DOCUMENTOS DE TRABAJODoes the Exposure to the Business Cycle Improve Consumer Perceptions for Forecasting? Microdata Evidence from Chile

Fernando FaureCarlos A. Medel

N° 888 Septiembre 2020BANCO CENTRAL DE CHILE

BANCO CENTRAL DE CHILE

CENTRAL BANK OF CHILE

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N° 888

Working Paper

N° 888

Does the Exposure to the Business Cycle Improve Consumer

Perceptions for Forecasting? Microdata Evidence from Chile

Abstract

Given the lag with which the official consumption series are released and the anticipation with which

consumption confidence indicators are published, there is latent attention in assessing the predictive

power of consumer confidence over consumer spending. In this article, we make use of a rich and

unique individual-level dataset obtained by merging a consumer sentiment survey with an

unemployment survey of the Greater Metropolitan area of Chile’s capital city. This is aiming to: (i)

analyse how forecasts of private consumption and components are improved by consumer sentiment

indexes constructed using the labour market characteristics of respondents and re-focusing aggregate

answers according to timing and subject, and (ii) analyse to what extent a greater exposure of

consumers/workers to the business cycle comes out as a better capability to nowcast and short-term

forecast consumption. Considering that consumers work in sectors where decisions are taken based

to a greater or lesser extent on the current and future economic situation, we assume a learning

mechanism permeable to the sentiment of workers that is present when they are surveyed as

consumers, referred to as “exposure”. Since the exposure is extensible to investment decisions, we

include total investment and its components in the analysis. By means of auto-regressions, our

results suggest that the in-sample adjustment of a simple model improves in most cases when any of

the newly built factors are included. Although there is no silver-bullet definition of the factor helping

all aggregates across all horizons simultaneously, future-oriented factors as well as information

coming from consumers working together in Commerce, Industry, Construction, and Personal

Services sectors provide material predictive gains, ranging from 4.5% to 40.2% at one-year

compared to the non-augmented auto-regression. Although surveys of consumers’ perceptions

provide rich information, these results are important since it is necessary to disentangle ideally from

the most disaggregate level to have a better revealing economic behaviour.

Resumen

Dado el rezago con el cual se publican las series oficiales de consumo y la anticipación con la que se

publican los indicadores de confianza de los consumidores, existe una latente atención en evaluar el

poder predictivo de la confianza de los consumidores sobre el gasto en consumo. En este artículo,

utilizamos una rica y única base de datos a nivel individual obtenida al fusionar una encuesta de

sentimiento de los consumidores con una encuesta de desempleo de la Gran Área Metropolitana de la

capital de Chile. Esto tiene como objetivo: (i) analizar cómo mejoran las proyecciones de consumo

privado y sus componentes mediante índices de sentimiento de los consumidores construidos

We thank comments and suggestions of José Miguel Alvarado, Pilar Cruz, Camila Gómez, Carlos Madeira,

Pablo Medel, Michael Pedersen, and Pablo Pincheira. Also, we thank Consuelo Edwards for editing services.

Any error or omission that remains at our own responsibility. The views and ideas expressed in this paper do

not necessarily represent those of the Central Bank of Chile or its authorities. E-mails: ffaure@fen.uchile.cl;

cmedel@bcentral.cl.

Fernando Faure

Universidad de Chile

Carlos A. Medel

Central Bank of Chile

utilizando las características del mercado laboral de los encuestados, y reenfocando las respuestas

agregadas según su temporalidad y sujeto, y (ii) analizar en qué medida una mayor exposición de los

consumidores/trabajadores al ciclo económico se manifiesta como una mejor capacidad para

pronosticar el consumo a corto plazo actual y a futuro. Considerando que los consumidores trabajan

en sectores donde se toman decisiones, en mayor o menor medida, basándose en la situación

económica actual y futura, asumimos un mecanismo de aprendizaje permeable al sentimiento de los

trabajadores que se presenta cuando se les encuesta como consumidores, denominado “exposición”.

Dado que la exposición es extensible a las decisiones de inversión, incluimos la inversión total y sus

componentes en el análisis. Mediante autoregresiones, nuestros resultados sugieren que el ajuste

dentro muestra de un modelo simple mejora en la mayoría de los casos cuando se incluye alguno de

los factores construidos. Aunque no existe una un factor tipo bala de plata que ayude a todos los

agregados en todos los horizontes simultáneamente, los factores reorientados hacia el futuro, así

como la información que proviene de los consumidores que trabajan juntos en los sectores de

Comercio, Industria, Construcción y Servicios Personales, entregan ganancias predictivas

importantes, que van desde 4.5% a 40.2% a un año en comparación con la misma autoregresión sin

aumentar. Si bien las encuestas sobre las percepciones de los consumidores entregan una rica

información, estos resultados son importantes ya que sugieren que necesario indagar, idealmente, al

nivel más desagregado para obtener un comportamiento económico más revelador.

1 Motivation, objectives, and main results

The confidence of consumers has played a key role in the development of modern theoretical economics. More-over, plenty of empirical literature has advocated analysing the relationship between consumer confidence andconsumer spending across world economies. This is relevant for different economic agents having to take impor-tant and irreversible decisions, and policymakers interested in future movements that shape the typically biggestcomponent of domestic demand. Given the lag with which the official consumption series are released, and theanticipation with which consumption confidence is published, there is latent attention in assessing the predictivepower of consumer confidence numeric indicators over consumer spending at the aggregate level.

This paper goes one step further by using microdata evidence of consumer sentiment predictability over aggregateconsumption and investment, taking advantage of a specific survey on consumers’ perceptions which, at the sametime, is linked to a survey of employment/unemployment of the Greater Santiago, Chile’s capital city. These arethe Survey of Employment and Unemployment in Greater Santiago (Encuesta de Ocupación y Desocupación en elGran Santiago, henceforth labelled as "EOD") and the Survey of Perception and Expectations on the EconomicSituation in Greater Santiago (Encuesta de Percepción y Expectativas sobre la Situación Económica en el Gran Santiago,"IEE"), both produced by the Centro de Microdatos of Universidad de Chile. The key advantage is that it is possibleto link, with no error, the perception of a consumer with her/his characteristics as a participant of the labourmarket, e.g. labour situation, economic activity, gender, income, and location. Thus, it is possible to exploitdatabase’s richness by re-grouping consumer perceptions indexes based on labour-market characteristics, aimingto improve their forecasting ability over macro aggregates and hypothesis testing. This treatment also aims todisentangle labour market characteristics more akin to the forecasting task.

By using the mentioned dataset, the aim of this article is two-fold: (i) to analyse the extent to which consumersentiment indexes better forecast aggregate consumption and its components, by constructing new indexes usingthe labour market characteristics of respondents and re-focusing aggregate answers according to timing and sub-ject, and (ii) analyse to what extent a greater exposure of consumers/workers to the business cycle comes out witha better capability to nowcast and short-term forecast consumption, compared to consumers/workers that partic-ipate in economic sectors less exposed to the business cycle. This latter exercise seeks to find the most accurateinformation of the survey when tracking the economy. Our claim assumes that consumers work in sectors wheredecisions are taken based to a greater or lesser extent on the current and future economic scenario. The consumerscan take these decisions themselves, be aware of them, or be affected by their consequences. Thus, we assume theexistence of a learning mechanism permeable to the sentiment of workers that is present when they are surveyedas consumers. We call this mechanism as "exposure" and we operationalize it by means of the correlation of work-ers’ economic sector with the output gap. Since this argument is extensible to investment decisions, we includetotal investment and its components in the analysis.

After checking the in-sample consumer-survey-based statistical inference within the simplest (and more trans-parent) econometric setup, we test our two proposals by means of out-of-sample comparisons exercises.1 Thus,the first hypothesis comes out as a multi-horizon forecast comparison between an atheoretical predictive autore-gressive model for a given macro aggregate and its corresponding survey-based factor-augmentation version,using different computations of consumer indexes. The second hypothesis consists of an out-of-sample compar-ison between two survey-based factors, one grouping indicators from consumers currently working in sectorsmore sensitive to the business cycle, and the other conformed with consumers working in the remaining sectorssurveyed. We proxy the business cycle by means of an output gap estimation.

Note that these hypotheses are tested for Private consumption, Non-durable consumption, and Durable con-sumption, plus Gross fixed capital formation (GFCF), Construction & works, and Machinery & equipment. Wealso make use of the same re-classification of answers used in Chanut, Marcel, and Medel (2019) in terms of tim-ing and subject, but now we are able to distinguish the economic sector where the consumer is currently working,adding new dimensions to exploit.

1These exercises consider a fixed vintage of the macroeconomic aggregates, which are subject to a revision policy. Thus, exercises are notconducted with real-time data.

1

Our in-sample results suggest that the adjusted goodness-of-fit coefficient of the first-best auto-regression im-proves in the majority of cases when including any of the considered consumer-perception-based factors. Ourbaseline results show that using specifically the re-classification by subject and timing, the Personal Future Expec-tation Index as well as the Overall Future Expectation Index improve for almost all macro aggregates consideringany sectorial definition of the factor. In contrast, the Personal Current Situation Index is less helpful to explainthe dynamics of any macro aggregate built with any sector. Most of these improved adjustments are found forGFCF and its components, and for Durable consumption to a lesser extent. Consumers working in Commerce andIndustry provide more useful information than remaining sectors, as well as when adding consumers in Construc-tion and Personal Services sectors without manufacturing. When accounting for the statistical significance of theconsumer-perceptions factor, there is a concentration of significant cases using future-based indexes for the samemacro aggregates, which exhibits better adjustments. Also, the evidence is mostly favourable for sectors moreclosely related to the business cycle rather than those that are less so or plainly insensitive to it.

Our out-of-sample results show, with a baseline added to alternative setups, predictive gains at all horizons for allvariables, in some cases of a sizable magnitude whereas in others non-statistically significant. The most fruitfulresults are obtained for Non-durable consumption and GFCF, which are statistically superior to the predictivebenchmark model when made up by sectors more akin to the business cycle. There is no silver-bullet definitionof the factor helping at the same time all aggregates across all horizons. However, in more consumption seriesthan not, the Personal Country Situation Index and the Country Current Situation Index lead to the best results. Inturn, the Overall Future Expectation Index does so for investment series. Regarding the economic sectors in whichconsumers participate and provide more useful predictive information, unquestionably the best forecasting resultsare concentrated in Commerce, Industry, Construction, and Personal Services (thus, out of 3,060 individuals surveyedper quarter, this factor is composed of 1,735 answers per quarter on average) and in Commerce, Construction, andPersonal Services (comprising 1,313 answers per quarter on average). When comparing between factors, the resultsare largely favourable to the factors based on consumers more exposed to the business cycle. In this line, themost fruitful results are obtained with Commerce, Industry, and Transportation sectors and Commerce, Construction,and Personal Services that outperform the remaining sectors less exposed to the business cycle. Although surveysof consumers perceptions provide rich information, these results are important as it is necessary to disentangleideally from the most disaggregate level to have a better revealing economic behaviour.

The remainder of the article proceeds as follows: in section II, we review the related literature on this topic. Insection III, we describe our econometric setup in terms of the individual and macro aggregates data, detailing theinformation contained in the two surveys and the construction of all consumer-based factors. It also describes thestatistical inference carried out to both in- and out-of-sample analyses. In section IV we display our results of thechosen baseline autoregressive model, and the in-sample and predictive evidence. Finally, section V provides theconclusions drawn from the study.

2 Literature review

Several articles set up the baseline stylised facts and common findings on this matter, specially analysing the caseof advanced economies such as the Euro Area and the United States; for the latter, specially using the Survey ofConsumers (SoC) produced by the University of Michigan.2 For instance, Fuhrer (1993) studied whether the SoCcan explain different economic phenomena with simple predictive models and a vector auto-regression (VAR).Their results suggest that a good part of the variation in the sentiment index is explained by macro aggregates,and that the SoC explains and improves a little on the actual consumption series and its forecasts. Carroll, Fuhrer,and Wilcox (1994) analyse if the information of the SoC predicts changes in private consumption, finding thatwithin a reduced-form model, the SoC anticipates consumption growth. Howrey (2001) makes use of part of theSoC to analyse the ability to anticipate recessions and recovery episodes using a VAR, finding that the SoC isbarely superior to a benchmark model when forecasting GDP one step ahead. Doms and Morin (2004) mimicsSoC answers using newspapers-based indexes, finding three transmission channels to consumers perceptionsthrough actual economic data, tone, and volume. The newly-built indexes come out as playing a role whenconsumers update their perceptions, which is directly dependent on the volume of economic news. Ludvigson

2For more details on the full content of the SoC, see Survey of Consumers, University of Michigan (2020).

2

(2004) shows that the SoC contains valuable information on the future path of aggregate consumption but yieldingmodest predictive gains, whereas the same SoC information could be found in economic/financial indicators.By exploiting the microdata of SoC, Souleles (2004) finds that aggregate shocks do not impact all householdsequally, and demographics explain this heterogeneity to a large extent. Particularly, people’s forecast errors aresystematically correlated with their demographics, and sentiment helps forecast consumption growth.

Geiger and Scharler (2019) use the SoC to show how consumers assess gasoline price shocks using a sign-restrictedVAR, finding that oil prices and unemployment guide consumer perceptions, and these perceptions are consistentwith economic developments. Lahiri, Monokroussos, and Zhao (2015) analyse the SoCs’ predictive ability overconsumption using a dynamic factor model and a large, real-time, jagged-edge dataset, finding a robust rolefor perceptions in improving consumption-forecast accuracy particularly through the services component. Allthese results are promising and call to analyse its potential extension to other countries with their correspondingsurveys. Moreover, valuing the predictive content of surveys for macro aggregates, and the way how it couldbe better handled, Bürgi and Sinclair (2015) suggests a nonparametric approach to refine the pool of respondentsparticipating in the Survey of Professional Forecasters conducted by the Federal Reserve of Philadelphia. Theirapproach leads to significant short-term predictive gains, which could certainly be interesting to further analysein the context of this article.

This list is not intended to be comprehensive; rather, it aims to show the evolution of the type of questions andresults that a rich consumer sentiment survey could provide for economic analysis. Outside the United States,the evidence is also substantial. Similar exercises to that conducted with SoC has been produced with specificconsumer sentiment and perceptions indexes for the Euro Area (Gayer, 2005; Girardi, Golinelli, and Pappalardo,2017; Basselier, Liedo, and Langenus, 2018), Germany (Schröeder amd Hüfner, 2002; Abberger, 2007), Italy (Brunoand Malgarani, 2002), Sweden (Hansson, Jansson, and Löf, 2003; Österholm, 2014), China (Li, 2011), South Korea(Moon and Lee, 2012), and Garnitz, Lehmann, and Wohlrabe (2017) for 44 countries. De Mello and Figuereido(2014) provide evidence for the Brazilian sentiment indicators acting as covariant when forecasting economicactivity in an econometric setup similar to this article’s.

In emerging market economies, as is the case of Chile, the evidence is scarce. Nonetheless, recent research suggeststhat aggregate consumer sentiment indicators do not perform well when trying to predict private consumptionand investment within a simple, statistical ensemble. However, when re-classifying survey answers according totiming (current/future) and subject (personal/country) dimensions, the evidence turns favourable to the use offorward-looking factors to predict specific components of the aforementioned macro aggregates (Chanut, Marcel,and Medel, 2019). By making use of an instrumental definition of consumer sentiment based on a different con-sumer confidence survey, Acuña, Echeverría, and Pinto-Gutiérrez (2020) find that consumer sentiment improvesin-sample modelling of private consumption as well as its out-of-sample forecast in a fundamental-based envi-ronment. Their results are robust to nonlinearities and, to some extent, they contradict theoretical predictions ofconsumer spending theories based on, for instance, the Precautionary Saving Hypothesis (Blanchard and Mankiw,1988).

Furthermore, using a subset of questions from a consumer perceptions survey, Albagli et al. (2019) find thatconfidence shocks impact consumption negatively up to eight quarters after returning to its previous growth rate,providing some support to consumer sentiment indicators acting as predictors. Also, Figueroa and Pedersen(2019), by picking specific questions of the same consumer confidence survey used in Chanut, Marcel, and Medel(2019) and Albagli et al. (2019), analyse its forecast ability on Chilean economic activity. Authors’ findings arefavourable to the use of consumer answers for horizons different from nowcast, suggesting that consumers indeedprovide good-quality frontward information.3 Interestingly, all these results have in common at least two limitingcharacteristics: (i) the need for a re-classification or refinement of quantitative indexes in search of actual harddata predictability, and (ii) the use of indexes in an aggregate way, in the sense that the mentioned re-shaping ofindicators makes use of all individuals’ data whatever the driver of the re-classification is, classified by eithertiming or subject.

3Some other applications of consumer sentiment indicators in Chile rely on its use as an aggregate covariate in a data-rich ensemble toforecast activity and inflation. See, for instance, Calvo and Ricaurte (2012) making use of one particular survey question, and Riquelme andRiveros (2018) using disaggregated survey indicators to build a coincident indicator of total monthly economic activity.

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3 Econometric setup

Firstly, it is relevant to distinguish between consumer expectations and consumer sentiment. In this article, we makeuse of consumer sentiment, which means the economic agents’ opinion on future relevant economic developmentsthat may be influenced by today’s actions (e.g. "Do you think the state of the economy has improved, stayedthe same, or deteriorated over the last year?"), in contrast to economic expectations in which agents state theirperceived most likely value on a particular targeted variable (e.g. "What do you think will be the year-on-yearrate of CPI inflation in the next quarter?"). It is generally believed that qualitative questions to report agents’sentiment, while less accurate, are better understood by a non-expert audience and, thus, better reflect their truesentiment, as opposed to a random guess. This is precisely a feature exploited in this article, testing whetherconsumers diverge in their opinions depending on the economic sector in which they participate. Naturally, thereis no wrong answer to a sentiment survey, whereas expectations allow us to even characterise a numeric errorterm fully.

A review of the econometric exercise conducted in this article is the following. First, we search the best stationaryautoregressive AR(p) forecasting model for each of the six macroeconomic variables considered. We search acrossp lags, p={1,...,4}, as actual macroeconomic data is released in quarterly frequency. Instead of using the traditionalin-sample information criteria to select the model with the best fit, we use a more demanding strategy by choosingthe best out-of-sample model when forecasting from 1 up to 4 quarters ahead. This is also the reason why wesearch among the simplest family of AR(p) models, i.e. to avoid the issue of overfitting by including regressorsthat exaggerate the dynamics of the series at the cost of spoiling out the predictive power of the model. Wealso choose this strategy to stress out the out-of-sample benefits of the exogenous factor without including anyadditional covariate.4

Secondly, we compare the multi-horizon forecast of the chosen AR(p) model extended with the exogenous consumer-survey-based factor. By performing this exercise, we can determine if this extension is fruitful from an out-of-sample perspective–and checking for our first hypothesis. We compare these forecasts by means of the root meanforecast error (RMSFE) and using the Clark and West (2007) test for statistical inference.

Thirdly, we build the exogenous consumer-survey-based factor by grouping consumers’ answers. These con-sumers are currently working in sectors that are more sensitive to the business cycle. This makes us consider ashare of total answers that compound the factor, and the complementary share compounding another factor withconsumers working in other sectors less sensitive to the business cycle. Hence, we compare the influence of bothfactors on the predictive ability of the chosen AR model, expecting that the consumers possibly more aware ofthe business cycle would provide more accurate information on their economic situation–and checking for oursecond hypothesis. This comparison is made by means of the RMSFE and the Harvey, Leybourne, and Newbold(1997) test. On top of this, we also re-classify some answers according to timing and subject. Thus, factors containthree dimensions: timing, subject, and economic sector, e.g. "Personal Current Situation Index of consumers workingin Commerce and Industry". An important drawback of this exercise is that it is not conducted in real time becauseof data vintages availability.

Fourthly, we try four different specifications of the economic sectors when building consumer-survey-based ex-ogenous factors. This is because the sensitivity to the output gap of the economic sectors of the surveyed con-sumers is evolving with the time difference (lags) with which the correlation coefficient is calculated.

Finally, we conduct a robustness exercise using the whole range of AR(p) models available combined with dif-ferent setups of the exogenous factor, namely, first differences or levels, and the number of terms included in theforecasting equation. These exercises are relevant because in some cases the best forecasting model is evolvingwith the forecast horizon for a given macro aggregate, and comparisons must be made with the best benchmarks.Also, there is no single manner to include the factor in the forecasting equation, and so, we try different specifica-tions.

4In Acuña, Echeverría, and Pinto-Gutiérrez (2019), the authors use another consumer-survey aggregate factor to predict private consump-tion with a fundamentals-based consumption model. The authors, however, do not check if the non-augmented model is better than anatheoretical simple benchmark. In this sense, the exercise conducted in this article is more motivated by the forecasting results.

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3.1 Consumer perceptions, labour market microdata, and the business cycle

As mentioned above, we make use of the microdata freely available (after submitting an online registry) by theUniversidad de Chile’s Centro de Microdatos (http://documentos.microdatos.cl/). This database is the result ofmerging the datasets of two surveys: the Survey of Employment and Unemployment in Greater Santiago (the EOD) andthe Survey of Perceptions and Expectations on the Economic Situation in Greater Santiago (the IEE). A unique feature isthat both databases are available (anonymously) at the individual level and are already merged since respondentsare asked about both their labour situation as a worker and her/his economic perception as a consumer. Theindependence in answering both surveys, especially that of sentiment, is ensured by the wording of the questions.Thus, the sentiment is not conditioned to her/his labour situation by survey design.

Naturally, the universe of the IEE is the same of that of EOD:5 inhabitants over 14 years old living in the San-tiago Metropolitan Region and in Puente Alto and San Bernardo counties. These add up to about 40% of theChilean population in 2017. The sample is composed of 3,060 individuals per quarter, consisting in a stratifiedrandom sampling with a panel data component–a rotating panel. In this method part of the whole panel is keptpermanently, and another part is a completely new cross-section sample. The sample of 3,060 individuals in eachquarter is divided into four subsamples of 765 individuals, where each subsample is independent and representsthe Greater Santiago. The rotation design is of the 2-2-2 type, where two selected individuals are interviewedtwice in a row, then they are not contacted in the following two rounds, and then they are interviewed again inthe following two rounds, covering a period of 18 months in total. The collection technique is face-to-face inter-view and the reported answer rate reaches 77.4% (informed on March 2014). The representativeness with respectto the universe could be considered adequate, but this is not the case when considering the whole country, asit focuses in Santiago only.6 The IEE is released quarterly and fully available since March 2001 (75 observationsavailable up until September 2019).

Note that across all questions asked in IEE there is a time dimension and a subject dimension, allowing us tore-classify them in these terms and the economic sector reported by each individual. These questions are thefollowing, responded in a qualitative manner (with two exceptions):

• Q1: How was the economic situation of the country a year ago? (better, same, worse)

• Q2: What are the three main problems of the country? (free answer)

• Q3: How did the income of your household vary in the last 12 months? (increased, same, decreased)

• Q4: How is the situation of your household in terms of indebtedness? (complicated, average, no problem)

• Q5a: Did a member of your household buy a durable good in the past three months? (yes/no)

• Q5b: If so, how have you financed it? (credit/cash)

• Q6: In one year, how will be the economic situation of the country compared to today? (better, same, worse)

• Q7: How will the income of your household vary within the next 12 months? (increase, same, decrease)

• Q8: What will be the CPI inflation rate in 12 months? (numeric answer)

• Q9a: Will a member of your household buy a durable good in the next three months? (yes/no)

• Q9b: If so, how will it be financed? (credit/cash)

• Q10: Are you or is a member of your household thinking of buying a house in the next 12 months? (yes/no).

5Specific details can be found in Centro de Microdatos (2016).6Santiago is Chile’s capital city with a population of 7.037 million, i.e., 37.57% of the country’s total of 18.730 million as of 2017.

5

It is important to look at the way in which qualitative answers are transformed into quantitative indicators. Thereare two steps. The first consists of aggregating the individual answers to the same question to get a number called"balance statistic," while the second step is to aggregate the balance statistic of each question to form a syntheticindicator. Intuitively, the balance statistic is the difference between the percentage of positive answers and thepercentage of negative answers.7 Any synthetic indicator (step 2) is constructed by taking the equally weightedaverage of the balance statistic of the questions composing the indicator.

Similarly to what Chanut, Marcel, and Medel (2019) sugget, we overcome the limitations of an aggregate indicatorthat blends all questions without a specific focus by re-grouping subsets of questions distinguishing betweentiming (current sentiment/future expectations) and subject (personal and country-wide ). Crossing these twodimensions originates four different indicators, in which the questions are mapped as:

1. Country Current Situation Index (CCSI ): Q1,

2. Country Future Expectation Index (CFEI ): Q6,

3. Personal Current Situation Index (PCSI ): 13Q3 + 1

3Q4 + 13Q5a,

4. Personal Future Expectation Index (PFEI ): 13Q7 + 1

3Q9a + 13Q10,

5. Overall Future Expectation Index (OFEI ): 14Q6 + 1

4Q7 + 14Q9a + 1

4Q10.

Note that we add a fifth indicator (OFEI) overriding the "subject" dimension (mixing country and personal) inorder to have an appraisal on the overall predictive ability of those answers. In turn, EOD asks for traditionalpersonal, demographic, and economic information: county, gender, age, marital status, educational level, em-ployment situation, reason of unemployment, availability, occupational position, number of workers hired underyour responsibility, economic activity, type of institution or establishment, total hours worked during the week ofreference, total days worked during the week of reference, duration of inactivity, willingness to work extra hours,effort in job search, reason for no job searching, type of contract, salary, income from independent activities, pen-sion, and total household income. Breaking over the "Employment Situation" answers (whose answers could beWorking, Unemployed, Studying, Housework, and Other), and particularly mapping the "Working" answer with the"Economic Activity", we found that 55.2% of the sample that reports working (average 2001.I-2019.III), 22.5% dothat in the Commerce sector, 18.2% in Commonality and Social Services, 15.6% in Public and Financial Services, 13.8%in Industry, 8.0% in Construction, 7.8% in Transportation, and the rest in four remaining smaller sectors (see Figure1).

Thus, our hypothesis propose that consumers in economic sectors that are more exposed to the business cycle couldbe able to forecast better overall consumption and investment than (i) a reasonable simple benchmark, and (ii)consumers in sectors less sensitive to the business cycle. But which is the group of consumers more exposed to thebusiness cycle? In our setup, this is equivalent to asking which economic sectors are more correlated to (a measureof) the output gap. There is no single way on how to determine the sensitivity or exposure of specific economicsectors to the business cycle. For instance, it is possible that those sectors with a higher GDP weight could bethe most exposed, but it ignores the dynamic relationship with the output gap. Thus, it could be the case that asector, while having a heavy weight on GDP, fluctuates less than other sectors with lighter weight throughout thebusiness cycle. This is actually the case of Financial Services (14.9%) and Mining (9.4%) with a weight greater than,for instance, Transportation (5.0%), but this latter with a greater correlation with the (lagged) output gap. Also, thecorrelation is calculated using the output gap instead of GDP to differentiate between, for instance, episodes of"GDP growth" from "GDP growth above the potential GDP".

7Formally, it is defined as balance statistic=100(∑Ni=1 ωixi), where N is the total number of individual surveyed, ωi is the weight of the

i-th sample unit, and xi is the response of the i-th sample unit, taking value one when the answer is "yes" or "increase", minus one when theanswer is "no" or "decrease", and zero when the answer is "stable" or "same". The weight of the i-th sample unit is chosen in such a way thatthe sample is representative: the weight is inversely proportional to the probability of unit i to be drawn; hence, if the sample is random, theweight is simply ωi=1/N.

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Figure 1. Composition of the Centro de Microdatos’ employment situation answersby situation and economic activity, 2001-2019 average (*)

55.2%

5.9%5.1%

16.8%

17.0%

Working UnemployedStudying Housew orkOther

I. Employment Situation

13.8%

8.0%22.5%

15.6%

12.4% 18.2%

7.8%

Agriculture MiningIndustry ConstructionCommerce Pub. & Fin. S.Personal S. Comm. S.Transp. S. Other

II. Employment by Economic Activity

(*) Source: Authors’ calculations based on Centro de Microdatos database.

The approximation used in this article for the output gap is obtained as the difference between the logarithmiclevel of actual GDP and potential GDP.8 The latter is defined as the logarithmic level of the seasonally-adjustedand filtered version of the GDP including up to five years of forecast observations coming from an ad-hoc ARIMAmodel. This last step is performed to avoid the "end-of-sample" identification problem when using the Hodrick-Prescott (λ=1,600) method to filter the series. The seasonal adjustment program used is the X-13ARIMA-SEATS,whereas the ARIMA forecasting model is the so-called airline model (Box and Jenkins, 1970; Ghysels, Osborn, andRodrigues, 2006).

Figure 2. Output gap and selected activity sectors (annual variation) (*)

­20

­16

­12

­8

­4

0

4

8

12

16

20

96 98 00 02 04 06 08 10 12 14 16 18

Output gap Construction Commerce Personal S.Industry Financial S. Public Adm. MiningTransportation

Per

cent

Percent

(*) Source: Authors’ calculations based on Central Bank of Chile’s database.

8The source of the GDP series is the Central Bank of Chile’s Quarterly National Accounts database(https://si3.bcentral.cl/Siete/secure/cuadros/home.aspx). We use the vintage available up to 2019.III.

7

We identify the economic sectors most sensitive to the output gap by means of cross correlation calculated withthe current and up to 4-quarter lagged output gap. Particularly, the correlation in period t of the activity sectorsConstruction, Commerce, Personal Services, Industry, Financial Services, Public Administration, Mining, and Transporta-tion, obtained from the Central Bank of Chile’s Quarterly National Accounts database, with the correlation in t, t-1,t-2, and t-3 quarters of the output gap. The time series plot of involved variables is presented in Figure 2, and theestimated correlations are presented in Table 1.

Table 1: Correlation coefficient between (lagged) output gap and economic activity sectors (*)Output gapt Output gapt−1 Output gapt−2 Output gapt−3 Output gapt−4

Output gapt 1.000 0.918 0.791 0.634 0.495Output gapt−1 0.918 1.000 0.918 0.789 0.636Output gapt−2 0.791 0.918 1.000 0.917 0.790Output gapt−3 0.634 0.789 0.917 1.000 0.921Output gapt−4 0.495 0.636 0.790 0.921 1.000Miningt 0.105 0.031 -0.013 -0.036 -0.040Industryt 0.330 0.108 -0.151 -0.362 -0.533Constructiont 0.541 0.477 0.302 0.068 -0.137Commercet 0.507 0.303 0.057 -0.190 -0.378Transportationt 0.213 0.072 -0.111 -0.315 -0.486Financial Serv.t 0.262 0.183 0.052 -0.126 -0.301Personal Serv.t 0.438 0.347 0.198 0.072 -0.058Public Adm.t 0.187 0.213 0.257 0.327 0.430

(*) Shaded cells=bigger correlation coefficient (≥ |30%|) for a comparable time difference.Sample: 2001.I-2019.III (75 observations). Source: Authors’ calculations.

Note that, as the sectors with an acceptably high correlation with the output gap are evolving with the lag withwhich the correlation is calculated, we make use of four different definitions of the factor combining more infor-mative sectors, thus:

1. CI: Commerce + Industry

2. CIT: Commerce + Industry + Transportation

3. CICS: Commerce + Industry + Construction + Personal Services

4. CCS: Commerce + Construction + Personal Services.

Notice that we consider for factor building all those sectors having more than twice a correlation coefficient above|30%| between t and t-4 output gap lags. Also, we opt to exclude Public Administration because it is merged withFinancial Services in the EOD/IEE that, in turn, exhibit a low correlation with the output gap for considered timedifferences. Recall that for our second hypothesis, we compare the predictive ability of each of these four factorsseparately in our AR(p) setup with those composed with the remaining activity sectors surveyed by IEE (seeFigure 1).

3.2 Macroeconomic aggregate data

We perform the same econometric exercise when predicting the six macroeconomic variables with the four con-sumer perception factors. Mentioned variables are Private consumption (PC) plus two out of three of its com-ponents separately—Durable consumption (DC) and Non-durable consumption (NDC)–, and Gross fixed capitalformation (GFCF) plus its two components–Construction & works (CWK) and Machinery & equipment (MEQ).

The source of all these variables is the Central Bank of Chile’s Quarterly National Accounts database; specifically, thevintage available until 2019.III. The transformation used to achieve stationarity is the annual percentage change.The series achieve stationarity with the full sample (2001.I-2019.III, 75 quarterly observations) according to theAugmented Dickey-Fuller (null hypothesis: the series has a unit root) using a trend, a constant, and 4 lags for PC(p-value: 0.193), a trend, a constant, and 4 lags for NDC (p-value: 0.147), a constant and 4 lags for DC (p-value:

8

0.145), a trend, a constant, and 4 lags for GFCF (p-value: 0.192), a constant and 4 lags for CWK (p-value: 0.127),and a trend, a constant, and 8 lags forMEQ (p-value: 0.381). No structural change is found in any of the series.

These macroeconomic aggregates are depicted in Figure 3, panels I and II, along with the indexes depicted bytiming/subject (CCSI, CFEI, PCSI, PFEI, and OFEI) in panels III to VII. Note that all these factors achieve station-arity with a trend, a constant, and 5 lags (but excluding the trend with PCSI and PFEI indexes) according to theAugmented Dickey-Fuller test at the 10% confidence level. This is important because although the factors aredeveloped in levels, they already refer to temporal comparisons according to their wording (see subsection 3.1).So, it could be unusual for one of these indicators to persistently grow over an extended time span. Thus, there isnot an econometric issue when including them in the AR model in levels.

3.3 In-sample and forecast evaluation framework

We use the estimation sample covering from 2001.I to 2014.IV (56 observations) to estimate the AR(1) to AR(4)models for the six macroeconomic variables to determine which of them is the best forecasting model makinguse of the remaining evaluation sample covering from 2015.I to 2019.III (19 observations). After finding the bestmodel, we then include four terms of the consumer-based factor and compare the resulting forecast with that ofthe non-augmented model. In our robustness exercises, we perform different setups on factor specification (levelor first differences) combined with different number of terms included in the auto-regression (from one to four),under different AR(p) models. There is not a clear way on how to include the factor. However, as mentionedabove, consumer data is evolving according to a 2-2-2 rotating panel scheme, and thus, include at least more thanone term imply consider different and ultimately more consumers in the forecasting task. We opt to set the 4-termfirst differences of the factor as a baseline setup, which will be naturally challenged by robustness exercises. Thebaseline specification thus is:

yt = y+P

∑i=1

ρiyt−i + φ1∆ ft + φ2∆ ft−1 + φ3∆ ft−2 + φ4∆ ft−3 + εt, (1)

where yt is any of the macro aggregates, ∆ ft corresponds to first difference of the consumer-based factor andits complementary versions, {y,ρi,φi} are to-be-estimated parameters once P ∈ {1, ..., 4} is determined accordingto its out-of-sample performance without including a factor, and εt is a white noise. Note that the factor entersthe equation with four terms, including a contemporaneous term. This is so because the survey data becomesavailable four to five months prior to macroeconomic aggregates.

For the same estimation sample, we compute the incremental adjusted goodness-of-fit coefficient with and withoutincluding the factor, and the joint statistical significance of the φi-coefficients in equation (1). We choose the Pcoefficient of equation (1) and also conduct the whole forecasting exercise making use of the evaluation sample in arolling window scheme. This is also required for the statistical inference framework.

The forecast evaluation statistic used is the root mean squared forecast error (RMSFE) defined as:

RMSFEh =

[1

P(h)

T+1−h

∑t=R

(yt+h − yt+h|t

)2] 1

2

, (2)

where yt+h|t represents the forecast of yt+h made with information known up until time t. We generate a total ofP(h) forecasts, satisfying P(h)=T + 2− h+ R, where h is the forecast horizon, h={1,2,3,4}, and R is the number ofobservations in the estimation sample (56 observations).

For simplicity, the results are reported using a relative measure of the RMSFE, easing a comparison across thealternative forecasts. Two comparisons are made:

(i) : Relative RMSFE1h=RMSFEFactor augmentedh /RMSFENo factorh , (3)

(ii) : Relative RMSFE2h=RMSFEFactor augmented (more exposed)h /RMSFEFactor augmented (less exposed)h ,

9

Figure 3. Macroeconomic aggregates and consumer-perceptions-based indexes (*)

­6

­4­20

246

8

101214

­40

­30­20­10

01020

30

405060

2002 2004 2006 2008 2010 2012 2014 2016 2018

Private Cons. Durable Cons. Non­durable Cons. (RHS)

I. Macroeconomic Aggregates: Consumption

Per

cent

age P

ercentage

Mean=4.74%; SD=3.15%Mean=10.34%; SD=13.58%Mean=4.04%; SD=2.75%

­40

­30

­20

­10

0

10

20

30

40

50

2002 2004 2006 2008 2010 2012 2014 2016 2018

Gross Fixed Cap. Fmtn. Const. and Works Machinery and Equipment

II. Macroeconomic Aggregates:  Investment

Per

cent

age P

ercentage

Mean=6.28%; SD=9.83%Mean=4.50%; SD=6.38%Mean=10.14%; SD=19.01%

24

28

32

36

40

44

48

52

56

60

2002 2004 2006 2008 2010 2012 2014 2016 2018

Comm. + Ind. Comm. + Ind. + Trans.Comm. + Ind. + Const. + Pers. Serv. Comm. + Const. + Pers. Services

III. Country Current Situation Index

Inde

x Index

202530354045505560657075

2002 2004 2006 2008 2010 2012 2014 2016 2018

Comm. + Ind. Comm. + Ind. + Trans.Comm. + Ind. + Const. + Pers. Services Comm. + Const. + Pers. Services

IV. Country Future Expectations Index

Inde

x Index

30

32

34

36

38

40

42

44

46

48

2002 2004 2006 2008 2010 2012 2014 2016 2018

Comm. + Ind. Comm. + Ind. + Trans.Comm. + Ind. + Const. + Pers. Services Comm. + Const. + Pers. Services

V. Personal Current Situation Index

Inde

x Index

22

24

2628

3032

34

363840

42

2002 2004 2006 2008 2010 2012 2014 2016 2018

Comm. + Ind. Comm. + Ind. + Trans.Comm. + Ind. + Const. + Pers. Services Comm. + Const. + Pers. Services

VI. Personal Future Expectations Index

Inde

x Index

24

28

32

36

40

44

48

52

56

2002 2004 2006 2008 2010 2012 2014 2016 2018

Comm. + Ind. Comm. + Ind. + Trans.Comm. + Ind. + Const. + Pers. Services Comm. + Const. + Pers. Services

VII. Overall Future Expectations Index

Inde

x Index

(*) Horizontal line in III-VII=mean of the mean of each depicted series. Source: Authors’ calculationsbased on Central Bank of Chile and Centro de Microdatos database.

10

where "more/less exposed" refers to the relationship with the output gap. Thus, values below unity imply a betterperformance in favour of our two proposed hypotheses.

For the first case, i.e. the forecast including the factor compared to the AR version with no augmentation, the Clarkand West (2007; CW) test is used because it consists of an adjusted RMSFE comparison due to model encompass-ing. Hence, the CW test evaluates model adequacy instead of forecast accuracy, as opposed to the Harvey, Leybourne,and Newbold (1997) test used to compare forecast accuracy between factors. Note that the CW is not the mostappropriate for small sample environments due to a reduction of its power. However, there is no small-samplecorrection available and results are presented for reference. Thus, we use it for want of a better alternative.

The CW test can be considered as both an encompassing test and an adjusted comparison of the MSFE. Theadjustment is made to ensure a fair comparison between nested models. Intuitively, the CW test removes a termthat introduces noise when a parameter, that should be zero under the null hypothesis of equal MSFE, is estimated.

The core statistic of the CW test is constructed as follow:

zt+h = (ε1,t+h)2 −

[(ε2,t+h)

2 −(

y1,t+h|t − y2,t+h|t)2]

, (4)

where

ε1,t+h = yt+h − y1,t+h|t, (5)ε2,t+h = yt+h − y2,t+h|t,

represent the corresponding forecast errors. Note that y1,t+h|t and y2,t+h|t denote the h-step-ahead forecasts gen-erated from the two models under consideration. "Model 1" is the parsimonious or small model without factor-augmentation that is nested in the larger "Model 2". In other words, Model 2 would become Model 1 of some ofits parameters were set to zero.

With a little algebra, it is straightforward to show that it could also be expressed as follows:

Sample MSFE-Adjusted=2

P(h)

T+1−h

∑t=R

ε1,t+h (ε1,t+h − ε2,t+h) . (6)

This statistic is used to test the following null hypothesis, against the alternative:

H0 : E [Sample MSFE-Adjusted] = 0, (7)H1 : E [Sample MSFE-Adjusted] > 0.

The CW test suggests a one-sided test for a t-type statistic based upon the core statistic in equation (4), i.e. asymp-totically normal critical values. In most of the analysis, it follows Clark and McCracken (2001, 2005). Theoreticalresults in those papers require models to be estimated with non-linear least squares (which we use in this article)and multi-step forecasts to be made with the direct method. As we make use of the iterated forecast method, weshow the results at more than one-step-ahead horizon just for reference.

For the second hypothesis considered in equation (3), i.e. comparing between the two factor-augmented forecasts,the equal predictive ability of Harvey, Leybourne, and Newbold (1997, HLN) test is used. This consists in a small-sample-corrected version of the Diebold and Mariano (1995) test, and plainly tests forecast accuracy. Accordingto the Diebold-Mariano original test, we focus on testing the following null hypothesis against the alternative:

H0 : E[dt(h)

]= 0, (8)

H1 : E[dt(h)

]6= 0,

wheredt(h) =

(yt+h − y1,t+h|t

)2−(

yt+h − y2,t+h|t)2

. (9)

11

Our null hypothesis posits that forecast generated from the nested model performs equally to those generatedfrom the larger model. As noted by HLN, using an approximately unbiased estimator of the mean’s varianceleads to a modified Diebold-Mariano test statistic:

HLNh =

[n+ 1− 2h+ n−1h(h− 1)

n

] 12 (

dt(h)/σdt(h)

), (10)

which must be contrasted with critical values from a Student’s t distribution with (n-1) degrees of freedom, anddt(h) corresponds to the sample mean and σdt(h) to the standard deviation of the term in equation (9). Notice thatthis test requires that the estimates be made with a rolling window scheme. Thus, we perform our estimations withrolling windows of a fixed size of 50 observations. It is important to emphasize that the two tests differ in a numberof aspects, the most important difference being that they are designed for different purposes. Consequently, weexpect these two tests to deliver different results.

4 Results

As mentioned above, we choose the best AR(p) model following its predictive performance. In Figure 4, we showthe (absolute) RMSFE of the AR(1) to AR(4) models for each horizon and macro aggregate. Two observationsare worth mentioning: (i) there are heterogeneous results across horizons for a given variable, and in some casesthe best model is evolving with the horizon, leading to further analyse other setups in an extensive robustnessexercise (subsection 4.3), and (ii) there are some variables that are more difficult to predict as they exhibit morevolatility than others, shedding some light on where is more likely to have room for improvement. Except for DCat h>1 andMEQ for h={2,3}, the best forecasting model is the AR(1). These two cases also motivate our robustnessexercises, where we analyse the same results but using an AR(4) model. Thus, we make use of this simple—butdemanding in terms of predictability—model to conduct our baseline forecasting exercise, but subject to furtheranalysis.

Figure 4: Multi-horizon RMSFE of the AR(p) models by macroeconomic aggregate (*)

0

1

2

3

4

5

6

7

8

9

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

p=1 p=2 p=3 p=4

RM

SFE

RM

SFE

Horizon:

Private            Durable            Non­durable        Gross Fixed      Construction        MachineryConsumption   Consumption         Consumption       Capital Fmtn.    and Public W.   and Equipment

(*) Each bar displays the out-of-sample RMSFE by horizon and macroeconomic aggregate,for a given p-lag, p={1,...,4}, of the AR(p) model. Source: Authors’ calculations.

12

4.1 In-sample diagnostics

Our first in-sample results comprise the incremental adjusted goodness-of-fit coefficient9 when comparing theAR(1) with and without including the consumer-based factor. The results are presented in Table 2, showing theratio between the adjusted goodness-of-fit coefficient of the AR(1) model including the factor upon the nativeAR(1). Hence, figures above unity are favourable for the factor. Note that we display two sets of columns: the firstwith the factors built with the sectors most associated to the output gap and the second with the complimentaryfactors.

Table 2. Adjusted R-squared ratio between AR(1) factor-augmented and native AR(1) model (*)Factor: More sensitive sectors Factor: Less sensitive sectors

PCSI PFEI CCSI CFEI OFEI PCSI PFEI CCSI CFEI OFEIFactor: Commerce + IndustryPC 0.977 1.013 0.984 0.996 1.009 0.977 0.992 1.004 0.991 0.995DC 0.981 1.026 0.985 1.003 1.020 0.974 0.993 0.993 0.985 0.992NDC 0.950 1.030 0.956 0.990 1.019 0.956 0.989 0.980 0.979 0.992GFCF 0.981 1.026 1.008 1.022 1.034 0.998 1.007 1.014 1.031 1.037CWK 0.983 1.025 1.013 1.060 1.058 0.982 1.015 0.997 1.034 1.039MEQ 0.986 1.021 1.029 1.023 1.033 .018 0.999 1.078 1.054 1.060Factor: Commerce + Industry + TransportationPC 0.980 1.010 0.991 0.995 1.005 0.976 0.995 1.000 0.991 0.996DC 0.986 1.025 0.986 0.998 1.013 0.972 0.993 0.993 0.987 0.994NDC 0.951 1.024 0.959 0.984 1.009 0.955 0.992 0.980 0.983 0.998GFCF 0.985 1.019 1.010 1.023 1.033 0.990 1.011 1.015 1.032 1.038CWK 0.981 1.028 1.006 1.058 1.059 0.982 1.014 1.001 1.034 1.038MEQ 0.997 1.010 1.032 1.020 1.030 1.001 1.006 1.087 1.059 1.066Factor: Commerce + Industry + Construction + Personal ServicesPC 0.980 0.990 1.002 0.990 0.992 0.980 1.017 0.987 0.997 1.010DC 0.971 0.995 0.991 0.987 0.994 0.988 1.018 0.988 0.998 1.012NDC 0.959 0.978 0.975 0.981 0.989 0.958 1.052 0.956 0.986 1.021GFCF 0.994 1.007 1.016 1.033 1.038 0.981 1.023 1.003 1.022 1.033CWK 0.986 1.020 0.997 1.034 1.039 0.981 1.015 1.009 1.058 1.056MEQ 1.010 1.000 1.078 1.061 1.066 0.986 1.017 1.035 1.020 1.032Factor: Commerce + Construction + Personal ServicesPC 0.978 0.997 1.001 0.993 0.999 0.983 1.015 0.992 0.991 1.002DC 0.972 1.003 0.988 0.992 1.002 0.990 1.017 0.997 0.989 1.002NDC 0.953 0.991 0.969 0.989 1.004 0.965 1.046 0.972 0.971 0.998GFCF 0.990 1.014 1.017 1.035 1.042 0.985 1.015 0.995 1.013 1.020CWK 0.985 1.022 1.001 1.042 1.046 0.979 1.015 1.006 1.051 1.051MEQ 1.004 1.012 1.075 1.062 1.070 0.994 0.995 1.028 1.001 1.008

(*) Adjusted R-squared ratio=Adjusted R-squared with the factor/Adjusted R-squaredwithout the factor. Orange-shaded cells=Adjusted R-squared ratio greater than 1.

Green-shaded cells=Adjusted R-squared ratio greater than 1.05 (5% of adjustment gain).Sample: 2001.I-2014.IV (56 observations). Source: Authors’ calculations.

Three salient features are worth mentioning. First, whatever the sectors included in the factor either more corre-lated to the output gap or not, the PCSI classification virtually in none of the cases provides material improve-ments. Consequently, the reading of this survey when including personal current situation questions (Q3, Q4, andQ5a) does not come out with relevant information for neither prospective consumption nor investment. Second,a comparison between a given factor with its complementary version is always favourable for the sectors moreakin to the output gap. However, an exception is made with the CICS sectors (Commerce + Industry + Construction

9Recall that the adjusted goodness-of-fit coefficient corresponds to Adjusted-R2=1− [(1− R2)(T − 1)/(T − P− 1)], where R2 is the ratiobetween the sum of regression squared residuals and total squared residuals, T is the sample size, and P the number of estimated coefficientsin the regression. Thus, the measure already considers the adjustment controlling for the number of regressors. This is particularly relevant toavoid the issue of overfitting.

13

+ Personal Services) in which 13 (out of 30) cases compared to 18 cases improves the model’s adjustment. This isimportant because this is the factor containing more information than the others and, despite this advantage, isunable to track better, specifically, DC and NDC. Third, there are two factors providing a satisfactory performanceindependently of the sectors considered and working well with all variables: PFEI and OFEI. As will be shownlater, these two specifications come out as the best for forecasting.

Our second in-sample result is regarding the statistical significance of the null hypothesis NH: φ1=...=φ4=0 ofequation (3). In this case, note that we test for this specific hypothesis being a number of different ways to considerit in terms of factor specification (level or differences), number of terms included in the regression, and the nativemodel by itself. Recall that we set this exercise obeying to a predictive criterion which has led to the best resultswith 4-term factor in levels with an AR(1) native model. Naturally, testing a particular economic theory willrequire a richer environment, such as that of Acuña, Echeverría, and Pinto-Gutiérrez (2020) to control for otherpossible effects occurring simultaneously. Having reported that there are numerous ways to carry out this typeof test, the issue of short sample is also latent. As the estimation sample comprises 56 observations (2001.I-2014.IV)and the evaluation sample 19 observations (2015.I-2019.III), we consider the full sample (2001.I-2019.III). Although75 observations could still be moderate to estimate six highly-correlated regression coefficients, we opt to conductthis exercise to disentangle and discriminate better between the proposed factors.

The results are presented in Table 3. First, in this exercise there are overall, fewer cases in which the factor comesout statistically significant compared to the previous case in which it may enhance the adjustment of the model.In this sense, this exercise could be considered as a refinement of the previous one and, thus, helping to focusin the most promising cases. Second, within those promising cases there is now a marked difference betweenPFEI and OFEI specifications, plainly favouring the OFEI index with sectors more related to the business cycle,and particularly for investment series. Third, following this exercise, the information from CITS sectors turnsspecifically useful to explain the dynamic of the investment series only (particularly MEQ), which is added to theprevious results of adjustment improvements.

In sum, PFEI and OFEI are the most fruitful re-classifications to explain the dynamic of the series considered,whereas in terms of the economic sectors in which the consumers participate, there is not a single specificationthat comes out as systematically superior—which will be determined predictively. Finally, there is supportingevidence for sectors more related to the business cycle than the remaining ones when explaining considered macroaggregates.

4.2 Out-of-sample results

Our first out-of-sample result concerns our first hypothesis, i.e. the extent to which consumer sentiment factorsbetter forecast macro aggregates and their components compared to the native un-extended chosen AR(p) model.The results are presented in Table 1A in Annex A.

Three facts are worth mentioning. First, although showing some important predictive gains (=1-RMSFE ratio%)specially at longer horizons, both PC and CWK do not deliver statistically significant results. For PC the best factorspecification is the PCSI compounded by the CICS sectors with the largest gain surrounding 18% at h=4. In turn,for CWK, there is not a single specification actually showing a predictive gain at the nowcast horizon, whereas forthe remaining horizons the CFEI specification with CI economic sectors comes out as the best forecasting strategy,with gains ranging from 4.1% to 11.3% at h=2 and 4, respectively.

Second, for DC and MEQ, there are noticeable predictive gains for all horizons, but statistically significant only ath=1 for DC, and at h=4 for MEQ. For DC, two cases provide significant results, using CFEI and OFEI both usinginformation from CIT sectors. Note that predictive gains coming from including the Transportation sector as thecomparison with CI sectors show a non-statistically significant, poorer performance. Also, the maximum gainwith CFEI achieves a material figure close to 14% (being 9.5% with the second-best alternative, OFEI). For MEQ,there are four statistically significant cases, all of them at h=4. Remarkably, all these results are obtained with theCFEI specification with each of the four economic sectors groups. Furthermore, there is virtually a tie betweenCI and CIT sectors (with gains of 7.8% and 7.7%), then a better performance is noticed with CICS sectors (8.5%),

14

and the best result is obtained with CCS (10.3%). Thus, it is important to note that the only factor that excludesconsumers working in Industry comes out as the best and, at the same time, by making pairwise comparisons,Construction seems to contribute more to the factor’s forecast ability.

Table 3. F-test results (p-value) of the consumer-based factor statistical significance (*)Factor: More sensitive sectors Factor: Less sensitive sectors

PCSI PFEI CCSI CFEI OFEI PCSI PFEI CCSI CFEI OFEIFactor: Commerce + IndustryPC 0.965 0.084 0.766 0.239 0.071 0.935 0.477 0.203 0.500 0.313DC 0.635 0.038 0.674 0.226 0.070 0.931 0.571 0.558 0.556 0.413NDC 0.976 0.042 0.875 0.209 0.048 0.872 0.430 0.592 0.429 0.273GFCF 0.971 0.105 0.380 0.127 0.028 0.756 0.334 0.161 0.103 0.076CWK 0.961 0.163 0.362 0.014 0.020 0.951 0.190 0.630 0.103 0.034MEQ 0.836 0.125 0.197 0.204 0.059 0.318 0.475 0.020 0.097 0.060Factor: Commerce + Industry + TransportationPC 0.923 0.091 0.525 0.293 0.102 0.971 0.411 0.317 0.480 0.268DC 0.504 0.028 0.612 0.345 0.148 0.981 0.561 0.564 0.488 0.348NDC 0.969 0.126 0.845 0.340 0.111 0.851 0.345 0.600 0.332 0.191GFCF 0.916 0.177 0.333 0.144 0.049 0.859 0.268 0.146 0.094 0.055CWK 0.986 0.124 0.513 0.023 0.014 0.962 0.239 0.508 0.090 0.035MEQ 0.697 0.230 0.170 0.213 0.083 0.446 0.418 0.010 0.095 0.048Factor: Commerce + Industry + Construction + Personal ServicesPC 0.802 0.529 0.164 0.515 0.364 0.900 0.063 0.750 0.242 0.065DC 0.981 0.545 0.581 0.521 0.343 0.431 0.032 0.553 0.307 0.157NDC 0.766 0.584 0.602 0.397 0.351 0.918 0.030 0.927 0.262 0.034GFCF 0.761 0.311 0.160 0.076 0.048 0.971 0.146 0.406 0.170 0.070CWK 0.847 0.099 0.637 0.086 0.023 0.986 0.331 0.439 0.027 0.030MEQ 0.408 0.481 0.026 0.066 0.037 0.794 0.176 0.128 0.251 0.104Factor: Commerce + Construction + Personal ServicesPC 0.932 0.269 0.144 0.365 0.180 0.882 0.071 0.563 0.400 0.165DC 0.965 0.308 0.647 0.382 0.209 0.364 0.047 0.224 0.499 0.373NDC 0.904 0.347 0.660 0.282 0.176 0.858 0.081 0.562 0.511 0.162GFCF 0.886 0.244 0.150 0.070 0.034 0.947 0.270 0.624 0.263 0.147CWK 0.899 0.069 0.553 0.049 0.013 0.992 0.395 0.465 0.056 0.060MEQ 0.573 0.346 0.028 0.058 0.026 0.720 0.467 0.141 0.426 0.254

(*) p-value of the null hypothesis: NH: φ1=...=φ4=0 (see equation 1) against the alternativeof at least one term is equal to zero. Green-shaded cells=p<10%. Orange-shaded

cells=p<15%. Sample: 2001.I-2019.III (75 observations). Source: Authors’ calculations.

Finally, the most fruitful results are obtained for NDC and GFCF. A common result between them is that no singlefactor is significant at the nowcast horizon, and this also is extended to NDC at h=2. However, for NDC, notablythe predictive gains at h=3 occurred all with the same PCSI factor using the four different groups of economicsectors. Moreover, the best results are obtained with CICS (20.9%) and CCS (19.1%) sectors. Consequently, the keyfeature leading to these results is the inclusion of the answers of consumers working in Personal Services, which iscorroborated with the results at h=4, where aforementioned two factors—PCSI-CICS and PCSI-CCS—comes outas the best forecasting alternatives with predictive gains of 24% and 20.9%, respectively.

Regarding GFCF, despite some important gains with CI and CIT sectors, none of them comes out as statisticallysignificant. In contrast, using CICS and CCS sectors the results with OFEI are always significant for h>1. It isimportant to remark that only in this case the best results in terms of the lowest RMSFE ratio are not statisticallysignificant, but the second-best alternative actually is so at conventional levels of significance. These are the casesof CFEI and OFEI indexes generated with CICS information comparing 0.862 versus 0.941 at h=2, 0.829 versus0.958 at h=3, and 0.810 versus 0.951 at h=4, where OFEI results are always statistically significant. The same isobtained with CCS when comparing CFEI with OFEI at h=2: 0.855 versus 0.923, h=3: 0.809 versus 0.935, and h=4:

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0.787 versus 0.928; all cases statistically significant with OFEI. Overall, however, for each considered case, the bestresults are always favourable to CCS sectors. In consequence, when considering the path of best results accordingto the lowest RMSFE ratio, this is composed by CFEI with CICS sectors at h=1, and CFEI with CCS sectors forh={2,3,4} despite the results of the CW test, but with a slightly different RMSFE ratio.

Regarding our second hypothesis, i.e. the extent to which consumers working in economic sectors more exposedto the business cycle provides better forecasting ability than those consumers working in the remaining sectors.The results are presented in Table 2A in Annex A.

The first salient feature is that a number of predictive gains are noticed favouring our hypothesis, but only a feware statistically significant. There is an overwhelming difference favouring the use of country-wide informationin the construction of the factor using either current sentiment or future expectation questions, plus the overallfuture expectation built jointly with the personal future expectation. On nine occasions, the OFEI indicator comesout as significant, and eight for CCSI, seven for CFEI, and two for PCSI. In terms of the economic sectors, theresults are spread across the four specifications, but the statistically significant cases are concentrated in CICSsectors (12), then CIT (8), and CI and CCS (3 cases each). Thus, our second hypothesis is mostly supported for DC,NDC, and GFCF using CFEI and OFEI factors with information coming from CICS sectors. These results, addedto the results of Table 1A, suggest a superior forecast ability of the CICS sectors over remaining ones when usingOFEI factor for GFCF, and reinforce the use of PCSI factor with the same sectors for NDC.

Given the number of specifications and results, in Table 4 we provide a summary of the best forecasting path ac-cording to the smaller RMSFE ratio for each variable. Note that in some cases, the smallest RMSFE ratio is achievedwith a non-statistically-significant setup, despite having available a second-best alternative with a slightly higherRMSFE ratio but rejecting the null hypothesis proposed by the CW test. This table highlights the importance ofthe PCSI specification for consumption, and the CFEI for investment series. It also makes clear that the most fruit-ful results in terms of predictive accuracy are found for NDC and GFCF, showing smaller RMSFE ratios. Finally,CICS and CCS sectors boldly provide the most valuable information for forecasting any of the considered macroaggregates.

4.3 Robustness results

In this subsection, we report the results of an extensive robustness exercise consisting in different twists to thebaseline setup. In particular, we assume different native best AR forecasting models, which is particularly relevantfor both DC and MEQ, as well as a different number of factor terms included in the regression. Notice that for DCand MEQ, according to Figure 4, the AR(4) model comes out as the best for some specific horizons (for all casesexcept MEQ at h=3 and 4). Unlike the baseline setup, we also consider the factor in levels. All these exercises areconducted to find the most fruitful way to consider the factor with an out-of-sample objective. Thus, the aim is tochallenge the results of Table 4.

All detailed results are presented in the Online Appendix, mimicking the results of Table 2 (Adjusted R-squaredratio), Table 3 (F-test results), Table 1A (RMSFE ratio between the native AR(1) and the factor-augmented ARmodel), and Table 1B (RMSFE ratio between the AR model augmented with the more sensitive factor and the ARmodel augmented with the less sensitive factor to the business cycle), but we provide a summary to ease compar-isons. Also, as we try the AR(2), AR(3), and AR(4) as native models, there is a new type of results when comparingto the native AR(1). However, these results are shown for reference only, as they are not fully comparable to theAR(1) because the factor-augmented AR(p) with p={2,3,4} could exhibit a better performance not exclusively tothe information contained in the factor but to a "larger p" (a model more suitable for the variable at hand).

Hence, the Online Appendix is organised according to the following scheme:

• A1: Native model: AR(2), factor specification: ∆x, number of factor terms: 4

• A2: Native model: AR(3), factor specification: ∆x, number of factor terms: 4

• A3: Native model: AR(4), factor specification: ∆x, number of factor terms: 4

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Table 4: Summary of the best forecasting baseline setupby macro aggregate (*)

Setup h=1 h=2 h=3 h=4PC RMSFE: 0.983 0.958 0.874 0.818

Sectors: CICS CICS/CCS CCS CICSIndex: PCSI PCSI PCSI PCSI

DC RMSFE: 0.863? 0.937 0.886 0.856Sectors: CIT CIT CCS CCSIndex: CFEI CFEI CCSI CCSI

NDC RMSFE: 0.958 0.872 0.791? 0.760??

Sectors: CICS CICS CICS CICSIndex: PCSI PCSI PCSI PCSI

GFCF RMSFE: 0.945 0.855† 0.809† 0.787†

Sectors: CICS CCS CCS CCSIndex: CFEI CFEI CFEI CFEI

CWK RMSFE: 1.002 0.959 0.983 0.887Sectors: CCS CI CCS CIIndex: CFEI CFEI OFEI CFEI

MEQ RMSFE: 0.992 0.980 0.976 0.897?

Sectors: CICS CICS CCS CCSIndex: PFEI CFEI CFEI CFEI

(*) “RMSFE” stands for Relative RMSFE1h (see equation 3). “Sectors” stands

for the economic sectors considered in the consumer-perception-based factor(see subsection 3.1). “Index” stands for the timing (current/ future) and subject(personal/country-wide) feature of the factor. (†) For this case there is available

a statistically significant result but with a slightly higher RMSFE ratio. Clarkand West (2007) test’s p-value: (???) p<1%, (??) p<5%, and (?) p<10%.

Sample: 2015.I-2019.III (19 observations). Source: Authors’ calculations.

• A4: Native model: AR(1), factor specification: ∆x, number of factor terms: 1

• A5: Native model: AR(1), factor specification: ∆x, number of factor terms: 2

• A6: Native model: AR(1), factor specification: ∆x, number of factor terms: 3

• A7: Native model: AR(1), factor specification: x, number of factor terms: 1

• A8: Native model: AR(1), factor specification: x, number of factor terms: 2

• A9: Native model: AR(1), factor specification: x, number of factor terms: 3

• A10: Native model: AR(1), factor specification: x, number of factor terms: 4.

Consequently, tabulated results are shown according to:

• Baseline Tables 2 and 3 (Adjusted R-squared ratio and F-test results) = merged to Tables 1.A1 to 1.A10,

• Baseline Table 1A (RMSFE ratio between the native AR(1) and the factor-augmented AR model) = Tables2.A1 to 2.A10,

• New tables comparing AR(p), p={2,3,4}models with the AR(1) = Tables 3.A1 to 3.A3,

• Baseline Table 2A (RMSFE ratio between factor-augmented AR models according to its relationship with thebusiness cycle) = Tables 4.A1 to 4.A10.

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Thus, for instance, for all series in which Figure 4 show that the best model is the AR(1), the comparisons should bemade across Table 2.A4 to Table 2.A10. In turn, for those series where the best model is the AR(4), the strength ofthe factor should be looked up in Table 3.A3. In this sense, and recalling that the primary interest is in forecastingand the comparison between sector, the primary conducting results are obtained from Tables 2.A4-2.A10 (or 3.A3)and Tables 4.A4-4.A10, with the in-sample results (Tables 1.A1 to 1.A10) analysed at the end.

The summary of robustness exercises is presented in Table 5. Notice that unlike Table 4, we consider two types ofresults, those statistically significant according to the CW test, and those not statistically significant. The latter areincluded to have an appraisal on the predictive gains on a small sample environment, where the CW test may notbe the most suitable but we use it as we have no better alternative, as well as to make it comparable to Table 4.

For PC, there are noticeable predictive gains for all horizons when comparing to baseline results, except at h=3in the non-statistically significant case. At h=1, there is a significant gain in neither the baseline nor alternativeestimations. However, the 2-term factor in levels with CIT sectors and OFEI index deliver better results as well asshowing better in-sample diagnostics. At h=2, there is a superior result in both RMSFE precision and significance.The results with the consumer-factor in levels including one and three terms, significant and non-statisticallysignificant, respectively, outperform the baseline results. More remarkably, the significant predictive gain of 4.9%with CIT sectors and CCSI index comes out as a better alternative than the remaining sectors less exposed to thebusiness cycle, and with better diagnostics. At h=3, the newly found statistically significant result does not providea greater predictive gain than the non-significant case, and its diagnostics are also non-supportive. For h=4, thebest results are obtained with the 4-term factor in levels, and its precision only improves for the non-significantcase. However, it is important to remark that robustness exercises find a superior statistically significant role forthe consumer-factor at any horizon (unlike the baseline results), except the nowcasting one, in which only onevariable exhibits a significant gain.

For DC, we present the results assuming that the best forecasting model is, first, the AR(1) and second the AR(4),which is in line with Figure 4. When assuming the AR(1) as the best model, the baseline results are still the bestperformers across all horizons, despite that for h>1 there are now statistically significant cases but with a smallerpredictive gain. The competing setup always includes a 2-term factor in levels. However, all these results for DCare due to the room opened by the use of the second-best forecasting model, the AR(1), and thus, it is relevantto delve in the results obtained with the AR(4). In this case, despite not finding statistically significant results, allpredictive gains are smaller than the AR(1) case, which is expected, but predictive gains nonetheless. Remarkably,all these results are obtained with the same sectors (CIT) and with two indexes: CFEI and CCSI. The best resultsare always obtained with the factor in first differences.

For NDC, robustness results provide enhanced predictive gains for h=1 and h=4. The case of NDC is the only onein the entire exercise showing a statistically significant predictive gain at the nowcasting horizon, which is also ofa material size (25.9%), and compounded by sectors (CCS) which are statistically superior to the remaining onesless exposed to the business cycle; and the PFEI index. For intermediate horizons, the results are mixed. In 8 out of9 cases the best setup is obtained with the factor in levels, and with a relatively high number of terms. For h=2, thestatistically significant result is obtained with CCS sectors and the PCSI index, which along with PFEI, are the twomost competitive indexes for this macro variable. Unlike the baseline case, for h=2 a statistically significant gainis found, completing all horizons with significant results. However, for these significant cases, the diagnostics arenot supportive, despite being superior at forecasting than the remaining sectors less exposed to the business cycle.Also, no clear pattern of sectors across horizons is found. At h=3 the baseline result remains the best, whereas h=4yields slightly better results (0.698 versus 0.760) with the factor in levels and replacing CICS by CI sectors.

For GFCF, none of the robustness results provides improvements. Thus, despite that the path of best results acrosshorizons does not provide statistically significant results, the significant ones show smaller gains also with the 4-term factor in first differences. From an in-sample point of view, all these results are very promising and favouringour hypotheses. Also, the out-of-sample comparison with sectors less exposed to the business cycle favours oursecond hypothesis, but being non-significant according to the HLN test.

For CWK, the situation with robustness exercises improves just a bit. At h=1, the baseline result with CICS sectorsand CFEI index show inexistent predictive gains, but using the factor in levels delivers a predictive gain of 4.9%

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(statistically non-significant) with same sectors but PCSI index. A similar situation is found at h=2 and 3, wheremild, statistically non-significant gains are obtained with different sectors, indexes, and consumer-factor setups.At h=4, the baseline result persists as the best with CI sectors and CFEI index, and with in-sample diagnosticsfavouring our hypotheses.

Finally, for MEQ we analyse the results assuming that the best model according to Figure 4 is the AR(4), whichclearly applies for h={1,2}, but is not the case at h={3,4}—where the AR(1) comes out as the best. When assumingthat the best model is the AR(1), the results tend to favour our first hypothesis, in the sense that using the factorin levels improves the predictive gains for h={1,2,3}. However, they do not support our second hypothesis, andsectors less exposed to the business cycle could be as good as those more exposed to it. At h=4, in turn, thebaseline result remains as the best option, corresponding to a statistically significant predictive gain of 10.3%with CCS sectors and CFEI index that, and at the same time, is better than the remaining sector less exposed tothe business cycle. Also, in-sample diagnostics give support to our out-of-sample results. When assuming theAR(4) as the best model, we find statistical gains for all horizons, despite not statistically significant. The resultsfor h={1,2} are more relevant in the light of Figure 4, and in both cases the RMSFE with CICS sectors and PFEIindex gives support to our hypotheses–first, showing predictive gains of 5.2% and 6% for h={1,2} and, second,predicting better than do sectors less exposed to the business cycle.

In sum, from our baseline setup we conclude that PCSI along with CCSI indexes provide the most fruitful resultsfor consumption series, and CFEI doing so for investment series. In turn, NDC and GFCF are the variables showingthe greatest predictive gains of the whole exercise. Lastly, CICS and CCS sectors undoubtedly lead to the bestforecasting results as well as better forecasts compared to remaining sectors less exposed to the business cycle.From the robustness exercises, we confirm that NDC and GFCG are the most benefited series when using theconsumer-based factor for forecasting as well as the pre-eminence of CCS and CICS sectors. However, a majorshift in favour of the OFEI index is found, which in our baseline setup leads to the best result in just one case,whereas in the alternative setups comes out as the best alternative for investment series. This shift is due tothe different way in which the factor is included in the forecasting regression. In this sense, the factor in levelscomes out as the best alternative at shorter horizons, i.e. h={1,2}, whereas the first differences are superior for theremaining horizons.

5 Concluding remarks

The aim of this article is two-fold: (i) to analyse the extent to which consumer sentiment indexes better forecastaggregate consumption and its components, by constructing new indexes using labour market characteristics ofrespondents using a unique dataset, and re-focusing aggregate answers according to timing and subject, and(ii) to analyse to what extent a greater exposure of consumers/workers to the business cycle comes out with abetter ability to nowcast and short-term forecast consumption, compared to consumers/workers that participatein economic sectors less exposed to the business cycle. Our claim assumes that consumers work in sectors wheredecisions are taken depending to a greater or lesser degree on the current and future economic situation. Theconsumers can take the decisions themselves, be aware of them, or be affected by their consequences. Thus, weassume the existence of a learning mechanism permeable to the sentiment of workers that is present when they aresurveyed as consumers. We call this mechanism "exposure" and we operationalize it by means of the correlationof worker’s economic sector with the output gap. Since this argument is extensible to investment decisions, weinclude total investment and its components in the analysis.

Despite the considerable amount of related literature, this article goes one step further by using microdata evi-dence of consumer sentiment predictability over aggregate consumption and investment, taking advantage of aspecific survey on consumers’ perceptions which, at the same time, is linked to a survey of employment/ un-employment of the Greater Metropolitan area of Chile’s capital city. These are the Survey of Employment andUnemployment in Greater Santiago and the Survey of Perception and Expectations on the Economic Situation inGreater Santiago, both elaborated by the Universidad de Chile’s Centro de Microdatos.

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Table 5: Summary of the best forecasting path by macro aggregate under different setups (*)h=1 h=2 h=3 h=4

Stat. s.1 Not stat. s.1 Stat. s.1 Not stat. s.1 Stat. s.1 Not stat. s.1 Stat. s.1 Not stat. s.1

Private Consumption (best native model2: AR(1))RMSFE3 - 0.837 0.951? 0.890 0.974? 0.874 0.914? 0.754Sectors4 - CIT CIT CICS CICS CCS CCS CIIndex5 - OFEI CCSI PFEI PCSI PCSI PCSI PCSIHLN test6 - 1.034 0.935 0.997 0.983 1.021 0.925 0.770Factor7 - x x x ∆x ∆x x xNo. of terms8 - 2 1 3 2 4 4 4Adj. R-sq. (more sens.)9 - 1.011 1.012 1.005 0.994 0.978 0.997 1.014Adj. R-sq. (less sens.)9 - 1.014 1.007 1.043 0.995 0.983 1.002 0.990F-Test (more sens.)10 - 0.122 0.075 0.618 0.813 0.932 0.645 0.215F-Test (less sens.)10 - 0.106 0.144 0.072 0.798 0.882 0.568 0.846

Durable Consumption (best native model2: AR(1))RMSFE3 0.863? 0.912 0.941?? 0.937 0.957? 0.886 0.955? 0.856Sectors4 CIT CI CI CIT CIT CCS CI CCSIndex5 CFEI CCSI OFEI CFEI OFEI CCSI OFEI CCSIHLN test6 0.922 0.961 0.976 0.952? 0.975 0.985 0.969 0.980Factor7 ∆x x x ∆x x ∆x x ∆xNo. of terms8 4 2 2 4 2 4 2 4Adj. R-sq. (more sens.)9 0.998 1.012 1.027 0.998 1.023 0.988 1.027 0.988Adj. R-sq. (less sens.)9 0.987 1.006 1.017 0.987 1.018 0.997 1.017 0.997F-Test (more sens.)10 0.345 0.162 0.022 0.345 0.031 0.647 0.022 0.647F-Test (less sens.)10 0.488 0.142 0.083 0.488 0.079 0.224 0.083 0.224

Durable Consumption (best native model2: AR(4))RMSFE3 - 0.885 - 0.978 - 0.928 - 0.919Sectors4 - CIT - CIT - CIT - CITIndex5 - CFEI - CFEI - CCSI - CCSIHLN test6 - 0.903? - 0.936? - 0.947 - 0.964Factor7 - ∆x - ∆x - ∆x - ∆xNo. of terms8 - 4 - 4 - 4 - 4Adj. R-sq. (more sens.)9 - 0.997 - 0.997 - 0.990 - 0.990Adj. R-sq. (less sens.)9 - 0.990 - 0.998 - 0.999 - 0.999F-Test (more sens.)10 - 0.411 - 0.411 - 0.476 - 0.476F-Test (less sens.)10 - 0.550 - 0.550 - 0.134 - 0.134

Non-durable Consumption (best native model2: AR(1))RMSFE3 0.741?? 0.769 0.896?? 0.653 0.791? 0.742 0.698? 0.700Sectors4 CCS CICS CCS CCS CICS CCS CI CITIndex5 PFEI PFEI PCSI PFEI PCSI PFEI PCSI PCSIHLN test6 0.831?? 0.809 0.870?? 0.932 0.866 0.964 0.697?? 0.694??

Factor7 x x x x ∆x x x xNo. of terms8 3 4 2 4 4 4 4 4Adj. R-sq. (more sens.)9 1.025 1.016 0.993 1.016 0.959 1.016 0.979 0.974Adj. R-sq. (less sens.)9 1.077 1.062 0.996 1.062 0.958 1.062 0.966 0.969F-Test (more sens.)10 0.352 0.450 0.555 0.450 0.766 0.450 0.710 0.784F-Test (less sens.)10 0.122 0.220 0.470 0.220 0.918 0.220 0.806 0.733

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Table 5 (cont.): Summary of the best forecasting path by macro aggregate under different setups (*)h=1 h=2 h=3 h=4

Stat. s.1 Not stat. s.1 Stat. s.1 Not stat. s.1 Stat. s.1 Not stat. s.1 Stat. s.1 Not stat. s.1

Gross Fixed Capital Formation (best native model2: AR(1))RMSFE3 - 0.945 0.923?? 0.855 0.935? 0.809 0.928?? 0.787Sectors4 - CICS CCS CCS CCS CCS CCS CCSIndex5 - CFEI OFEI CFEI OFEI CFEI OFEI CFEIHLN test6 - 0.938 0.873 0.879 0.867 0.878 0.876 0.876Factor7 - ∆x ∆x ∆x ∆x ∆x ∆x ∆xNo. of terms8 - 4 4 4 4 4 4 4Adj. R-sq. (more sens.)9 - 1.033 1.042 1.035 1.042 1.035 1.042 1.035Adj. R-sq. (less sens.)9 - 1.022 1.020 1.013 1.020 1.013 1.020 1.013F-Test (more sens.)10 - 0.076 0.034 0.070 0.034 0.070 0.034 0.070F-Test (less sens.)10 - 0.170 0.147 0.263 0.147 0.263 0.147 0.263

Construction and Works (best native model2: AR(1))RMSFE3 - 0.951 - 0.950 - 0.944 - 0.887Sectors4 - CICS - CICS - CCS - CIIndex5 - PCSI - PCSI - CFEI - CFEIHLN test6 - 0.984 - 0.992 - 0.996 - 0.980Factor7 - x - x - ∆x - ∆xNo. of terms8 - 4 - 4 - 3 - 4Adj. R-sq. (more sens.)9 - 0.978 - 0.978 - 0.993 - 1.060Adj. R-sq. (less sens.)9 - 0.982 - 0.982 - 0.998 - 1.034F-Test (more sens.)10 - 0.848 - 0.848 - 0.433 - 0.014F-Test (less sens.)10 - 0.817 - 0.817 - 0.768 - 0.103

Machinery and Equipment (best native model2: AR(1))RMSFE3 - 0.976 0.937?? 0.933 0.928?? 0.922 0.897? 0.941Sectors4 - CICS CCS CICS CICS CICS CCS CITIndex5 - OFEI OFEI OFEI OFEI OFEI CFEI PFEIHLN test6 - 1.047 1.017 0.998 1.025 1.015 0.934 0.960Factor7 - x x x x x ∆x xNo. of terms8 - 2 2 3 2 3 4 2Adj. R-sq. (more sens.)9 - 1.002 1.003 1.092 1.002 1.092 1.062 0.998Adj. R-sq. (less sens.)9 - 0.998 0.996 1.056 0.998 1.056 1.001 1.002F-Test (more sens.)10 - 0.491 0.480 0.006 0.491 0.006 0.058 0.708F-Test (less sens.)10 - 0.639 0.691 0.025 0.639 0.025 0.426 0.641

Machinery and Equipment (best native model2: AR(4))RMSFE3 - 0.948 - 0.940 - 0.956 - 0.987Sectors4 - CICS - CICS - CICS - CITIndex5 - PFEI - PFEI - PFEI - PCSIHLN test6 - 0.869 - 0.916 - 0.959 - 0.993Factor7 - ∆x - ∆x - ∆x - ∆xNo. of terms8 - 4 - 4 - 4 - 4Adj. R-sq. (more sens.)9 - 0.987 - 0.987 - 0.987 - 0.997Adj. R-sq. (less sens.)9 - 0.980 - 0.980 - 0.980 - 1.012F-Test (more sens.)10 - 0.483 - 0.483 - 0.483 - 0.674F-Test (less sens.)10 - 0.652 - 0.652 - 0.652 - 0.159

(*) Notes to Table 5. (1) “Stat. s.” stands for statistically significant; “Not stat. s.” denotes non-statistically significant resultaccording to the Clark and West (2007) test. p-value: (???) p<1%, (??) p<5%, and (?) p<10%. (2) “Best native model” reports thebest forecasting AR(p) model according to Figure 4. For PC, NDC, GFCF, and CWK the best model is the AR(1) for all horizonswhereas for DC andMEQ it is the AR(4) for some specific horizons. (3) “RMSFE” stands for Relative RMSFEh

1 (see equation 3).(4) “Sectors” stands for the economic sectors considered in the consumer-based factor (see subsection 3.1): CI, CIT, CICS, and

21

CCS. (5) “Index” stands for the timing (current/future) and subject (personal/country-wide) feature of the factor: CCSI, CFEI,PCSI, PFEI, and OFEI. (6) “HLN test” stands for Relative RMSFEh

2 (see equation 3) and the results of the Harvey, Leybourne,and Newbold (1997) test between factor-augmented AR models according to its relationship with the business cycle. p-value:(???) p<1%, (??) p<5%, and (?) p<10%. Orange-shaded cells=Figures below 1. Green-shaded cells= Figures below 1 andstatistically significant. (7) “Factor” stands for the way in which the consumer-based factor enters the forecasting equation (seeequation 1) either in levels (x) or first differences (∆x). (8) “No. of terms” refers to the number of factor terms included in theforecasting equation (see equation 1). 1=x/∆x, 2=x x(-1)/∆(x) ∆(x(t-1)), 3=x x(-1) x(t-2)/∆(x) ∆(x(t-1)) ∆(x(t-2)), and 4=xx(t-1) x(t-2) x(t-3)/∆(x) ∆(x(t-1)) ∆(x(t-2)) ∆(x(t-3)). (9) “Adj. R-sq. (more sens.)” and “Adj. R-sq. (less sens.)” stands for theAdjusted R-squared ratio between factor-augmented and native AR models, for the factors built with sectors more and lesssensitive to the business cycle. Orange-shaded cells=Adjusted R-squared ratio greater than 1. Green-shaded cells=AdjustedR-squared ratio greater than 1.05 (5% of adjustment gain). (10) “F-Test (more sens.)” and “F-Test (less sens.)” stands for thep-value of the consumer-based factor statistical significance. NH: φ1=...=φp=0 (see equation 1) against the alternative of at leastone term is equal to zero. Green-shaded cells=p<10%. Orange-shaded cells=p<15%. Sample: 2015.I-2019.III (19 observations).Source: Authors’ calculations.

The key advantage is that it is possible to link, with no error, the perception of a consumer with her/his character-istics as a labour market participant. Thus, it is possible to exploit databases’ richness by re-grouping consumerperceptions indexes based on labour-market characteristics, aiming to improve their forecasting ability over macroaggregates and hypothesis testing. This treatment also aims to disentangle labour market characteristics more akinto the forecasting task.

Our first hypothesis comes out as a multi-horizon forecast comparison between a simple AR model for a givenmacro aggregate and its corresponding survey-based factor-augmentation version, using different computationsof consumer indexes. The second hypothesis consists in an out-of-sample comparison between two survey-basedfactors, one grouping indicators from consumers currently working in sectors more sensitive to the business cycle,and the other conformed by consumers working in the remaining sectors surveyed. We proxy the business cycleby means of an output gap estimation.

These hypotheses are tested for Private consumption, Non-durable consumption, and Durable consumption, plusGross fixed capital formation, Construction & works, and Machinery & equipment, using the quarterly samplecovering from 2000.I to 2019.III (75 observations). We also make use of a re-classification of answers based ontiming (current/future) and subject (personal/country). Remarkably, we are able to distinguish the economicsector in which the consumer is currently working, adding new dimensions to exploit on top of the previousre-classification.

Our in-sample results suggest that the adjusted goodness-of-fit coefficient of the AR model improves in most caseswhen including any of the consumer-based factors. In particular, the PFEI and the OFEI specifications improvefor almost all macro aggregates considering any sectorial definition of the factor. In contrast, the PCSI is lesshelpful in explaining the dynamics of any macro aggregate built with any sector. Most of these improvements arefound for GFCF and its components, andDC somewhat less. Consumers working in Commerce and Industry sectorsprovide more useful information than remaining sectors, as well as when adding consumers on Construction andPersonal Services sectors without manufacturing. When accounting for the statistical significance of the consumer-based factor, there is a concentration of significant cases using future-based indexes (PFEI, CFEI, and OFEI) for thesame macro aggregates that exhibit a better adjustment (GFCF and DC). Also, the evidence is most favourable forsectors mostly related to the business cycle–proxied by the output gap–rather than those that are less so or plainlyinsensitive to it.

Our out-of-sample results show, with a baseline added to alternative setups, predictive gains at all horizons forall variables, in some cases of a sizable magnitude and statistically non-significant in others. The most fruitfulresults are obtained for NDC and GFCF, which are statistically superior to the predictive benchmark model whenconformed by sectors more akin to the business cycle. There is not a silver-bullet definition of the factor helpingat the same time for all aggregates across all horizons. However, more often than not for consumption series, thePCSI followed by the CCSI lead to the best results. In turn, the OFEI do so for investment series. Regarding theeconomic sectors in which consumers participate and provide more useful predictive information, unquestionably

22

the best forecasting results are concentrated in Commerce, Industry, Construction, and Personal Services (thus, outof 3,060 individuals surveyed per quarter, this factor is composed by an average of 1,735 answers per quarter)and in Commerce, Construction, and Personal Services (comprising 1,313 answers per quarter on average). Whencomparing between factors, the results are largely favourable to the factors based on consumers more exposed tothe business cycle. In this line, the most fruitful results are obtained with Commerce, Industry, and Transportationsectors and Commerce, Construction, and Personal Services that outperform the remaining sectors less exposed tothe business cycle.

Although surveys of consumers perceptions provide rich information, these results are important as it is necessaryto disentangle ideally from the most disaggregate level to have a better revealing economic behaviour.

References

1. Abberger, K., 2007, "Forecasting Quarter-on-Quarter Changes of German GDP with Monthly Business TendencySurvey Results," Working Paper 40, ifo Leibniz Institute for Economic Research at the University of Munich.

2. Acuña, G., C. Echeverría, and C. Pinto-Gutiérrez, 2020, " Consumer Confidence and Consumption: Empiri-cal Evidence from Chile," International Review of Applied Economics 34(1): 75-93.

3. Albagli, E., J.A. Fornero, M.A. Fuentes, and R. Zúñiga, 2019, " On the Effects of Confidence and Uncertaintyon Aggregate Demand: Evidence from Chile," Economía Chilena 22(3): 8-33.

4. Basselier, R., D. de A. Liedo, G.L. Langenus, 2018, "Nowcasting Real Economic Activity in the Euro Area:Assessing the Impact of Qualitative Surveys," Journal of Business Cycle Research 14: 1-46.

5. Blanchard, O.J. and N.G. Mankiw, 1988, "Consumption: Beyond Certainty Equivalence," American EconomicReview 78(2): 173-177.

6. Box, G.E.P. and G.M. Jenkins, 1970, Time Series Analysis: Forecasting and Control, first edition, San Francisco,USA: Holden Day.

7. Bruno, G. and M. Malgarini, 2002, "An Indicator of Economic Sentiment for the Italian Economy," Documenti diLavoro 28, ISAE Istituto di Studi e Analisi Economica.

8. Bürgi, C. and T.M. Sinclair, 2015, "A Nonparametric Approach to Identifying a Subset of Forecasters that Outper-forms the Simple Average," Research Program on Forecasting, Working Paper 2015-006, The George Washing-ton University.

9. Calvo, G. and M. Ricaurte, 2012, "Indicadores Sintéticos para la Proyección de Imacec en Chile," Working Paper656, Central Bank of Chile.

10. Carroll, C.D., J.C. Fuhrer, and D.W. Wilcox, 1994, "Does Consumer Sentiment Forecast Household Spending?If So, Why?" American Economic Review 84(5): 1397-1408.

11. Centro de Microdatos, 2016, Diseño Muestral Encuesta de Ocupación y Desocupación en el Gran Santiago, Centrode Microdatos, University of Chile.

12. Chanut, N., M. Marcel, and C.A. Medel, 2019, "Can Economic Perceptions Surveys Improve MacroeconomicForecasting in Chile?," Economía Chilena 22(3): 34-97.

13. Clark, T.E. and M.W. McCracken, 2001, "Tests of Equal Forecast Accuracy and Encompassing for NestedModels," Journal of Econometrics 105: 85-110.

14. Clark, T.E. and M.W. McCracken, 2005, "Evaluating Direct Multistep Forecasts," Econometric Reviews 24: 369-404.

15. Clark, T.E. and K.D. West, 2007, "Approximately Normal Tests for Equal Predictive Accuracy in NestedModels," Journal of Econometrics 138(1): 291-311.

23

16. De Mello, E.P.G. and F.M.R. Figueiredo, 2014, "Assessing the Short-term Forecasting Power of Confidence Indices,"Working Paper 371, Banco Central do Brasil.

17. Diebold, F.X. and R.S. Mariano, 1995, "Comparing Predictive Accuracy," Journal of Business and EconomicStatistics 13: 153-263.

18. Doms, M. and N. Morin, 2004, "Consumer Sentiment, the Economy, and the News Media," Finance and Eco-nomics Discussion Series, Staff Working Paper 2004-51, Federal Reserve Board.

19. Figueroa, C. and M. Pedersen, 2019, "Extracting Information on Economic Activity from Business and Con-sumer Surveys in an Emerging Economy (Chile)," Economía Chilena 22(3): 98-131.

20. Fuhrer, J.C., 1993, "What Role Does Consumer Sentiment Play in the U.S. Economy?" New England EconomicReview January: 32-44.

21. Garnitz, J., R. Lehmann, and K. Wohlrabe, 2017, "Forecasting GDP all over the World: Evidence from Compre-hensive Survey Data," Working Paper 40, ifo Leibniz Institute for Economic Research at the University ofMunich.

22. Gayer, C., 2005, "Forecast Evaluation of European Commission Survey Indicators," Journal of Business CycleMeasurement and Analysis 2(2): 157-183.

23. Geiger, M. and J. Scharler, 2019, "How Do Consumers Assess the Macroeconomic Effects of Oil Price Fluctu-ations? Evidence from U.S. Survey Data," Journal of Macroeconomics 62: 103134.

24. Ghysels, E., D. Osborn, and P.M. Rodrigues, 2006, Forecasting Seasonal Time Series, in G. Elliot, C.W.J. Granger,and A. Timmermann (Eds.), Handbook of Economic Forecasting, volume 1, North Holland: Elsevier.

25. Girardi, A., R. Golinelli, and C. Pappalardo, 2017, "The Role of Indicator Selection in Nowcasting Euro-areaGDP in Pseudo-real Time," Empirical Economics 53: 79-99.

26. Hansson, J., P. Jansson, and M. Löf, 2003, "Business Survey Data: Do They Help in Forecasting the Macro Econ-omy?," Working Paper 84, National Institute of Economic Research, Stockholm, Sweden.

27. Harvey, D., S. Leybourne, and P. Newbold, 1997, "Testing the Equality of Prediction Mean Squared Errors,"International Journal of Forecasting 13: 281-291.

28. Howrey, E.P., 2001, "The Predictive Power of the Index of Consumer Sentiment," Brookings Papers on EconomicActivity 2001(1): 175-207.

29. Lahiri, L., G. Monokroussos, and Y. Zhao, 2015, "Forecasting Consumption: The Role of Consumer Confi-dence in Real Time with Many Predictors," Journal of Applied Econometrics 31(7): 1254-1275.

30. Li, C., 2011, "Consumer Expectation and Output Growth: The Case of China," Economics Letters 113: 298-300.

31. Ludvigson, S., 2004, "Consumer Confidence and Consumer Spending," Journal of Economic Perspectives 18:29-50.

32. Moon, H. and J. Lee, 2012, Forecast Evaluation of Economic Sentiment Indicator for the Korean Economy, in Bankfor International Settlements (Ed.), Proceedings of the Sixth IFC Conference on Statistical Issues and Activitiesin a Changing Environment 36: 180-190.

33. Österholm, P., 2014, "Survey Data and Short-term Forecasts of Swedish GDP Growth," Applied EconomicsLetters 21(2): 135-139.

34. Riquelme, V. and G. Riveros, 2018, "Un Indicador Contemporáneo de Actividad (ICA) para Chile," EconomíaChilena 21(1): 134-149.

35. Shröeder, M. and F.P. Hüfner, 2002, "Forecasting Economic Activity in Germany: How Useful are Sentiment Indica-tors?" Discussion Paper 02-56, Zentrum für Europäische Wirtschaftsforschung GmbH / Centre for EuropeanEconomic Research.

24

36. Souleles, N.S., 2004, "Expectations, Heterogeneous Forecast Errors, and Consumption: Micro Evidence fromthe Michigan Consumer Sentiment Survey," Journal of Money, Credit and Banking 36: 39-72.

37. Survey of Consumers, University of Michigan, 2020, Survey Description, accessed on July 7, 2020.

25

AB

asel

ine

resu

lts:

AR

(1)m

odel

Tabl

e1A

.Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

nati

veA

R(1

)and

fact

or-a

ugm

ente

dA

R(1

)mod

el(*

)PCSI

PFEI

CCSI

CFEI

OFEI

PCSI

PFEI

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OFEI

PCSI

PFEI

CCSI

CFEIOFEI

PCSI

PFEI

CCSI

CFEIOFEI

Com

mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

.C

omm

.+In

d.+

Con

st.+

Pers

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v.C

omm

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rs.S

erv.

hPr

ivat

eC

onsu

mpt

ion

11.

006

1.17

5???

1.07

2?1.

015

1.08

8??

0.99

41.

178???

1.08

4??

1.01

51.

086??

0.98

31.

171?

1.12

6??

1.03

71.

095?

0.98

91.

164?

1.11

4??

1.02

91.

088?

20.

974

1.37

3??

1.08

61.

079

1.21

7???

0.96

11.

367??

1.10

4?1.

106

1.21

7???

0.95

81.

314??

1.15

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1.17

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223??

0.95

81.

314??

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30.

919

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81.

099

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0.90

41.

489??

1.01

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128

1.25

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01.

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1.05

61.

217?

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874

1.45

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51.

192?

1.27

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947

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81.

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143

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830

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91.

203?

1.26

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996

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932

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893

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926

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989

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ures

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26

Tabl

e2A

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ti-h

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Era

tio

betw

een

fact

or-a

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ente

dA

R(1

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els

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(*)

PCSIPFEI

CCSI

CFEIOFEIPCSI

PFEI

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PFEI

CCSI

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PCSI

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Com

mer

ce+

Indu

stry

Com

mer

ce+

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stry

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ansp

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Con

st.+

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mpt

ion

11.

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11.

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61.

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986

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933

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60.

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965

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981

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31.

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60.

962

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93

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119?

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80.

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50.

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874

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11.

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830

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984

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40.

857

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70.

932

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41.

070

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10.

911

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50.

757?

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909

1.04

30.

992

0.77

31.

038

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41.

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Dur

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sum

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989

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60.

942

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20.

994

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90.

962

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30.

989

0.97

50.

944

0.93

30.

965

21.

003

1.02

91.

042

0.96

11.

017

0.99

31.

028

1.02

70.

942

0.99

01.

025

1.00

31.

018

0.98

60.

983

1.02

11.

006

0.98

41.

011

1.01

23

1.01

61.

040

1.08

31.

015

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71.

005

1.03

61.

064

0.99

31.

010

1.05

71.

026

1.05

70.

995

1.01

01.

047

1.03

01.

040

1.00

71.

041

41.

015

1.03

91.

090

1.04

11.

045

1.00

01.

040

1.06

91.

016

1.02

31.

048

1.03

61.

032

1.00

11.

032

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044

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81.

004

1.06

9h

Non

-dur

able

Con

sum

ptio

n1

0.97

61.

097??

0.96

20.

943

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60.

964

1.09

9??

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80.

943

1.02

10.

928

1.06

00.

969

0.97

70.

978

0.91

21.

005

1.01

00.

953

0.94

32

0.96

11.

119???

0.91

80.

803

0.94

00.

944?

1.12

0???

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30.

840

0.94

90.

807

1.10

2??

0.85

50.

959

0.96

80.

818

1.07

10.

856

0.93

10.

952

30.

949

1.12

7???

0.91

7??

0.76

4?0.

917

0.93

5?1.

132??

0.88

2??

0.79

1?0.

925

0.74

21.

156??

0.81

0?0.

966

0.96

30.

760

1.11

0?0.

816??

0.94

40.

953

40.

988

1.08

80.

907?

0.75

4?0.

885

0.97

31.

093?

0.86

8?0.

781?

0.89

30.

719?

1.17

7???

0.80

30.

987

0.96

70.

750?

1.13

5???

0.82

90.

976

0.97

1h

Gro

ssFi

xed

Cap

ital

Form

atio

n1

1.06

00.

998

0.99

51.

014

0.97

01.

063

1.02

60.

999

1.04

01.

004

1.12

61.

002

0.92

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934

0.94

61.

112

0.93

30.

896

0.92

10.

906

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007

0.93

50.

925

1.00

60.

922

1.01

00.

973

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041

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090

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922

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00.

858

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90.

896

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10.

812

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23

1.00

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896

0.84

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944

0.87

11.

004

0.92

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844?

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20.

925

1.04

10.

889

0.90

5?0.

870

0.81

11.

039

0.83

30.

898

0.76

40.

728?

41.

031

0.89

10.

826??

0.90

50.

850?

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909

0.82

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901

1.01

60.

852

0.89

7??

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40.

793?

1.02

00.

809

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0.74

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715??

hC

onst

ruct

ion

and

Wor

ks1

1.00

50.

984

0.95

61.

004

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41.

004

0.99

70.

971

1.01

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000

0.98

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016

0.95

20.

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955

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20.

989

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989

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1.01

40.

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00.

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016

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995

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965

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909

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993

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906??

0.98

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991

0.99

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996

0.90

3??

1.00

11.

004

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90.

969

0.98

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015

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60.

998

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00.

954

0.96

00.

897

40.

994

0.97

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0.87

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0.94

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971

0.99

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979

0.86

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991

0.96

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0.97

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999

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0.96

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929

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0.87

2??

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achi

nery

and

Equi

pmen

t1

1.06

31.

098

1.06

11.

017

1.02

61.

060

1.11

11.

066

1.02

21.

039

1.13

11.

045

0.95

50.

978

1.02

31.

129

1.01

30.

930

0.99

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023

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020

0.99

90.

996

0.99

40.

955

1.01

81.

028

1.02

41.

001

0.98

21.

113

1.00

50.

967

0.93

50.

958

1.09

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964

0.94

60.

937

0.93

83

1.01

80.

975

0.86

00.

869

0.88

71.

004

0.98

00.

874

0.89

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923

1.03

20.

912

0.91

00.

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0.90

51.

044

0.86

5?0.

892

0.88

50.

860

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044

0.98

40.

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0.91

80.

923

1.04

10.

984

0.89

90.

937

0.95

11.

121

0.93

60.

941

0.92

20.

920

1.12

60.

909

0.93

00.

878

0.87

5(?

)Rel

ativ

eR

MSF

E2 h(s

eeeq

uati

on3)

.Ora

nge-

shad

edce

lls=F

igur

esbe

low

1.G

reen

-sha

ded

cells

=Fi

gure

sbe

low

1an

dst

atis

tica

llysi

gnifi

cant

.H

arve

y,Le

ybou

rne,

and

New

bold

(199

7)te

st’s

p-va

lue:

(???

)p<

1%,(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

27

Does the Exposure to the Business Cycle Improve Consumer Perceptionsfor Forecasting? Microdata Evidence from Chile∗

Online Appendix

Fernando Faure†

Universidad de ChileCarlos A. Medel‡

Central Bank of Chile

September 1, 2020

Abstract

This is the Online Appendix of the Faure, F. and C.A. Medel (2020), "Does the Exposure to the Business CycleImprove Consumer Perception for Forecasting? Microdata Evidence from Chile" paper containing robustness exercises’results referred in subsection 4.3. These exercises are different variations of the baseline setup displayed accordingto the following scheme:

Factor In-sample Out-of-sample

No. Model Spec. Terms Adj. R-sq. F-test ARX/AR(1) ARX(p)/AR(p) ARX1/ARX2

Baseline AR(1) ∆y 4 Table 2 Table 3 Table 1A - Table 2A

1 AR(2) ∆y 4 Table 1.A1 Table 2.A1 Table 3.A1 Table 4.A1

2 AR(3) ∆y 4 Table 1.A2 Table 2.A2 Table 3.A2 Table 4.A2

3 AR(4) ∆y 4 Table 1.A3 Table 2.A3 Table 3.A3 Table 4.A3

4 AR(1) ∆y 1 Table 1.A4 Table 2.A4 - Table 4.A4

5 AR(1) ∆y 2 Table 1.A5 Table 2.A5 - Table 4.A5

6 AR(1) ∆y 3 Table 1.A6 Table 2.A6 - Table 4.A6

7 AR(1) y 1 Table 1.A7 Table 2.A7 - Table 4.A7

8 AR(1) y 2 Table 1.A8 Table 2.A8 - Table 4.A8

9 AR(1) y 3 Table 1.A9 Table 2.A9 - Table 4.A9

10 AR(1) y 4 Table 1.A10 Table 2.A10 - Table 4.A10

∗The views and ideas expressed in this paper do not necessarily represent those of the Central Bank of Chile or its authorities. Any error oromission remains at authors’ sole responsibility.

†BA in Economics and Administration undergraduate, Universidad de Chile. E-mail: ffaure@fen.uchile.cl.‡Economic Adviser to the Governor, Central Bank of Chile. E-mail: cmedel@bcentral.cl.

1R

obus

tnes

sre

sult

sI:

AR

(2)n

ativ

em

odel

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erm

fact

orin

diff

eren

ces

Tabl

e1.

A1.

Adj

uste

dR

-squ

ared

rati

obe

twee

nA

R(2

)fac

tor-

augm

ente

dan

dna

tive

AR

(2)m

odel

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and

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stre

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cons

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ctor

stat

isti

cals

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fican

ce(*

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or:L

ess

sens

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ors

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or:L

ess

sens

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or:C

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ryPC

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024

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000

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021

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002

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80.

100

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50.

277

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274

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004

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001

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000

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044

0.97

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176

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082

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70.

997

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024

1.01

90.

603

0.64

50.

475

0.10

70.

134

0.94

70.

922

0.38

10.

059

0.09

6M

EQ1.

012

1.00

51.

074

1.04

41.

051

0.99

60.

977

1.01

60.

990

0.99

20.

322

0.44

20.

015

0.23

20.

108

0.67

60.

777

0.17

50.

743

0.61

0(*

)Adj

uste

dR

-squ

ared

rati

o=A

djus

ted

R-s

quar

edw

ith

the

fact

or/A

djus

ted

R-s

quar

edw

itho

utth

efa

ctor

.Ora

nge-

shad

edce

lls=A

djus

ted

R-s

quar

edra

tio

grea

ter

than

1.G

reen

-sha

ded

cells

=Adj

uste

dR

-squ

ared

rati

ogr

eate

rth

an1.

05(5

%of

adju

stm

entg

ain)

.Sam

ple:

2001

.I-20

14.IV

(56

obse

rvat

ions

).(*

*)p-

valu

eof

the

null

hypo

thes

is:N

H:φ

1=...

=φ

4=0

(see

equa

tion

1)ag

ains

tthe

alte

rnat

ive

ofat

leas

tone

term

iseq

ual

toze

ro.G

reen

-sha

ded

cells

=p<

10%

.Ora

nge-

shad

edce

lls=p<

15%

.Sam

ple:

2001

.I-20

19.II

I(75

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

1

Tabl

e2.

A1.

Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

nati

veA

R(1

)and

fact

or-a

ugm

ente

dA

R(2

)mod

el(*

)PCSI

PFEI

CCSI

CFEI

OFEI

PCSI

PFEI

CCSI

CFEI

OFEI

PCSI

PFEI

CCSI

CFEI

OFEI

PCSI

PFEI

CCSI

CFEI

OFEI

Com

mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

.C

omm

.+In

d.+

Con

st.+

Pers

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v.C

omm

.+C

onst

.+Pe

rs.S

erv.

hPr

ivat

eC

onsu

mpt

ion

11.

254

1.32

8??

1.25

4?1.

236?

1.28

6??

1.23

91.

334??

1.26

31.

233

1.28

3?1.

183

1.35

3??

1.29

51.

244

1.29

4?1.

201

1.34

2?1.

297?

1.23

91.

288?

21.

351???

1.61

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1.42

3??

1.50

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3??

1.61

1???

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4?1.

484??

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9??

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2???

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1?1.

471??

1.51

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31.

416???

1.79

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(?)R

elat

ive

RM

SFE2 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=

Figu

res

belo

w1

and

stat

isti

cally

sign

ifica

nt.

Har

vey,

Leyb

ourn

e,an

dN

ewbo

ld(1

997)

test

’sp-

valu

e:(???

)p<

1%,(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

4

2R

obus

tnes

sre

sult

sII

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(3)n

ativ

em

odel

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erm

fact

orin

diff

eren

ces

Tabl

e1.

A2.

Adj

uste

dR

-squ

ared

rati

obe

twee

nA

R(3

)fac

tor-

augm

ente

dan

dna

tive

AR

(3)m

odel

(*)

and

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stre

sult

s(p

-val

ue)o

fthe

cons

umer

-bas

edfa

ctor

stat

isti

cals

igni

fican

ce(*

*)Fa

ctor

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ese

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ive

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ors

Fact

or:L

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sens

itiv

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ese

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or:L

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itiv

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quar

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ith

the

fact

or/A

djus

ted

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quar

edw

itho

utth

efa

ctor

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nge-

shad

edce

lls=A

djus

ted

R-s

quar

edra

tio

grea

ter

than

1.G

reen

-sha

ded

cells

=Adj

uste

dR

-squ

ared

rati

ogr

eate

rth

an1.

05(5

%of

adju

stm

entg

ain)

.Sam

ple:

2001

.I-20

14.IV

(56

obse

rvat

ions

).(*

*)p-

valu

eof

the

null

hypo

thes

is:N

H:φ

1=...

=φ

4=0

(see

equa

tion

1)ag

ains

tthe

alte

rnat

ive

ofat

leas

tone

term

iseq

ual

toze

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reen

-sha

ded

cells

=p<

10%

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nge-

shad

edce

lls=p<

15%

.Sam

ple:

2001

.I-20

19.II

I(75

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

5

Tabl

e2.

A2.

Mul

ti-h

oriz

onR

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tio

betw

een

nati

veA

R(1

)and

fact

or-a

ugm

ente

dA

R(3

)mod

el(*

)PCSI

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CCSI

CFEI

OFEI

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CFEI

OFEI

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mer

ce+

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stry

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mer

ce+

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stry

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ansp

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st.+

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(?)R

elat

ive

RM

SFE2 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=

Figu

res

belo

w1

and

stat

isti

cally

sign

ifica

nt.

Har

vey,

Leyb

ourn

e,an

dN

ewbo

ld(1

997)

test

’sp-

valu

e:(???

)p<

1%,(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

8

3R

obus

tnes

sre

sult

sII

I:A

R(4

)nat

ive

mod

el,4

-ter

mfa

ctor

indi

ffer

ence

s

Tabl

e1.

A3.

Adj

uste

dR

-squ

ared

rati

obe

twee

nA

R(4

)fac

tor-

augm

ente

dan

dna

tive

AR

(4)m

odel

(*)

and

F-te

stre

sult

s(p

-val

ue)o

fthe

cons

umer

-bas

edfa

ctor

stat

isti

cals

igni

fican

ce(*

*)Fa

ctor

:Mor

ese

nsit

ive

sect

ors

Fact

or:L

ess

sens

itiv

ese

ctor

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ctor

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ese

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ive

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ors

Fact

or:L

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sens

itiv

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ctor

sPCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEI

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or:C

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the

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or/A

djus

ted

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edw

itho

utth

efa

ctor

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nge-

shad

edce

lls=A

djus

ted

R-s

quar

edra

tio

grea

ter

than

1.G

reen

-sha

ded

cells

=Adj

uste

dR

-squ

ared

rati

ogr

eate

rth

an1.

05(5

%of

adju

stm

entg

ain)

.Sam

ple:

2001

.I-20

14.IV

(56

obse

rvat

ions

).(*

*)p-

valu

eof

the

null

hypo

thes

is:N

H:φ

1=...

=φ

4=0

(see

equa

tion

1)ag

ains

tthe

alte

rnat

ive

ofat

leas

tone

term

iseq

ual

toze

ro.G

reen

-sha

ded

cells

=p<

10%

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nge-

shad

edce

lls=p<

15%

.Sam

ple:

2001

.I-20

19.II

I(75

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

9

Tabl

e2.

A3.

Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

nati

veA

R(1

)and

fact

or-a

ugm

ente

dA

R(4

)mod

el(*

)PCSI

PFEI

CCSI

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OFEI

PCSI

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CFEI

OFEI

PCSI

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CCSI

CFEI

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PFEI

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mer

ce+

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stry

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mer

ce+

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stry

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ansp

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d.+

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st.+

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8

(?)R

elat

ive

RM

SFE2 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

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ures

belo

w1.

Gre

en-s

hade

dce

lls=

Figu

res

belo

w1

and

stat

isti

cally

sign

ifica

nt.

Har

vey,

Leyb

ourn

e,an

dN

ewbo

ld(1

997)

test

’sp-

valu

e:(???

)p<

1%,(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

12

4R

obus

tnes

sre

sult

sIV

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(1)n

ativ

em

odel

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erm

fact

orin

diff

eren

ces

Tabl

e1.

A4.

Adj

uste

dR

-squ

ared

rati

obe

twee

nA

R(1

)fac

tor-

augm

ente

d(1

-ter

m)a

ndna

tive

AR

(1)m

odel

(*)

and

F-te

stre

sult

s(p

-val

ue)o

fthe

cons

umer

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edfa

ctor

stat

isti

cals

igni

fican

ce(*

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ctor

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ese

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ors

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or:L

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uste

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ted

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ith

the

fact

or/A

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ted

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edw

itho

utth

efa

ctor

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nge-

shad

edce

lls=A

djus

ted

R-s

quar

edra

tio

grea

ter

than

1.G

reen

-sha

ded

cells

=Adj

uste

dR

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ared

rati

ogr

eate

rth

an1.

05(5

%of

adju

stm

entg

ain)

.Sam

ple:

2001

.I-20

14.IV

(56

obse

rvat

ions

).(*

*)p-

valu

eof

the

null

hypo

thes

is:N

H:φ

1=...

=φ

4=0

(see

equa

tion

1)ag

ains

tthe

alte

rnat

ive

ofat

leas

tone

term

iseq

ual

toze

ro.G

reen

-sha

ded

cells

=p<

10%

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nge-

shad

edce

lls=p<

15%

.Sam

ple:

2001

.I-20

19.II

I(75

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

13

Tabl

e2.

A4.

Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

nati

veA

R(1

)and

fact

or-a

ugm

ente

dA

R(1

)mod

el,1

-ter

mfa

ctor

(*)

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PFEICCSI

CFEI

OFEI

PCSI

PFEICCSI

CFEI

OFEI

PCSI

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mer

ce+

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stry

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mer

ce+

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stry

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ansp

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omm

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d.+

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st.+

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v.C

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ple:

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hors

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cula

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0.32

10.

319

0.16

40.

105

0.89

00.

520

0.05

90.

037

0.04

2C

WK

0.98

70.

987

0.98

70.

991

0.99

00.

991

0.98

80.

987

0.99

50.

991

0.99

00.

961

0.96

60.

737

0.77

70.

738

0.92

70.

984

0.42

40.

629

MEQ

1.00

51.

024

1.04

01.

042

1.04

70.

991

1.02

01.

084

1.08

01.

083

0.41

10.

208

0.14

60.

075

0.03

40.

996

0.22

70.

006

0.02

10.

011

Fact

or:C

omm

erce

+In

dust

ry+

Con

stru

ctio

n+

Pers

onal

Serv

ices

PC0.

994

1.00

21.

006

1.00

41.

006

0.99

51.

021

0.99

61.

007

1.01

50.

813

0.54

70.

267

0.37

00.

314

0.79

80.

155

0.75

90.

299

0.16

1D

C0.

988

1.00

20.

999

1.00

11.

006

0.99

11.

025

0.99

21.

009

1.02

00.

933

0.49

20.

376

0.35

70.

254

0.66

50.

056

0.63

30.

255

0.12

6N

DC

0.98

61.

006

1.00

20.

998

1.00

20.

979

1.03

50.

982

0.99

71.

013

0.53

80.

407

0.34

30.

369

0.39

30.

950

0.15

10.

892

0.39

70.

205

GFC

F0.

995

0.99

91.

026

1.02

81.

027

0.99

51.

012

1.00

71.

014

1.01

90.

660

0.56

90.

055

0.03

60.

044

0.84

90.

282

0.39

80.

154

0.09

5C

WK

0.99

30.

989

0.98

60.

995

0.99

10.

988

0.98

80.

987

0.99

10.

991

0.57

70.

869

0.99

40.

433

0.66

90.

921

0.89

30.

967

0.73

00.

732

MEQ

0.99

31.

018

1.08

31.

079

1.08

11.

002

1.02

81.

035

1.04

41.

050

0.91

80.

233

0.00

80.

016

0.00

90.

562

0.19

10.

188

0.07

80.

037

Fact

or:C

omm

erce

+C

onst

ruct

ion

+Pe

rson

alSe

rvic

esPC

0.99

41.

007

1.00

51.

005

1.00

90.

995

1.02

20.

996

1.00

51.

012

0.82

50.

363

0.26

50.

327

0.25

80.

797

0.07

10.

810

0.31

00.

150

DC

0.98

81.

008

0.99

81.

005

1.01

10.

993

1.02

70.

991

1.00

31.

014

0.93

30.

335

0.41

40.

298

0.20

50.

578

0.03

90.

668

0.31

60.

172

ND

C0.

985

1.01

30.

996

1.00

11.

008

0.98

01.

035

0.98

40.

992

1.00

50.

643

0.28

60.

457

0.32

90.

314

0.92

30.

095

0.84

80.

523

0.29

0G

FCF

0.99

51.

001

1.02

41.

028

1.02

70.

996

1.01

01.

004

1.00

91.

013

0.72

10.

506

0.06

40.

043

0.04

40.

776

0.31

80.

567

0.21

70.

144

CW

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991

0.98

80.

987

0.99

50.

991

0.98

80.

991

0.98

60.

990

0.99

20.

738

0.91

00.

990

0.44

90.

640

0.90

40.

744

0.99

80.

798

0.76

3M

EQ0.

993

1.02

41.

083

1.08

11.

083

1.00

61.

016

1.02

01.

027

1.03

20.

881

0.20

90.

010

0.01

40.

008

0.45

40.

332

0.35

30.

156

0.09

7(*

)Adj

uste

dR

-squ

ared

rati

o=A

djus

ted

R-s

quar

edw

ith

the

fact

or/A

djus

ted

R-s

quar

edw

itho

utth

efa

ctor

.Ora

nge-

shad

edce

lls=A

djus

ted

R-s

quar

edra

tio

grea

ter

than

1.G

reen

-sha

ded

cells

=Adj

uste

dR

-squ

ared

rati

ogr

eate

rth

an1.

05(5

%of

adju

stm

entg

ain)

.Sam

ple:

2001

.I-20

14.IV

(56

obse

rvat

ions

).(*

*)p-

valu

eof

the

null

hypo

thes

is:N

H:φ

1=...

=φ

4=0

(see

equa

tion

1)ag

ains

tthe

alte

rnat

ive

ofat

leas

tone

term

iseq

ual

toze

ro.G

reen

-sha

ded

cells

=p<

10%

.Ora

nge-

shad

edce

lls=p<

15%

.Sam

ple:

2001

.I-20

19.II

I(75

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

16

Tabl

e2.

A5.

Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

nati

veA

R(1

)and

fact

or-a

ugm

ente

dA

R(1

)mod

el,2

-ter

mfa

ctor

(*)

PCSI

PFEI

CCSI

CFEIOFEIPCSI

PFEI

CCSI

CFEIOFEIPCSI

PFEI

CCSI

CFEIOFEIPCSI

PFEI

CCSI

CFEIOFEI

Com

mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

.C

omm

.+In

d.+

Con

st.+

Pers

.Ser

v.C

omm

.+C

onst

.+Pe

rs.S

erv.

hPr

ivat

eC

onsu

mpt

ion

10.

997

1.00

10.

912

0.96

70.

983

0.99

41.

014

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30.

945

0.98

10.

992

1.02

50.

949

0.93

70.

983

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21.

017

0.95

30.

934

0.97

7

20.

994

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029

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025

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038

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986

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019

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017

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042

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hD

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mpt

ion

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001

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972

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975

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10.

943

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30.

991

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50.

960

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40.

979

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992

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955

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5

21.

002

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009

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008

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10.

990

1.00

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026

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999

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70.

993

1.05

0?1.

013

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90.

996

0.99

31.

043?

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2

31.

002

1.00

00.

993

1.01

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003

1.00

00.

999

0.98

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006

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91.

000

0.99

90.

980

1.01

31.

001

1.00

11.

000

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01.

011

1.00

1

41.

005

0.99

80.

985

0.99

60.

992

1.00

30.

998

0.98

10.

993

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11.

003

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80.

972

0.98

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992

1.00

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999

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991

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3

hN

on-d

urab

leC

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mpt

ion

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00.

961

0.96

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998

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029

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10.

970

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00.

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01.

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935

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9

20.

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00.

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007

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975

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002

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40.

982

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963

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9

hG

ross

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rmat

ion

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005

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026

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81.

013

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41.

005

0.99

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001

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013

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00.

988

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008

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993

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5

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000

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015

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972?

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006

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80.

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001

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000

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989

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5??

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006

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989

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005

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002

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992

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008

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and

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ks

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019

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003

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998

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006

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998

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11.

002

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015

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001

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002

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980

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005??

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001

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008??

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6

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achi

nery

and

Equi

pmen

t

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004

1.01

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011

1.00

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995

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014

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00.

998

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80.

996

1.01

61.

003

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51.

001

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21.

015

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20.

996

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1

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996

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009

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00.

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61.

000

1.01

50.

987

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00.

996

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993

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982?

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995

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971

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7?

30.

995

1.00

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968

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10.

996

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41.

005

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984

0.99

90.

991

1.01

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957

0.97

10.

997

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51.

016

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80.

974

0.99

2

40.

997

1.00

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70.

999

0.99

80.

995?

1.00

20.

978

0.99

60.

999

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61.

013

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00.

990

1.00

70.

998

1.01

80.

981

0.99

31.

007

(*)R

elat

ive

RM

SFE1 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=F

igur

esbe

low

1an

dst

atis

tica

llysi

gnifi

cant

.C

lark

and

Wes

t(20

07)t

est’s

p-va

lue:

(???

)p<

1%,

(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

17

Tabl

e4.

A5:

Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

2-te

rmfa

ctor

-aug

men

ted

AR

(1)m

odel

sac

cord

ing

toit

sre

lati

onsh

ipw

ith

the

busi

ness

cycl

e(*

)PCSIPFEI

CCSICFEIOFEIPCSIPFEI

CCSICFEIOFEIPCSIPFEICCSI

CFEIOFEI

PCSIPFEICCSI

CFEIOFEI

Com

mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

.C

omm

.+In

d.+

Con

st.+

Pers

.Ser

v.C

omm

.+C

onst

.+Pe

rs.S

erv.

hPr

ivat

eC

onsu

mpt

ion

11.

001

1.02

10.

957

1.17

21.

118?

0.99

71.

053

0.95

31.

110

1.11

1?1.

042

1.05

21.

039

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11.

089

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999

1.06

01.

021

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5

21.

005

1.01

90.

977

0.99

31.

008

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71.

026

0.96

60.

980

1.00

30.

982

1.01

20.

958

1.02

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015

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61.

000

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81.

007

1.00

2

31.

005

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50.

998

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002

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016

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953

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003

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50.

998

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31.

019

1.00

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40.

995

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004

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11.

013

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012

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982

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006

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30.

993

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013

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7

hD

urab

leC

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mpt

ion

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0.97

80.

987

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981

1.01

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5

21.

008

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50.

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008

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944

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996

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994

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012

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005

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027

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001

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000

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003

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019

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011

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(?)R

elat

ive

RM

SFE2 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=

Figu

res

belo

w1

and

stat

isti

cally

sign

ifica

nt.

Har

vey,

Leyb

ourn

e,an

dN

ewbo

ld(1

997)

test

’sp-

valu

e:(???

)p<

1%,(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

18

6R

obus

tnes

sre

sult

sV

I:A

R(1

)nat

ive

mod

el,3

-ter

mfa

ctor

indi

ffer

ence

s

Tabl

e1.

A6.

Adj

uste

dR

-squ

ared

rati

obe

twee

nA

R(1

)fac

tor-

augm

ente

d(3

-ter

m)a

ndna

tive

AR

(1)m

odel

(*)

and

F-te

stre

sult

s(p

-val

ue)o

fthe

cons

umer

-bas

edfa

ctor

stat

isti

cals

igni

fican

ce(*

*)Fa

ctor

:Mor

ese

nsit

ive

sect

ors

Fact

or:L

ess

sens

itiv

ese

ctor

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ctor

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ese

nsit

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ors

Fact

or:L

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sens

itiv

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364

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7(*

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uste

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ared

rati

o=A

djus

ted

R-s

quar

edw

ith

the

fact

or/A

djus

ted

R-s

quar

edw

itho

utth

efa

ctor

.Ora

nge-

shad

edce

lls=A

djus

ted

R-s

quar

edra

tio

grea

ter

than

1.G

reen

-sha

ded

cells

=Adj

uste

dR

-squ

ared

rati

ogr

eate

rth

an1.

05(5

%of

adju

stm

entg

ain)

.Sam

ple:

2001

.I-20

14.IV

(56

obse

rvat

ions

).(*

*)p-

valu

eof

the

null

hypo

thes

is:N

H:φ

1=...

=φ

4=0

(see

equa

tion

1)ag

ains

tthe

alte

rnat

ive

ofat

leas

tone

term

iseq

ual

toze

ro.G

reen

-sha

ded

cells

=p<

10%

.Ora

nge-

shad

edce

lls=p<

15%

.Sam

ple:

2001

.I-20

19.II

I(75

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

19

Tabl

e2.

A6.

Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

nati

veA

R(1

)and

fact

or-a

ugm

ente

dA

R(1

)mod

el,3

-ter

mfa

ctor

(*)

PCSI

PFEICCSI

CFEIOFEI

PCSI

PFEICCSI

CFEIOFEI

PCSI

PFEICCSI

CFEI

OFEI

PCSI

PFEICCSI

CFEI

OFEI

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mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

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omm

.+In

d.+

Con

st.+

Pers

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v.C

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rs.S

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mpt

ion

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uste

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ared

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ted

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ith

the

fact

or/A

djus

ted

R-s

quar

edw

itho

utth

efa

ctor

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nge-

shad

edce

lls=A

djus

ted

R-s

quar

edra

tio

grea

ter

than

1.G

reen

-sha

ded

cells

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uste

dR

-squ

ared

rati

ogr

eate

rth

an1.

05(5

%of

adju

stm

entg

ain)

.Sam

ple:

2001

.I-20

14.IV

(56

obse

rvat

ions

).(*

*)p-

valu

eof

the

null

hypo

thes

is:N

H:φ

1=...

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4=0

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equa

tion

1)ag

ains

tthe

alte

rnat

ive

ofat

leas

tone

term

iseq

ual

toze

ro.G

reen

-sha

ded

cells

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10%

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nge-

shad

edce

lls=p<

15%

.Sam

ple:

2001

.I-20

19.II

I(75

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

22

Tabl

e2.

A7.

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ti-h

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onR

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tio

betw

een

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veA

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)and

fact

or-a

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ente

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el(1

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m,i

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vels

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elat

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equa

tion

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rang

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ures

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w1.

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nd(?

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ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

23

Tabl

e4.

A7:

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ti-h

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onR

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ugm

ente

d(1

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nle

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odel

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ing

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sre

lati

onsh

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ith

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busi

ness

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954

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029

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094

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008

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027

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016

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075

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052

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4

(?)R

elat

ive

RM

SFE2 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=

Figu

res

belo

w1

and

stat

isti

cally

sign

ifica

nt.

Har

vey,

Leyb

ourn

e,an

dN

ewbo

ld(1

997)

test

’sp-

valu

e:(???

)p<

1%,(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

24

8R

obus

tnes

sre

sult

sV

III:

AR

(1)n

ativ

em

odel

,2-t

erm

fact

orin

leve

ls

Tabl

e1.

A8.

Adj

uste

dR

-squ

ared

rati

obe

twee

nA

R(1

)fac

tor-

augm

ente

d(2

-ter

m,i

nle

vels

)and

nati

veA

R(1

)mod

el(*

)an

dF-

test

resu

lts

(p-v

alue

)oft

heco

nsum

er-b

ased

fact

orst

atis

tica

lsig

nific

ance

(**)

Fact

or:M

ore

sens

itiv

ese

ctor

sFa

ctor

:Les

sse

nsit

ive

sect

ors

Fact

or:M

ore

sens

itiv

ese

ctor

sFa

ctor

:Les

sse

nsit

ive

sect

ors

PCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEI

Fact

or:C

omm

erce

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ryPC

1.00

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011

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008

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40.

998

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012

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012

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149

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598

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70.

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00.

126

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995

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017

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166

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066

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142

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443

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ctor

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223

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005

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792

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325

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Fact

or:C

omm

erce

+In

dust

ry+

Con

stru

ctio

n+

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onal

Serv

ices

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156

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002

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or:C

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onst

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ion

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alSe

rvic

esPC

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008

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009

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004

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019

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008

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268

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157

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40.

416

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127

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009

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015

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003

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134

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70.

258

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80.

072

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027

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993

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996

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019

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000

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40.

996

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10.

555

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10.

466

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237

0.47

00.

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002

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011

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200

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00.

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70.

829

0.87

00.

760

0.49

20.

678

0.82

80.

694

0.81

20.

614

0.57

8M

EQ0.

994

1.00

41.

016

0.99

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003

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90.

993

1.03

30.

996

0.99

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00.

190

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10.

480

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70.

890

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20.

682

0.69

1(*

)Adj

uste

dR

-squ

ared

rati

o=A

djus

ted

R-s

quar

edw

ith

the

fact

or/A

djus

ted

R-s

quar

edw

itho

utth

efa

ctor

.Ora

nge-

shad

edce

lls=A

djus

ted

R-s

quar

edra

tio

grea

ter

than

1.G

reen

-sha

ded

cells

=Adj

uste

dR

-squ

ared

rati

ogr

eate

rth

an1.

05(5

%of

adju

stm

entg

ain)

.Sam

ple:

2001

.I-20

14.IV

(56

obse

rvat

ions

).(*

*)p-

valu

eof

the

null

hypo

thes

is:N

H:φ

1=...

=φ

4=0

(see

equa

tion

1)ag

ains

tthe

alte

rnat

ive

ofat

leas

tone

term

iseq

ual

toze

ro.G

reen

-sha

ded

cells

=p<

10%

.Ora

nge-

shad

edce

lls=p<

15%

.Sam

ple:

2001

.I-20

19.II

I(75

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

25

Tabl

e2.

A8.

Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

nati

veA

R(1

)and

fact

or-a

ugm

ente

dA

R(1

)mod

el(2

-ter

m,i

nle

vels

)(*)

PCSI

PFEI

CCSI

CFEIOFEI

PCSI

PFEI

CCSI

CFEI

OFEI

PCSI

PFEI

CCSI

CFEI

OFEI

PCSI

PFEI

CCSI

CFEIOFEI

Com

mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

.C

omm

.+In

d.+

Con

st.+

Pers

.Ser

v.C

omm

.+C

onst

.+Pe

rs.S

erv.

hPr

ivat

eC

onsu

mpt

ion

10.

899

0.87

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60.

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0.92

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843

0.83

70.

997

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841

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024

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027

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7?1.

004

1.03

1?

41.

012

1.00

81.

031??

0.98

51.

037?

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01.

007

1.02

9??

0.99

21.

040?

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31.

006

1.05

6???

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41.

035?

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31.

009

1.04

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51.

033?

hM

achi

nery

and

Equi

pmen

t

11.

027

0.98

61.

019

1.02

6?0.

983

1.02

90.

985

1.01

21.

024

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01.

050

0.99

61.

001

1.00

20.

976

1.04

30.

999

1.00

71.

008?

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4

21.

019

0.97

70.

975

0.99

20.

944??

1.02

20.

985

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50.

994

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0??

1.06

10.

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962

0.93

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2??

31.

028

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60.

999

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017

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985

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079

1.01

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001

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928??

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018

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00.

954

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9?

41.

036

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996

1.02

20.

959??

1.04

30.

941

0.99

71.

018

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5?1.

106

0.97

20.

997

0.97

30.

947?

1.08

90.

976

0.99

70.

988

0.95

9??

(*)R

elat

ive

RM

SFE1 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=F

igur

esbe

low

1an

dst

atis

tica

llysi

gnifi

cant

.C

lark

and

Wes

t(20

07)t

est’s

p-va

lue:

(???

)p<

1%,

(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

26

Tabl

e4.

A8:

Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

fact

or-a

ugm

ente

d(2

-ter

m,i

nle

vels

)AR

(1)m

odel

sac

cord

ing

toit

sre

lati

onsh

ipw

ith

the

busi

ness

cycl

e(*

)PCSI

PFEI

CCSI

CFEIOFEIPCSI

PFEI

CCSI

CFEIOFEIPCSI

PFEI

CCSI

CFEIOFEIPCSI

PFEICCSI

CFEIOFEI

Com

mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

.C

omm

.+In

d.+

Con

st.+

Pers

.Ser

v.C

omm

.+C

onst

.+Pe

rs.S

erv.

hPr

ivat

eC

onsu

mpt

ion

10.

893

1.01

60.

903

0.99

21.

057

0.91

21.

114

0.90

90.

924

1.03

41.

119

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71.

055

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91.

007

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60.

915

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905

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7

20.

921

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906

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41.

067

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31.

251??

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909

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00.

944

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8??

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045

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913

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975

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058

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920

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976

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908

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01.

006

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881?

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052

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096

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121?

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6

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906

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888?

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110

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056

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41.

053

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urab

leC

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mpt

ion

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996

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957??

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078

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008

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7

30.

997

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010

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025?

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100

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993

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001

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999

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7

40.

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015

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003

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001

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897??

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857?

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883?

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931?

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989

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895??

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80.

884??

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846???

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984

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837???

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979

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ross

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021

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033

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3

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025

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961??

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002

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005

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019

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992

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022

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000

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014

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006

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010

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018

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994

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009

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023

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ruct

ion

and

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ks

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005

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011

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014

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020

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001

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003

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010

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018

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017

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4

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008

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985

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007

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012

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000

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003

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999

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006

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11.

029

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71.

001

1.00

0

31.

010

1.01

60.

980

0.98

31.

010

1.01

01.

018

0.97

50.

991

1.01

30.

998

1.03

1?1.

009

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91.

010

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71.

039

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30.

995

1.00

5

41.

014

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30.

977

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51.

013

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31.

022

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00.

984

1.01

60.

988

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010

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010

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030

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80.

991

1.00

5

hM

achi

nery

and

Equi

pmen

t

11.

008

0.99

81.

015

1.03

11.

019

1.01

20.

994

1.00

61.

027

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21.

055

1.00

30.

974

0.98

81.

001

1.04

71.

011

0.97

50.

998

1.01

5

20.

995

0.97

10.

987

1.03

81.

020

0.99

60.

981

0.98

51.

046

1.02

9?1.

054

0.99

40.

967

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81.

006

1.04

50.

991

0.96

11.

001

1.01

7

31.

003

1.00

01.

003

1.10

51.

089?

1.01

10.

988

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61.

102

1.07

71.

087

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00.

990

1.00

81.

025

1.07

50.

980

0.97

71.

017

1.03

3

40.

994

0.96

70.

983

1.08

91.

067

1.00

10.

960

0.98

21.

091

1.05

81.

110

1.01

40.

970

1.00

21.

032

1.09

11.

030

0.95

91.

026

1.05

5

(*)R

elat

ive

RM

SFE2 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=

Figu

res

belo

w1

and

stat

isti

cally

sign

ifica

nt.

Har

vey,

Leyb

ourn

e,an

dN

ewbo

ld(1

997)

test

’sp-

valu

e:(???

)p<

1%,(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

27

9R

obus

tnes

sre

sult

sIX

:AR

(1)n

ativ

em

odel

,3-t

erm

fact

orin

leve

ls

Tabl

e1.

A9.

Adj

uste

dR

-squ

ared

rati

obe

twee

nA

R(1

)fac

tor-

augm

ente

d(3

-ter

m,i

nle

vels

)and

nati

veA

R(1

)mod

el(*

)an

dF-

test

resu

lts

(p-v

alue

)oft

heco

nsum

er-b

ased

fact

orst

atis

tica

lsig

nific

ance

(**)

Fact

or:M

ore

sens

itiv

ese

ctor

sFa

ctor

:Les

sse

nsit

ive

sect

ors

Fact

or:M

ore

sens

itiv

ese

ctor

sFa

ctor

:Les

sse

nsit

ive

sect

ors

PCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEI

Fact

or:C

omm

erce

+In

dust

ryPC

1.01

21.

030

1.05

01.

032

1.03

90.

996

1.01

31.

078

1.03

81.

042

0.46

70.

160

0.00

30.

040

0.02

00.

822

0.46

50.

000

0.02

10.

021

DC

1.00

51.

042

1.05

01.

047

1.05

70.

991

1.00

81.

062

1.04

01.

043

0.29

40.

006

0.00

20.

018

0.00

30.

855

0.26

70.

001

0.01

50.

007

ND

C0.

997

1.04

61.

031

1.02

71.

042

0.98

41.

030

1.06

11.

034

1.04

70.

555

0.22

70.

060

0.09

70.

035

0.68

70.

371

0.01

40.

059

0.03

8G

FCF

1.00

01.

007

1.03

81.

008

1.01

30.

994

0.99

41.

070

1.02

31.

022

0.45

70.

417

0.02

30.

262

0.15

40.

687

0.68

70.

001

0.10

70.

106

CW

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984

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20.

981

0.99

80.

999

0.98

80.

984

0.98

80.

990

0.98

80.

894

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70.

984

0.60

80.

575

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40.

923

0.72

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692

0.82

5M

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006

1.02

71.

113

1.05

11.

056

0.98

71.

020

1.17

01.

081

1.08

70.

517

0.21

80.

001

0.04

10.

016

0.89

20.

205

0.00

00.

024

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0Fa

ctor

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mer

ce+

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stry

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tion

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61.

058

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41.

040

0.99

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015

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038

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10.

538

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001

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025

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409

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001

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054

1.04

51.

055

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21.

007

1.06

11.

039

1.04

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472

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002

0.02

30.

004

0.80

80.

282

0.00

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013

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6N

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21.

044

1.03

61.

026

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20.

988

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061

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61.

048

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00.

372

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0.04

50.

584

0.27

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30.

032

GFC

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997

1.00

21.

043

1.00

71.

011

0.99

40.

995

1.07

11.

025

1.02

50.

529

0.50

30.

013

0.29

20.

198

0.73

90.

698

0.00

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087

0.08

6C

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0.98

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989

0.98

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995

0.99

50.

987

0.98

50.

987

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989

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30.

766

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40.

691

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10.

770

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40.

720

0.61

40.

768

MEQ

1.00

11.

026

1.11

61.

048

1.05

40.

987

1.01

81.

177

1.08

71.

092

0.53

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223

0.00

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054

0.02

00.

892

0.24

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000

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10.

008

Fact

or:C

omm

erce

+In

dust

ry+

Con

stru

ctio

n+

Pers

onal

Serv

ices

PC0.

994

1.00

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078

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039

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043

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21.

034

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882

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000

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10.

029

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70.

072

0.00

40.

038

0.01

3D

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987

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060

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041

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048

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41.

047

1.05

70.

915

0.43

40.

001

0.01

60.

007

0.30

60.

003

0.00

10.

020

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3N

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21.

017

1.06

11.

037

1.04

50.

999

1.06

81.

031

1.02

51.

046

0.70

10.

459

0.01

40.

048

0.05

00.

467

0.11

00.

071

0.11

20.

026

GFC

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991

0.99

31.

068

1.02

51.

023

1.00

21.

006

1.04

71.

008

1.01

30.

754

0.73

20.

001

0.08

20.

087

0.37

90.

460

0.00

70.

278

0.17

9C

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991

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50.

992

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00.

988

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983

0.99

50.

994

0.72

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734

0.82

00.

614

0.76

30.

784

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50.

917

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696

MEQ

0.98

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1.16

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1.09

21.

005

1.02

51.

125

1.05

01.

056

0.94

10.

204

0.00

00.

014

0.00

60.

506

0.24

10.

000

0.06

10.

025

Fact

or:C

omm

erce

+C

onst

ruct

ion

+Pe

rson

alSe

rvic

esPC

0.99

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010

1.07

51.

035

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010

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051

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048

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475

0.00

00.

029

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495

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003

0.02

40.

007

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11.

007

1.05

71.

039

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005

1.06

21.

059

1.05

01.

063

0.84

50.

311

0.00

20.

022

0.01

10.

297

0.00

10.

001

0.01

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001

ND

C0.

983

1.02

51.

054

1.03

51.

046

0.99

91.

077

1.03

61.

026

1.04

60.

739

0.35

20.

026

0.05

70.

048

0.46

00.

122

0.04

00.

120

0.02

8G

FCF

0.99

20.

995

1.06

41.

023

1.02

21.

008

1.00

41.

046

1.00

41.

009

0.76

40.

687

0.00

20.

095

0.09

30.

310

0.49

00.

006

0.35

10.

232

CW

K0.

985

0.99

10.

984

0.99

40.

992

0.99

00.

985

0.98

20.

992

0.99

10.

822

0.70

70.

874

0.59

40.

688

0.73

90.

861

0.89

70.

761

0.76

1M

EQ0.

986

1.02

51.

166

1.08

71.

091

1.01

51.

013

1.11

51.

036

1.04

10.

920

0.20

00.

000

0.01

30.

005

0.40

20.

365

0.00

00.

103

0.05

2(*

)Adj

uste

dR

-squ

ared

rati

o=A

djus

ted

R-s

quar

edw

ith

the

fact

or/A

djus

ted

R-s

quar

edw

itho

utth

efa

ctor

.Ora

nge-

shad

edce

lls=A

djus

ted

R-s

quar

edra

tio

grea

ter

than

1.G

reen

-sha

ded

cells

=Adj

uste

dR

-squ

ared

rati

ogr

eate

rth

an1.

05(5

%of

adju

stm

entg

ain)

.Sam

ple:

2001

.I-20

14.IV

(56

obse

rvat

ions

).(*

*)p-

valu

eof

the

null

hypo

thes

is:N

H:φ

1=...

=φ

4=0

(see

equa

tion

1)ag

ains

tthe

alte

rnat

ive

ofat

leas

tone

term

iseq

ual

toze

ro.G

reen

-sha

ded

cells

=p<

10%

.Ora

nge-

shad

edce

lls=p<

15%

.Sam

ple:

2001

.I-20

19.II

I(75

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

28

Tabl

e2.

A9.

Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

nati

veA

R(1

)and

fact

or-a

ugm

ente

dA

R(1

)mod

el(3

-ter

m,i

nle

vels

)(*)

PCSI

PFEI

CCSI

CFEIOFEI

PCSI

PFEI

CCSI

CFEIOFEIPCSI

PFEI

CCSI

CFEIOFEIPCSI

PFEI

CCSI

CFEIOFEI

Com

mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

.C

omm

.+In

d.+

Con

st.+

Pers

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v.C

omm

.+C

onst

.+Pe

rs.S

erv.

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ivat

eC

onsu

mpt

ion

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974

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040

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996

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997

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2

(*)R

elat

ive

RM

SFE1 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=F

igur

esbe

low

1an

dst

atis

tica

llysi

gnifi

cant

.C

lark

and

Wes

t(20

07)t

est’s

p-va

lue:

(???

)p<

1%,

(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

29

Tabl

e4.

A9:

Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

fact

or-a

ugm

ente

d(3

-ter

m,i

nle

vels

)AR

(1)m

odel

sac

cord

ing

toit

sre

lati

onsh

ipw

ith

the

busi

ness

cycl

e(*

)PCSI

PFEI

CCSICFEIOFEIPCSI

PFEI

CCSICFEIOFEIPCSI

PFEI

CCSI

CFEIOFEI

PCSI

PFEICCSI

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Com

mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

.C

omm

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d.+

Con

st.+

Pers

.Ser

v.C

omm

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onst

.+Pe

rs.S

erv.

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ivat

eC

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mpt

ion

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(*)R

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RM

SFE2 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=

Figu

res

belo

w1

and

stat

isti

cally

sign

ifica

nt.

Har

vey,

Leyb

ourn

e,an

dN

ewbo

ld(1

997)

test

’sp-

valu

e:(???

)p<

1%,(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

30

10R

obus

tnes

sre

sult

sX

:AR

(1)n

ativ

em

odel

,4-t

erm

fact

orin

leve

ls

Tabl

e1.

A10

Adj

uste

dR

-squ

ared

rati

obe

twee

nA

R(1

)fac

tor-

augm

ente

d(4

-ter

m,i

nle

vels

)and

nati

veA

R(1

)mod

el(*

)an

dF-

test

resu

lts

(p-v

alue

)oft

heco

nsum

er-b

ased

fact

orst

atis

tica

lsig

nific

ance

(**)

Fact

or:M

ore

sens

itiv

ese

ctor

sFa

ctor

:Les

sse

nsit

ive

sect

ors

Fact

or:M

ore

sens

itiv

ese

ctor

sFa

ctor

:Les

sse

nsit

ive

sect

ors

PCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEIPCSIPFEICCSICFEIOFEI

Fact

or:C

omm

erce

+In

dust

ryPC

1.01

41.

037

1.05

41.

039

1.04

80.

990

1.01

61.

074

1.03

91.

045

0.21

50.

144

0.00

10.

035

0.01

00.

846

0.19

90.

000

0.03

20.

017

DC

1.00

71.

059

1.06

61.

076

1.08

80.

981

1.01

51.

061

1.05

71.

062

0.20

10.

002

0.00

00.

000

0.00

00.

941

0.02

90.

001

0.00

10.

000

ND

C0.

979

1.03

41.

031

1.02

51.

040

0.96

61.

018

1.05

01.

029

1.04

20.

710

0.34

80.

062

0.11

30.

034

0.80

60.

547

0.01

60.

091

0.05

6G

FCF

1.00

51.

001

1.03

21.

001

1.00

60.

995

0.99

01.

065

1.01

71.

016

0.27

90.

566

0.05

50.

407

0.27

60.

537

0.69

60.

003

0.18

90.

166

CW

K0.

977

0.98

90.

974

0.99

10.

993

0.97

90.

979

0.98

40.

985

0.98

30.

918

0.68

80.

899

0.75

00.

688

0.81

70.

946

0.35

00.

707

0.76

3M

EQ1.

011

1.02

01.

102

1.04

41.

047

0.98

61.

014

1.16

01.

074

1.07

90.

425

0.31

20.

004

0.06

50.

032

0.80

10.

289

0.00

00.

035

0.01

6Fa

ctor

:Com

mer

ce+

Indu

stry

+Tr

ansp

orta

tion

PC1.

006

1.03

51.

058

1.03

81.

047

0.99

21.

018

1.07

11.

039

1.04

40.

459

0.20

00.

001

0.04

40.

016

0.78

50.

178

0.00

00.

026

0.01

4D

C0.

998

1.05

81.

061

1.07

21.

084

0.98

31.

014

1.06

21.

058

1.06

20.

528

0.00

10.

001

0.00

00.

000

0.89

80.

038

0.00

00.

001

0.00

0N

DC

0.97

41.

032

1.03

31.

026

1.04

10.

969

1.02

01.

049

1.02

91.

041

0.78

40.

501

0.06

50.

131

0.03

70.

733

0.41

30.

014

0.06

90.

048

GFC

F0.

996

0.99

71.

036

1.00

11.

004

0.99

90.

991

1.06

81.

018

1.01

80.

481

0.64

20.

034

0.42

50.

324

0.41

00.

659

0.00

30.

166

0.13

6C

WK

0.97

40.

986

0.97

50.

987

0.98

80.

980

0.98

00.

984

0.98

70.

987

0.95

60.

784

0.86

40.

826

0.78

10.

798

0.94

10.

301

0.58

60.

655

MEQ

1.00

01.

020

1.10

51.

042

1.04

80.

991

1.01

31.

168

1.07

91.

083

0.55

50.

320

0.00

30.

066

0.03

30.

710

0.30

80.

000

0.03

70.

016

Fact

or:C

omm

erce

+In

dust

ry+

Con

stru

ctio

n+

Pers

onal

Serv

ices

PC0.

995

1.01

31.

075

1.03

91.

044

1.00

71.

043

1.05

21.

038

1.04

80.

621

0.18

20.

000

0.03

10.

015

0.42

00.

114

0.00

20.

039

0.01

2D

C0.

980

1.01

21.

060

1.05

71.

063

1.00

21.

058

1.06

31.

072

1.08

20.

941

0.05

5.0

010.

001

0.00

00.

369

0.00

00.

001

0.00

00.

000

ND

C0.

969

1.01

01.

051

1.03

11.

042

0.98

11.

053

1.02

31.

024

1.04

00.

706

0.53

00.

015

0.07

60.

060

0.67

30.

219

0.07

30.

128

0.03

3G

FCF

0.99

30.

988

1.06

31.

018

1.01

61.

005

1.00

21.

041

1.00

21.

007

0.63

10.

765

0.00

40.

169

0.15

40.

242

0.55

60.

020

0.37

10.

273

CW

K0.

978

0.98

40.

981

0.98

50.

985

0.98

20.

981

0.97

80.

989

0.98

90.

848

0.87

40.

420

0.65

20.

735

0.81

70.

852

0.70

00.

804

0.77

0M

EQ0.

987

1.01

31.

159

1.07

91.

083

1.00

41.

019

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51.

043

1.04

90.

785

0.28

90.

000

0.02

50.

011

0.51

50.

318

0.00

20.

075

0.03

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ctor

:Com

mer

ce+

Con

stru

ctio

n+

Pers

onal

Serv

ices

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997

1.01

81.

071

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81.

044

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050

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41.

040

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00.

645

0.17

60.

000

0.03

50.

016

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80.

059

0.00

10.

029

0.00

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C0.

984

1.02

11.

057

1.06

01.

067

0.99

81.

069

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91.

072

1.08

20.

874

0.04

40.

001

0.00

10.

000

0.41

20.

000

0.00

10.

000

0.00

0N

DC

0.96

81.

016

1.04

21.

031

1.04

30.

983

1.06

21.

030

1.02

31.

040

0.78

80.

450

0.03

20.

081

0.05

40.

677

0.22

00.

032

0.14

20.

042

GFC

F0.

991

0.99

01.

058

1.01

61.

016

1.01

61.

004

1.04

00.

999

1.00

40.

675

0.79

10.

006

0.18

30.

168

0.11

40.

384

0.01

50.

445

0.29

7C

WK

0.97

60.

985

0.98

00.

988

0.98

80.

986

0.98

10.

979

0.98

40.

984

0.91

70.

837

0.50

90.

649

0.69

00.

731

0.84

00.

662

0.87

30.

861

MEQ

0.98

51.

017

1.15

61.

079

1.08

21.

017

1.01

31.

105

1.03

11.

036

0.82

40.

322

0.00

00.

022

0.01

20.

381

0.28

40.

002

0.11

00.

055

(*)A

djus

ted

R-s

quar

edra

tio=

Adj

uste

dR

-squ

ared

wit

hth

efa

ctor

/Adj

uste

dR

-squ

ared

wit

hout

the

fact

or.O

rang

e-sh

aded

cells

=Adj

uste

dR

-squ

ared

rati

ogr

eate

rth

an1.

Gre

en-s

hade

dce

lls=A

djus

ted

R-s

quar

edra

tio

grea

ter

than

1.05

(5%

ofad

just

men

tgai

n).S

ampl

e:20

01.I-

2014

.IV(5

6ob

serv

atio

ns).

(**)

p-va

lue

ofth

enu

llhy

poth

esis

:NH

:φ1=

...=

φ4=

0(s

eeeq

uati

on1)

agai

nstt

heal

tern

ativ

eof

atle

asto

nete

rmis

equa

lto

zero

.Gre

en-s

hade

dce

lls=p<

10%

.Ora

nge-

shad

edce

lls=p<

15%

.Sam

ple:

2001

.I-20

19.II

I(75

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

31

Tabl

e2.

A10

.Mul

ti-h

oriz

onR

MSF

Era

tio

betw

een

nati

veA

R(1

)and

fact

or-a

ugm

ente

dA

R(1

)mod

el(4

-ter

m,i

nle

vels

)(*)

PCSI

PFEICCSI

CFEIOFEIPCSI

PFEICCSI

CFEIOFEIPCSI

PFEI

CCSI

CFEI

OFEIPCSI

PFEI

CCSI

CFEI

OFEI

Com

mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

.C

omm

.+In

d.+

Con

st.+

Pers

.Ser

v.C

omm

.+C

onst

.+Pe

rs.S

erv.

hPr

ivat

eC

onsu

mpt

ion

10.

960

0.96

41.

223??

1.23

4?1.

046?

0.97

50.

988

1.25

5??

1.23

71.

047?

1.16

0??

0.99

71.

320???

1.21

81.

062?

1.11

0?0.

977

1.30

8???

1.21

81.

055?

21.

082??

0.97

41.

534???

1.45

4?1.

114?

1.06

9??

0.95

31.

594???

1.48

6?1.

130?

1.27

3??

0.93

71.

543???

1.46

8?1.

153??

1.20

6??

0.93

21.

529???

1.46

0?1.

151??

30.

955

0.92

41.

314???

1.37

9??

1.03

70.

922

0.89

91.

360???

1.39

9??

1.05

91.

140??

0.93

91.

372???

1.38

6??

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063?

0.93

71.

360???

1.37

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1.09

8?

40.

754

0.95

51.

025??

1.21

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0.98

50.

761

0.94

11.

054???

1.19

7???

0.99

60.

983??

0.90

31.

166???

1.24

6???

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914?

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11.

137???

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3?

hD

urab

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mpt

ion

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007

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951

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932

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60.

995

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60.

928

0.92

71.

022

1.01

70.

994

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20.

968

1.01

51.

015

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50.

955

0.96

3

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030?

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988

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006

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005

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041

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002

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994

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022

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051

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071?

1.02

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51.

000

1.06

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030

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21.

048

1.00

1

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30.

985

1.06

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977

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004

0.98

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084?

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012

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0

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862

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100

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788

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769

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317??

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656

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653

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149

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6

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ross

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040

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040

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059

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2

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029

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0

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116???

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053

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60.

967

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61.

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0.97

10.

970

1.08

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050?

1.02

20.

972

1.07

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51.

050?

1.02

10.

983

1.09

7??

1.03

5

(*)R

elat

ive

RM

SFE1 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=F

igur

esbe

low

1an

dst

atis

tica

llysi

gnifi

cant

.C

lark

and

Wes

t(20

07)t

est’s

p-va

lue:

(???

)p<

1%,

(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

32

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e4.

A10

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onR

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tio

betw

een

fact

or-a

ugm

ente

d(4

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odel

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lati

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ith

the

busi

ness

cycl

e(*

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PFEI

CCSICFEIOFEIPCSI

PFEI

CCSICFEIOFEIPCSI

PFEICCSI

CFEIOFEI

PCSI

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Com

mer

ce+

Indu

stry

Com

mer

ce+

Indu

stry

+Tr

ansp

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omm

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d.+

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st.+

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v.C

omm

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onst

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rs.S

erv.

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ivat

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mpt

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10.

919

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4

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015

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20.

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1.04

31.

047

1.00

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91.

023

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01.

064

1.05

3

(?)R

elat

ive

RM

SFE2 h

(see

equa

tion

3).O

rang

e-sh

aded

cells

=Fig

ures

belo

w1.

Gre

en-s

hade

dce

lls=

Figu

res

belo

w1

and

stat

isti

cally

sign

ifica

nt.

Har

vey,

Leyb

ourn

e,an

dN

ewbo

ld(1

997)

test

’sp-

valu

e:(???

)p<

1%,(??

)p<

5%,a

nd(?

)p<

10%

.Sam

ple:

2015

.I-20

19.II

I(19

obse

rvat

ions

).So

urce

:Aut

hors

’cal

cula

tion

s.

33

Documentos de Trabajo

Banco Central de Chile

NÚMEROS ANTERIORES

La serie de Documentos de Trabajo en versión PDF

puede obtenerse gratis en la dirección electrónica:

www.bcentral.cl/esp/estpub/estudios/dtbc.

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pueden hacer por fax: +56 2 26702231 o a través del

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DTBC – 887

Railroads, specialization, and population growth in small open economies: Evidence

from the First Globalization

Andrés Forero, Francisco A. Gallego, Felipe González, Matías Tapia

DTBC – 886

High Dimensional Quantile Factor Analysis

Andrés Sagner

DTBC – 885

Heterogeneous Paths of Industrialization

Federico Huneeus, Richard Rogerson

DTBC – 884

Does the Commodity Super Cycle Matter?

Andrés Fernández, Stephanie Schmitt-Grohé, Martín Uribe

DTBC – 883

Twitter-Based Economic Policy Uncertainty Index for Chile

Andrés Sagner, Juan Sebastián Becerra

DTBC – 882

Corporate-Sector Functional Currency: An International Comparison

Jorge Fernández, Fernando Pino, Francisco Vásquez

DTBC – 881

Back testing fan charts of activity and inflation: the Chilean case

Jorge Fornero, Andrés Gatty

DTBC – 880

Financing Firms in Hibernation during the COVID-19 Pandemic

Tatiana Didier, Federico Huneeus, Mauricio Larrain, Sergio L. Schmukler

DTBC – 879

Choice Aversion in Directed Networks

Jorge Lorca, Emerson Melo

DTBC – 878

Big G

Lydia Cox, Gernot Muller, Ernesto Pasten, Raphael Schoenle, Michael Weber

DTBC – 877

Sticky Capital Controls

Miguel Acosta-Henao, Laura Alfaro, Andrés Fernández

DTBC – 876

Measuring the perceived value of an MBA degree

Carlos Madeira

DTBC – 875

The Real Effects of Monetary Shocks: Evidence from Micro Pricing Moments

Gee Hee, Matthew Klepacz, Ernesto Pasten, Raphael Schoenle

DTBC – 874

Measuring Systemic Risk: A Quantile Factor Analysis

Andrés Sagner

DTBC – 873

The impact of information laws on consumer credit access: evidence from Chile

Carlos Madeira

DOCUMENTOS DE TRABAJO • Septiembre 2020