the predictive power of survey results in macroeconomic analysis lawrence r. klein...

The Predictive Power of Survey Results

in

Macroeconomic Analysis

Lawrence R. Klein*

Suleyman Ozmucur*

MACROMODELS’ 2001

Krag, Poland

5-8 December 2001

* University of Pennsylvania, Department of Economics, 3718 Locust Walk, Philadelphia, PA 19104-6297. USA, Tel: 215 898 6765, Fax: 215 8984477

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The Predictive Power of Survey Results in Macroeconomic Analysis

Lawrence R. Klein / Suleyman Ozmucur

Abstract

Many indicators are helpful in improving statistical performance for forecasting and policy analysis. We do believe, however, no single indicator (or type of indicator) can do the necessary work by itself. Any new finding is likely to make a better contribution in combination with others that have been found to be useful. Timeliness, flexibility, and foresight are important properties of indicators, and we are especially interested in information that reflects subjective feelings of participants in the economy. Results of surveys covering consumers, producers or managers are useful in forecasting major macroeconomic variables, such as personal consumption expenditures, personal income, employment, retail sales, and industrial production. Preliminary results indicate that models including survey results perform better than those that do not include such results. There are five survey results considered in this paper (i) The index of consumer sentiment by the University of Michigan, (ii) The index of consumer confidence by the Conference Board, (iii) The purchasing management composite index by the National Association of Purchasing Management, (iv) The consumer comfort index by the ABC News/Money Magazine, and (v) The index of investor optimism by UBS/Paine Webber.

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1. Introduction

The surveys of investors provide fresh insight on the functioning of the US economy. The present paper is designed to appraise the performance of the various index values produced by these surveys over their history and, in particular, to examine their use in analyzing the present economic turbulence that arises from the effects of the terrorist attacks on the US since September 11th

, and their continuation in a biological mode. Surveys are very informative, not only for the present critical situation but for analysis of the economy in a more normal environment.

The objectives of this assessment are as follows: (i) What niche in the information annals of quantitative economics

is covered by the indexes? (ii) How do various surveys conducted compare with other surveys

that are often used in economic analysis? (iii) What is the performance record of the Indexes? (iv) How have the indexes provided contemporary insight at this

and other critical phases? (v) What are some potential extensions and enlargements of the

indexes that can render them even more informative?

The economic information system is vast and developing in many dimensions. The information is more and more frequent – decennial, annual, quarterly, monthly, weekly, daily, hourly, ... real time. The scope is both macro and microeconomic. The history dates from colonial times and grows intensively, mainly as a result of advances in the use of information technology. Our ability to process this enormous information flow is made possible by the advances in computer science, both in terms of hardware and software supply.

Vast as this information flow has become, it is focused on objective, quantitative information such as prices, transaction volumes, production, sales, costs, exports, imports, interest rates, exchange rates, and so on. These pieces of information are all readily available in quantitative form, but they often lack a qualitative dimension. They are objective but economic decision making has a large subjective component. It is this subjective and qualitative property that finds expression in responses to surveys of human populations. There are some well-known surveys of households, firms, and bureaucrats but few, if any, of investors. This is the dimension in economic behavior that has been missing, but is now filled by the results of the surveys of investor optimism.

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The population that is being sampled every month has well-considered thoughts about the economy, their personal economic circumstances and other relevant issues. The qualitative responses in coded quantitative index form provide both microeconomic and macroeconomic information that enables one to determine their influence on performance of markets, consumption patterns, and production patterns.

Subjective feelings are always important for the economy, but the present situation highlights their extreme significance because personal attitudes have quickly and radically been changed as a result of calculated terrorism within US boundaries. Consumers and producers are no longer being guided mainly by objective market signals, and surveys of the investor population can quickly fill the void in our analyses of the economy.

There are five survey results considered in this paper (i) The index of consumer sentiment by the University of Michigan, (ii) The index of consumer confidence by the Conference Board, (iii) The purchasing management composite index by the National Association of Purchasing Management, (iv) The consumer comfort index by the ABC News/Money Magazine, and (v) The index of investor optimism by UBS/Paine Webber. The paper is in six sections. The second section deals with time series properties of indexes and indicators used in this study. The explanatory power of these surveys are given in the third section. Results are also compared with the help of various model selection criteria. The fourth section is devoted to models with principal components. Ex-post and ex-ante forecasts based on alternative models are reported in section five. Major conclusions are stated in the final section. 2. Tests of Stationarity

Augmented Dickey-Fuller and Phillips-Perron unit root tests are implemented to study time series properties of the series used in this analysis. Under the null hypothesis of a unit root, the t-statistic does not have the conventional t distribution. Therefore, MacKinnon critical values based on Monte Carlo simulations are used in testing for unit roots. The estimated model may have serial correlation in residuals. To alleviate the problem Dickey-Fuller recommends the use of lagged differences (which gives the Augmented Dickey-Fuller statistic), while Phillips-Perron recommends a non-parametric method of correction for serial correlation. It is not possible to reject the null hypothesis (non-stationary series) based on both Augmented Dickey-Fuller and Phillips-Perron tests (Table 1a). Both of these tests are asymptotic tests, and may not be sufficient to indicate stationarity

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clearly in small samples. Therefore, in addition to these two common tests, a correlogram is also used. Autocorrelation (ACF) and partial autocorrelation (PACF) functions of the index clearly indicate the presence of an AR(1) process. The index of investor optimism is not a stationary series. On the other hand, change in the index (D(INDEX)) is a stationary series, as indicated by very high (negative) ADF and PP statistics, no significant ACF or PACF, and a low Ljung-Box Q statistic. Therefore, all three statistics indicate the following: The level of the index of investor optimism is a non-stationary series integrated of order one, I (1). The monthly change of the index is of order zero, I (0). Monthly personal consumption expenditures is a non-stationary series integrated of order one, I (1). The monthly change of the log of personal consumption expenditures is of order zero, I (0). Test results are given in Table 1b. Similar results are obtained for other variables used in this analysis, not presented here. 3. Polynomial Distributed Lags (Almon lags)

The polynomial distributed lag (PDL) of the index is used to explain personal consumption expenditures. Using individual lags may be a major cause of multicollinearity which, in turn, causes low t-ratios for individual regression coefficients. PDL alleviates this problem and enables the use of more than one lag of the variable, with some constraints on coefficients.

The polynomial distributed lag of the change in the index was used to explain the growth in real personal consumption expenditures (Table 2). Three lags are used. Experiments with higher lags did not improve the performance of the model. Moving average (MA(1)) is also used to alleviate the problem of serial correlation of residuals. Since there is serial correlation in residuals, Newey-West heteroscedasticity and autocorrelation consistent (HAC) standard errors are used. The determination coefficient is rather low, around 0.2; all coefficients have correct signs and are significant at the five percent level. The sum of distributed lag coefficients is 0.00015. Real personal consumption expenditures are estimated to increase by 0.015 percent with a point change in the index. In addition to Durbin-Watson statistics, more general statistics on serial correlation are used. Ljung-Box Q-statistics indicate that there is no serial correlation up to the 12th order. Breusch-Godfrey Lagrange multiplier (LM) statistics are for the second order serial correlation. Both the F statistics, and the χ2 statistics indicate that there is no serial correlation. First, and 12 order LM tests also indicate

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no serial autocorrelation. The ARCH (Autoregressive conditional heteroscedasticity) test due to Engle indicates that there is no autoregressive conditional heteroscedasticity. Ramsey’s RESET test gives support to “no specification error” in the model. The Jarque-Bera statistic rejects the assumption of normality of residuals. With the exception of the last test, this specification passes a battery of tests. The “actual, fitted, and residual” diagram indicate some problems in certain selected periods.

This model is used for one-period ahead forecasts. The performance of the model is quite satisfactory. The mean absolute percentage error is 0.20 for the sample period. The Theil inequality coefficient is 0.00129, very close to zero. The covariance proportion is 0.992, very close to one, and the bias proportion is very small. These results indicate that the forecasting performance of the model is relatively good.

The index of investor optimism explains in a regression sense about 19 percent of the variance in the growth of real personal consumption expenditures. Although, R2 = 0.187 is low, it is significant at the five percent level, as indicated by the F statistics. The personal index component of the index of investor optimism has the highest R2, with 0.25. The economic index has an R2=0.17. The index performs better than other surveys, namely those of the University of Michigan on consumer sentiment, the Conference Board, and the National Association of Purchasing Management (NAPM) (Table 4). The Conference Board index has an R2= 0.14. The University of Michigan index has an R2=0.14. The National Association of Purchasing Management index has an R2=0.13. The ABC News/Money Magazine index has an R2=0.10. Similar ordering is obtained by using adjusted R2, Akaike information criterion (AIC) and Schwarz (Bayesian) information criterion (BIC). The personal component of the index has the lowest AIC with –9.0, and the lowest BIC with –8.9. Since, the number of explanatory variables and/or lags are the same in all models, this result is expected.

The ranking of models in terms of within-sample forecasting performance is similar. The personal component of the index of investor optimism has the lowest mean absolute percentage error with 0.2038, and the lowest Theil inequality coefficient of 0.001239. The index of investor optimism and its economic component also outperform other surveys, though by a small margin.

Although, performance indicators like the mean absolute percentage error are very useful, they do not really say much about the statistical significance of the difference. The Diebold-Mariano test statistic may also be used to test forecast accuracy. The test statistic is standard normal,

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therefore the critical value of 1.96 may be used for the 95 percent level of confidence.

The index of investor optimism is compared with others, one at a time. A DM value less than –1.96 shows that the index performs better than the others. A DM value between –1.96 and 1.96 indicates that the performance of the index is not significantly different from the other models. The Diebold-Mariano statistic is 1.57 for the Conference Board index of consumer confidence, -1.40 for the University of Michigan index of consumer sentiment, and –7.46 for the NAPM index. DM statistics show that the forecasting performance of the index is significantly better than the NAPM index. The difference between the Conference Board and the University of Michigan indexes are not statistically significant at the 95 percent confidence level, or even at the 90 percent level.

Since the UBS/Paine Webber indexes are based on surveys of investors, a universe that is undoubtedly interested in, and concerned with, financial market dynamics, it is worthwhile looking into the relationships between various indexes obtained from responses obtained from the surveys and market measures, such as equity and bond price indexes. We have, accordingly estimated values for such indexes as S&P 500, Dow-Jones, MSCI and Bond Prices.

In each case we regressed a market index on a four-month distributed lag of each of several different index values based on survey responses. Nearly all the regression estimates are significantly related to domestic equity price indexes and the results are mixed for the international indexes (MSCI) or the bond price index. In the interests of space we report the overall correlation between the identical specification of a distributed lag in a survey index and the value of the percentage change in the financial index.

The results are summarized in Table 3. Judging the results by the correlation coefficients, we can say that the index is most closely related to the S & P 500, the Dow Jones, and to the MSCI index for total return. It is close to being the most highly correlated with the MSCI index, itself. We can say, however, that the whole set of indexes are indicative of movements on financial markets.

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4. Principal Components The method of principal components is used to find a linear

combination of more economic and financial variables. The first component (linear combination of variables) extracts the highest explanatory power of the whole set being considered, the second, the next largest explanatory power, and so on. It should be noted that data requirements in principal component analysis are also greater than when using only a few variables. There are 27 variables used in this analysis. These variables are: NEWORDERS – Manufacturers’ new orders, consumer goods, chained 1996 Dollars UNFILLEDORDERS – Manufacturers’ unfilled orders, 1996 Dollars INVENTORYSALESRATIO – Manufacturing and trade inventories to sales ratio HOUSINGSTARTS – new privately owned housing units started CONSTRUCTION – value of new construction put in place, 1996 Dollars BUILDINGPERMITS – building permits for new private housing units EMPLOYMENT – establishment data, payrolls, all employees UNEMPLOYMENTRATE – rate of unemployment HOURLYEARNINGS – average hourly earnings, private establishments HOURS – average weekly hours, private establishments CPI – consumer price index PPI – producer price index for finished goods EXPORTIMPORTRATIO – the ratio of exports of goods and services to imports of goods and services EXCHANGERATE – trade weighted value of the dollar SANDP500 – S & P 500 Index DOWJONES – Dow Jones Composite index BONDPRICEINDEX - bond price index MSCI - MSCI FEDFUNDSRATE – Federal funds rate PRIMERATE – prime rate CORPORATEBONDRATE – corporate bond rate (AAA) TBILL3M – US Treasury bill rate, 3 month MONEYMARKETRATE – money market rate TENYEARMINUSFEDFUNDS – interest spread ( 10 year bond yield – federal funds rate) MONEY – Broad money supply (M2) deflated by the consumer price index CONSUMERCREDIT – consumer credit outstanding deflated by the consumer price index BUDGET – Federal receipt/outlay ratio

The correlation of individual variables with each component help to give some interpretation of the separate principal components. For example, the first component is highly correlated with interest rates.

Principal components improve the explanatory power significantly. R2

increases to 0.60, but adjusted R2 (which takes the number of explanatory variables used in the model into consideration) is 0.44. Furthermore, parameters associated with the index and most of the principal components are not statistically different from zero. Therefore, a new equation is estimated with statistically significant principal components. The results are

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more satisfactory (Table 4). The adjusted R2 increases to 0.59. The model also passes tests on serial correlation, ARCH, and specification (test results are not given here).

The index also performs slightly better than the competitors. The model using the Conference Board index of consumer confidence has an adjusted R2=0.57, very close to the one obtained with the index of investor optimism. The University of Michigan index of consumer sentiment gives an adjusted R2 =0.55, while the index of the National Association of Purchasing Management delivers an adjusted R2 =0.56. The ABC News/Money Magazine index gives an adjusted R2 ==0.55. 5. Ex-post and ex-ante forecasts (within sample) Forecasts based on the entire sample are provided in order to see the forecasting power of the model. The percentage errors are rather low. The mean absolute percentage error is 0.15. The Diebold-Mariano statistic is 1.49 for the Conference Board index of consumer confidence, -1.39 for the University of Michigan index of consumer sentiment, and –7.24 for the NAPM index. DM statistics show that the forecasting performance of the index of investor optimism is significantly better than the economic component, the personal component, and the NAPM index. The difference between the index of investor optimism and the indexes of the Conference Board and the University of Michigan are not statistically significant at the 95 percent confidence level, even at the 90 percent level. The first step in analysis of new information sources and methods is to examine, retrospectively, how closely and meaningfully the new approaches could interpret actual data for the macroeconomy. The regression equations, relying to a significant extent on indexes derived from sample surveys, show the degree of correlation over an historical period, together with various diagnostic statistics that tell how well the equations separate signal from noise, where some theoretical assumptions are placed on the structure of noise. In effect we assume that the noise factor is additive and random. To a great extent, we feel that we have isolated the noise factor.

A more severe test of our modeling efforts is given by an examination of the predictive power of the equations. By predictive power we mean that historical data, up to a point in time, are used to estimate the regression equations and the equations, based on the survey indexes, are extrapolated ahead by one month at a time to generate estimates of consumer expenditures and also other important magnitudes that can be numerically compared with observed data. The observations do not reveal the complete

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“truth”, but they are the best available single equation estimates of what actually happened in the economy.

We replicate this extrapolative test for the whole year 2000 and the months of 2001 through September. This is as close as we can come to simulation of the forecasting situation in a non-experimental science, such as econometrics. The emphasis is on extrapolation (as opposed to interpolation) and to replication (as opposed to a single experimental test).

We have two kinds of equations for testing, one using distributed lags of indexes and some time-series properties of residual error, the other using principal components of many economy-wide variables together with survey indexes and with time-series properties of residual error.

First we shall look at the mean-absolute-percentage errors for prediction (one month ahead) for consumer expenditure, industrial production, employment, personal income, manufacturing sales, and retail sales. In Table 5, we find that the error statistics are smallest for UBS/Paine Webber indexes of economic conditions in the case of consumption, industrial production, and employment and almost as small for the index of substantial investors. In the case of sales (manufacturing and retail) the smallest errors are for substantial investors. The Michigan index is the smallest for personal income, but the substantial investor index is fairly close to the Michigan index in this respect.

The equations that combine principal components and survey indexes show (Table 6) that consumption is best predicted by the equation using the index of substantial investors, if the principal component terms are given their historically observed values. It is more work and involves more uncertainty if the principal component values must be separately estimated for the extrapolations. We have used time-series analysis to project (one month ahead) values of the principal components and find that the index of economic conditions from the UBS/Paine Webber family of indexes performs best, by a fairly wide margin.

There is yet another relevant comparison to be made; that is the longevity of the explanatory power of the index. We cannot test or examine this aspect directly, since the index was introduced as recently as October 1996. We can gather some indirect information about longevity of such indexes by estimating equations for the Michigan, Conference Board, and National Association of Purchasing Management surveys over much longer periods. Monthly values of the Michigan index date back to 1978:05, the Conference Board back to 1977:10 and the National Association of Purchasing Management back to 1959:05.

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These estimates suggest that there is staying power in these relationships and that the recent findings are not simply chance events with low probability of occurrence. In the longer sample periods, the Michigan and Conference Board indexes are quite strongly correlated with changes in industrial production and total employment, as well as with changes in consumption. The index of the National Association of Purchasing Management is, as noted above, mainly related to explanation of industrial production and other business variables.

6. Conclusion

Survey of people in households and also in enterprises add a psychological dimension that can be quantified for use in the study of economic decision making. The UBS/Paine Webber surveys of investor optimism provide quantitative information from a strategic universe that has the potential for enlarging the information content of existing economic surveys from such sources as the University of Michigan, the Conference Board, and the National Association of Purchasing Management.

Since the UBS/Paine Webber surveys have a much shorter life history than the others, it is an objective of this study to examine its performance since inception (late 1996, early 1997). In comparison with the older surveys in existence to see how it performs in accuracy, economic insight, timeliness, and breadth of scope.

We find that it is at least as good and probably better in terms of accuracy, judging from its degree of correlation with key economic magnitudes such as consumer spending, personal income, industrial production, employment, and stock market averages. We also consider its lead time as a predictor of major economic variables, and it has excellent timeliness, in being available early each month for use in prediction of target variables with outstanding accuracy.

We have tested the UBS/Paine Webber series jointly with as many as 27 other monthly indicators and find that it performs well in one-month ahead projections of important variables. In this connection, we find that specific focus on certain groups of respondents such as substantial investors and experienced investors is promising in that they show relatively greater perception in a predictive sense.

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Table 1a. Time Series Properties of the Index of Investor Optimism1

Augmented Dickey-Fuller test for unit root ( INDEX) ADF Test Statistic 0.540795 1% Critical Value* -3.5457

5% Critical Value -2.9118 10% Critical Value -2.5932

*MacKinnon critical values for rejection of hypothesis of a unit root.

Phillips-Perron test for unit root (INDEX): PP Test Statistic 0.380244 1% Critical Value* -3.5437



Lag truncation for Bartlett kernel: 3

( Newey-West suggests: 3 )

Residual variance with no correction 114.3663Residual variance with correction 101.8748

1 Prior to 1999:02, monthly values are interpolated and fluctuates less.

20

40

60

80

100

120

140

160

1997 1998 1999 2000 2001

INDEX

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Table 1a. Time Series Properties of the Index of Investor Optimism

(Continued)2 Autocorrelation and Partial Autocorrelation (INDEX) Sample: 1996:10 2001:10 Included observations: 60

Autocorrelation Partial Correlation AC PAC Q-Stat Prob . |*******| . |*******| 1 0.848 0.848 45.371 0.000 . |****** | . |*. | 2 0.760 0.144 82.411 0.000 . |***** | .*| . | 3 0.655 -0.067 110.45 0.000 . |**** | . | . | 4 0.561 -0.041 131.34 0.000 . |**** | . |*. | 5 0.504 0.090 148.55 0.000 . |*** | .*| . | 6 0.406 -0.143 159.92 0.000 . |*** | . | . | 7 0.328 -0.048 167.48 0.000 . |** | .*| . | 8 0.229 -0.106 171.24 0.000 . |*. | . | . | 9 0.141 -0.052 172.69 0.000 . | . | .*| . | 10 0.061 -0.062 172.97 0.000 . | . | . | . | 11 0.006 0.044 172.97 0.000 .*| . | .*| . | 12 -0.063 -0.100 173.28 0.000

2 Prior to 1999:02, monthly values are interpolated and fluctuates less.

-30

-20

-10

0

10

20

30

1997 1998 1999 2000 2001

D(INDEX)

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Table 1a. Time Series Properties of the Index of Investor Optimism

(Continued)

Augmented Dickey-Fuller test for unit root ( D(INDEX)) ADF Test Statistic -5.018092 1% Critical Value* -3.5478



Phillips-Perron test for unit root (D(INDEX)): PP Test Statistic -8.179872 1% Critical Value* -3.5457






Autocorrelation and Partial Autocorrelation (D(INDEX)) Sample: 1996:10 2001:10 Included observations: 59

Autocorrelation Partial Correlation AC PAC Q-Stat Prob .*| . | .*| . | 1 -0.125 -0.125 0.9688 0.325 . |*. | . | . | 2 0.069 0.054 1.2678 0.531 . |*. | . |*. | 3 0.067 0.083 1.5547 0.670 **| . | **| . | 4 -0.217 -0.208 4.6291 0.328 . |*. | . |*. | 5 0.183 0.135 6.8728 0.230 .*| . | .*| . | 6 -0.128 -0.078 7.9792 0.240 . |*. | . |*. | 7 0.081 0.074 8.4346 0.296 . |*. | . |*. | 8 0.172 0.150 10.528 0.230 . | . | . |*. | 9 0.063 0.170 10.816 0.289 . |*. | . | . | 10 0.119 0.058 11.850 0.295 . |*. | . |*. | 11 0.121 0.196 12.948 0.297 . | . | . | . | 12 -0.027 0.017 13.005 0.369

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Table 1b. Time Series Properties of Real Personal Consumption

Expenditures

Augmented Dickey-Fuller test for unit root ( CONSUMPTION) ADF Test Statistic -0.188299 1% Critical Value* -3.5437



Phillips-Perron test for unit root (CONSUMPTION) PP Test Statistic -0.250744 1% Critical Value* -3.5437






5200

5400

5600

5800

6000

6200

6400

6600

1997 1998 1999 2000 2001

CONSUMPTION

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Expenditures (Continued)

Autocorrelation and Partial Autocorrelation (CONSUMPTION) Sample: 1996:10 2001:10 Included observations: 59

Autocorrelation Partial Correlation AC PAC Q-Stat Prob . |*******| . |*******| 1 0.955 0.955 56.598 0.000 . |*******| . | . | 2 0.909 -0.035 108.77 0.000 . |*******| . | . | 3 0.863 -0.019 156.69 0.000 . |****** | . | . | 4 0.819 -0.017 200.53 0.000 . |****** | . | . | 5 0.773 -0.037 240.31 0.000 . |****** | . | . | 6 0.725 -0.040 276.04 0.000 . |***** | . | . | 7 0.677 -0.042 307.75 0.000 . |***** | .*| . | 8 0.625 -0.064 335.33 0.000 . |**** | . | . | 9 0.575 -0.014 359.15 0.000 . |**** | . | . | 10 0.528 -0.003 379.59 0.000 . |**** | . | . | 11 0.479 -0.044 396.80 0.000 . |*** | .*| . | 12 0.428 -0.059 410.83 0.000

-.002

.000

.002

.004

.006

.008

.010

.012

.014

1997 1998 1999 2000 2001

DLOG(CONSUMPTION)

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Expenditures (Continued)

Augmented Dickey-Fuller test for unit root ( DLOG(CONSUMPTION)) ADF Test Statistic -7.112755 1% Critical Value* -3.5437



Phillips-Perron test for unit root (DLOG(CONSUMPTION)) PP Test Statistic -9.592873 1% Critical Value* -3.5437





Residual variance with no correction 7.96E-06Residual variance with correction 5.87E-06

Autocorrelation and Partial Autocorrelation (DLOG(CONSUMPTION)) Sample: 1996:10 2001:10 Included observations: 59

Autocorrelation Partial Correlation AC PAC Q-Stat Prob **| . | **| . | 1 -0.198 -0.198 2.4220 0.120 .*| . | **| . | 2 -0.170 -0.217 4.2439 0.120 . | . | . | . | 3 0.052 -0.035 4.4163 0.220 . |*. | . |*. | 4 0.097 0.071 5.0339 0.284 .*| . | .*| . | 5 -0.144 -0.108 6.4247 0.267 . |*. | . |*. | 6 0.192 0.185 8.9177 0.178 . | . | . | . | 7 -0.026 0.010 8.9642 0.255 .*| . | . | . | 8 -0.072 -0.013 9.3261 0.316 . |*. | . |*. | 9 0.115 0.124 10.277 0.329 . |*. | . |*. | 10 0.177 0.192 12.584 0.248 .*| . | . | . | 11 -0.114 0.055 13.564 0.258 .*| . | . | . | 12 -0.058 -0.041 13.825 0.312

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Table 2. Real Personal Consumption Expenditures and Distributed Lags of the Index Dependent Variable: DLOG(CONSUMPTION) Method: Least Squares Sample(adjusted): 1997:02 2001:08 Included observations: 55 after adjusting endpoints Convergence achieved after 13 iterations Newey-West HAC Standard Errors & Covariance (lag truncation=3) Backcast: 1997:01

Variable Coefficient Std. Error t-Statistic Prob. C 0.003710 0.000191 19.47245 0.0000

PDL01 3.80E-05 8.13E-06 4.670430 0.0000MA(1) -0.536421 0.086533 -6.199053 0.0000

R-squared 0.187091 Mean dependent var 0.003508Adjusted R-squared 0.155825 S.D. dependent var 0.002965S.E. of regression 0.002724 Akaike info criterion -8.920269Sum squared resid 0.000386 Schwarz criterion -8.810778Log likelihood 248.3074 F-statistic 5.983894Durbin-Watson stat 1.740112 Prob(F-statistic) 0.004582Inverted MA Roots .54 Lag Distribution of

D(INDEX) i Coefficien

t Std. Error T-Statistic

. * | 0 3.0E-05 6.5E-06 4.67043 . *| 1 4.6E-05 9.8E-06 4.67043 . *| 2 4.6E-05 9.8E-06 4.67043 . * | 3 3.0E-05 6.5E-06 4.67043

Sum of Lags

0.00015 3.3E-05 4.67043

-.010

-.005

.000

.005

.010-.004

.000

.004

.008

.012

.016

1997 1998 1999 2000 2001

Residual Actual Fitted

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Table 2. Real Personal Consumption Expenditures and Distributed Lags of the Index (Continued) Sample: 1997:02 2001:08 Included observations: 55

Q-statistic probabilities

adjusted for 1 ARMA term(s)

Autocorrelation Partial Correlation AC PAC Q-Stat Prob . |*. | . |*. | 1 0.123 0.123 0.8825 .*| . | .*| . | 2 -0.123 -0.140 1.7786 0.182 . | . | . |*. | 3 0.043 0.080 1.8905 0.389 . |*. | . |*. | 4 0.142 0.112 3.1363 0.371 . | . | .*| . | 5 -0.046 -0.070 3.2695 0.514 . |*. | . |*. | 6 0.092 0.147 3.8086 0.577 . | . | .*| . | 7 -0.021 -0.092 3.8371 0.699 . | . | . | . | 8 0.012 0.052 3.8463 0.797 . |*. | . |*. | 9 0.157 0.155 5.5277 0.700 . |*. | . | . | 10 0.121 0.046 6.5476 0.684 .*| . | .*| . | 11 -0.150 -0.116 8.1511 0.614 .*| . | . | . | 12 -0.066 -0.045 8.4686 0.671

Breusch-Godfrey Serial Correlation LM Test: (2 lags) F-statistic 1.123107 Probability 0.333334Obs*R-squared 2.325845 Probability 0.312571

ARCH Test (1 lag): F-statistic 0.012307 Probability 0.912093Obs*R-squared 0.012778 Probability 0.910001

Ramsey RESET Test : F-statistic 0.849038 Probability 0.433901Log likelihood ratio 1.836866 Probability 0.399144

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Table 2. Real Personal Consumption Expenditures and Distributed Lags of the Index (Continued)

0

2

4

6

8

10

12

-0.005 0.000 0.005

Series: ResidualsSample 1997:02 2001:08Observations 55

Mean -7.19E-05Median -0.000173Maximum 0.008576Minimum -0.007869Std. Dev. 0.002672Skewness 0.352926Kurtosis 4.527468

Jarque-Bera 6.488595Probability 0.038996

5200

5400

5600

5800

6000

6200

6400

6600

1997 1998 1999 2000 2001

CONSUMPTIOF

Forecast: CONSUMPTIOFActual: CONSUMPTIONForecast sample: 1997:02 2001:10Adjusted sample: 1997:02 2001:09Included observations: 55

Root Mean Squared Error 15.32737Mean Absolute Error 11.93892Mean Abs. Percent Error 0.204414Theil Inequality Coefficient 0.001290 Bias Proportion 0.000456 Variance Proportion 0.007207 Covariance Proportion 0.992337

21

Table 3. Relationship With Financial Variables (Determination coefficients) Indicator S & P 500 Dow-Jones MSCI Bond price

index

Index 0.185 0.071 0.118 0.015

Michigan 0.108 0.055 0.070 0.011

Conference 0.073 0.042 0.049 0.017

NAPM 0.027 0.020 0.023 0.069

ABC News/Money Magazine

0.078 0.026 0.032 0.028

22

Table 4. Polynomial Distributed Lags and Principal Components: The model with the Index of Investor Optimism Dependent Variable: DLOG(CONSUMPTION)*100 Method: Least Squares Sample(adjusted): 1997:05 2001:09 Included observations: 53 after adjusting endpoints Convergence achieved after 16 iterations Newey-West HAC Standard Errors & Covariance (lag truncation=3) Backcast: 1997:04

Variable Coefficient Std. Error t-Statistic Prob. C 0.367338 0.009240 39.75676 0.0000

C1 -0.013532 0.007844 -1.725266 0.0917C2 0.043492 0.012420 3.501765 0.0011C4 -0.075825 0.016338 -4.641021 0.0000C12 0.061213 0.020827 2.939144 0.0053

PDL01 0.003077 0.001514 2.032606 0.0483PDL02 -0.001332 0.001591 -0.837014 0.4072AR(2) -0.380785 0.113302 -3.360795 0.0016AR(1) -0.445955 0.127644 -3.493750 0.0011MA(1) -0.958033 0.010429 -91.86620 0.0000

R-squared 0.661167 Mean dependent var 0.331644Adjusted R-squared 0.590249 S.D. dependent var 0.373128S.E. of regression 0.238846 Akaike info criterion 0.142274Sum squared resid 2.453044 Schwarz criterion 0.514027Log likelihood 6.229752 F-statistic 9.322920Durbin-Watson stat 1.782006 Prob(F-statistic) 0.000000Inverted AR Roots -.22+.58i -.22 -.58i Inverted MA Roots .96 Lag Distribution of D(UBSPAINEWEBBE

R)

i Coefficient

Std. Error T-Statistic

. *| 0 0.00451 0.00188 2.39310 . * | 1 0.00308 0.00151 2.03261 . * | 2 0.00185 0.00208 0.88938 . * | 3 0.00082 0.00164 0.50062

Sum of Lags

0.01026 0.00505 2.03261

-.004

-.002

.000

.002

.004 -.004

.000

.004

.008

.012

.016

1997 1998 1999 2000 2001

Residual Actual Fitted

23

Table 5. Mean Absolute Percent Errors (%) Based on One-period ahead Ex-ante Forecasts

Consumption

Industrial production

Employment

Income Manufacturing and trade sales

Retail sales

Index 0.2895 0.4122 0.1087 0.3807 0.5873 0.6714

Indexeconomic 0.2602 0.3848 0.1077 0.3720 0.5970 0.6766

Indexpersonal 0.3317 0.5090 0.1104 0.4115 0.5714 0.6738

Indexsubstantial 0.2616 0.4266 0.1078 0.3756 0.5095 0.6659

Michigan 0.3137 0.5675 0.1300 0.3639 0.5936 0.6910

Conference 0.3923 0.5551 0.1381 0.3754 0.6134 0.7022

NAPM 0.3051 0.3969 0.1250 0.4031 0.5289 0.6707

Table 6. Mean Absolute Percent Errors (%) Based on One-period ahead Ex-ante Forecasts (Using Principal Components)

using actual values of principal components

using predicted values of principal components

Index 0.2702 0.3060

Indexeconomic 0.2461 0.2888

Indexpersonal 0.2165 0.3655

Indexsubstantial 0.2000 0.3815

Michigan 0.2400 0.3765

Conference 0.2329 0.3771

NAPM 0.2237 0.3424

the predictive power of survey results in macroeconomic analysis lawrence r. klein...

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