Inflation and Output Volatility: Evidence from International Historical Data

Bruno Ćorić

University of Split, Faculty of Economics, Business and Tourism

and CERGE-EI Foundation Teaching Fellow

Cvite Fiskovića 5

21000 Split, Croatia

telephone: +385914430724,

email: bcoric@efst.hr

Abstract

This study adopts a historical perspective to investigate variations in output volatility within

and across world economies. The analysis uses annual data for 37 OECD and non-OECD

countries covering the last two centuries. We focus on the relationship between inflation and

output volatility. The results of a panel analysis show a positive effect of inflation on output

volatility. This finding is consistent with the view that low inflation has a stabilizing effect on

output volatility over the long term.

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1. Introduction

Macroeconomic stability is high on the list of economic priorities in most societies.

Accordingly, the question of what determines the size of output volatility is important for

policymakers. The need to better understand output volatility determinants may be

particularly urgent today, when the economic and political turmoil due to the most recent

financial crisis threatens to undermine the foundation of democratic institutions in many

countries.

To address this issue, we analyse variations in output volatility across 19 OECD and

18 non-OECD countries over the last two hundred years, concentrating on the link between

the average level of inflation and output volatility. The analysis of output data in Ćorić (2019)

reveals that, historically, variations in output volatility within countries are often larger than

the variations across countries. Figure 1 illustrates the output data employed in our research.

The descriptive statistics show that the standard deviation of output volatility across the 37

countries in the sample is 1.82. In 27 countries, the standard deviations of output volatility

was larger than 1.82, while the average value of the standard deviations of output volatility

within all countries is 2.91. Accordingly, an analysis of the historical data might provide

valuable insights into the potential sources of output volatility.

Our data also show a positive relationship between the average level of inflation and

output volatility (see Figure 2). The idea that low inflation reduces output volatility is not

new in the literature. As argued in Logue and Sweeney (1981), a high inflation rate makes it

more difficult for producers to distinguish between nominal and real demand shifts and thus

causes higher fluctuations in relative prices than are seen in a low-inflation regime. As

relative price variations create additional producer uncertainty, the result will be more

variability in real investment and economic activity.

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More recently, a number of studies have argued that the low rate of inflation

contributed to low output volatility in the US during the Great Moderation.1 Blanchard and

Simon (2001) noted in one of the first studies on the Great Moderation that the observed

decline in US output volatility in the early 1980s coincided with a sharp decline in inflation

rates, while Clarida et al. (2000) found a significant change in US monetary policy,

suggesting a more aggressive response to inflation after Paul Volcker became chairman of

the Board of Governors of the Federal Reserve System (Fed) in 1979. Canova (2009) claims

that, by the early 1980s, the Fed had learned that the output–inflation trade-off was not

exploitable and that it concentrated instead on fighting inflation. A low-inflation regime

ensued, making the macroeconomic environment less volatile. The link between the Fed’s

stronger commitment to a low-inflation regime and the reduction in output volatility is

supported by a number of studies that estimated different types of structural macroeconomic

models to distinguish among the possible causes of the Great Moderation (Lubik and

Schorfheide 2004; Boivin and Giannoni 2006; Benati and Surico 2009; Canova 2009; Inoue

and Rossi 2011).2

The Great Moderation was not confined to the US. Similar periods of low output

volatility at the end of the 20th century were seen in a number of countries (Dalsgaard et al.

1 McConnell and Perez-Quiros’s (2000) analysis of the US data revealed a large decline in

output volatility after 1984, known in the literature as the “Great Moderation.”

2 A burst in volatility associated with the sharp recession of 2008/2009 seems to have ended

the Great Moderation. However, the results of the latest empirical research show that the

crisis merely interrupted, and did not end, the low-output volatility period in the US and other

developed economies (Charles, Darné and Ferrara 2018; Check and Piger 2018).

Consequently, the suggested link between inflation and output volatility still appears

theoretically and empirically plausible.

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2002; Stock and Watson 2003; Ćorić 2012). This swing in volatility was also not historically

unique. Variations in output volatility levels had been observed before World War Two

(WWII; Bergman, Bordo and Jonung 1998; Basu and Taylor 1999; Ćorić 2019). Therefore,

we employ historical data on output and inflation constructed by Barro and Ursúa (2008,

2012) and Reinhart and Rogoff (2011), respectively, to investigate the link between inflation

and output volatility. To account for the variations in output volatility detected within each

country, we use the results of tests for structural breaks reported in Ćorić (2019) and

organize the data into country–periods with significantly different output volatility levels.

The results of a panel regression analysis reveal a significantly positive relationship between

the average level of inflation and output volatility. These results appear to be robust to

variations in model specification, corresponding variations in sample size, an alternative

construction of the timespans in the data sample, and different estimation techniques.

Our analysis contributes to the literature on output volatility in several ways. First, in

contrast to the Great Moderation literature, our study does not concentrate just on the lower-

volatility episode in the US economy but also considers the structural changes in output

volatility that occurred across many OECD and non-OECD countries. Second, by focusing on

historical data and by explicitly considering the structural changes in output volatility within

countries, our study expands on existing analyses of cross-country variations in output

volatility. In particular, output has been systematically more volatile in some countries than

in others since WWII. The possible sources of these differences have been extensively

studied; these include the quality of institutions (Acemoglu et al. 2003; Mobarak 2005; Yang

2011; Williams 2014; Mathonnat and Minea 2019), geographical characteristics (Malik and

Temple 2006), financial development and integration (Beck, Lundberg and Majnoni 2006;

Manganelli and Popov 2015; Sahoo, Badri and Rath 2019) and international trade (di

Giovanni and Levchenko 2009; Haddad et al. 2013; Balavac and Pugh 2016). However, the

literature does not account for the structural changes in output volatility within countries or

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attempt to glean the additional insights that might be obtained from variations of output

volatility over a longer period of time. Finally, our results improve our understanding of the

factors influencing output volatility levels. Specifically, our results suggest that the beneficial

effects on volatility of low inflation were not limited to the Great Moderation, and that low

inflation helped reduce output volatility in general.

The rest of this paper is organised as follows. Section 2 describes the study’s model,

data, and methodology. Section 3 presents the results of the empirical analysis. Finally,

section 4 concludes the paper.

2. Empirical model and data description

2.1. Model

The hypothesized relationship between inflation and output volatility is tested with a

panel linear regression model:

Volatilityi , t=βInflationi ,t+ X i ,t θ+ηi+μ t+ε i, t (1)

where superscripts i and t represent country and time period, respectively. Volatilityi , t

represents the volatility of output. Inflationi ,t denotes the average rate of inflation, while X i , t

is a 1×k vector of k control variables. ηi and μt denote unobserved country- and time-specific

effects, respectively. ε i ,t is the idiosyncratic error term. The model is used to analyse a panel

of non-overlapping averages of annual data. The grouping of the data into country–periods

and the corresponding datasets are described in section 2.3 below.

2.2. Variables and data sources

The study’s variables are listed in Table 1. Our research is based on Barro and Ursúa’s

(2008, 2012) historical output data, which are an upgraded and improved form of Maddison’s

historical data. The dataset includes annual real GDP per capita data for 42 countries up to

2009. Country starting dates vary, ranging from 1790 to 1913. We employ data for 19 OECD

and 18 non-OECD countries for which continuous output series without missing observations

5

are available. A complete list of these countries is given in Table 2. These data are used to

construct the dependent variable. Output volatility is constructed as the logarithm of the

standard deviation of annual real GDP per capita growth rates.

Our main variable of interest is the average rate of inflation. This variable is

constructed as the logarithm of the average annual rate of inflation. The annual inflation rates

for the 37 countries in our sample are obtained from Reinhart and Rogoff’s (2011) dataset.

Reinhart and Rogoff (2011) combined International Monetary Fund data on inflation with the

work of a number of economic historians to construct historical annual rates of inflation for

70 countries. The dataset starts as early as 1265 (depending on the country).

We account for possible alternative determinants of output volatility by including a

number of control variables in the analysis, following the literature on output volatility.

However, our set of control variables is inevitably constrained by limited data availability

since our study of output volatility variations covers the last two centuries.3

The negative relationship between democracy and output volatility has been

documented in several studies (Rodrik 2000; Quinn and Woolley 2001; Mobarak 2005;

Klomp and de Haan 2009). Democracy can reduce volatility through various channels. For

example, Quinn and Woolley (2001) has argued that democratic government tends to require

more effort to stabilize economic volatility because voters punish politicians electorally for

economic instability. To address the possible relationship between democracy and output

volatility we use the indicator democ from the Polity IV Project. The Polity IV online

database (available at http://www.systemicpeace.org/inscrdata.html) provides annual

3 Note also that the observations for some explanatory variables are not available for all years.

Hence, two general principles are adopted. In country–periods where less than 20 percent of

the observations for a certain variable are missing, the average values of that variable are

calculated. In cases where more than 20 percent of the observations are missing, the country–

periods are excluded from the analysis.6

estimates on the characteristics of political regimes across the world. The democ indicator

measures democracy levels on a scale from zero to 10. The indicator is reported for every

independent country starting in 1800.4 Our variable for democracy is constructed as the

average value of the democ indicator.

The literature suggests that output volatility might be negatively related to a nation’s

development level due to diversification. For example, Acemoglu and Zilibotti (1997) argue

that output in less-developed countries is more volatile because diversification opportunities

are limited in the early stages of development in economies with indivisible risky projects

due to the scarcity of capital. Koren and Tenreyro (2007) suggest that poorer countries

specialize in not only fewer sectors but also more volatile sectors. We consider the possible

relationship between development levels and output volatility by including a variable for

initial output in the model, calculated as the logarithm of the average level of real GDP per

capita in the first five years of each country–period.5 The relevant data are obtained from the

Barro and Ursúa (2008, 2012) database.

Mobarak (2005) points to population size as another source of economic

diversification, as larger countries may have a greater capacity to diversify because their

resource base is likely to be broader. Following Mobarak (2005), then, we employ a variable

for population size, constructed as the logarithm of the total population in the first year of

each country–period using population data from Maddison (2010). Maddison’s historical data

provide periodic estimates of GDP and population for global and national economies from

4 We assign the lowest score for the years before independence for India, Indonesia, Korea,

Sri Lanka, Taiwan, and Finland.

5 Since the country–periods are, on average, shorter in data sample 2 (see explanation below),

in this sample we use the logarithm of the average level of real GDP per capita in the first

three years.7

the first year of a new era. Depending on the country, continuous annual observations on

population size are available starting in 1820.

According to Malik and Temple (2006), variations in output volatility are related to

nations’ geographic characteristics and locations. They argue that remote countries are more

likely to have undiversified exports and thus experience greater output volatility. Following

Malik and Temple (2006), we include variables reflecting distance to the equator, coast

distance, and distance to market in the model. The variable for distance to the equator is

calculated as the absolute value of the geographic latitude of the country centroid; latitude

data are obtained from the Geography dataset of the Centre for International Development at

Harvard University (available at http://www.cid.harvard.edu/ciddata/geographydata.htm). We

construct the coast distance variable using the same dataset. For each country, the coast

distance variable shows the mean distance (in km) to the nearest coastline or sea-navigable

river. The distance-to-market variable is constructed as the logarithm of country distance (in

km) to the nearest major market (in Europe, the United States, or Japan). The distance data

are obtained from CEPII’s GeoDist data on geographic distances (available at

http://www.cepii.fr/cepii/en/bdd_modele/bdd.asp). We use the variable distcr, which reflects

the distance between two countries based on the bilateral distances between the largest cities

of those two countries (the EU capital, Brussels, is used for Europe).

The possible link between low inflation and output volatility is not the only proposed

explanation for the Great Moderation. A number of authors have attributed the low volatility

in the US between 1984 and 2007 merely to the lack of large economic shocks (Stock and

Watson 2003; Ahmed, Levin and Wilson 2004; Primiceri 2005; Kim, Morley and Piger

2008). Therefore, it is particularly important to control for the effects of large economic

shocks on output volatility. For this purpose, we use the estimates of economic disasters

provided in Barro and Ursúa (2008, 2012). The term ‘economic disaster’ was introduced by

Barro (2006) to describe abnormally severe economic recessions. An economic disaster is

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defined as a cumulative decline in output of at least 10 percent over one or more years. Barro

and Ursúa (2008, 2012) used the historical data on real GDP per capita described above to

detect economic disasters for each country in their sample. We employ these data to construct

a measure for economic disaster frequency. For each country–period, we construct an

economic disaster variable, defined as the ratio of a number of economic disasters over a

number of years in a country–period.

We also use additional controls. A trade openness variable is introduced to consider

the possible effect of economic diversification, through international trade, on output

volatility (di Giovanni and Levchenko 2009; Haddad et al. 2013). The variable is constructed

as the logarithm of the average share of international trade (import plus export) in GDP; data

on international trade are obtained from Barbieri and Keshk’s (2012) Correlates of War

Project Trade Data Set. Barbieri and Keshk (2012) provide historical data on bilateral trade

flows and total national imports and exports starting in 1870.

Acemoglu et al. (2003) argue that the quality of institutions is the main determinant of

output volatility. Hence, as an alternative to the democracy variable, we use a variable

reflecting constraints on the executive employed by Acemoglu et al. (2003). We use the

indicator xconst taken from the Polity IV database described above. A variable for institutions

is constructed as the average value of xconst. The indicator reflects the extent of

institutionalized constraints on the decision-making powers of chief executives, measured on

a scale from zero to seven.

Following Klomp and de Haan’s (2009) findings that political instability might

increase economic volatility, we include a regime durability variable, constructed using the

durable indicator from the Polity VI database. This indicator reflects the number of years

since the most recent regime change. The regime durability variable is constructed as the

logarithm of the average value of durable.

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We also employ a variable for average output growth, defined as the average annual

growth rate of real GDP per capita; GDP data are obtained from Barro and Ursúa’s (2008,

2012) database. Prior to WWII, the monetary base was tied to the gold reserves. Hence, the

average growth of the monetary base was usually relatively small. After WWII, the creation

of the monetary base became independent of gold reserves, leading to higher inflation. In

parallel, the rate of output growth increased dramatically after WWII in many sample

countries. When economies grow faster, the growth will likely also be more volatile. Hence,

the positive relationship between inflation and output volatility may reflect the correlation

between the money supply and output growth.6

Finally, the time trend is employed to address the possible effect of improvement(s) in

national accounting standards on output volatility (Romer 1986; Sheraffin 1988; Bacus and

Kehoe 1992). It is plausible to assume that the accuracy of GDP measurements evolved over

the last two centuries. If the improvement(s) in national accounting contributed substantially

to the reduction in the observed output volatility across countries, we should observe

significantly a negative coefficient of the time trend variable after the other determinants of

output volatility are taken into account.

2.3. Data samples construction

The data are organised into country–periods. To avoid an arbitrary selection of the

length of these country–periods, we use the results of the time series analysis of historical

variations in output volatility reported in Ćorić (2019). This study uses the Barro and Ursúa

(2008, 2012) output data to test for structural changes (breaks) in conditional output

volatility. Ćorić (2019) modelled output growth as a linear autoregressive (AR) process and

tested for breaks in the mean of the absolute values of the AR model residuals for each

country separately. The breaks in the mean of the absolute values of the AR model residuals

(i.e. breaks in conditional output volatility) are estimated using Bai and Perron’s (1998) test

6 We thank an anonymous referee for drawing our attention to this possibility. 10

for detecting multiple structural breaks at unknown time points. Each detected break point

marks a year of a change in output volatility levels, which splits the annual output

observations of the considered country into periods with significantly different levels of

output volatility.

We employ the structural breaks reported by Ćorić (2019) to construct data sample 1.

For each country in our sample, we use the detected break points (years) in output volatility

to construct time spans with significantly different output volatility levels. For example, three

statistically significant breaks in output volatility are reported for Belgium; the breaks are

detected in 1893, 1913, and 1951. Correspondingly, the data for Belgium are organized in

four time periods. The first includes annual observations between 1847 and 1893, in which

the output volatility measured by the standard deviation (SD) of output growth was 1.74. The

second period comprises observations between 1894 and 1913, in which the SD of output

growth was 0.68. The third period includes observations between 1914 and 1952, in which

the SD of output growth was 14.36. The last period includes observations between 1952 and

2009, in which the SD of output growth was 1.89. The same procedure is applied to all other

countries in the sample. Since the number of detected breaks differs across countries, the

number of constructed time periods also differs across countries. The length as well as the

initial and end years of the periods are unique for each country and depend on the position of

the detected break points. To make this procedure clearer, the structure of data sample 1 is

shown in Appendix (see Table A1).

Data sample 1 has the advantage of corresponding directly to the detected significant

structural changes in output volatility. This data construction approach should enhance the

precision and reliability of the estimated coefficients because it avoids mixing observations

across periods with significantly different levels of output volatility. However, its

construction also imposes several limits on our analysis. The number and duration of the

periods in data sample 1 are unique for each country, depending on the break points.

11

Consequently, the years included in the particular time periods are not identical for all

countries. As the above example indicates, for example, time period two for Belgium

comprises annual observations from 1894 to 1913, whereas the corresponding time period

two for Brazil comprises observations from 1932 to 2009 (see Appendix Table A1). The

unique time periods preclude us from addressing the issue of cross-sectional dependence. The

construction of data sample 1 also resulted in an unbalanced panel in which the time

dimension appears to be insufficiently long to construct valid internal instruments. This limits

our ability to address the problem of potential endogeneity, since the construction of time-

variant external instruments is constrained by the lack of historical data.

To address these issues, we employ data sample 2. In this sample, the data for all

countries are organized into 20-year country–periods. Since the starting year for the output

data varies across the countries, we obtained an unbalanced panel with at most 10 time

periods per country (the structure of data sample 2 is shown in Appendix Table A2). The

country–periods of the same length enable us to consider possible unobserved time-specific

effects and address the issue of cross-sectional dependence. The larger number of the time

periods allows the use of internal instruments to address the problem of endogeneity. Finally,

the empirical simulations show that Bai and Peron’s (1998) testing procedure employed in

Ćorić (2019) is appropriate in small samples, but that method is conservative and captures

only major changes (Bai and Perron 2006; Jones and Olken 2008). Hence, data sample 2 is

also used to ensure that the results of our panel analysis are not an artefact of the approach

used to construct data sample 1.

2.4. Methodology

To estimate the relationship between inflation and output volatility, we several

estimators and model specifications. We first employ data sample 1 and polled OLS

estimates of the model that include inflation and the set of our controls with all time-invariant

geographical covariates. As noted above, our set of control variables is constrained by the

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limited availability of historical data. Therefore, it is particularly important to control not just

for geographic characteristics but for all kinds of country-specific characteristics that might

influence output volatility. To consider the possible unobserved country-specific effects

related to output volatility, we include country dummies and estimate a fixed effects model.

As a robustness check, we also estimate fixed effects models that include additional controls.

Data sample 1 has the advantage of corresponding directly to the results of the test for

structural breaks in output volatility. However, as explained above, the too-short time

dimension of the dataset and the uniqueness of the time periods for each country preclude us

from addressing the issues of endogeneity and cross-sectional dependence. Therefore, in the

next step, we employ data sample 2. To address cross-sectional dependence, we use the time

dummies and estimate the dynamic fixed effects models. The lagged dependent variable is

included in the models to account for the autocorrelation in residuals, while Everaert and

Pozzi’s (2007) bootstrap-based bias-corrected fixed effects estimator is used to address the

problem of dynamic panel bias.

The fixed effects help to address endogeneity caused by omitted country- and time-

specific variables that may be important in this study since the number of control variables is

limited due to data availability. Nonetheless, the estimated coefficient of inflation does not

necessary imply the causal effect of inflation on output volatility. Since higher inflation may

be a consequence of economic turmoil in some country–periods, we use two approaches to

address the potential endogeneity of inflation: (a) Blundel–Bond (1998) system GMM

estimation and (b) Lewbel’s (2012) estimation.

The Blundel–Bond (1998) method is widely used to handle endogeneity and dynamic

panel bias in dynamic fixed effects models. The method exploits the time series dimension of

a panel dataset to create internal instruments. The Blundel–Bond system GMM estimator

combines the regression equation in differences and the regression equation in levels into one

system. Therefore, the instrument matrix is also composed of two distinct parts: one part with

13

the second and deeper lags of endogenous explanatory variables in levels as instruments for

the endogenous explanatory variables in the first-differenced equation, and the other part with

the second and deeper lags of endogenous explanatory variables in first-differences as

instruments for the endogenous explanatory variables in the equation in levels.

Unfortunately, system GMM estimates can be biased due to the week instruments

problem, and no tests for weak instruments in dynamic panel GMM regressions are available

(Bazzi and Clemens 2013). Hence, we also employ Lewbel’s (2012) method to address

endogeneity. Lewbel’s (2012) estimator allows the identification of structural parameters in

regression models with endogenous regressors by using instruments that are constructed as

functions of the model’s data. Identification is achieved by having regressors that are

uncorrelated with the product of heteroscedastic standard errors.

3. Results

Table 3 reports the results of estimating our panel regression model by using data

sample 1. We first report the polled OLS estimates in column 1. The standard diagnostic tests

reveal that the reported models are well-specified with respect to multicollinearity, normality,

heteroscedasticity, and autocorrelation. We are concerned about the possible effect of outliers

related to the extreme values of inflation in some country–periods. Hence, we drop the

second observation for inflation in Germany from the sample.7 As an additional check, we

employ a robust regression analysis. The outlier-robust estimates (available on request) show

that the results reported in column 1 are not influenced by undue ‘leverage’ on the

regressions exerted by observations with extreme values.8

7 The observation for 1914–1945, during which the average value of inflation was above 6

million due to the well-known hyperinflationary periods in 1922 and 1923.

8 The results remain robust when clustered standard errors and wild-bootstrap cluster standard

errors are used (see discussion below).14

The results reveal a significantly positive relationship between inflation and output

volatility. The positive coefficient of inflation supports Logue and Sweeney’s (1981) findings

on the positive cross-sectional relationship between inflation and output volatility from 1950

to 1970. The result is also in line with the finding that attributes the reduction in US output

volatility in the early 1980s to the low-inflation regime caused by the Fed’s more aggressive

response to inflation (Clarida et al. 2000; Lubik and Schorfheide 2004; Boivin and Giannoni

2006; Benati and Surico 2009; Canova 2009; Inoue and Rossi 2011). Regarding the controls,

the significantly negative coefficient on initial output is consistent with the link between the

level of development and output volatility found by Acemoglu and Zilibotti (1997) and

Koren and Tenreyro (2007). As expected, the coefficient on economic disasters appears to be

significantly positive.9 The positive historical relationship between economic disasters and

output volatility is in line with findings that relate the Great Moderation to smaller and less-

frequent economic shocks (Stock and Watson 2003; Ahmed, Levin and Wilson 2004;

Primiceri 2005; Kim, Morley and Piger 2008).

The results of the fixed effects models are reported in columns 2 to 7 of Table 3. Due

to the introduction of country dummies, the time-invariant covariates (distance to equator,

distance to market, coast distance) drop out of the models. In addition to the country

dummies, the models reported in columns 3 to 7 also include the additional control variables

for trade openness, regime durability, time trend, quality of institutions, and output growth,

separately. The reported results suggest that all models are well-specified with respect to

autocorrelation. The modified Wald test indicates that the standard errors of the fixed effects

9 Since output volatility and economic disasters are parts of the same data-generating process,

the significantly positive empirical relationship between them is expected. Therefore, the

main role of the variable for economic disasters in our model is to control for the effect of

large economic shocks on volatility, and thus help us to assess the importance of the other

potential sources of variations in output volatility.15

models are not homoscedastic. Hence, we report the clustered standard errors. The results

show that the coefficients of inflation, economic disasters, and initial output remain

consistent with respect to sign, size, and statistical significance with the coefficients reported

in the benchmark model (see column 1).

Table 4 reports the results of estimating our panel regression model by using data

sample 2. We first run our fully specified model – that which includes time-invariant

variables for geographic characteristics and hence does not include country dummies. The

results of diagnostic tests do not indicate problems of multicollinearity, normality, and cross-

sectional dependence. However, the tests reject the hypotheses of no autocorrelation and

constant variance of residuals (available on request). To address the autocorrelation and

heteroscedasticity issues, we include the lagged dependent variable in the model and employ

cluster-robust standard errors. Since the result of Pesaran’s (2015) test indicates a problem of

cross sectional dependence (p = 0.001), we also introduce time dummies in the dynamic

version of our fully specified model. Although the reported diagnostic test indicates that the

time dummies address the issue of cross-sectional dependence, we are concerned that the

model’s standard errors might still be inappropriate. Particularly, clustered standard errors are

based on the asymptotic theory and may perform poorly if the number of clusters is small.

The literature does not provide a clear-cut definition of ‘small’. The suggested threshold level

ranges from 20 to 50 (Cameron and Miller 2015). Since the number of clusters in our case is

smaller than the suggested upper threshold bound, we report the wild cluster bootstrapped

standard errors proposed by Cameron, Gelbach and Miller (2008) for the estimates with a

small number of clusters.10 The results of the model are reported in column 1 of Table 4.

We then run the models that include the country dummies and the additional controls.

To take advantage of the longer time dimension of data sample 2, we also use the country-

specific time trend as an additional control (see column 8). Since the diagnostic test rejects

10 Estimations are implemented using cgmwildboot in STATA.16

the null of no autocorrelation at the standard level of statistical significance for all models

(available on request), we include the lagged dependent variable. To address the problem of

dynamic panel bias caused by the introduction of the lagged dependent variable in the models

with country dummies, we employ Everaert and Pozzi’s (2007) bootstrap-based bias-

corrected fixed effects estimator for dynamic panel data models.11 The reported diagnostics

suggest that, after we control for the time fixed effects, cross-sectional dependence does not

pose serious estimation or inferential problems. The results of the models are reported in

columns 2 to 8 in Table 4.

The estimates reported in columns 1 to 8 of Table 4 show that the results on inflation

and economic disasters are similar to those reported in Table 3. Both variables keep the same

sign and remain statistically significant in all specifications. The results on initial output

appear to be less robust. The coefficients of initial output remain negative, but are statistically

insignificant in all models.

Taken together, the results on inflation reported in Tables 3 and 4 reveal a persistently

significant relationship between the average level of inflation and output volatility.

Nonetheless, the significant coefficient on inflation does not necessarily imply a causal effect

of inflation on output volatility. To address the potential endogeneity of inflation caused by

reverse causality, we perform a Blundel–Bond (1998) system GMM estimation of the model

that includes the country dummies (model in column 2 of Table 4) and Lewbel’s (2012)

11 In our case, this estimator has advantages over the standard Kiviet (1995) and Bruno (2005)

bias-corrected fixed effects estimators because it enables us to allow for the

heteroscedasticity of residuals and to report wild bootstrapped standard errors. All

estimations are implemented using xtbcf (De Vos et al. 2015) in STATA.17

estimation of the pooled OLS model that includes the time-invariant geographic covariates12

(model in column 1 of Table 4).

The instrumental variable (IV) estimates are reported in columns 9 and 10 of Table 4.

Column 9 reports model diagnostics from the system GMM estimation, in which second and

deeper lags of the inflation, lagged output volatility, and regime durability are used as

instruments for the inflation and lagged output volatility.13 The results suggest that first-order

serial correlation in the first-differenced errors cannot be rejected, whereas second-order

serial correlation is rejected at the standard levels of statistical significance. The Hansen test

comfortably exceeds the conventional threshold. Column 10 reports model diagnostics from

the IV estimation with the inflation instrumented by its own first lags and instruments

generated by Lewbel’s (2012) method. If the instruments are uncorrelated, or weakly

correlated, with the endogenous variable(s), then IV estimators can perform poorly (Baum et

al., 2007). Hence, tests for underidentification and weak identification of instruments are

reported. The Kleibergen and Paap (2006) test statistic reveals that the null hypothesis of zero

correlation between instruments and endogenous variables can be rejected at conventional

levels of significance, suggesting that underidentification is not a problem. The value of the

Kleibergen–Paap rk Wald F statistic indicates that the null of a weak correlation of

instruments and endogenous variables should also be rejected.14 The orthogonality of the

12 The method is implemented using Baum and Schaffer’s (2012) ivregh2 Stata module,

which allows the application of Lewbel’s (2012) estimator in panel data regressions.

13 The estimation was implemented using xtabond2 (Roodman, 2009a) in STATA. We

employ a two-step system GMM estimator robust to heteroscedasticity with Windmeijer

(2005) small-sample correction to the standard errors. Following Roodman (2009b), the

number of instruments is restricted to be less than the number of groups (countries).

14 The reported Kleibergen–Paap rk LM statistic for underidentification is robust to

heteroscedasticity (Baum, Schaffer and Stillman 2007). For weak identification, Baum, 18

instruments is tested by the Hansen test of overidentification that is consistent in the presence

of heteroscedasticity. The reported result suggests that the instruments are uncorrelated with

the error term.

The IV estimates on inflation reported in columns 9 and 10 appear to be similar to the

results presented in columns 1 to 8. The coefficients of inflation are positive, statistically

significant, and of similar sizes, suggesting that the detected effect of inflation on output

volatility is not a mere reflection of reverse causality.

4. Conclusion

This study contributes to a better understanding of variations in output volatility over

the last two centuries. A number of studies suggest that low inflation was an important cause

of the macroeconomic stability that occurred in the US during the Great Moderation. This

study’s key contribution is constructing a historical dataset for 37 OECD and non-OECD

countries and testing the hypothesis that a lower average inflation rate has a stabilizing effect

on output volatility. The results from panel regression analysis do not reject this hypothesis.

The estimated coefficients on inflation suggest that the average inflation level had a positive

impact on output volatility. Instrumental variable estimates suggest that this effect is unlikely

to be driven only by endogeneity. This finding remains robust after controlling for the effects

of large economic crises, institutions, and a number of other time-variant and -invariant

covariates. Additional checks indicate that the effect is robust with respect to different

construction of time-spans and corresponding variations in output volatility and different

model formulation and estimation techniques.

Schaffer and Stillman (2007) suggest reporting the Kleibergen–Paap rk Wald F statistic in

cases when i.i.d. residuals are not assumed. Since Stock and Yogo’s (2005) tabulated critical

values are calculated for the case of i.i.d. residuals, they suggest applying the older ‘rule of

thumb’ that the F statistic should be at least 10 for weak identification not to be considered a

problem.19

Our findings enhance the results of previous research by suggesting that the low rate

of inflation was not just one of the important causes of the low output volatility in the US

during the Great Moderation but also had a stabilizing effect on output volatility in a number

of OECD and non-OECD countries over the last two centuries. The results of our analysis

also contribute to the literature on cross-countries differences in output volatility during the

post WWII period. For instance, the influential study of Acemoglu et al. (2003) finds that the

average rate of inflation appears to have had only a minor impact on output volatility between

1970 and 1997, especially after the effect of institutions is controlled for. Our results show

that, when historical variations in output volatility within and across countries are considered,

average inflation levels emerge as an important factor in output stabilization. This seems to

prevail even when we control for the effect of institutions and a number of other potential

determinants of output volatility.

The literature attributes the low rate of inflation in the US since the early 1980s to the

good conduct of monetary policy. The average rate of inflation is also used as an indicator of

the quality of economic policy by Acemoglu et al. (2003) and other empirical studies of

cross-country differences in volatility after WWII (Bekaert, Harvey and Lundbland 2006;

Yang 2008; Williams 2014). The positive relationship between average inflation rates and

output volatility revealed in our study might suggest that good economic policy also has

beneficial effects on output volatility. However, interpreting inflation as an indicator of

economic policy quality is not entirely appropriate in our case. Our analysis uses historical

data that, depending on the country, cover annual observations starting as early as 1790 – a

time when no central banks were controlling money creation and when the monetary base

was largely exogenous, being tied to the trade balance and to the performance of silver- and

gold-mining activity. Thus, while this interpretation makes sense after WWII, it cannot be

considered appropriate for periods as early as the 19th century.15

15 I thank an anonymous referee for suggesting this point.20

This caveat does not imply that our results are irrelevant with respect to the

importance of sound economic policy. As long as demand for government bonds is sufficient,

central banks can control money creation and thus inflation rates. Therefore, by showing that

low inflation has historically contributed to lower output volatility, our results provide

additional empirical evidence in support of policymakers’ commitment to maintaining low

inflation rates. This support might be valuable amid the turbulent political circumstances

since the most recent crisis, when some central banks – even in developed democracies with

formally independent institutions – have been put under pressure by political leaders to

loosen the emphasis on the low inflation objective and pursue a more expansionary monetary

policy to stimulate the economy in the short run.

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Tables

Table 1. Definitions and sources of the variables

Variable name DefinitionOutput volatility Logarithm of the standard deviation of the real GDP p.c. annual growth rates

Inflation Logarithm of the average annual rate of inflation

Democracy Average value of the Polity IV indicator democ (measured on the 0 to 10 scale,

27

with 10 corresponding to the highest degree of democracy)

Initial output Logarithm of the average real GDP p.c. over the first five/three years in the country-period

Economic disasters Ratio of a number of economic disasters over a number of years in the country-period

Population Logarithm of the size of population in the first year of the country-period

Distance to equator Absolute value of geographic latitude of country centroid

Distance to market Logarithm of country distance (in km) to the nearest major market: Europe (Brussels), US or Japan.

Coast distance Mean distance (in km) to nearest coastline or sea navigable river

Trade openness Logarithm of the average share of international trade (import plus export) in GDP

Institutions Average value of the Polity IV indicator xconst (measured on the 0 to 7 scale, with 7 corresponding to the highest constraints on executives)

Regime durability Logarithm of the average value of the Polity IV indicator durable

Output growth Average annual growth rate of real GDP p.c.

Table 2. Countries

included in the data

sample

28

OECD Countries time period non OECD Countries time periodAustralia 1820-2009 Argentina 1875-2009Austria 1870-2009 Brazil 1850-2009Belgium 1846-2009 Chile 1860-2009Canada 1870-2009 China 1890-2009Denmark 1818-2009 Colombia 1905-2009Finland 1860-2009 Egypt 1894-2009France 1820-2009 India 1872-2009Germany 1851-2009 Indonesia 1880-2009Italy 1861-2009 Korea 1911-2009Japan 1870-2009 Mexico 1895-2009Netherlands 1807-2009 Peru 1896-2009New Zealand 1860-2009 Russia 1860-2009Norway 1830-2009 S. Africa 1911-2009Portugal 1865-2009 Sri Lanka 1870-2009Spain 1850-2009 Taiwan 1901-2009Sweden 1800-2009 Turkey 1875-2009Switzerland 1851-2009 Uruguay 1870-2009United Kingdom 1830-2009 Venezuela 1883-2009United States 1790-2009

Note: Countries are classified across the groups of OECD and non OECD countries based on the original Barro and Ursúa’s (2008, 2012) classification. The time period denotes period for which annual output data are available.

Table 3. Results of the panel data analysis of output volatility - data sample 1

Dependent variable Output volatility(1) (2) (3) (4) (5) (6) (7)

Inflation 0.110*** 0.133*** 0.159*** 0.127*** 0.132*** 0.140*** 0.117***(0.029) (0.037) (0.052) (0.038) (0.041) (0.035) (0.038)

Democracy 0.010 0.029 0.040 0.031 0.027 0.043

29

(0.017) (0.024) (0.026) (0.027) (0.026) (0.030)Initial output -0.249*** -0.390*** -0.283** -0.384*** -0.402*** -0.347*** -0.463***

(0.058) (0.093) (0.128) (0.112) (0.135) (0.080) (0.107)Economic disasters 0.147*** 0.133*** 0.136*** 0.128*** 0.133*** 0.135*** 0.128***

(0.011) (0.018) (0.020) (0.018) (0.018) (0.018) (0.017)Population -0.014 -0.040 -0.043 -0.035 -0.043 -0.071 0.062

(0.028) (0.145) (0.206) (0.155) (0.147) (0.138) (0.157)Distance to equator 0.005

(0.003)Distance to market -0.037

(0.041)Coast distance 0.000

(0.000)Trade openness -0.149

(0.160)Regime durability -0.074

(0.081)Time trend 0.017

(0.129)Institutions 0.046

(0.038)Output growth -4.332

(4.589)Constant -1.711** -.304 -1.500 -0.183 -0.182 -0.229 -1.343

(0.754) (1.914) (2.574) (2.048) (2.062) (1.842) (2.000)

Number of observations 86 86 62 79 86 86 86

Number of countries 37 37 35 36 37 37 37Country dummies No Yes Yes Yes Yes Yes YesCameron & Trivedi test for:heteroscedasticity 0.365skewness 0.193kurtosis 0.278Brush-Pagan test for heterosced. 0.918Wooldridge test for autocorrelation 0.117 0.117 0.128 0.177 0.120 0.092 0.166Variance inflation factor: Maximum 2.99Variance inflation factor: Mean 1.92Wald modified test for groupwise het. 0.000 0.000 0.000 0.000 0.000 0.000Notes: *,**,*** indicate 10, 5 and 1 percent of significance.

Table 4. Results of the panel data analysis of output volatility - data sample 2

Dependent variable Output volatility(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Lagged output volatility 0.271*** 0.222*** 0.240*** 0.232*** 0.222*** 0.220*** 0.252*** 0.159* 0.086 0.255***(0.039) (0.060) (0.070) (0.073) (0.060) (0.058) (0.068) (0.093) (0.135) (0.053)

Inflation 0.068* 0.110*** 0.106* 0.119*** 0.110*** 0.110*** 0.096** 0.150*** 0.110** 0.090**(0.030) (0.044) (0.057) (0.043) (0.044) (0.044) (0.048) (0.057) (0.056) (0.043)

Democracy -0.014 -0.004 0.003 -0.016 -0.004 0.000 -0.012 -0.002 -0.007

30

(0.009) (0.018) (0.018) (0.020) (0.018) (0.017) (0.022) (0.015) (0.011)Initial output -0.045 -0.098 -0.091 -0.019 -0.098 -0.104 -0.191 -0.060 -0.063 -0.042

(0.042) (0.112) (0.159) (0.113) (0.115) (0.099) (0.137) (0.197) (0.051) (0.056)Economic disasters 0.080*** 0.084*** 0.082*** 0.081*** 0.085*** 0.085*** 0.081*** 0.084*** 0.071*** 0.074***

(0.011) (0.012) (0.012) (0.012) (0.012) (0.012) (0.011) (0.016) (0.015) (0.013)Population -0.038* -0.151 -0.130 -0.179 -0.151 -0.148 -0.138 -0.180 -0.026 -0.059**

(0.019) (0.151) (0.193) (0.157) (0.155) (0.154) (0.156) (0.392) (0.022) (0.027)Distance to equator -0.000 -0.001

(0.002) (0.002)Distance to market -0.025 -0.023

(0.042) (0.046)Coast distance 0.000 0.000

(0.000) (0.000)Trade openness 0.073

(0.118)Regime durability -0.005

(0.049)Time trend -0.037

(0.048)Institutions -0.003

(0.028)Output growth -4.418

(2.945)Constant -1.843* -2.819***

(0.627) (0.703 )Number of observations195 182 158 174 182 182 182 182 195 173Number of countries 36 36 36 36 36 36 36 36 36 36Number of instruments 28Country dummies No Yes Yes Yes Yes Yes Yes Yes Yes NoTime period dummies Yes Yes Yes Yes Yes Yes Yes Yes Yes YesCountry specific trends No No No No No No No Yes No NoCross sectional dependence

0.214 0.642 0.658 0.766 0.642 0.667 0.594 0.678 0.276 0.208

Underidentification test 0.005Weak identification test 16.823Overidentification test 0.600 0.198Arellano-Bond AR(1) 0.071Arellano-Bond AR(2) 0.141Notes: *,**,*** indicate 10, 5 and 1 percent of significance. The reported diagnostic tests are as follows: for cross sectional dependence, the Paseran (2015) test; for underidentification, Kleibergen and Paap’s (2006) test; for weak identification, the Kleibergen-Paap rk Wald F statistic; for overidentification, the Hansen J statistic; first-order and second-order serial correlation, Arellano-Bond AR(1) and AR(2) tests. The reported values for the diagnostic tests are their respective p-values, except for the weak identification test (for which we report the F-statistic).

31

Figures(a) OECD countries

-20

-10

010

2030

1800 1850 1900 1950 2000Year

Australia

-80

-60

-40

-20

020

1800 1850 1900 1950 2000Year

Austria

-40

-20

020

40

1800 1850 1900 1950 2000Year

Belgium

-20

-10

010

20

1800 1850 1900 1950 2000Year

Canada

-20

-10

010

20

1800 1850 1900 1950 2000Year

Denmark-2

0-1

00

1020

1800 1850 1900 1950 2000Year

Finland

-40

-20

020

40

1800 1850 1900 1950 2000Year

France

-100

-50

050

1800 1850 1900 1950 2000Year

Germany

-30

-20

-10

010

20

1800 1850 1900 1950 2000Year

Italy

-40

-20

020

1800 1850 1900 1950 2000Year

Japan

-40

-20

020

4060

1800 1850 1900 1950 2000Year

Netherland

-20

-10

010

20

1800 1850 1900 1950 2000Year

New Zealand

-10

-50

510

15

1800 1850 1900 1950 2000Year

Norway

-10

-50

510

15

1800 1850 1900 1950 2000Year

Portugal

-30

-20

-10

010

1800 1850 1900 1950 2000Year

Spain

-20

-10

010

20

1800 1850 1900 1950 2000Year

Sweden

-20

-10

010

20

1800 1850 1900 1950 2000Year

Switzerland

-10

-50

510

1800 1850 1900 1950 2000Year

United Kingdom

-20

-10

010

20

1800 1850 1900 1950 2000Year

United Sates

32

(b) non-OECD countries

-30-

20-1

00

1020

1800 1850 1900 1950 2000Year

Argentina

-20

-10

010

20

1800 1850 1900 1950 2000Year

Brazil

-20

-10

010

20

1800 1850 1900 1950 2000Year

Chile

-20

-10

010

20

1800 1850 1900 1950 2000Year

China

-50

510

1800 1850 1900 1950 2000Year

Colombia-1

00

1020

30

1800 1850 1900 1950 2000Year

Egypt

-20

-10

010

20

1800 1850 1900 1950 2000Year

India

-30-

20-1

00

1020

1800 1850 1900 1950 2000Year

Indonesia

-40

-20

020

1800 1850 1900 1950 2000Year

Korea

-20

-10

010

1800 1850 1900 1950 2000Year

Mexico

-20

-10

010

1800 1850 1900 1950 2000Year

Peru

-40

-20

020

1800 1850 1900 1950 2000Year

Russia

-30-

20-1

00

1020

1800 1850 1900 1950 2000Year

South Africa

-10

-50

510

15

1800 1850 1900 1950 2000Year

Sri Lanka

-60

-40

-20

020

1800 1850 1900 1950 2000Year

Taiwan

-40

-20

020

40

1800 1850 1900 1950 2000Year

Turkey

-20

-10

010

20

1800 1850 1900 1950 2000Year

Uruguay

-20-

100

1020

30

1800 1850 1900 1950 2000Year

Venezuela

Figure 1. Output volatilityNote: Countries are classified across the groups of OECD and non OECD countries based on the original Barro and Ursúa’s (2008, 2012) classification. The graphs show the annual growth rates of real GDP per capita.Source: Author’s calculation based on Barro and Ursúa’s (2008, 2012) historical GDP data.

33

-5-4

-3-2

-1Lo

g. o

f the

sta

ndar

d de

viat

ion

of o

utpu

t gro

wth

-5 -4 -3 -2 -1 0 1 2 3 4 5 6Log. of the average rate of inflation

Fitted values

Figure 2. Inflation and Output volatilityNote: Data are organised in the 20-year country-periods.Source: Author’s calculation based on Barro and Ursúa’s (2008, 2012) historical GDP data.

34