Inflation uncertainty and unemployment: Some International evidence.

Seyfried, William L. ; Ewing, Bradley T.

William L. Seyfried (*)

Bradley T. Ewing (**)

Introduction

Understanding the relationships between prices, output, and unemployment is a central theme in both theoretical and empirical macroeconomics. The impact of macroeconomic policy on jobs and inflation is of interest to both economists and policy-makers alike. For instance, the ability of the monetary authority to lower the unemployment rate depends critically on whether or not money is neutral. In this paper, we examine the linkage between the uncertainty associated with inflation variability and the unemployment rate for a sample of industrialized countries over the last two decades.

First developed by Phillips (1958) and later modified by Friedman (1968) and Phelps (1967), the standard expectations-augmented Phillips curve relationship is as follows:

[pi] = [[pi].sup.e] -- k (ur -- [ur.sup.*]) (1)

where [pi] represents the inflation rate, [[pi].sup.e] represents expected inflation, (1) ur the unemployment rate, [ur.sup.*] the natural rate of unemployment, and k > 0 indicates the extent to which the inflation rate is associated with the deviation of the actual unemployment rate from the natural rate of unemployment. The short-run Phillips curve suggests a trade-off between unemployment and unexpected inflation. Only if expected inflation changes will the short-run Phillips curve shift. Consequently, any observed relationship between unemployment and actual inflation will change over time as expected inflation changes. Thus we may observe actual inflation being high even when unemployment is higher than the natural rate. With regard to unemployment, it is unexpected inflation that is relevant, not its level. Rearranging (1) expresses the unemployment rate as a function of the natural rate of unemployment and unexpected inflation.

ur = [ur.sup.*] -- (1/k)([pi] - [[pi].sup.e] (2)

It is clear that uncertainly regarding inflation has associated with it a number of costs, including the costs associated with the redistribution of resources. Perhaps even more costly to the economy are the negative effects brought on by inflation uncertainty which distorts information provided by relative prices. These relative prices provide signals to economic agents as to how to best allocate resources. Uncertainty about changes in prices can lead to agents spending an inefficient amount of time collecting and processing price information and thus wasting scarce resources. (2) It is reasonable to think that risk-averse agents might adjust inflation expectations upwards, at least in the short run, when faced with heightened uncertainty about inflation (as proxied by its variability), since expectations formation is more difficult. Cuikerrnan and Meltzer (1986) formulate a game-theoretic model that predicts higher inflation uncertainty raises the average inflation rate. Reagan and Stulz (1993) confirm thi s hypothesis by developing a theoretical model that suggests one should expect higher inflation when there is an increase in the variability of prices. In a sense, a risk premium will be incorporated into expected inflation. Thus, we have [[pi].sup.e] = f([sigma][pi]) with f > 0, where [sigma][pi] denotes the variability of inflation and is our proxy for inflation uncertainty. As seen in (2), is higher expected level of inflation due to the variability of inflation will result in higher unemployment.

In the long run, rational expectations of inflation will equal expected inflation on average. Thus according to the expectations-augmented Phillips curve, the actual unemployment rate will coincide with the natural rate in the long run and the long-run Phillips curve is vertical. This implies that changes in the nominal money supply cannot affect output or unemployment in the long run and therefore money is long-run neutral.

In this paper, we explicitly focus on the relationship between unemployment in the G7 countries and the uncertainty associated with the variability of inflation underlying the theory described above. To examine the relationship between inflation uncertainty and unemployment, we consider how the unemployment rate in each of the G7 countries has responded to inflation uncertainty as measured by the variability of the inflation. Furthermore, by using standard time-series estimation techniques, we are able to distinguish short-run effects of inflation uncertainty on unemployment from long-run equilibrium relationships.

Inflation uncertainty and the harm that it can do has not gone unnoticed by the Federal Reserve, either. The President of the Richmond Fed has suggested that the risk associated with "uncertainty regarding future inflation ... could harm the economy in a variety of ways." (3) In fact, according to Logue and Sweeney (p. 500, 1981), "given the uncertainty induced by inflation, it does not seem unreasonable that the inflation-unemployment trade-off may actually slope upwards." Individual nations may behave quite differently. Consequently, we believe it is important to study the effects of inflation uncertainty using data from several industrialized countries. The paper proceeds with a brief review of the literature, discussion of the empirical methodology and presentation of the results. Concluding remarks are then offered the closing section.

Review of Related Literature

Several researchers have studied the effects of anticipated inflation. For instance, Fischer and Summers (1989 and 1993) and Agell and Ysander (1993) focused on how to insulate an economy from the potential harmful effects of unanticipated inflation. Logue and Sweeney (1981) conducted a cross-sectional study of twenty-four countries for the period of 1950-1971 to examine the relationship between inflation and real growth, including testing the proposition that inflation variability may impact average real growth and the variability of real growth. They found some evidence that inflation variability significantly impacts the variability of real growth. Thornton (1988) examined time-series data from eighteen countries including those of the G7 over the 1955-1984 period to determine the impact of inflation on industrial production. His results indicated that in the G7 countries inflation variability impacted the variability of industrial production only in Germany and Italy. Finding only limited support for the hypothesis that there is a causal relationship between inflation uncertainty and the variability of output growth, Thornton contends that the cross-section results of Logue and Sweeney (1981) should be treated with caution.

Weber (1994) conducted tests of long-run neutrality for the G7 countries. Using a bivariate vector-autoregression, Weber examined the relationship between changes in inflation and changes in unemployment rates. (4) He provides little evidence against the long-run neutrality of money and also finds that the data in the G7 countries do not reject the hypotheses of a long-run vertical Phillips curve. Weber's results are consistent in spirit with those of King and Watson (1992) who find little evidence to refute the existence of a long-run vertical Phillips curve.

In a study of ten industrialized economies, Serletis and Krause (1996) concluded that the data support the quantity-theoretic proposition that money is neutral in the long run. Others have also provided support for the long-run money neutrality argument. The findings of Lucas (1980), Mills (1982), and Geweke (1986) are all consistent with the proposition that money is neutral in the long run. Additionally, McCandless and Weber (1995) studied a cross-section of 110 countries over a thirty-year period and determined that there was no correlation between inflation and real output growth.

Methodology and Results

We hypothesize that greater variability of inflation is associated with an increase in the unemployment rate. In order to test this hypothesis, we use data from the G7 countries with sample periods given in parentheses: Canada (1980:1-96:1), France (1985:1-96:1), Germany (1980:1-89:4), Italy (1980:1-90:4), Japan (1980:1-95:4), United Kingdom (1980:1-96:1), and the United States (1980:1-96:1). The data are quarterly observations and sample periods differ due to data availability. The sample period for Germany stops at 1989:4 to avoid any problems associated with reunification. Inflation is computed using the consumer price index obtained from the International Financial Statistics CD-ROM database. Inflation variability is calculated as the eight-quarter standard deviation of inflation. (5) Unemployment rate data are from the Main Economic Indicators from the OECD. In what follows, we let ur denote the unemployment rate and [sigma][pi] inflation variability.

Before proceeding with tests of Granger-causality, we examined univariate time series properties of the unemployment rate and our proxy for inflation variability to determine whether or not cointegration and error-correction modeling is warranted. (6) Augmented Dickey-Fuller unit root tests revealed that unemployment is first-difference stationary in France, Italy, Japan, United Kingdom, and the United States and stationary in levels in Canada and Germany. Inflation variability was found to be first difference stationary in France, Italy, Japan, United Kingdom, and the United States and level stationary in Canada and Germany. These unit root test results are presented in the third and fourth columns of Table 1. Appendix 1 provides a description of the ADF unit root test.

Given that the respective inflation uncertainty and unemployment measures are integrated of order zero (I(0)) in Canada and Germany, no cointegration exists between inflation variability and unemployment. However, it is appropriate to test for cointegration between inflation variability and employment in the cases of France, Italy, Japan, United Kingdom, and the United States since each of the variables was found to be integrated of order one (I(1)).

A pair of I(1) time series are said to be cointegrated if some linear combination of them is stationary. Tests for cointegration seek to discern whether or not a stable long-run relationship exists among a set of variables. The existence of a common trend among unemployment and inflation variability means that in the long run the behavior of the common trend will drive the behavior of the two variables. Shocks that are unique to one series (e.g., inflation uncertainty induced by the momentary authority) will die out as the variables adjust back to their common trend. In the context of this study, a finding of cointegration would simply mean that the transmission mechanism between the variability of inflation in a particular country and its unemployment rate is stable and thus more predictable over long periods. In the presence of a cointegrating relationship, the long-run behavior of the two variables will be highly correlated, even though they may diverge considerably in the short run, and consequently this relationship may be exploited. Cointegration test results based on the Engle-Granger (1987) procedure are; presented in the fifth column of Table 1. Appendix 2 provides a description of the cointegration test.

In each case, the null hypothesis of no cointegration cannot be rejected implying there is no long run trade-off between inflation variability and unemployment. Given these findings, we can proceed to utilize the conventional vector-autoregressive format and standard Granger-causality tests.

We now turn our attention to the estimation of vector-autoregressions (VAR) for each of the countries in our study. Variables in the VAR are entered in first-differences for France, Italy, Japan, UK, and US and in levels for Canada and Germany. The lag specifications were chosen based on Akaike's information criterion and F-tests were conducted to see if inflation variability Granger-causes the unemployment rate. The unemployment rate equation is specified as:

u[r.sub.1] = [B.sub.0] + [SIGMA][[alpha].sub.i]u[r.sub.t-i] + [SIGMA][B.sub.i][sigma][[pi].sub.t-i] + [[epsilon].sub.t] (3)

A time-series ([sigma] [pi]) is said to Granger-cause another time-series (ur) if the prediction error of current ur declines by using past values of [sigma][pi] in addition to past values of ur. We thus test the null hypothesis that all of the coefficients of the lagged values of [sigma][pi] are jointly insignificant. Rejection of the null hypothesis implies that movements in past values of inflation variability Granger-cause the unemployment rate.

The last column of Table 1 reports the F-statistics that test for the joint significance of the coefficients on the lagged inflation variability terms in the estimation of the unemployment rate equation for each of the country-specific vector autoregressions in the study. (7) The F-statistics are significant for Canada, France, Italy, and the United States indicating that past values of inflation variability significantly impact unemployment. The F-statistics are insignificant for Germany, Japan, and the United Kingdom. (8)

The above findings suggest that inflation volatility is a precursor to changes in the unemployment rate for some of the G7 countries, namely, Canada, France, Italy, and the United States. In order to study this issue further, we examine impulse response functions for each of these cases in which a significant statistical relationship was detected. The dynamic characteristics of the empirical model can be described by impulse response functions which trace the response of the dependent variable (ur) to an innovation in the explanatory variable ([sigma][pi]).

Let [X.sub.t] be a vector of stationary variables, in our case, ur and [sigma][pi], and let [U.sub.t] be a vector of structural shocks. We can represent [X.sub.t] as [X.sub.t] = A (L) [U.sub.t], where Var([U.sub.t]) = I. The responses are generated by accumulating the [A.sub.i] coefficients. For our purposes, we focus on the effect of a one standard deviation shock to inflation variability on current and future values of the unemployment rate. Panels A-D of Figure 1 present the impulse response functions of the unemployment rate to one standard deviation-innovations to [rho][pi] generated from the VARs for Canada, France, Italy, and the United States. The impulse response functions show the cumulative impulse responses to these disturbances for up to 20 quarters and were calculated using a Cholesky decomposition so at the covariance matrix of the resulting innovations is diagonal.

Generally speaking, in each case except Italy, a one-time positive shock to [sigma][pi] has a substantial positive effect on the unemployment rate. For the US, the effect lasts for about 7-8 quarters before dying Out while for France the effect lasts even longer. The effect of the shock for Canada is more cyclical at the beginning but then is overwhelmingly positive out until the 20th quarter. The effect for Italy is also cyclical but dies out rather quickly. The positive effect on the unemployment rate of shocks to inflation variability for Canada, France and the United States suggests that, at least in these countries, policies that minimize the variability of inflation may prove very beneficial.

Concluding Remarks

This paper has focused on the relationship between the uncertainty associated with inflation volatility and the unemployment rate in the G7 countries. We provide additional empirical evidence using cointegration techniques, VAR estimation and Granger-causality tests, as well as impulse response functions to analyze the impact of inflation uncertainty on unemployment. The results indicate that, for the sample period studied, inflation variability had a significant effect in the short run upon the unemployment rate in Canada, France, Italy, and the US. This is consistent with the results of Reagan and Stulz (1993) who showed that price variability leads to decreased real output via higher contracting costs. Impulse response functions generally indicated that for the countries in which inflation variability was found to Granger-cause the unemployment rate, positive shocks to inflation variability raised the unemployment rate for periods of interest in a business cycle context. No significant statistical relatio nship was found for Germany, Japan, or the UK. Consistent with economic theory, we find no evidence of a long-run trade-off between inflation variability and unemployment.

(*.) Department of Accounting, Finance and Economics, College of Business Administration, Winthrop University, Rock Hill, SC 29733

(**.) Department of Economics, Texas Tech University, Lubbock, TX 79409

Notes

(1.) Payne (1995) provides evidence on the usefulness of the expectations-augmented Phillips curve relationship at the state level.

(2.) It has been found that monetary surprises were more important for determining output than actual money growth in the US (Barro, 1977).

(3.) J. Alfred Broaddus (1995, p. 8).

(4.) Our research is distinct from Weber's because we focus on inflation variability in order to capture the effect of uncertainty.

(5.) This technique is borrowed from the money demand and velocity literature where it has been used to proxy for the uncertainty of money growth (McMillin, 1991; Hall and Noble, 1987, and others). A similar measure of inflation variability can he found in Thornton (1988), who studied the impact of inflation on industrial production. Plosser and Rouwenhorst (1994) use the sample variance of price growth when studying the term structure of interest rates.

(6.) It is now common practice to examine the time-series properties of individual variables by conducting unit root tests and, if applicable, tests for cointegration. For a practical discussion of cointegration and unit roots, see Dickey et al (1991). Failure to properly account for these time series properties may lead to the problem of spurious regression.

(7.) CUSUM tests indicated that the models were free of parameter instability No ARCH effects were found except for the case of Germany, where evidence of first-order ARCH effects was present. Full regression results are available from the authors upon request.

(8.) The results for Germany may be suspect given the presence of ARCH effects. In addition, the data indicate a persistent rise in the rate of unemployment for Germany consistent with hysteresis. It is also interesting to note that the shape of the impulse response function for Germany was consistent with the hypothesis of the paper.

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TABLE 1

Empirical Results

Country Variable ADF for Levels ADF for 1st-Differences

Canada ur -2.72 (***) --
 [sigma][pi] -3.60 (**) --
France ur -1.33 -2.62 (***)
 [sigma][pi] -1.94 -4.36 (*)
Germany ur -3.42 (*) --
 [sigma][pi] -2.75 (***) --
Italy ur -2.47 -6.35 (*)
 [sigma][pi] -2.07 -7.39 (*)
Japan ur -0.57 -3.17 (**)
 [sigma][pi] -2.46 -7.01 (*)
UK ur -2.31 -2.77 (***)
 [sigma][pi] -2.42 -3.50 (*)
US ur -2.00 -2.97 (**)
 [sigma][pi] -1.59 -5.04 (*)

Country E-G Statistic VAR: Granger F

Canada NA 3.01 (**)
 (3)
France -1.38 4.61 (**)
 (1)
Germany NA 0.77
 (2)
Italy -2.41 4.10 (**)
 (1)
Japan -2.46 1.68
 (2)
UK -1.96 0.01
 (1)
US -2.04 4.95 (**)
 (1)

Notes: (*), (**), (***)denote significance at 1%, 5%, and 10% levels.
E-G Statistic refers to the Engle-Granger cointegration test. Critical
values for ADF and E-G are found in MacKinnon (1991). VAR Granger F is
the F-statistic that tests the hypothesis that all the coefficients on
[sigma][pi] are zero. The number of lags in the VAR was chosen based on
Akaike's Information Criterion and is given in parentheses.

Appendix 1: Unit Root Test

The augmented Dickey-Fuller (ADF) test is used in this study to check for the presence of unit roots, and is conducted from the ordinary least squares estimation of equation (A1).

[DELTA][x.sub.t] = [[rho].sub.0] + ([[rho].sub.t] - l)[x.sub.t-1] + [[rho].sub.2]t + [summation over (m/i=1)][[phi].sub.i][DELTA][x.sub.t-1] + [[epsilon].sub.t] (A1)

where x is the individual time series under investigation; [DELTA] is the first-difference operator; t is a linear time trend; [[epsilon].sub.t] is a covariance stationary random error and m is determined by Akaike's information criterion to ensure serially uncorrelated residuals. The null hypothesis is that [x.sub.t] is a nonstationary time series and is rejected if ([[rho].sub.1] - 1) < 0 and statistically significant. The finite sample critical values for the ADF test developed by MacKinnon (1991) are used to determine statistical significance.

Appendix 2: Cointegration Test

Given the bivariate nature of this study, the Engle-Granger (1987) procedure is used to test for the presence of cointegration between the unemployment rate and the variability of inflation. If both time series are integrated of the same order, then one can proceed with the estimation of the following cointegrating regression for each country:

u[r.sub.t] = [a.sub.1] + [b.sub.1][sigma][[pi].sub.t] + [e.sub.t] (A2)

where ur is the unemployment rate, [sigma][pi] represents inflation variability (as defined above), and e is the error term. Individual country subscripts are suppressed. The residuals from the above cointegrating regression are then tested for stationarity to determine whether or not the two time series are cointegrated using the following ADF unit root test on the respective residuals:

[DELTA][e.sub.t] = [[alpha].sub.0] + [[delta].sub.t][e.sub.t-i] + [summation over (n/i=1)][[alpha].sub.i][delta][e.sub.t-i] + [v.sub.t] (A3)

where [e.sub.t], is the residual from equation (A2), [v.sub.t] represents the respective stationary random error and n is determined by Akaike's information criterion. The null hypothesis of nonstationarity (no cointegration) is rejected when [[delta].sub.1] is significantly negative. If the residuals from (A2) are determined to be stationary using the ADF unit root test then the two variables are cointegrated.