Monetary policy and inflation uncertainty in the United States and Germany.

• Author: Sauer, Christine

1. Introduction

   Friedman's [16] proposition that increased inflation uncertainty may adversely affect real economic variables has received much attention over the last decade.(1) The theoretical arguments for such real effects are compelling; however, the empirical evidence on their presence and magnitude in different countries is mixed. Most results for the postwar US. economy strongly support the proposition [28; 25; 26; 19; 24; 7] whereas it is generally rejected for the German economy [23; 17; 8].(2) While a direct comparison of the U.S. and German results is difficult due to a lack of uniform sample periods, data definitions, estimation techniques, and/or measures of inflation uncertainty, the evidence to date nevertheless suggests that the role of inflation uncertainty differs sharply between the two countries. The question then arises what factor(s) can explain the difference.

   One popular explanation is that the monetary authorities in the United States and Germany respond quite differently to accelerating inflation,(3) so that the behavior of uncertainty differs across countries.(4) The U.S. Federal Reserve is often criticized for switching frequently between the primary policy goals of price stability and full employment, possibly due to political pressures [21; 30]. Since inflation is primarily a monetary phenomenon in the long run, it is likely that such stop-and-go policies increase the uncertainty about future (steady-state) inflation, which in turn can adversely affect real output growth by reducing overall economic efficiency. The German Bundesbank, on the other hand, is reputed for its staunch and credible commitment to price stability, which often takes precedence over other policy goals. A more consistent and predictable policy may reduce the uncertainty about future inflation sufficiently to avert the negative real effects described by Friedman [16].

   The purpose of this study is to investigate the empirical foundations of these arguments. First, however, it must be confirmed that the real effects of inflation uncertainty differ across countries when identical sample periods, data definitions, estimation techniques, and uncertainty proxies are used. The second step is to examine whether and how the U.S. and German uncertainty measures differ with respect to their sources and properties. Third, we test the hypothesis of different central bank responses to inflation by estimating monetary reaction functions, which are specified as time-varying parameter models to allow for shifting policy objectives and/or changing economic conditions over time. Finally, the analysis explores the link between monetary policy, inflation, and inflation uncertainty to explain the difference in real effects.

   Results for the 1966-90 sample period indicate (i) that inflation uncertainty reduces real output growth in the United States but not in Germany, (ii) that uncertainty about (steady-state) inflation is lower, less variable, and less persistent in Germany, (iii) that German inflation uncertainty declines along with actual inflation whereas (long-term) U S. uncertainty remains at high levels, and (iv) that the Federal Reserve does not respond as strongly and systematically to inflationary pressures as the Bundesbank.

2. Inflation Uncertainty and Real Activity

   Previous studies typically test the Friedman hypothesis along with the Macro Rational Expectations (MRE) hypothesis that only unanticipated inflation or policy has real output effects [28; 25; 26; 19; 24; 7]. Such a "nested" framework is implied by the underlying theoretical model, namely a Lucas supply curve modified to incorporate the adverse effects of inflation uncertainty on the natural level of output [17]. The reduced form is

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   where GY is the growth rate of real GNP, CVI is a measure of inflation uncertainty, SHOCKI is unanticipated inflation, ANTI is anticipated inflation,(5) computed as the difference between actual and unanticipated values, and [[mu].sub.t], is a white noise error term. According to the Friedman hypothesis, [[Alpha].sub.1i] 0 and [[Alpha].sub.3.sub.i] = 0 in the short run. Contemporaneous as well as lagged values of the regressors are allowed since the underlying model does not indicate what the lag length should be [27].

   The unobservable regressors are obtained from a time-varying parameter (TVP) model of inflation, which allows for structural changes in the inflation process over time as agents adjust to changes in the economic environment due, for example, to exogenous price shocks and/or policy regime breaks. Stability test results confirm the validity of the TVP specification for the U.S. and German inflation equations (see tables A-I and A-II in the appendix)(6) The TVP model consists of the forecasting or measurement equation (2) and the transition equation (3) describing the evolution of the time-varying coefficients:

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   and

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   where [Z.sub.t-1] is the vector of variables (including a constant term), known at time t - 1, used to forecast next period's inflation rate ([INF.sub.t]), [[Beta].sub.t] is a vector of time-varying coefficients, and [e.sub.t] is the orthogonal measurement error, assumed to be normally distributed with constant variance [[Sigma].sup.2]. In the transition equation, [Phi] is a diagonal matrix of autoregressive (AR) parameters, [Psi] is the identity matrix, and [[Theta].sub.t], is a vector of independently normally distributed error terms with covariance matrix Q. Thus, each time-varying coefficient [[Beta].sub.it] (i = 1, ...,k) depends only on its own past; for [Phi] = identity matrix, the coefficients follow a random walk.

   A two-step estimation procedure is adopted. In the first step, the TVP model of the inflation process (2)-(3) is estimated by Kalman filtering.(7) The information set [Z.sub.t-1] used to forecast the quarterly inflation rate is motivated by Froyen and Waud's [17] theoretical model; it includes a constant term, lagged nominal income/GNP growth (demand-pull), lagged M1 money growth, lagged relative oil price changes (cost-push), and lagged inflation.(8) Kalman filter estimates of the US. and German inflation models are presented in table A-111 in the appendix. The models are consistent with the rationality principle since the residuals are white noise. Furthermore, there is no evidence of any ARCH effects (see table A-X in the appendix).

   The Kalman filter estimates are used to generate the measures of unanticipated inflation and inflation uncertainty -- the time-varying innovations [[Eta].sub.t\-1] and the time-varying conditional variance [H.sub.t\t-1] respectively. Note that [H.sub.t\t-1] is a short-term measure that reflects the forecaster's uncertainty about next period's inflation rate, but not necessarily about inflation over longer time horizons.(9) We therefore compute the time-varying conditional variance of steady-state inflation as a proxy for uncertainty in the longer run.(10)

   In the second step, the generated regressors -- the conditional variance of inflation (CVI), the inflation innovations (SHOCKI), and the anticipated rate of inflation (ANTI) - are included in the output growth equation (1) to test the Friedman and MRE hypotheses. Several issues need to be addressed with respect to the estimation of this equation. First, what is the appropriate measure of inflation uncertainty? According to the signal extraction model of the Lucas supply curve, output varies from period to period as changes in the variance of next period's inflation make it more difficult for firms to distinguish aggregate from relative price fluctuations.(11) This suggests that changes in short-term inflation uncertainty have short-term real effects. On the other hand, Friedman [16] argues that higher uncertainty shortens the optimal length of non-indexed contracts, thus reducing overall economic efficiency. Such institutional changes and the implied long-term economic costs seem more likely in connection with long-term inflation uncertainty. To cover all possible channels through which uncertainty may affect the real economy, we consider both measures to estimate alternative specifications of the model.

   Second, the two-step estimation procedure is subject to the generated regressor bias because it treats the rationality of expectations as the maintained hypothesis. Specifically, the procedure may falsely reject the MRE hypothesis that only unanticipated inflation/policy matters due to a failure of the rationality assumption alone. To avoid this potential bias, we correct the standard errors and t-statistics for the generated regressor bias within the two-step framework.(12)

   Third, to control for multicollinearity between the generated regressors, the U. S. and German output growth equations are estimated by polynomial distributed lags (PDL). We employ Akaike's Information Criterion (AIC) and over- and underfitting tests to determine the polynomial degree (r) and the lag length (n). The specification search over r = 1, 2, 3 and n = 4, 8, 12 identifies a PDL (2,8) model for the United States and a PDL(1,8) model for Germany (see Table A-IV in the appendix). Note that the German output growth equation requires the presence of four own lags to assure white noise residuals.

   Fourth, the reduced-form equation may suffer from an omitted variable problem if output growth and inflation uncertainty are both affected by oil price shocks.[13] If the direct output effects are not controlled for, the effects of oil price shocks may be captured by inflation uncertainty, thus creating a bias in favor of the Friedman hypothesis. To check the robustness of our results, we add contemporaneous and lagged values of the growth rate of relative oil prices (GROIL) to all regressions.

   Tests of the Friedman and MRE hypotheses are performed by excluding the...