Expectations and monetary neutrality: an empirical reexamination.

• Author: Poitras, Marc

1. Introduction

   Modern monetary business cycle models feature rational expectations and natural rate assumptions which imply that unanticipated changes in nominal aggregates affect real output, but anticipated changes do not. Initial tests conducted by Barro [3] and by Barro and Rush [4] supported the neutrality of anticipated money growth. In a particularly influential study, Mishkin [21; 22] rejected the neutrality of anticipated policy. Mishkin's paper [21] has become one of the most frequently cited studies in empirical macroeconomics. The influence of the study probably derives in large part from the unequivocal nature of the results. In particular, Mishkin showed that i) the hypothesis that anticipated policy has no effect on output is strongly rejected; ii) anticipated nominal changes have a greater estimated effect on output than do unanticipated nominal changes; iii) lags as long as 17 quarters have significant coefficients, implying that Barro's eight-lag model was underspecified; iv) in some specifications, the estimated sign of the effect of nominal innovations is opposite to the prediction of monetary business cycle theory. Frydman and Rappoport [9] used Mishkin's empirical model to provide further evidence against the neutrality hypothesis by showing that the data provide no evidence for distinguishing between the output effects of anticipated policy and those of unanticipated policy.

   Although several subsequent studies have supported the neutrality hypothesis [7; 12], Mishkin's careful study and a small number of additional studies suggest that the neutrality hypothesis is not robust. The empirical rejection of the neutrality hypothesis contradicts a wide range of modern monetary models, including those based on imperfect information [14; 18; 19], and those based on imperfect competition [8; 20].(1) As a consequence, the focus of macroeconomists has in recent years shifted to non-monetary models in which money responds passively to changes in aggregate output [16; 17].

   This paper explores the robustness of Mishkin's results using an updated data set. The model yields results that are more consistent with the neutrality hypothesis than those of Mishkin. In particular, the results contradict each of Mishkin's four salient findings described above. The study also presents evidence which suggests rejection of the Frydman-Rappoport hypothesis regarding the irrelevance of the distinction between the output effects of anticipated and unanticipated policy.

   Section II describes the empirical model. In particular, I describe the approach to specifying forecasting equations for M1 and inflation. The forecasting equations allow decomposition of nominal changes into anticipated and unanticipated components. The extended data set yields specifications that differ from those obtained by Mishkin. Section III presents and interprets the results and section IV concludes.

2. Econometric Issues

   The Model

   I test the neutrality hypothesis in the context of the model employed by Mishkin and Frydman and Rappoport. The model consists of two equations:

   [Mathematical Expression Omitted], (1a)

   and

   [X.sub.t] = [Z.sub.t][Gamma] + [[Mu].sub.t]. (1b)

   Equation (1a) is the output equation, where [y.sub.t] is the log of real GNP and [Mathematical Expression Omitted] is the natural rate. Equation (1b) is the forecasting equation for the nominal aggregate. The variable [X.sub.t] represents the rate of growth of the nominal aggregate, and [Mathematical Expression Omitted] is the expectation of [X.sub.t] at time t - 1. The term [Z.sub.t] is a matrix of variables used to forecast [X.sub.t], and [Gamma] is a vector of parameters. The variables in [Z.sub.t] are known in period t - 1, and [v.sub.t] is assumed uncorrelated with any information available in period t - 1. These assumptions imply that the fitted values from equation (1b) represent optimal forecasts of [X.sub.t], hence

   [Mathematical Expression Omitted]. (2)

   Following Mishkin, I represent [Mathematical Expression Omitted] by a linear time trend, and allow [u.sub.t] to follow a second-order autoregressive process.(2) Equation (1a) can be written more specifically as

   [y.sub.t] = [Alpha]t + [summation over i] [[Beta].sub.i]([x.sub.t-i] - [Z.sub.t-i][Gamma]) + [summation over i] [[Delta].sub.i][Z.sub.t-i][Gamma] + [[Rho].sub.1][u.sub.t-1] + [[Rho].sub.2][u.sub.t-2] + [[Epsilon].sub.t], (1a[prime])

   where t is time and [[Epsilon].sub.t] is normally distributed and uncorrelated. The neutrality hypothesis states that expected changes in the nominal aggregate leave real output unaffected, which implies [[Delta].sub.i] = 0 for all i.

   I explore Mishkin's claim that a specification which includes long lags rejects the neutrality hypothesis. Hence I extend the lag distributions of [Mathematical Expression Omitted] and [Mathematical Expression Omitted] to twenty quarters. Mishkin found that lags of nominal shocks as long as seventeen quarters significantly affect output. Barro's model, which includes only eight quarterly lags, risks leaving out significant lags which can cause inconsistent estimates and incorrect test statistics.(3)

   I estimate two different specifications of the model: one with M1 growth and the other with inflation as the nominal aggregate, [X.sub.t]. (Mishkin used M1 in one study [21], and inflation in another study [22]). Like Mishkin, I restrict the coefficients [[Beta].sub.i] and [[Delta].sub.i] to follow a fourth-degree polynomial distributed lag (PDL) with the endpoint constrained to zero. The fourth-degree PDL represents a relatively flexible lag distribution which the data rarely reject in practice. The neutrality hypothesis predicts zero values for the four PDL coefficients on anticipated policy.

   Consistent estimation of the output equation requires exogeneity of M1 and inflation with respect to output. Negative correlation between unanticipated inflation and the equation (1) error term follows directly from the Equation of Exchange: cetera paribus, an increase in the growth rate of...