A Theory-Based, State-Dependent Phillips Curve and its Estimation

Abstract

To explain the existing empirical irregularity about the slope of a Phillips curve, this article provides a model of imperfect competition to short that the slope of a Phillips curve is shock-dependent. We empirically apply a state-space, Markov-switching model to examine the impact of inflation surprise on the unemployment gap, resulting in the state-dependent Phillips curve fitting quite well. Our empirical evidence indicates that an unexpected monetary, expansion does produce effects in reducing unemployment rates and that supply shocks should not be ignored in estimating the Phillips curve because they dominate demand shocks in several nonoil shock periods. (JEL C51, E24, E52) I. INTRODUCTION It is well known that a downward-sloping short-run Phillips curve implies a trade-off between the inflation rate and unemployment rate. However, empirical findings point out that the slope of the Phillips curve depends on the selected sample periods. (1) Does any theoretical model explain the changes in the slope of a short-run Phillips curve as displayed in the data? Can we find empirical support for our model that implies a slope-changeable Phillips curve? To answer these questions, this article provides a theoretical model implying that the slope of the Phillips curve is shock-dependent. We then apply a state-space, Markov-switching model to investigate the empirical support of the theoretical model. Although a stable, negative, short-run Phillips curve is crucial for producing inflation forecasts in policy-making institutions, there is no general consensus about the negative slope of the Phillips curve in empirical literature. (2) One of the explanations to the previous empirical irregularity, as suggested by King and Watson (1994) is that the relationship between unemployment and inflation is shock-dependent, which means that the slope of a Phillips curve relies on the dominance of the demand or supply shocks. Therefore the conventional single-equation regression based on the state independent framework is not appropriate. Apart from neglecting the state-dependent characteristic of the Phillips curve, there are several other drawbacks for conventional empirical studies when investigating the Phillips curve. First, many articles assume that forecast errors of inflation are homoscedastic, which is challenged in the literature. The homoscedastic assumption is debatable because several studies, such as Engle (1983), Jansen (1989), Evans (1991), and Brunner and Hess (1993), point out significant heteroscedasticity in the U.S. inflation rate. ARCH- or GARCH-type models provide estimates of how the conditional variance of inflation varies over time within a given structure and therefore they ignore the possibility of structural changes caused by changing regimes. A Markov-switching heteroscedasticity model is an alternative that allows regime changes in the variance structure. Instead of applying ARCH-type models to estimate the time-varying conditional variance of inflation within a given structure, this article takes into account the influence of regime changes on inflation's variance. We apply the state-dependent conditional heteroscedasticity approach provided by Brunner and Hess (1993) and Evans and Wachtel (1993) to estimate the forecasting errors of inflation. The second drawback is a constant natural rate assumption. The unemployment gap is the difference between the unemployment rate and the natural rate. Conventional literature assumes a constant natural rate, which is challenged theoretically and empirically as stated by Gordon (1997). The existence of unionization, unemployment insurance programs, and labor force demographics leads to a highly persistent unemployment rate. We therefore assume that the unobservable natural rate is time-varying and behaves in accordance with the hysteresis of unemployment rates. (3) Recent empirical works of a regime-switching approach on the Phillips curve have focused on whether the relationship between inflation and unemployment rates is nonlinear, as in Ferri et al. …