Identification of New Keynesian Phillips Curves from a Global Perspective

Article excerpt

NEW KEYNESIAN PHILLIPS CURVES (NKPC) have been widely used in the macroeconomic literature. Yet their empirical implementation raises a number of issues that continue to be of some concern. In this paper, we shall focus on two of these issues--the weak instrument problem and the characterization of the steady states--and propose some solutions from a global perspective.

The first issue relates to the quality of the instruments used to estimate the NKPC model. The problem arises because in a closed economy setting it turns out that there are not many variables that can be used to produce inflation forecasts that improve significantly over a first-order autoregressive model of inflation. Under the NKPC lagged observations are admissible as instruments, in the sense that they are not correlated with the error terms. However, in order to be valid instruments the variables also need to be sufficiently correlated with the endogenous explanatory variables so that the necessary rank condition is satisfied. The solution of the rational expectations (RE) model indicates that this rank condition will not be satisfied unless the lag order of the equation determining the driving variable is greater than that of the NKPC and the extra lags significantly improve the prediction of the driving variable (see, e.g., Mavroeidis 2005, Nason and Smith 2008). In this paper, by taking a global perspective, we suggest some possible routes to resolving the weak instrument problem at least for NKPC models of small open economies.

In addition, the NKPC is typically derived from the first-order optimization conditions of a representative firm, subject to staggered pricing behavior, in the context of a dynamic stochastic general equilibrium (DSGE) framework. Because these first-order conditions are complicated nonlinear stochastic equations, usually they are log-linearized around a steady state. Such an approximation procedure is appropriate if a unique steady state exists, the log-linearization is carried out around the correct steady state, and the approximation errors are relatively small. In cases where the steady states exist and are not time varying the analysis of the DSGE equations as deviations from the steady states does not pose any new difficulties. Inclusion of intercepts in the log-linearized version of the first-order conditions will suffice. Similarly, when the steady state values follow deterministic trends, residuals from regressions on such trend components can be used in the log-linearized DSGE model. The problem arises if the first-order conditions contain variables with stochastic trends that could be cointegrated. In such cases any misspecification of the steady states can seriously bias the estimates of the DSGE equations. In practice, the stochastic trends, for example in the case of output, are often approximated by statistical methods such as the Hodrick-Prescott (HP) filter or a variety of the band pass filters as discussed in Christiano and Fitzgerald (2003). These procedures are purely statistical, in the sense that they are not derived from the assumed DSGE model and need not be consistent with it. In this paper, we present an alternative approach where the derivation of steady states is made consistent with the underlying DSGE model. We propose to measure the steady states by the long-horizon expectations, where expectations are taken consistently with respective to the underlying DSGE model. This is in line with the idea of the model consistent expectations that underpin the NKPC and simply extends it to the long run.

In the empirical section of the paper the steady states are estimated using a global model for 33 countries estimated over the period 1979Q1-2006Q4. Using these estimates NKPC equations are estimated for eight developed economies where it is shown that using global instruments and economic measures of the steady states provide better determined estimates of the NKPC not only for the United States but also for a number of European economies, notably United Kingdom, France, and Spain. …