Academic journal article Economic Quarterly - Federal Reserve Bank of Richmond

DSGE Model-Based Estimation of the New Keynesian Phillips Curve

Academic journal article Economic Quarterly - Federal Reserve Bank of Richmond

DSGE Model-Based Estimation of the New Keynesian Phillips Curve

Article excerpt

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An important building block in modern dynamic stochastic general equilibrium (DSGE) models is the price-setting equation for firms. In models in which the adjustment of nominal prices is costly, this equation links inflation to current and future expected real marginal costs and is typically referred to as the New Keynesian Phillips curve (NKPC). Its most popular incarnation can be derived from the assumption that firms face quadratic nominal price adjustment costs (Rotemberg 1982) or that firms are unable to re-optimize their prices with a certain probability in each period (Calvo 1983). The Calvo model has a particular appeal because it generates predictions about the frequency of price changes, which can be measured with microeconomic data (Bils and Klenow 2004, Klenow and Kryvtsov 2008). The slope of the NKPC is important for the propagation of shocks and determines the output-inflation tradeoff faced by policymakers. The Phillips curve relationship can also be used to forecast inflation.

This article reviews estimates ofNKPCparameters that have been obtained by fitting fully specified DSGE models to U.S. data. By now, numerous empirical papers estimate DSGE models with essentially the same NKPC specification. In this literature, the Phillips curve implies that inflation can be expressed as the discounted sum of expected future marginal costs, where marginal costs equal the labor share. We document that the identification of the Phillips curve coefficients is tenuous and no consensus about its slope and the importance of lagged inflation has emerged from the empirical studies.

We begin by examining how the NKPC parameters are identified in a DSGE model-based estimation. This is a difficult question. Many estimates are based on a likelihood function, which is the model-implied probability distribution of a set of observables indexed by a parameter vector. The likelihood function peaks at parameter values for which the model-implied autovariance function of a vector of macroeconomic time series matches the sample autocovariance function. Unfortunately, this description is not particularly illuminating. More intuitively, the NKPC parameters are estimated by a regression of inflation on the sum of discounted future expected marginal costs. The likelihood function corrects the bias that arises from the endogeneity of the marginal cost regressor. We show that if one simply uses ordinary leastsquares (OLS) to regress inflation on measures of expected marginal costs, the slope coefficient is very close to zero. This finding is quite robust to the choice of detrending method and marginal cost measure. Hence, much of the variation in the estimates reported in the literature is due to the multitude of endogeneity corrections that arise by fitting different DSGE models that embody essentially the same Phillips curve specification.

The review of empirical studies distinguishes between papers in which marginal costs are included in the observations and, hence, are directly used in the estimation and studies that treat marginal costs as a latent variable. In the latter case, NKPC estimates are more sensitive to the specification of the households' behavior, the conduct of monetary policy, and the law of motion of the exogenous disturbances. Estimates of the slope of the Phillips curve lie between 0 and 4. If the list of observables spans the labor share, then the slope estimates fall into a much narrower range of 0.005 to 0.135. No consensus has emerged with respect to the importance of lagged inflation in the Phillips curve. We compare estimates of the relative movement of inflation and output in response to a monetary policy shock, which captures an important tradeoff for monetary policymakers. We find that the estimates in the studies that are surveyed in this article range from 0.07 to 1.4. Avalue of 0.07 (1.4) implies that a 1 percent increase in output due to a monetary policy shock is accompanied by a quarter-to-quarter inflation rate of 7 (140) basis points. …

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