Exact and asymptotic identification-robust inference for dynamic structural equations with an application to New Keynesian Phillips Curves

Many models in econometrics involve endogeneity and lagged dependent variables. We start by observing that usual identification-robust (IR) tests are unreliable when model variables are nonstationary or nearly nonstationary. We propose IR methods which are also robust to nonstationarity: one Anderson-Rubin type procedure and two split-sample procedures. Our procedures are also robust to missing instruments. For distributional theory, three different sets of assumptions are considered. First, on assuming Gaussian structural errors, we show that two of the proposed statistics follow the standard F distribution. Second, for more general cases, we assume that the distribution of errors is completely specified up to an unknown scale factor, allowing the Monte Carlo test method to be applied. This assumption enables one to deal with non-Gaussian error distributions. For example, even when errors follow heavy-tailed distribution, such as the Cauchy distribution or more generally the family of stable distributions—which may not have moments and thus make inference difficult—our procedures provide simple and exact solutions. Third, we establish the asymptotic validity of our procedures under quite general distributional assumptions. We present simulation results showing that our procedures control their level correctly and have good power properties. The methods are applied to an empirical example, the New Keynesian Phillips curve, in which both weak identification and nonstationarity present challenges. The results of this empirical study suggest forward-looking behavior of U.S. inflation.