GMM and OLS Estimation and Inference for New Keynesian Phillips Curve

This paper considers estimation situations where identification, endogeneity and non-spherical regression error problems are present. Instead of always using GMM despite weak instruments to solve the endogeneity, it is possible to first check whether endogeneity is serious enough to cause inconsistency in the particular problem at hand. We show how to use Maximum Entropy bootstrap (meboot) for nonstationary time series data and check `convergence in probability' and `almost sure convergence' by evaluating the proportion of sample paths straying outside error bounds as the sample size increases. The new Keynesian Phillips curve (NKPC) ordinary least squares (OLS) estimation for US data finds little endogeneity-induced inconsistency and that GMM seems to worsen it. The potential `lack of identification' problem is solved by replacing the traditional pivot which divides an estimate by its standard error by the Godambe pivot, as explained in Vinod (2008) and Vinod (2010), leading to superior confidence intervals for deep parameters of the NKPC model.