Advances in Econometrics for Treatment Effect Bounds, Time-Varying-Parameter Nonstationary/Stationary Autoregressive Models, and Identification-Robust Inference

Yale University, New Haven CT

Investigators

Abstract

This research project includes five different topics. The first develops new treatment effect bounds for the average treatment effect (ATE) in models with two continuous or discrete potential outcome variables, a binary treatment variable, and a binary instrumental variable (IV) that is independent of the potential outcomes. The ATE is not identified due to treatment effect heterogeneity. The research develops bounds on ATE that exploit the independence condition and an IV restriction by first considering the case where the treatment effect distribution is binary. The bounds hold for arbitrary treatment effect distributions. The bounds depend explicitly on the probability limit of the IV estimator and are of a simple form, which is conducive to inference. The assumptions imposed are neither stronger nor weaker than those currently considered in the literature. The results are applicable to treatment effect analysis in economics and to the analysis of medical randomized trials with incomplete compliance. The second portion develops deterministically time-varying autoregressive (AR) models that may exhibit (local) nonstationarity or stationarity and smooth transitions between the two. The PI considers estimation of the parameters by nonparametric smoothing in the time domain. Standard methods of reducing bias due to the time-varying parameters fail in the (locally) nonstationary case. Hence, new bias reduction methods will need to be introduced. Another important issue to be addressed is the endogenous character of the initial conditions for the local smoothing estimator, which are determined by the time-varying path of the sum of the AR coefficients. The PI analyzes methods for estimation, testing, CS construction, and forecasting. He also develops tests for the presence of time-varying parameters. This research will provide a useful new time series model that allows for time-varying nonstationarity/stationarity. Third, he develops inference methods that are robust to weak identification and identification failure in moment condition models. Several existing methods employ conditional likelihood ratio-type (CLR) tests and CS's that generalize the CLR test of Moreira (2003) for the linear IV regression model. Existing procedures (i) do not necessarily have correct asymptotic size when the dimension of the parameter is two or greater and (ii) do not reduce to Moreira?s CLR test in the linear IV model, which is known to have optimal power properties. The PI introduces new CLR-type procedures that do not have these deficiencies. The last two areas of research are on inference in partially-identified models that are defined by inequality restrictions on nonlinear functions of infinitely-many conditional moments and Lagrange multiplier tests under weak identification or lack of identification. This research develops new methods for the statistical analysis of social science data. The project will benefit society because it will improve the quality of data analysis used for a variety of important questions. These methods will be useful for economic policy analysis but will also be used by medical and engineering researchers who analyze data with similar statistical features.