Monte Carlo two-stage indirect inference (2SIF) for autoregressive panels

Abstract

Persistence and mean-nonstationarity often undermine reliability of asymptotically justified inference in dynamic panels. We combine the Monte Carlo test (MCT) and the indirect inference estimation (IIE) principles to construct confidence regions for autoregressive panel parameters with valid coverage whether mean-stationarity is imposed or relaxed and whether autoregressive roots are at or close to the unit boundary or far from unity. Procedures are based on the standard least squares dummy variables (LSDV) estimator and an augmented counterpart which we introduce to restore finite sample exactness in mean-nonstationary settings. We also put forth a ‘Durbin–Wu–Hausman-type’ test for mean-stationarity given a tested autoregressive parameter, based on the distance between the LSDV and its augmented counterpart. Location-scale invariance is shown analytically, and the MCT methods involve multiple stages that preserve exchangeability. The above are formally shown to control size exactly for finite N and T, and provide a new perspective to a literature that is primarily asymptotic. The advantages of the proposed approaches are also illustrated via comparative simulation studies. The identification problems arising from relaxing mean-stationarity are assessed and addressed; we also consider heteroskedastic directions. Results show concrete promise even with very small sample sizes and more broadly, underscore the usefulness of combining MCT and IIE principles.