# Asymptotics and Inference for Possibly Non-Stationary Panel in thePresence of High-Dimensional Nuisance Parameters

### Abstract

This paper studies asymptotic theory for a possibly nonstationary panel AR(1) model when cross-sectionaldimension (n) and time dimension (T) are large. We considers the nonstationary case ($\theta_0$= 1) in the pres-ence of both cross-sectional and time fixed effects, which is not investigated in existing literature of dynamicpanel (e.g., Hahn and Kuersteiner (2002) and Hahn and Moon (2006). We derive the limiting distributionof the bias-corrected (quasi-)maximum likelihood estimator with Gaussian or non-Gaussian error terms.Because of the discontinuity between stationary and non-stationary limits, practitioners can face difficultiesin choosing between stationary and non-stationary bias corrected confidence intervals. We extend Andrews(1993)’ method to a panel data framework and construct a valid confidence interval without knowing the (non)-stationarity.

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##### Dingxian Cao
###### Ph.D. Candidate in Econometrics

My research interests include High-dimensional Non-asymptotics and Uniform analysis of possible persistent Panel AR(1) model.