Dynamic panel data models can suffer greatly from incidental parameter bias due to correlation between past realizations of the data and the unobserved heterogeneity, and this bias is a function of included regressors. This paper uses simulation-based methods that require explicit models and sets of assumptions to obtain consistent point estimates and exact confidence sets. A parametric discontinuous starting value is assumed for simulated series that jointly allows for stationary and unit root processes, where only the stationary case was considered in Gouriéroux, Phillips, and Yu (2010). This discontinuous assumption leads to least squared dummy variable (LSDV) estimator that are nuisance parameter free and location-scale invariant. These properties are conferred to the indirect inference objective function (IIOF) used to obtain bias-corrected estimates.Discontinuities are problematic for traditional asymptotic methods of constructing confidence sets. To account for this the indirect confidence set inference method is introduced, which uses a second round of Monte Carlo simulations [Dufour (2006)] to calibrate the distribution of the IIOF. The confidence set is constructed with test inversion, so the parameters are set to known values, the model is tested at that point, and all points that fail to reject the null hypothesis are in the confidence set. The confidence set is exact and level correct, since the IIOF is pivotal and both simulation rounds are exchangeable under the null.Adding regressors into panel data models can distort estimates, as this paper demonstrates with respect to the X-differencing method of Han, Phillips, and Sul (2014) with regressors. By introducing a model augmentation approach, the influence of regressors are corrected. The augmentation uses a projection of the regressors for iii all time periods onto the model, giving the augmented-LSDV and the augmented-IIOF that are provably location-scale invariant and nuisance parameter free.The framework presented is robust to non-Gaussian errors, which is demonstrated with bank cost data where the dynamic technical efficiency framework allows for skew-Normal errors. Simulation studies support all theoretical results, with confidence sets that are level correct with good coverage properties, even for asymmetric confidence regions.iv ACKNOWLEDGMENTS A special thank you to my supervisor Lynda Khalaf, that without your patience, support, and knowledge I would likely not have been able to advance as quickly and cleanly as I have. I would also like to thank Russell Davidson (McGill) for pointing out that the initial observation could be random. I would like to thank Jeffery Wooldridge, for our brief discussion in Budapest, and for indicating that he had given a block-diagonal Mundlak device some consideration in response to query at a conference a few years prior.
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