Dynamic panel data models can suffer greatly from the 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 a simulation-based methods that require explicit model and set 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) estimates 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 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 and Phillips (2014) with regressors. By introducing a model augmentation approach, the influence of regressors are corrected. The augmentation uses a projection of the regressors for all time periods onto the model, giving the augmented-LSDV and the augmented-IIOF that are provably location-scale invariant properties 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.