Spatial Dynamic Panel Data Models with Small T

This dissertation consist of three papers which contribute to the estimation and inference theory of the spatial dynamic panel data model with small T. In the first chapter, we develop M-estimation and inference methods for spatial dynamic panel data (SDPD) models with correlated random effects, based on short panels. The unobserved individual-specific effects are assumed to be correlated linearly with the observed time- varying regressors, giving the so-called correlated random effects model, which allows the estimation of the effects of time-invariant regressors. The unbiased estimating functions are obtained by adjusting the conditional quasi-scores given the initial observations, leading to M-estimators that are consistent, asymptotically normal, and free from the initial conditions except the process starting time. The standard errors are obtained by representing the estimating functions as sums of martingale differences with respect to the individual-specific errors given the idiosyncratic errors, which again depend only on the process starting time. Monte Carlo results are presented to show the good finite sample properties of the developed methods. In the second chapter We consider the estimation and inference of fixed effects SDPD models under small T and unknown heteroskedasticity by extending the M-estimation strategy for homoskedastic FE-SPDP model of Yang (2018). Unbiased estimating equations are obtained by adjusting the conditional quasi-score functions given the initial observations, leading to robust M-estimators that are free from the initial conditions and robust against unknown cross-sectional heteroskedasticity. Consistency and asymptotic normality of the proposed M-estimator are established. The standard errors are obtained by representing the estimating equations as sums of martingale differences. Monte Carlo results show that the proposed M-estimators have good finite sample performance. The practical importance and relevance of allowing for heteroskedasticity in the model is illustrated using a data on sovereign risk spillover. In the third chapter we develop an adjusted quasi-score estimator for SDPD model with interactive fixed effect under small T. Consistency and asymptotic normality of the proposed estimator are established. Monte Carlo results show that the proposed estimator have good finite sample performance.