QML estimation of dynamic panel data models with spatial errors

Abstract

We propose quasi maximum likelihood (QML) estimation of dynamic panel models with spatial errors when the cross-sectional dimension n is large and the time dimension T is fixed. We consider both the random effects and fixed effects models, and prove consistency and derive the limiting distributions of the QML estimators under different assumptions on the initial observations. We propose a residual-based bootstrap method for estimating the standard errors of the QML estimators.Monte Carlo simulation shows that both the QML estimators and the bootstrap standard errors perform well in finite samples under a correct assumption on initial observations, but may perform poorly when this assumption is not met.

Instrumental variable estimation of a spatial dynamic panel model with endogenous spatial weights whenTis small

“…For the initial value of the stochastic process, we adopt a similar framework as Su and Yang () where the starting position of data process can be either exogenous or endogenous. (a)Data collection starts from the first period; the process starts from the th period, i.e., periods before the start of data collection, and then evolves according to the model specified by and . (b)The data starting period .…”

“…() investigate various specifications with error components. For the fixed effects model, Elhorst (), Korniotis (), Su and Yang (), Yu et al. (, ) and Lee and Yu () study static or dynamic models under various spatial structures with the fixed effects specification.…”

Estimation of fixed effects panel regression models with separable and nonseparable space–time filters

“…The model (1) can be extended to include the spatial dynamics in the main regression (see Yu et al (2008Yu et al ( , 2012). When T is short, we can use GMM estimation similar to Kelejian and Prucha (1998), or use MLE with initial observation approximation as in Elhorst (2005) and Su and Yang (2007) where the information of X nt for t = 1, . .…”

“…However, when T is fixed, the information in the first period should not be easily discarded. In panel models where the spatial dependence is present in the disturbances rather than the dependent variables, treatment of the initial period observations has been found to be important (Su and Yang, 2007). 9 In obtaining (15) …”

“…These spatiotemporal interactions can be specified in dependent variables as in Su and Yang (2007), Yu et al (2008), Elhorst (2010) among others. They can also be specified in the error components such as in Elhorst (2004), Baltagi et al (2007), LeSage (2011, 2012) ✩ We would like to thank participants of 18th International Conference on Panel Data (Paris, 2012), International Conference on Policy Analysis Using Modern Econometric Methods (Beijing, 2012), 1st China Meeting of the Econometric Society (Beijing, 2013), seminars at South Western University of Finance and Economics (Chengdu, 2013), two anonymous referees and the co-editor, Professor Peter M. Robinson, of this journal for helpful comments.…”