Dynamic spatial panel data models with interactive fixed effects: M-estimation and inference under fixed or relatively small T

We propose an M-estimation method for dynamic spatial panel data models with interactive fixed effects based on (relatively) short panels. Unbiased estimating functions are constructed by adjusting the concentrated conditional quasi scores, given the initial values and with the factor loadings being concentrated out, to account for the effects of conditioning and concentration. Solving the estimating equations gives the M-estimators of the common parameters and common factors. Under fixed T, n-consistency and joint asymptotic normality of the M-estimators are established. Under T = o(n), the M-estimators of the common parameters are shown to be nT-consistent and asymptotically normal. For inference, difficulty lies in the estimation of the variance-covariance (VC) matrix of the estimating functions. We decompose the estimating functions into a sum of n nearly uncorrelated terms, using their outer products with a covariance adjustment to obtain a consistent VC estimator under both fixed T and T = o(n). Monte Carlo results show that the proposed methods perform well in finite samples. We apply our methods to examine peer effects in firms’ innovation decisions, using data from publicly listed Chinese firms. The results reveal significant spillovers in R & D investment within industries and spatial correlations in unobserved shocks among geographically proximate firms.