A two-step estimator for a spatial lag model of counts: Theory, small sample performance and an application

Abstract

Several spatial econometric approaches are available to model spatially correlated disturbances in count models, but there are at present no structurally consistent count models incorporating spatial lag autocorrelation. A two-step, limited information maximum likelihood estimator is proposed to fill this gap. The estimator is developed assuming a Poisson distribution, but can be extended to other count distributions. The small sample properties of the estimator are evaluated with Monte Carlo experiments. Simulation results suggest that the spatial lag count estimator achieves gains in terms of bias over the aspatial version as spatial lag autocorrelation and sample size increase. An empirical example deals with the location choice of single-unit start-up firms in the manufacturing industry in the US between 2000 and 2004. The empirical results suggest that in the dynamic process of firm formation, counties dominated by firms exhibiting (internal) increasing returns to scale are at a relative disadvantage even if localization economies are present.

A Spatial-Filtering Zero-Inflated Approach to the Estimation of the Gravity Model of Trade

“…Among those works, many focus on the issue of MTR, which can be considered as a main source of spatial heterogeneity (Behrens et al 2012;Baier and Bergstrand 2009). One way to relax this independence assumption is by incorporating spatial dependence in the Poisson gravity model by means of spatial autoregressive techniques (Sellner et al 2013;Lambert et al 2010). Another is ESF (Griffith 2003).…”

“…Spatial generalized linear models (GLMs) (Sellner et al 2013;Lambert et al 2010): these models extend the previous approaches by allowing for estimation based on Poisson-type models, therefore accommodating the concerns expressed in Santos Silva and Tenreyro (2006). • Semi-parametric (ESF) models (Fischer and Griffith 2008;Scherngell and Lata 2013;Krisztin and Fischer 2015;Chun 2008;): these models mix a parametric and a non-parametric approach, by employing ESF within Poisson-type models.…”

Analysis of Discrete Dependent Variable Models with Spatial Correlation

“…Direct extensions of this spatial count data approach, which is amenable to standard ML estimation, are the specication of Kaiser and Cressie (1997) based upon a truncated (Winzorized) Poisson distribution and the semi-parametric Negative-Binomial (Negbin) specication proposed by Basile et al (2010). Observation-driven count data models where the expected value of a count variable is specied as a function of spatially lagged expectations are analyzed by Hays and Franzese (2009) and Lambert et al (2010). In order to estimate those models the former study rely on a nonlinear Least Squares (LS) approach and the Generalized Method of Moments (GMM), while Lambert et al (2010) use a two-step limited information ML (LIML) procedure.…”

“…Observation-driven count data models where the expected value of a count variable is specied as a function of spatially lagged expectations are analyzed by Hays and Franzese (2009) and Lambert et al (2010). In order to estimate those models the former study rely on a nonlinear Least Squares (LS) approach and the Generalized Method of Moments (GMM), while Lambert et al (2010) use a two-step limited information ML (LIML) procedure. For an overview of further spatial observation-driven count data models see Lambert et al (2010).…”

“…In order to estimate those models the former study rely on a nonlinear Least Squares (LS) approach and the Generalized Method of Moments (GMM), while Lambert et al (2010) use a two-step limited information ML (LIML) procedure. For an overview of further spatial observation-driven count data models see Lambert et al (2010).…”