Dynamic panel estimation of a regional adjustment model with spatial-temporal robust covariance
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Dynamic panel estimation of a regional adjustment model with spatial‑temporal robust covariance Dayton M. Lambert1 Received: 12 February 2020 / Accepted: 29 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper extends the Arellano-Bond dynamic panel regression model’s covariance estimator to one robust to spatial autocovariance and heteroskedasticity. We apply Kelejian and Prucha’s semi-parametric procedure for estimating covariance matrices that accommodate spatial heteroskedastic autocovariance processes to augment the usual Arellano-Bond covariance estimator. The empirical application examines the jobs-topeople/people-to-jobs conundrum with Carlino and Mill’s regional adjustment model using employment and population data from 2001 to 2018 for Oklahoma’s 77 counties. Keywords Dynamic panel · Spatial-temporal covariance · Regional adjustment model · Instrumental variables JEL Classification C4 · C51 · R12
1 Introduction In their 1974 study, Steinnes and Fisher (1974) explained the intraurban movement of jobs and people as a codetermined process, with the geographic outcome of one predicting the other. Carlino and Mills (1987) extended Steinnes and Fisher’s model by endogenizing the adjustment process. This class of regional adjustment models portrays economic growth as advancing along a trajectory towards an unknown equilibrium where the spatial allocation of jobs, industry profits, employers, and household income are optimized with respect to geographic location (Carruthers and Vias 2005). The resulting equilibrium is a relative concept. Employers and people organize themselves such that growth in jobs and people advances as a proportional constant. Equilibrium are ephemeral, which is why researchers routinely describe the spatial economy as existing in a state of constant adjustment towards a theoretical equilibrium, subject to initial conditions (Carruthers and Mulligan 2007). * Dayton M. Lambert [email protected] 1
Oklahoma State University, 410 Agricultural Hall, Stillwater, OK, USA
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The geographically explicit features of jobs-to-people/people-to-jobs feedback naturally lends itself to analysis as a spatial process to model the effects of local and regional context on inter-regional migration and the allocation of capital to regions with comparative advantage (Boarnet et al. 2005; Monchuk et al. 2011; Gebremariam et al. 2011)1. Previous studies using spatial process models to explain the geographic distribution of jobs and residential patterns typically represented spatial dependence through neighborhood contiguity or inverse-distance matrices, in turn estimating the adjustment process with spatial lag, error, lag-error, or spatial Durbin models.2 Other studies maintain an agnostic stance regarding the structure of spatial error components, using spatial heteroskedastic-autocorrelation consistent covariance estimators (spatial HAC estimators) (Kelejian and Prucha 2007) to adjust the standard errors of parameter
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