GMM gradient tests for spatial dynamic panel data models

Abstract

4In this study, we formulate the adjusted gradient tests when the alternative model used to construct tests deviates from the true data generating process for a spatial dynamic panel data 6 model (SDPD). Following Bera et al. (2010), we introduce these adjusted gradient tests along with the standard ones within a GMM framework. These tests can be used to detect the presence 8 of (i) the contemporaneous spatial lag terms, (ii) the time lag term, and (iii) the spatial time lag terms in an higher order SDPD model. These adjusted tests have two advantages: (i) 10 their null asymptotic distribution is a central chi-squared distribution irrespective of the misspecified alternative model, and (ii) their test statistics are computationally simple and require 12 only the ordinary least-squares (OLS) estimates from a non-spatial two-way panel data model. We investigate the finite sample size and power properties of these tests through Monte Carlo

Specification tests for spatial panel data models

“…Based on Bera and Yoon (1993), Montes-Rojas (2010) has proposed an adjusted RS test for autocorrelation in presence of random effects and vice-versa, after estimating the spatial dependent parameter using ML and instrumental variable estimation methods. Similar adjusted tests are suggested by Taşpınar et al (2017) for a higher order spatial dynamic panel data model in a generalized method of moments (GMM) framework. However, the specification tests proposed in the above papers require the ML estimation of nuisance parameters [except for the adjusted tests in Taşpınar et al (2017)], and such a strategy will get more complex as we add more parameters to generalize the model in multiple directions.…”

“…Similar adjusted tests are suggested by Taşpınar et al (2017) for a higher order spatial dynamic panel data model in a generalized method of moments (GMM) framework. However, the specification tests proposed in the above papers require the ML estimation of nuisance parameters [except for the adjusted tests in Taşpınar et al (2017)], and such a strategy will get more complex as we add more parameters to generalize the model in multiple directions.…”

Generalized Method of Moment Estimation Method Lagrange Multiplier Test for Simultaneous Spatial of Dynamic Panel Data

“…The last use of the LM test for dynamic panel data spatial models was carried out by [13], where [13] used [22] model as a model that tested its spatial dependency, is:…”

“…The LM test by [13] uses the GMM estimation method which can detect dependencies on spatial lag, time lag and spatial time lag. The test begins with estimating the optimal GMM on a limited model.…”

“…The spatial dependency test was first described by [10] with the Moran's I test, which is more in the direction of testing the spatial autocorrelation in the model. In the development of the spatial dependency test for panel data using Lagrange Multiplier and Likelihood Ratio as has been done by [11], while the spatial dependency test with the GMM approach was carried out by [12] and the spatial dependency test for dynamic panel data with the GMM approach was carried out by [13]. All spatial dependency tests that have been done above are still carried out for a single model.…”