Concentrated Partial Ml Estimation for Dynamic Spatial Panel Data Probit Models with Fixed Effects

In this paper we propose three different concentrated partial maximum likelihood estimators (CPMLE) for a new specification of a spatial dynamic panel data probit (SDPDprobit) model, which allows to deal with cross-sectional dependence, time dependence and individual (spatial) or time fixed effects in a nonlinear setting. The first ML-based estimator is a panel version of the bivariate PMLE proposed by Wang et al. (2013) and Bill´e and Leorato (2020); the second one is the same estimator based on univariate (rather than bivariate) probabilites. We adjust the MLE and concentrate out the fixed effects following Carro (2007) and Fern´andez-Val (2009). Proper marginal effects for this new model specification are also defined. We provide extensive Monte Carlo simulations for the finite sample properties of those estimators, as well as their asymptotic properties using the increasing domain definition for the spatial component and under the assumption of near-epoch dependence. Finally, the third estimator is a feasible version of PMLE which make use of the coding technique, see Besag (1974) and Arbia (2014), and a block-diagonal structure of the variance-covariance matrix which can be used to overcome computational issues raised by very large datasets