Generalized spatial autocorrelation in a panel-probit model with an application to exporting in China

Without using a particular notation for it, it should be noted that any spatial lags of the observable explanatory variables would already be incorporated in the matrix X (Kelejian and Prucha 1999).

Earlier contributions based on MCMC estimation of spatial probit models include: LeSage (2000) who proposed a cross-sectional spatial probit model with spatial correlation in the disturbances and the dependent variable; Smith and LeSage (2004) who allowed for a spatially correlated individual effect in their cross-sectional probit model; LeSage and Pace (2009) who considered spatial correlation in the dependent variable in cross-sectional univariate and multinomial probit models; Baltagi et al. (2017) who analyzed a bivariate panel-probit with spatial correlation in the dependent variable of both equations; Wang and Kockelmann (2009) who proposed a dynamic ordered probit model with spatial correlation in the individual-specific error term. While the aforementioned papers focus on some forms of spatial correlation, it is the goal of the current paper to propose a unified approach accounting for several forms of spatial correlation in the dependent variable and all components of the error term.

After thinning and discarding burn-in draws, the sample of the MCMC draws is split into three parts. Then, the equality of the sample means based on the first 20% and the last 50% of the draws of the chain is tested.

Others such as LeSage and Pace (2009), LeSage et al. (2011), or Elhorst et al. (2017) proposed calculating marginal average effects of covariates in spatial probit models as well.

For the non-spatial model, we calculate the vector of total (which are the direct) effects \(\widehat{d}_{k}^{d}=\widehat{d}_{k}^{t}\) and use this in calculating the counterfactual \(\widetilde{y}\).