Searching for correct specification in spatial probit models. Classical approaches versus Gradient Boosting algorithm

Selecting correct specification in spatial model frameworks is a relevant research topic in spatial econometrics. The purpose of this paper is to examine and contrast two well-known model selection strategies, Specific-to-General, Stge, and General-to-Specific, Gets, in the context of spatial probit models. The results obtained from these classical methods are juxtaposed with those generated through the utilization of a powerful machine learning algorithm: Gradient Boosting. The paper includes an extensive Monte Carlo experiment to compare the performance of these three strategies with small and medium sample sizes. The results show that under ideal conditions, both classical strategies obtain similar results for medium-sized samples, but for small samples, Stge performs slightly better than Gets. The Gradient Boosting algorithm obtains slightly higher success rates than the classical strategies, especially with small samples sizes. Finally, the flow of both strategies is illustrated using a well-known dataset on the probability of businesses reopening in New Orleans in the aftermath of Hurricane Katrina.