Estimating a probit model with a continuous endogenous covariate and using complex survey data: An application to socioeconomic mobility analysis in Mexico

We use Stata to estimate the probability of having a high socioeconomic destination as a function of education, parental economic level, and other explanatory variables. Given the potential endogeneity of the education variable, we estimate a probit model with an instrumental variable under the context of a complex survey dataset. The maximum-likelihood estimation procedure of the structural parameters is carried out using two equivalent strategies that consider Stata functions and reporting options. Following Long and Freese (2014), we first estimate the model using the ivprobit command with sampling weights and clustered robust standard errors, allowing us to obtain the report of the Wald exogeneity test. As a second strategy, we use the ivprobit command with survey data analysis estimation. We performed additional steps needed to compute the overall rate of correctly classified results after estimation under survey data analysis or using sampling weights. The validity of an instruments test remains challenging for ivprobit models with survey data. Our analysis of the estimation results is extended and enriched with the calculation of odds ratios (testing whether they are statistically different from one) and average probabilities by region in Mexico and educational level.