A control function approach to estimating dynamic probit models with endogenous regressors, with an application to the study of poverty persistence in China

This paper proposes a parametric approach to estimating a dynamic binary response panel data model that allows for endogenous contemporaneous regressors. This approach is of particular value for settings in which one wants to estimate the effects of an endogenous treatment on a binary outcome. The model is next used to examine the impact of rural-urban migration on the likelihood that households in rural China fall below the poverty line. In this application, it is shown that migration is important for reducing the likelihood that poor households remain in poverty and that non-poor households fall into poverty. Furthermore, it is demonstrated that failure to control for unobserved heterogeneity would lead the researcher to underestimate the impact of migrant labor markets on reducing the probability of falling into poverty.