Bayesian Estimation of Panel Data Fractional Response Models with Endogeneity: An Application to Standardized Test Rates.

摘要

n this paper I propose Bayesian estimation of a nonlinear panel data model with a fractional dependent variable (bounded between 0 and 1). Specifically, I estimate a panel data fractional probit model which takes into account the bounded nature of the fractional response variable. I outline estimation under the assumption of strict exogeneity as well as when allowing for potential endogeneity. Furthermore, I illustrate how transitioning from the strictly exogenous case to the case of endogeneity only requires slight adjustments. For comparative purposes I also estimate linear specifications of these models and show how quantities of interest such as marginal effects can be calculated and compared across models. Using data from the state of Florida, I examine the relationship between school spending and student achievement, and find that increased spending has a positive and statistically significant effect on student achievement. Furthermore, this effect is roughly 50% larger in the model which allows for endogenous spending. Specifically, a