Multiple Fractional Response Variables with Continuous Endogenous Explanatory Variables

Multiple fractional response variables have two features. Each response is between zero and one, and the sum of the responses is one. In this paper, I develop an estimation method not only accounting for these two features, but also allowing for endogeneity. It is a two step estimation method employing a control function approach: the first step generates a control function using a linear regression, and the second step maximizes the multinomial log likelihood function with the multinomial logit conditional mean which depends on the control function generated in the first step. Monte Carlo simulations examine the performance of the estimation method when the conditional mean in the second step is misspecified. The simulation results provide evidence that the method's average partial effects (APEs) estimates approximate well true APEs and that the method's approximations is preferable to an alternative linear method. I apply this method to the Michigan Educational Assessment Program data in order to estimate the effects of public school spending on fourth grade math test outcomes, which are categorized into one of four levels. The effects of spending on the top two levels are statistically significant while almost those on the others are not.