Multiple Fractional Response Variables with Continuous Endogenous Explanatory Variables
AbstractMultiple 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 42696.
Date of creation: Oct 2012
Date of revision:
Multiple fractional responses; Endogeneity; Partial effects; Two step estimation; Control function approach; Misspecified conditional mean; Monte Carlo simulation;
Find related papers by JEL classification:
- I2 - Health, Education, and Welfare - - Education
- H75 - Public Economics - - State and Local Government; Intergovernmental Relations - - - State and Local Government: Health, Education, and Welfare
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
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