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Multiple Fractional Response Variables with Continuous Endogenous Explanatory Variables

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  • Nam, Suhyeon

Abstract

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.

Suggested Citation

  • Nam, Suhyeon, 2012. "Multiple Fractional Response Variables with Continuous Endogenous Explanatory Variables," MPRA Paper 42696, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:42696
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    File URL: https://mpra.ub.uni-muenchen.de/42696/1/MPRA_paper_42696.pdf
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    References listed on IDEAS

    as
    1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    2. Papke, Leslie E. & Wooldridge, Jeffrey M., 2008. "Panel data methods for fractional response variables with an application to test pass rates," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 121-133, July.
    3. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    4. Papke, Leslie E., 2005. "The effects of spending on test pass rates: evidence from Michigan," Journal of Public Economics, Elsevier, vol. 89(5-6), pages 821-839, June.
    5. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
    6. John Mullahy, 2010. "Multivariate Fractional Regression Estimation of Econometric Share Models," NBER Working Papers 16354, National Bureau of Economic Research, Inc.
    7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    8. Maarten L. Buis, 2008. "FMLOGIT: Stata module fitting a fractional multinomial logit model by quasi maximum likelihood," Statistical Software Components S456976, Boston College Department of Economics, revised 16 Feb 2017.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Multiple fractional responses; Endogeneity; Partial effects; Two step estimation; Control function approach; Misspecified conditional mean; Monte Carlo simulation;
    All these keywords.

    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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