Nam, Suhyeon (2012): Multiple Fractional Response Variables with Continuous Endogenous Explanatory Variables.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Multiple Fractional Response Variables with Continuous Endogenous Explanatory Variables.|
|Keywords:||Multiple fractional responses; Endogeneity; Partial effects; Two step estimation; Control function approach; Misspecified conditional mean; Monte Carlo simulation|
|Subjects:||I - Health, Education, and Welfare > I2 - Education and Research Institutions
H - Public Economics > H7 - State and Local Government ; Intergovernmental Relations > H75 - State and Local Government: Health ; Education ; Welfare ; Public Pensions
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General
|Depositing User:||Suhyeon Nam|
|Date Deposited:||18. Nov 2012 13:56|
|Last Modified:||23. Aug 2015 10:21|
Bethany Wicksall amd Mary Ann Cleary, The basics of the foundation allowance – FY 2006-07, House Fiscal Agency, January 2009, memorandum.
David Arsen and David N. Plank, Michigan School Finance Under Proposal A: State Control, Local Consequences, State Tax Notes 31 (2004).
Maarten L. Buis, Fmlogit: Stata module fitting a fractional multinomial logitmodel by quasi maximum likelihood, Statistical Software Components, Boston College Department of Economics, June 2008.
Christian Gourieroux, Alain Monfort, and Alain Trognon, Pseudo maximum likelihood methods: Theory, Econometrica 52 (1984), no. 3, 681–700.
William H. Greene, Econometric analysis, Prentice Hall, August 2008.
John Mullahy, Multivariate fractional regression estimation of econometric share models, NBER Working Papers 16354, National Bureau of Economic Research, Inc, September 2010.
Leslie E. Papke, The effects of spending on test pass rates: evidence from michigan, Journal of Public Economics 89 (2005), no. 5-6, 821–839.
Leslie E Papke and Jeffrey M Wooldridge, Econometric methods for fractional response variables with an application to 401(k) plan participation rates, Journal of Applied Econometrics 11 (1996), no. 6, 619–32.
Leslie E. Papke and Jeffrey M. Wooldridge, Panel data methods for fractional response variables with an application to test pass rates, Journal of Econometrics 145 (2008), no. 1-2, 121–133.
Amil Petrin and Kenneth Train, A Control Function Approach to Endogeneity in Consumer ChoiceModels, JOURNAL OFMARKETINGRESEARCH47 (2010), no. 1, 3–13.
Aruna Sivakumar and Chandra Bhat, Fractional split-distribution model for statewide commodity-flow analysis, Transportation Research Record 1790 (2002), no. 1, 80–88.
Douglas Staiger and James H. Stock, Instrumental variables regression with weak instruments, Econometrica 65 (1997), no. 3, 557–586.
Jeffrey M Wooldridge, Unobserved heterogeneity and estimation of average partial effects, Identification and Inference for Econometric Models Essays in Honor of Thomas Rothenberg (2005), 27–55.
Jeffrey M Wooldridge, Econometric analysis of cross section and panel data, vol. 1, MIT Press Books, no. 0262232588, The MIT Press, January 2010.