Multivariate Fractional Regression Estimation of Econometric Share Models

Abstract This paper describes and applies econometric strategies for estimating regression models of economic share data outcomes where the shares may take boundary values (zero and 1) with nontrivial probability. The main focus of the paper is on the conditional mean structures of such data. The paper proposes an extension of the fractional regression methodology proposed by (Papke, L. E., and J. M. Wooldridge. 1996. “Econometric Methods for Fractional Response Variables with an Application to 401(k) Plan Participation Rates.” Journal of Applied Econometrics 11: 619–632; Papke, L. E. and J. M. Wooldridge. 2008. “Panel Data Methods for Fractional Response Variables with an Application to Test Pass Rates.” Journal of Econometrics 145: 121–133.), in univariate cross-sectional and panel contexts. The paper discusses the stochastic aspects of share definition and measurement, and summarizes important features of the existing literature on econometric strategies for share model estimation. The paper then goes on to discuss the univariate fractional regression estimation strategies proposed by Papke and Wooldridge and to extend the fractional regression approach to estimation of and inference about regression models describing the multivariate share data. Some issues involving outcome aggregation/disaggregation are considered, as is a full likelihood estimation approach based on Dirichlet-multinomial models. The paper demonstrates the workings of these various empirical strategies by estimating models of financial asset portfolio shares using data from the 2001, 2004, and 2007 US Surveys of Consumer Finances.