A Sample Selection Approach to Censored Demand Systems

The use of micro survey data has been popular in estimating consumer demand equations. Important features of microdata include censored dependent variables. Estimation procedures for censored consumer demand systems include the primal (Kuhn-Tucker) approach of Wales and Woodland (1983), dual (virtualprice) approach of Lee and Pitt (1986), and the Tobit system (Amemiya 1974) estimated by generalized maximum entropy (Golan, Perloff, and Shen 2001) and maximum simulated likelihood (Dong, Gould, and Kaiser 2004; Yen, Lin, and Smallwood 2003) procedures. Less efficient alternatives include the quasi-maximum likelihood estimator (Yen, Lin, and Smallwood 2003), the generalized method of moments estimator (Meyerhoefer, Ranney, and Sahn 2005), and a number of two-step estimators (Heien and Wessells 1990; Perali and Chavas 2000; Shonkwiler and Yen 1999). Yen (2005) recently proposed a maximum likelihood (ML) procedure for the multivariate sample selection model (MSSM), an extension of the bivariate sample selection model (Heckman 1979), which had motivated the procedures of Heien and Wessells (1990) and Shonkwiler and Yen (1999). The MSSM was developed in the context of linear equations and, in addition, is not strictly applicable for a partially selective equation system, viz.,