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Cross Product Censoring in a Demand System with Limited Dependent Variables: A Multivariate Probit Model Approach Open Access


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Chen, Kevin Z.
Chen, Chen
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probit models
cross sectional demand
consumer demand
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The most challenging problem in cross sectional demand analyses is to deal with zero expenditure because OLS estimates tend to be biased towards zero in a regression model where a large proportion of the dependent variable is zero. The problem arises as households participating in the survey do not report or consume all types of good products during the survey period. While several econometric approaches have been proposed to deal with zero expenditure problems, the most common strategy adopted in the food demand literature is to employ an extension of Tobin's (1958) limited dependent variable model for single equations, later generalized by Ameniya (1974) for systems of equations. In empirical applications, the Heckman (1979) two-step type estimation procedure for a demand system with limited dependent variables proposed by Heien and Wessells (1990) has become increasingly popular in applied demand analysis. The practice, however, has been recently been questioned doe to an apparent internal inconsistency problem associated with the Heien and Wessells procedure. Shonkwiler and Yen (1999) and Su and Yen (2000) therefore proposed a consistent two-step estimation of a censored demand system, which is also adopted here. A remaining problem with the Heien and Wessells procedure is that consumers' market participation in each product is model as an independent process and estimated by the univariate probit model. Though attractive because of the ease with which the model can be estimated, correction factors obtained from univariate probit equations do not capture cross-product censoring impacts in multiple equations. In the same spirited as the seemingly unrelated regression model, this could result in inefficient probit estimates when cross product censoring occurs. These inefficient probit estimates likely affect the estimation of the second stage censored demand system. The greater the cross product censoring (the correlation of disturbances), the greater the efficiency gain one would gain if using a multivariate probit model. However, in practice this has rarely been evaluated because the estimation of the multivariate normal density function. This, combined with the necessity of using an iterative technique to maximize the likelihood function, has made the application of the multivariate probit model computationally difficult. With the development of various simulation techniques, estimation of the multivariate probit has recently become more feasible.
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