On-site samples' regression

Abstract

The paper corrects an estimation problem that has not yet been recognized in previous estimates of demand functions using on-site samples. There are three kinds of problems that one faces in on-site samples, namely, non-negative integers, truncation and endogenous stratification. Two theoretically correct maximum likelihood methods are developed based on two different assumptions about the variable distribution: the normal distribution and the Poisson distribution. A simulation is performed to compare the two methods using generated data sets of known models. We should not use OLS and instead should use the maximum likelihood methods developed here to estimate demand functions that use on-site samples. If forecasting is the purpose of estimation, then the simulation indicates that the Poisson ML method may be better.