Econometrica: Apr, 1965, Volume 33, Issue 2
Joint Estimation of Relationships Involving Discrete Random Variables
Arnold Zellner, Tong Hun Lee
In this paper we present several models which have been utilized to "explain" the variation of proportions. For these models, we review single equation estimation techniques which yield asymptotically efficient estimators. We then go on to consider the analysis of a set of correlated sample proportions and develop a joint estimation procedure which yields asymptotically efficient estimators. The joint estimation procedure, by taking account of heteroscedasticity as well as the correlations existing between proportions, produces estimators with smaller asymptotic variances than do single equation techniques which take account only of heteroscedasticity. Data on consumer decisions with respect to durable purchases and use of installment credit are analyzed to illustrate one use of these techniques in economics.