COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1767 Identifying Finite Mixtures in Econometric Models Marc Henry, Yuichi Kitamura and Bernard Salanié September 2010 We consider partial identification of finite mixture models in the
presence of an observable source of variation in the mixture weights that leaves component
distributions unchanged, as is the case in large classes of econometric models. We first
show that when the number J of component distributions is known a priori, the family of
mixture models compatible with the data is a subset of a J(J –
1)-dimensional space. When the outcome variable is continuous, this subset is defined by
linear constraints which we characterize exactly. Our identifying assumption has testable
implications which we spell out for J = 2. We also extend our results to the case
when the analyst does not know the true number of component distributions, and to models
with discrete outcomes. |
