Novel Approaches to Coherency Conditions in LDV Models
The paper discusses the major identification issue of *coherency conditions* in LDV models with endogeneity and flexible temporal and contemporaneous correlations in the unobservables. Conditions for coherency as discussed in the existing literature are reviewed and shown to be rather esoteric. Two novel methods for establishing coherency conditions are presented, which have intuitive interpretations and are easy to implement and generalize. The constructive consequence of the new approaches is that they indicate how to achieve coherency in models traditionally classified as incoherent through the use of prior sign restrictions on model parameters. This allows us to develop estimation strategies based on Conditional MLE for simultaneous LDV models without imposing recursivity. Econometric applications are used to illustrate the methods in practice and extensions are given to simultaneous ordered probit models with multiple regions. A set of extensive Monte-Carlo experiments are used to evaluate the properties of the proposed Conditional MLE and the consequences of employing estimators that make overly restrictive coherency assumptions about the DGP. These experiments confirm very substantive improvements in terms of estimation Mean-Squared-Error by employing the CMLE developed in this paper. They also show that estimators based on the Linear Probability approximation perform poorly in this context. Our CMLE approach allows for the first time to obtain estimates of the reverse as well as direct interaction terms in LDV models with simultaneity.
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