Simultaneous equations in ordered discrete responses with regressor-dependent thresholds

The parameters of ordered discrete response (ODR) models are identified only up to a positive scale. In this paper, we examine the identification issue for simultaneous equations with ODR, where the well-known identification problem in simultaneous equations of recovering structural-form parameters from reduced-form parameters is compounded with the ODR identification problem. We allow the thresholds in ODR to be regressor dependent as well as constant; the former is particularly challenging because threshold parameters get mixed with regression parameters, adding one more dimension to the identification problem. We also explore a cross-equation restriction on threshold differences, under which the structural form parameters are fully identified as if the dependent variables are continuously distributed. An empirical example with farm--household joint labour supply is provided to illustrate the identification issues, to show how our proposals work and to apply tests devised for the threshold constancy and cross-equation restrictions. Copyright 2005 Royal Economic Society