Simultaneous Equation Models
This chapter introduces the concept of endogenous attributes and discusses J. J. Heckman analysis of sample selectivity bias. It presents a case study to illustrate more fully the principles. Heckman approaches the discrete endogenous variable problem by assuming that they are generated by continuous latent variables crossing thresholds. His model is outlined together with some situations in which it is applicable, in particular in cases of sample separation and sample selectivity. To estimate the parameters in this model, the likelihood function formulated for the joint probabilities of various combinations of alternatives must be specified. Consider a situation where the investigator has a set of Q observations available with which to attempt the estimation of some behavioural relationships but that some of the observations have some data missing. The existence of endogenous attributes in travel choice models has been discussed in a casual way since the early 1970s.