CMP: Stata module to implement conditional (recursive) mixed process estimator
cmp estimates multi-equation, recursive mixed process models. "Mixed process" means that different equations can have different kinds of dependent variables. The choices are: continuous (like OLS), tobit (left-, right-, or bi-censored), probit, and ordered probit. A dependent variable in one equation can appear on the right side of another equation. "Recursive" means, however, that cmp can only fit "recursive" models with clearly defined stages, not ones with simultaneous causation. A and B can be determinants of C and C a determinant of D--but D cannot be a determinant of A, B, or C. So cmp can fit many IV and SUR models, among others. "Conditional" means that the model can vary by observation. An equation can be dropped for observations for which it is not relevant--if, say, a worker retraining program is not offered in a city then the determinants of uptake cannot be modeled there. Or the type of dependent variable can vary by observation. cmp's modeling framework therefore embraces those of the official Stata commands probit, oprobit, ivprobit, biprobit, tobit, and ivtobit, in principle even regress, sureg, ivreg, as well as the user-written triprobit, mvprobit, bitobit, and mvtobit. It goes beyond them in offering far more flexibility in model construction. To take one arbitrary example, one could regress a continuous variable, on two endogenous variables, one binary and the other sometimes left-censored, instrumenting each with additional variables. In some cases, the gain is consistent estimation where it was difficult before. In other cases, the gain is just in efficiency. For example if y is continuous, x is a sometimes-left-censored determinant of y, and z is an instrument, then the effect of x on y can be consistently estimated with 2SLS (Kelejian 1971). However, a cmp estimate that uses the information that x is censored will be efficient, based as it is on a more accurate model. The routine runs faster under Stata 10, but will run under Stata 9.2 as well.
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