Self-selection and direct estimation of across-regime correlation parameter

Abstract

A direct Maximum Likelihood (ML) procedure to estimate the "generally unidentified" across-regime correlation parameter in a two-regime endogenous switching model is here provided.The results of a Monte Carlo experiment confirm consistency of our direct ML procedure, and its relative efficiency over widely applied models and methods. As an empirical application, we estimate a Two-Regime simultaneous equation model of domestic work of Italian married women in which the two regimes are given by their working status (employed or unemployed).

Maximum likelihood estimation of an across-regime correlation parameter

“…An example on the use of ρ 12 to obtain information about the skills of the agents is provided by Calzolari and Di Pino (2017), who estimated the time devoted to domestic work by employed and unemployed women in Italy. In this case, a positive sign of ρ 12 indicated that common latent factors positively influence the domestic work supply of women in both regimes.…”

“…3 Methodological issues Calzolari and Di Pino (2017) specified an endogenous switching model with two regression equations whose dependent variables (outcomes) are mutually exclusive in a cross-sectional framework and where selection is simply based on the choice of the larger outcome.…”

“…Differently from these approaches, which provide an "indirect" estimation of the across-regime correlation parameter, Calzolari and Di Pino (2017) suggested that identification and direct ML estimation of the across-regime correlation parameter are possible if the model specification is closer to the traditional Roy model rather than its more widely used generalized versions. The model is specified as "two equation", implying a sort of "rational" behavior of the agent, who simply chooses the regime with the higher outcome.…”

“…This approach allows us to obtain a reliable simultaneous point estimation of both the outcome equations without introducing a further selection equation explaining the choice of the subject, such as in the specification of the "generalized" Roy model (for example, Carneiro, Hansen, and Heckman [2003]). This allows us to obtain more efficient estimates than those provided applying two-stage estimation methods.…”

“…This allows us to obtain more efficient estimates than those provided applying two-stage estimation methods. 2 In this article, we describe the mlcar command, which implements the two-equation ML method of Calzolari and Di Pino (2017) to estimate simultaneously the coefficients of an (endogenous switching) two-equation model including the across-regime correlation coefficient. This full-information approach relies on the assumption of joint normality of the error terms of each of the two outcome equations in the respective regime.…”