A Causal Interpretation of Extensive and Intensive Margin Effects in Generalized Tobit Models

Abstract

Abstract:The usual decomposition of effects in corner solution models into extensive and intensive margins is generally incompatible with a causal interpretation. This paper proposes a decomposition based on the joint distribution of potential outcomes which is meaningful in a causal sense. The difference between decompositions can be substantial and yield diametrically opposed results, as shown in a standard Tobit model example. In a generalized Tobit application exploring the effect of reducing firm entry regulation on bilateral trade flows between countries, estimates suggest that using the usual decomposition would overstate the contribution of the extensive margin by around 15%.

Extensive and Intensive Margin Effects in Sample Selection Models: Racial Effects on Wages

“…Comparing our set‐up with that of Staub (), first, Staub () used the term ‘switchers’ instead of changers. Second, Staub () considered mainly Y with P ( Y =0)>0 without splitting Y into Q and and then examined the sample selection case briefly as a generalization. Third, Staub () pursued non‐parametric bounds for the above effects, whereas we focus on point identification adopting linear models.…”

“…Second, Staub () considered mainly Y with P ( Y =0)>0 without splitting Y into Q and and then examined the sample selection case briefly as a generalization. Third, Staub () pursued non‐parametric bounds for the above effects, whereas we focus on point identification adopting linear models. Fourth, Staub () also explored point identification; however, the entities identified include error term conditional means whose estimation was not addressed, whereas much of this paper is on estimating such terms.…”

“…In the treatment effect literature, Lee () and Staub () have already examined the above subeffects; however, they had only limited success because their approaches are non‐parametric. In contrast, we use semiparametric models that are linear in D and Z for the latent Q ‐ and ‐equations without specifying the error term distributions.…”

A Dynamic Hurdle Model for Zero-Inflated Count Data: With an Application to Health Care Utilization

“…Note that the extensive margin effect is the change in the probability of participation times the average outcome of participants. This may overstate the true causal effect if those at the margin of participation have below average outcomes once they participate (Staub, 2013).…”

A GMM-Based Test for Normal Disturbances of the Heckman Sample Selection Model

“…The derived LM test is similar to the widely used Jarque 1 An example is the estimation of gravity models of bilateral trade flows with missing and/or zero trade. Here, the assumption of bivariate normality turns out important for deriving comparative static results with respect changes in the external and internal margin of trade following Yen and Rosinski (2008) [1] and Staub (2014) [2]. 2 There is also work available that proposes normality tests for the Tobit model (see Skeels and Vella, 1999 [4] and Drukker, 2002 [5]).…”