Heterogeneous rebound effects: Comparing estimates from discrete-continuous models

Discrete-continuous models have become a common technique for addressing selectivity biases in data sets with endogenously partitioned observational units. Alternative two-stage approaches have been suggested by LEE (1983), DUBIN and MCFADDEN (1984), and DAHL (2002), all of which capture the first-stage discrete choice by the multinomial logit model, while the second-stage outcome equation is estimated using OLS. The nonlinearity introduced by the selection bias correction implies that the second-stage coefficients cannot be interpreted as marginal effects. Instead, the marginal effects are obtained using the estimates from both the first and second stages, a step that has been widely neglected in the applied literature. After deriving formulae for the marginal effects obtained from these selection correction approaches, we estimate a joint model of automobile ownership and distance driven to quantify the rebound effect, the behaviorally induced increase in driving that results from higher fuel economy. Our example illustrates that the pattern of rebound effects varies substantially depending on the method of selection bias correction.