Another Look at the Identification at Infinity of Sample Selection Models

It is often believed that without instrument, endogenous sample selection models are identified only if a covariate with a large support is available (see Chamberlain, 1986, and Lewbel, 2007). We propose a new identification strategy mainly based on the condition that the selection variable becomes independent of the covariates when the outcome, not one of the covariates, tends to infinity. No large support on the covariates is required. Moreover, we prove that this condition is testable. We finally show that our strategy can also be applied to the identification of generalized Roy models.identification at infinity, sample selection model, Roy model

Inference on a Generalized Roy Model, with an Application to Schooling Decisions in France

This paper considers the identification and estimation of an extension of Roy's model (1951) of occupational choice, which includes a non-pecuniary component in the decision equation and allows for uncertainty on the potential outcomes. This framework is well suited to various economic contexts, including educational and sectoral choices, or migration decisions. We focus in particular on the identification of the non-pecuniary component under the condition that at least one variable affects the selection probability only through potential earnings, that is under the opposite of the usual exclusion restrictions used to identify switching regressions models and treatment effects. Point identification is achieved if such variables are continuous, while bounds are obtained otherwise. As a result, the distribution of the ex ante treatment effects can be point or set identified without any usual instruments. We propose a three-stages semiparametric estimation procedure for this model, which yields root-n consistent and asymptotically normal estimators. We apply our results to the educational context, by providing new evidence from French data that non-pecuniary factors are a key determinant of higher education attendance decisions.Roy model, nonparametric identification, exclusion restrictions, schooling choices, ex ante returns to schooling

The Effect of Public Policies on Consumers' Preferences: Lessons from the French Automobile Market

In this paper, we investigate whether French consumers have modified their preferences towards environmentally-friendly vehicles between 2003 and 2008. We estimate a model of demand for automobiles incorporating both consumers' heterogeneity and CO2 emissions of the vehicles. Our results show that there has been a shift in preferences towards low-emitting cars, with an average increase of 367 euros of the willingness to pay for a reduction of 10 grams of carbon dioxide per kilometer. We also stress a large heterogeneity in the evolution of preferences between consumers. Rich and young people are more sensitive to environmental issues, and our results are in line with votes for the green party at the presidential elections. We relate these changes with two environmental policies that were introduced at these times, namely the obligation of indicating energy labels by the end of 2005 and a feebate based on CO2 emissions of new vehicles in 2008. Our results suggest that such policies have been efficient tools to shift consumers utility towards environmentally-friendly goods, the shift in preferences accounting for 20% of the overall decrease in average CO2 emissions of new cars on the period

Another look at the identification at infinity of sample selection models

It is often believed that without instrument, endogenous sample selection models are identified only if a covariate with a large support is available (see Chamberlain, 1986, and Lewbel, 2007). We propose a new identification strategy mainly based on the condition that the selection variable becomes independent of the covariates when the outcome, not one of the covariates, tends to infinity. No large support on the covariates is required. Moreover, we prove that this condition is testable. We finally show that our strategy can also be applied to the identification of generalized Roy models

Two-way Fixed Effects Regressions with Several Treatments

We study regressions with period and group fixed effects and several treatment variables. Under a parallel trends assumption, the coefficient on each treatment identifies the sum of two terms. The first term is a weighted sum of the effect of that treatment in each group and period, with weights that may be negative and sum to one. The second term is a sum of the effects of the other treatments, with weights summing to zero. Accordingly, coefficients in those regressions are not robust to heterogeneous effects, and may be contaminated by the effect of other treatments. We propose alternative estimators.Comment: 25 pages. Compared to the previous version, we have added in particular Corollary 1, Section 4.2 on dynamic effects and an applicatio

Identification of peer effects using group size variation

This paper considers the semiparametric identification of endogenous and exogenous peer effects based on group size variation. We show that Lee (2006)'s linear-in-means model is generically identified, even when all members of the group are not observed. While unnecessary in general, homoskedasticity may be required in special cases to recover all parameters. Extensions to asymmetric responses to peers and binary outcomes are also considered. Once more, most parameters are semiparametrically identified under weak conditions. However, recovering all of them requires more stringent assumptions. Eventually, we bring theoretical evidence that the model is more adapted to small group

Late Again with Defiers

We show that the Wald statistic still identifies a causal effect if instrument monotonicity is replaced by a weaker condition, which states that the potential propensities to be treated with or without the instrument should have the same distribution, conditional on potential outcomes. This holds for instance if the slippages between these potential propensities and the average propensity are independent of potential outcomes. In this framework, the Wald statistic identifies a LATE on a population which comprises both compliers and always takers

Automobile Prices in Market Equilibrium with Unobserved Price Discrimination

In markets where sellers are able to price discriminate, individuals pay different prices that may be unobserved by the econometrician. This paper considers the structural estimation of a demand and supply model à la Berry et al. (1995) with such price discrimination and limited information on prices taking the form of, e.g., observing list prices from catalogues or average prices. Within this framework, identification is achieved by using supply-side conditions, provided that the marginal costs of producing and selling the goods do not depend on the characteristics of the buyers. The model can be estimated by GMM using a nested fixed point algorithm that extends BLP’s algorithm to our setting. We apply our methodology to estimate the demand and supply in the French new automobile market. Our results suggest that discounting arising from price discrimination is important. The average discount is estimated to be 9.6%, with large variation depending on buyers’ characteristics and cars’ specifications. Our results are consistent with other evidence on transaction prices in France

Difference-in-Differences Estimators of Intertemporal Treatment Effects

We consider the estimation of the effect of a treatment, using panel data where groups of units are exposed to different doses of the treatment at different times. We consider two sets of parameters of interest. The first are the average effects of having changed treatment for the first time $\ell$ periods ago. Those parameters generalize the average effect of having started receiving the treatment $\ell$ periods ago that has often been estimated in applications with a binary treatment and staggered adoption. We also consider cost-benefit ratios a planner may use to compare the treatments actually assigned to a counterfactual \textit{status quo} scenario where groups receive their period-one treatment throughout the panel. We show that under common trends conditions, all these parameters are unbiasedly estimated by weighted sums of differences-in-differences. Our estimators are valid if the treatment effect is heterogeneous, contrary to the commonly-used dynamic two-way fixed effects regressions. We also propose estimators of a dynamic linear model, with group-specific but time-invariant effects of the current and lagged treatments, which may be used to evaluate ex-ante the effect of future policies. In an application, we find that our estimators differ substantially from those obtained with dynamic two-way fixed effects regressions.Comment: Compared to v5, we added in particular the parameters delta_{+/-,ell}, an inference section and an application (plus another one in the web appendix). 62 pages overall, with the web appendix starting at page 4