Testing and Relaxing the Exclusion Restriction in the Control Function Approach
In a nonparametric triangular structure typical of the control function literature, and provided the instrument satises a “local irrelevance” condition, we show that we can test the exclusion restriction. Second, if the “instrument” also directly affects the outcome variable, we show that the identication of average causal effects can be achieved in linear random coefficients models and single index models.
(Find here Y. Sasaki’s webpage for the Stata command testex implementing our test of the exclusion restriction)
Empirical Process Results for Exchangeable Arrays
We show the weak convergence of empirical processes and some bootstrap processes with multiadic (e.g., dyadic) data or multiway clustering. These results imply asymptotic normality and the validity of the bootstrap for a large class of nonlinear estimators. We illustrate our results with trade data.
The last version of the WP can be found here: https://arxiv.org/abs/1906.11293
(this paper supersedes our previous paper “Asymptotic results under multiway clustering”).
Rationalizing Rational Expectations: Characterization and Tests
We construct the best possible test of rational expectations (RE) when we observe expectations on future variables on a certain sample, and realizations of that variable on another sample of different units. we apply our methodology to test for RE about future earnings.
You can find the corresponding R package here: https://github.com/cgaillac/RationalExp
Note: this version supersedes “Rationalizing Rational Expectations: Tests and Deviations” (v1 on arXiv), which also considers deviations from RE.
Segregsmall: A command to estimate segregation in the presence of small units
The Stata command Segregsmall estimates usual segregation indices (e.g. Duncan or Theil) when units (=geographical areas, firms, classrooms…) are small. In such cases, naive estimators are biased upwards. The command computes in particular the estimators described in R. Rathelot’s JBES paper and in our join, QE paper.
The Provision of Wage Incentives: A Structural Estimation Using Contracts Variation
To what extent do people react to incentives? Are observed contracts (nearly) optimal? We answer to these questions using a nonparametric principal agent model and an exogenous variation in contracts between the French national institute of statistics and its interviewers.
Estimating Selection Models without Instrument with Stata
This paper presents the Stata command eqregseg, which computes the extremal quantile regression estimator for sample selection developed in our paper “Extremal Quantile Regressions for Selection Models and the Black-White Wage Gap”.
Two-way fixed effects estimators with heterogeneous treatment effects
We show that if treatment effects are not constant, regressions with groups and time fixed effects identify weighted averages of treatment effects across groups and time periods, with potentially (many) negative weights. We suggest sensitivity checks and better estimands under testable restrictions on the design.
See https://arxiv.org/abs/1803.08807 for the last WP version
A cautionary tale on instrument vector calibration for the treatment of unit nonresponse in surveys
We show that the calibration method based on instruments, proposed by Deville (2002), leads to a large variance when the instrumental variable are poorly related to the calibrating variables. If the exclusion restriction is violated, the bias is also large under the same condition.
Fuzzy differences-in-differences with Stata
This paper presents the Stata command fuzzydid, which computes various estimators of the LATE and LQTE for fuzzy DID designs, following our paper “Fuzzy DID”. It can handle non-binary treatments, multiple periods and groups, covariates and partial identification.
Fuzzydid Stata package available from the SSC repository. You can find the files to replicate the application on Clément’s webpage.
Automobile Prices in Market Equilibrium with Unobserved Price Discrimination
We consider inference on a demand and supply model for differentiated products with price discrimination that is unobserved by the econometrician. We show how to extend BLP’s GMM estimation to this setting, using restrictions on marginal costs. We apply our framework to the French automobile market.
Extremal Quantile Regressions for Selection Models and the Black-White Wage Gap
We consider models with endogenous selection and no instrument nor large support regressors. Identification relies on the independence between the covariates and selection, when the outcome tends to infinity. We propose a simple estimator based on extremal quantile regressions and apply it to the evolution of the black-white wage gap in the US.
In many applications of the DID method, the treatment rate only increases more in the treatment group. In such fuzzy designs, we show that the popular “Wald-DID” (the DID of the outcome divided by the DID of the treatment) identifies a LATE only if two homogeneous treatment effect assumptions hold. We then propose two alternative estimands that do not rely on such assumptions.
Measuring Segregation on Small Units: A Partial Identification Analysis
Suppose that an individual in a small unit j (a classroom, a small firm…) belongs to a minority with a probability pj. To measure segregation of this minority, one would ideally use an inequality index on the pj, but they are unobserved. Using the observed proportion instead leads to an overestimation. The segregation indices are actually partially identified. We provide tractable bounds and develop inference.
The supplement and code can be found following the link to the journal’s website.
Identification of Additive and Polynomial Models of Mismeasured Regressors Without Instruments
Suppose that Y = g(X*) + h(Z) + U, E(U|X*,Z)=0 but X* is measured with error. We show that g and h can be identified nonparametrically without side information provided that, basically, Z affects X*. A similar result holds when Y=P(X*,Z) + U, with P polynomial.
A Convenient Method for the Estimation of the Multinomial Logit Model with Fixed Effects
Disentangling Sources of Vehicle Emissions Reduction in France: 2003-2008
We study the factors of the decrease in average CO2 emissions of new cars in France between 2003 and 2008. We show that the evolution of consumers’ preferences account for 43% of this decrease, and that these changes follow two environmental policies put in place during this period.
Identification of Nonseparable Triangular Models with Discrete Instruments
Consider a model Y = g(X,U) with X endogenous, and suppose that we have instruments Z such that X = h(Z,V). If Z is independent of (U,V) and both g(X,.) and h(Z,.) are strictly monotonic, then g can be partially or pointly identified if Z is binary. It is fully identified in general if Z takes three values or more.
Identification of Mixture Models Using Support Variation
Suppose that observed variables (X1,…,XK) are independent conditional on a continuous and unobserved variable X*. We show that the distributions of Xi conditional on X* are identified if the bounds of the conditional support of Xi are strictly increasing with X*. We also develop a test of this condition.
The Environmental Effect of Green Taxation: the Case of the French “Bonus/Malus”
In 2008 was introduced in France a feebate system for new automobiles. We investigate the effect of this policy on CO2 emissions. We find that the policy actually led to an increase in these emissions, mostly because of a substantial increase in the sales of new automobiles.
La régression quantile en pratique
This article (in French) is an introduction to quantile regression, with an emphasis on its interpretation.
Another Look at Identification at Infinity of Sample Selection Models
The sample selection model can be identified without instrument if basically, the probability of selection, conditional on the potential outcome and covariates, does not depend on covariates as the potential outcome tends to infinity.
Inference on an Extended Roy Model, with an Application to Schooling Decisions in France
Consider an extended Roy model where a binary decision depends on expected gains and an unobserved cost. The model is identified without instruments if, basically, the unobserved cost only depends on covariates. Applying our results to French data, we show that nonpecuniary components are a key factor for going to college.
On the Completeness Condition for Nonparametric Instrumental Problems
Sufficient conditions for the completeness condition (E(g(X)|Z) = 0 => g(X)=0) used in nonparametric IV problems are given. It holds in particular under a large support condition on n(Z) and technical restrictions on V in the generalized additive model X = m(n(Z) + V).
Le coût du bonus/malus écologique : que pouvait-on prédire ?
A New Instrumental Method for Dealing with Endogenous Selection
Consider the sample selection model under the nonstandard IV restriction that D is independent of Z conditional on Y. Nonparametric identification is achieved under a completeness condition between Y and Z. Partial identification can also be obtained if one replaces independence by monotonicitiy restrictions.
Identification of Peer Effects Using Group Size Variation
A linear-in-means model close to the one of Manski (1993) is identified provided that we observe groups with three distinct sizes. This applies even if one does not observe all members of the group, and can also be extended to binary outcomes.