Selecting Strong and Exogenous Instruments via Structural Error Criteria

Job Market Paper

Abstract: Instrumental variables (IVs) allow consistent estimation of the causal effect of endogenous variables on outcomes. However if IVs are not exogenous and jointly strong, estimators are inconsistent and t-test based Gaussian confidence intervals are invalid. Thus in this paper I design a procedure to select a subset of strong and exogenous IVs among a larger set of potentially weak and / or endogenous IVs in a linear setting. To do so I formally build losses, risks and risk estimators which are based on the structural errors being implicitly minimized when performing IV estimation. I shed light into the empirical and theoretical properties of the risks and find that IV subset selection via risk estimators minimization consistently select strong and exogenous subsets of IVs for the two-stage least squares (2SLS) estimator. More specifically, efficiency and consistency results are established by considering standard asymptotics, weak IV asymptotics and locally invalid IV asymptotics, while maintaining the total number of IVs fixed. I confirm the performances of my IV selection procedures against competing ones' using Monte Carlo simulations and lastly I estimate the causal effect of pre-trial detention on offenders guilt by selecting judge dummy IVs in the first stage.

Presented: TSE Job Market Presentations (2022), TSE Econometrics Workshop (2021, 2022), TSE PhD Workshop (2021, 2022), University of Oxford Econometrics Lunch (2022)

Testing and Relaxing Distributional Assumptions on Random Coefficients in Demand Models

Joint with Gökçe Gökkoca and Max Lesellier

Abstract: The BLP demand model for differentiated products is the workhorse model for demand estimation with market-level data. This model uses random coefficients to account for unobserved preference heterogeneity. The shape of the distribution of random coefficients matters greatly for many counterfactual quantities, such as the cost pass-through. In this paper, we develop new econometric tools to test this distribution and improve its estimation under a flexible parametrization. First, we construct new instruments that are designed to detect deviations from the true distribution of random coefficients. Second, we develop a formal moment-based specification test on the distribution of random coefficients. Third, we show that our instruments can be successfully used to estimate a flexible distribution of random coefficients. Finally, we validate our approach with Monte Carlo simulations and an empirical application using data on car purchases in Germany. We also show that these methods extend to the mixed logit demand model with individual-level data.

Presented: TSE Econometrics Workshop (2020, 2021), TSE PhD Workshop (2021, 2022), IAAE 2022 London (2022), 4th QMUL Finance and Economics Workshop (2022), AMES Tokyo (2022), AFES Addis Ababa (2022)

A Pivotal Nonparametric Test for Identification-Robust Inference in Linear IV Models

Abstract: In linear models with endogenous regressors it is well-known that weak instruments (IVs) bias the 2 Stage Least Squares (2SLS) and other k-class IV estimators and make standard Gaussian confidence intervals invalid. Inference can still be performed by inverting tests, however there are no known method to account for a non-linear first stage except Antoine and Lavergne (2019). Their method requires simulations of the distribution of the test statistic under the null which makes it difficult to apply when sample size is moderate to large. For the above reasons I build a pivotal test statistic based on a score of integrated conditional moments which allows to easily infer on the model's structural parameters regardless of instruments' strength and the shape of the first stage conditional mean. For heteroskedastic or independent and identically distribution data with normal or non-normal errors I prove that the test is valid regardless of the degree of identification of the structural parameter of interest, and also prove that the test is consistent as long if the parameter of interest is at least semi-strongly identified. I compare the performances of the test against competing ones and revisit the effect of education on wage using Angrist and Krueger (1991) data and prove that it is strictly positive.

Presented: TSE MRe Workshop (2018), TSE Econometrics Workshop (2019, 2020)

SpeTestNP: An R package on nonparametric specification tests for linear models

Joint with Pascal Lavergne

Description: This R package performs nonparametric tests of parametric specifications. Five heteroskedasticity-robust tests are available: Bierens (1982), Zheng (1996), Escanciano (2006), Lavergne and Patilea (2008), and Lavergne and Patilea (2012). Specific bandwidth and kernel methods can be chosen along with many other options. Allows parallel computing to quickly compute p-values based on the bootstrap.

Published on CRAN