Joint work with: Alexis Derumigny and Yannick Guyonvarch.

History or status: in progress.

Joint work with: Elia Lapenta.

History or status: in progress.

Joint work with: Alexis Derumigny and Yannick Guyonvarch.

Building upon earlier reflections as regards the construction of confidence intervals (CIs) for ratios of expectations and using tools from first-order Edgeworth expansions of standardized sums of independent variables, we develop nonasymptotic CIs (i.e., with guaranteed coverage for any sample size) for expectations and individual coefficients in linear models while being exact and efficient at the limit, when the sample size tends to infinity.

History or status: In fact, we divide the initial project focused on linear regression into two parts. The endogeneity case is left for future articles. The current article focuses on the case of an expectation and the coefficients of a linear regression model (without endogeneity). It is better motivated/supported by general (impossibility and possibility) results about the construction of nonasymptotically valid confidence intervals. It has been submitted.

arXiv preprint: here. Latest version: here.

Takeaway. We construct confidence intervals for expectations and linear regressions’ coefficients with non-asymptotic validity guarantees while maintaining the precision of standard intervals as sample size grows to infinity.

Abstract. We contribute to bridging the gap between large- and finite-sample inference by studying confidence sets (CSs) that are both {non-asymptotically valid} and {asymptotically exact uniformly} (NAVAE) over semi-parametric statistical models. NAVAE CSs are not easily obtained; for instance, we show they do not exist over the set of Bernoulli distributions. We first derive a generic sufficient condition: NAVAE CSs are available as soon as uniform asymptotically exact CSs are. Second, building on that connection, we construct closed-form NAVAE confidence intervals (CIs) in two standard settings — scalar expectations and linear combinations of OLS coefficients — under moment conditions only. For expectations, our sole requirement is a bounded kurtosis. In the OLS case, our moment constraints accommodate heteroskedasticity and weak exogeneity of the regressors. Under those conditions, we enlarge the Central Limit Theorem-based CIs, which are asymptotically exact, to ensure non-asymptotic guarantees. Those modifications vanish asymptotically so that our CIs coincide with the classical ones in the limit. We illustrate the potential and limitations of our approach through a simulation study.

Joint work with: Elia Lapenta.

History or status: submitted.

This article focuses on estimating the average marginal effect of a treatment in the context of nonparametric instrumental variables regression (NPIV). We propose to adapt nonparametric estimation based on Reproducing Kernel Hilbert Spaces (RKHS) to this framework, which presents several computational advantages: a single hyperparameter when most current methods require two, and a closed form for our estimator. We prove the asymptotic normality of our estimator and construct bootstrap tests to conduct inference.

Latest version: here.

Takeaway. We develop a computationally efficient single-tuning-parameter method for estimating and conducting inference on the average treatment effect in nonparametric instrumental variable models, with theoretical guarantees and good small-sample performance. The companion R package rkhsiv implements our procedure.

Abstract. We propose a novel procedure for estimating and conducting inference on average marginal effects in partially linear instrumental regressions using Reproducing Kernel Hilbert Space methods. Our procedure relies on a single regularization parameter. We obtain the consistency and asymptotic normality of our estimator. Since the variance of the limiting distribution has a complex analytical form, we propose a Bayesian bootstrap method to conduct inference and establish its validity. Our procedure is easy to implement and exhibits good finite-sample performance in simulations. Three empirical applications illustrate its implementation on real data, showing that it yields economically meaningful results.

History or status: working paper.

Latest version: here.

Takeaway. We document that residential segregation has remained stable over five decades in France but varies substantially across dimensions, being strongest for nationality and ethnicity and weakest for labor market status.

Abstract. This article takes advantage of the sampling scheme of the French Labor Force Survey, which draws clusters of around thirty adjacent housing, to study several dimensions of residential segregation in France from 1968 to 2019. Such clusters form relevant neighborhoods to study residential segregation provided the indices account for the small-unit bias so that they can be compared over time or across different dimensions of segregation (French versus non-French people, jobseekers versus employed, college graduates versus non-graduate, white-collar versus blue-collar workers, etc.).
Applying the methodology developed in D’Haultfoeuille and Rathelot (Quantitative Economics, 2017) and Rathelot (Journal of Business and Economic Statistics, 2012), we estimate annual segregation indices for different specifications of the “minority” and “majority” groups, aiming to quantify several dimensions of residential segregation and compare them.
The results suggest two main conclusions.
First, whatever the dimension under study (ethnicity, immigrant, nationality, occupational category, labor market status, education), the estimated indices do not reveal any substantial evolution over time: within each dimension, the magnitude of residential segregation has remained globally constant for the past decades.
Second, they reveal the magnitude of segregation differs across the different dimensions according to the following decreasing ranking (in parentheses, order of magnitude of the corresponding Duncan segregation index, on average over the period 1968-2019):

– nationality (0.65)

– ethnicity, using as a proxy parents’ country of birth, and being an immigrant (0.50)

– social status, as measured by occupational category or college education (0.40)

– labor market status, specified here as unemployed or employed (0.25)

A conditional analysis, separating neighborhoods that belong to urban areas of 200,000 inhabitants or more from neighborhoods belonging to smaller urban areas, complements the unconditional analysis.

Joint work with: Xavier D’Haultfoeuille and Roland Rathelot.

In “Measuring Group Differences in High-Dimensional Choices: Method and Application to Congressional Speech” (Econometrica 2019), M. Gentzkow, J. M. Shapiro, and M. Taddy propose a novel method to quantify to which extent two exogenous groups make different choices among a set of alternatives or options. In the context of high-dimensional choices, that is only a few choices per option is observed, their method deals with the so-called small-unit bias, which, otherwise, precludes relevant comparisons over time or across settings. Such a problem arises in various applications: residential segregation between immigrants and natives; occupational segregation between men and women; speech polarization between Democrats and Republicans in the US Congress; etc. Their methodology relies on the penalized estimation of a structural discrete choice model. As a consequence, it requires data at the chooser-level (in the example of congressional speech, it means knowing the map between speeches and speaker identities). Moreover, as the number of possible options might be large (in the same example, the vocabulary is made of hundreds of thousands of distinct bigrams), they use a Poisson approximation and distributed computing to be able to perform the estimation. In this setting of high-dimensional choices, we propose an alternative method to estimate a polarization index. Our method has formal identification, estimation, and inference results under a simple and testable statistical model. Our estimators and confidence intervals have closed-form expressions, hence they are very light to compute. Besides, our method only uses aggregated data, namely the counts of choices per group and option.

History or status: a complete working paper version can be found in Chapter 3 of my PhD manuscript (link); slides (link). The project is currently resting since our main application (speech polarization) uses a bag-of-word approach, which is most likely superseded by more modern Natural Language Processing (NLP) methods, in particular word embedding. Nonetheless, the general methodological contribution (measuring group differences in high dimensional choice sets) remains relevant and can be interesting for other applications.

Takeaway. We develop a method to measure speech polarization in congressional discourse, showing that partisan language differences reached historic highs in 2008-2016 after rising since the 1980s-1990s.

Abstract. We quantify the extent to which Democrats and Republicans use different words during debates in the U.S. Congress. Such reliable measures are a prerequisite to study the causes or consequences of the polarization of political discourse. To do so, we propose a partially testable statistical framework, formal identification results for a speech polarization index, and easily computable estimators and confidence intervals for this index. The results suggest an increase in speech polarization starting in the 1980s-1990s, reaching its highest historical level between 2008 and 2016. However, this phenomenon is not entirely new as the analysis also reveals a period of relatively high polarization during the first decade of the XXth century and, to a lesser extent, around the 1930s.

Joint work with: Alexis Derumigny and Yannick Guyonvarch.

Ratios of expectations are frequent parameters of interest in applied economics. In particular, any conditional expectation can be expressed as such. Inference for these quantities usually stems from asymptotic normality and the delta method. Their properties are therefore only asymptotic. In settings where the denominator is close to zero, we document through simulations that the asymptotic approximation may require hundreds of thousands of observations. In finite samples, it entails that the confidence intervals used in practice can have a probability to contain the target parameter far below their nominal level. To address this issue, we investigate how to conduct reliable inference in settings with a denominator close to zero.

History or status: resting working paper arXiv:1904.07111 (we have reorganized the paper – dividing it to separate asymptotic and nonasymptotic results and extending the nonasymptotic results to linear regressions).

Abstract. In econometrics, many parameters of interest can be written as ratios of expectations. The main approach to construct confidence intervals for such parameters is the delta method. However, this asymptotic procedure yields intervals that may not be relevant for small sample sizes or, more generally, in a sequence-of-model framework that allows the expectation in the denominator to decrease to 0 with the sample size. In this setting, we prove a generalization of the delta method for ratios of expectations and the consistency of the nonparametric percentile bootstrap. We also investigate finite-sample inference and show a partial impossibility result: nonasymptotic uniform confidence intervals can be built for ratios of expectations but not at every level. Based on this, we propose an easy-to-compute index to appraise the reliability of the intervals based on the delta method. Simulations and an application illustrate our results and the practical usefulness of our rule of thumb.