arXiv subjects

Xavier D'Haultfœuille

Publications and source records attributed to Xavier D'Haultfœuille.

16 recordsLinked to original sources

arXiv2026

Difference-in-Differences Estimators When No Unit Remains Untreated

We study difference-in-differences designs in which all units are initially untreated and later receive heterogeneous, strictly positive treatment doses. When quasi-untreated units receive doses close to zero, a difference-in-difference estimand using those units as the control group identifies a weighted average treatment effect per unit of treatment, under a parallel-trends assumption. We develop a nonparametric estimator and bias-corrected confidence intervals for this parameter. We also show that the assumptions justifying the usual two-way fixed-effects estimator imply testable linearity restrictions, and propose specification tests that can guide its use.

econ.EM↗

arXiv2026

Is Inference Conditional on Not Rejecting a Pre-test Less Reliable than Unconditional Inference?

Researchers often report an estimate and confidence interval only if a specification test does not reject - for example, only if a pre-trend test supports a difference-in-differences design. Does this make the reported confidence interval less reliable? We show that when the identifying assumptions hold, the answer is no: conditional on passing the pre-test, the confidence interval may over-cover but cannot under-cover. When the assumptions fail, pre-testing can reduce coverage, but under an additional condition it still improves coverage relative to not pre-testing. A calibration to 12 differences-in-differences examples suggests modest effects of pre-testing on coverage.

econ.EM↗

arXiv2026

Instrument-Free Demand Estimation Using Relative Prices Variation, with an Application to Railway Transportation

We develop a new identification strategy for demand estimation when cost shifters may not be available and there are substantial variations in demand over time. This approaches relies on a kind of nonlinear difference-in-differences, in which price elasticities are identified by relating changes over time in relative purchases between two goods to changes in their relative prices. We apply this strategy to the context of French railway transportation. Our price elasticity estimates are in line with those on airlines, but substantially higher, in absolute terms, than those generally obtained on railway transportation. We then use our demand estimation to compare the current pricing with several counterfactual pricing strategies. Our results suggest similar or better performance of the actual revenue management compared to optimal uniform pricing, but also substantial losses compared to the optimal pricing strategy. Finally, we highlight the key role of revenue management in acquiring information when demand is uncertain.

econ.GN↗

arXiv2026

Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period

When studying the effects of taxes, tariffs, or prices using panel data, the treatment is often continuously distributed in every period. We develop difference-in-differences (DID) estimators for such settings. We partition units into switchers, whose treatment changes between consecutive periods, and stayers, whose treatment remains constant. Under a parallel-trends assumption, we show that the slopes of switchers' potential outcomes with respect to the treatment are nonparametrically identified by DID comparisons between switchers and stayers sharing the same baseline treatment level. Conditioning on the baseline treatment is key, as it ensures that the underlying parallel-trends assumption accommodates time-varying treatment effects. We then study two weighted averages of these slopes, discuss their respective advantages, and propose for each a doubly robust, semiparametrically efficient, and $\sqrt{n}$-consistent estimator. Finally, we extend our framework to instrumental variables and illustrate it by estimating the effects of gasoline taxes on prices and fuel consumption.

econ.EM↗

arXiv2026

Asymptotic Properties of Empirical Quantile-Based Estimators

We consider inference for parameters of the form $θ_0 = E[F_Y^{-1}\circ F_Z(X)]$ for some variables $X$, $Y$ and $Z$. Such parameters appear, in particular, in the ``changes-in-changes'' model of \cite{AtheyImbens2006}. We first establish that $\widehatθ$, a plug-in estimator of $θ_0$, is root-$n$ consistent and asymptotically normal under weaker conditions than those previously available, allowing in particular for unbounded variables. Next, we propose a new estimator of the asymptotic variance of $\widehatθ$ and show its consistency, also allowing for unbounded variables. Monte Carlo simulations suggest that the conditions for root-$n$ consistency and asymptotic normality are, in some sense, minimal. These simulations highlight that our variance estimator also leads to more accurate inference than some alternative approaches.

econ.EM↗

arXiv2026

Difference-in-Differences Estimators of Intertemporal Treatment Effects

We study treatment-effect estimation using panel data. The treatment may be non-binary, non-absorbing, and the outcome may be affected by treatment lags. We make a parallel-trends assumption, and propose event-study estimators of the effect of being exposed to a weakly higher treatment dose for $\ell$ periods. We also propose normalized estimators, that estimate a weighted average of the effects of the current treatment and its lags. We also analyze commonly-used two-way fixed-effects regressions. Unlike our estimators, they can be biased in the presence of heterogeneous treatment effects. A local-projection version of those regressions is biased even with homogeneous effects.

econ.EM↗

arXiv2026

Analytic inference with two-way clustering

This paper studies analytic inference along two dimensions of clustering. In such setups, the commonly used approach has two drawbacks. First, the corresponding variance estimator is not necessarily positive. Second, inference is invalid in non-Gaussian regimes, namely when the estimator of the parameter of interest is not asymptotically Gaussian. We consider a simple fix that addresses both issues. In Gaussian regimes, the corresponding tests are asymptotically exact and equivalent to usual ones. Otherwise, the new tests are asymptotically conservative. We also establish their uniform validity over a certain class of data generating processes. Independently of our tests, we highlight potential issues with multiple testing and nonlinear estimators under two-way clustering. Finally, we compare our approach with existing ones through simulations.

econ.EM↗

arXiv2025

Treatment-Effect Estimation in Complex Designs under a Parallel-trends Assumption

This paper considers the identification of dynamic treatment effects with panel data, in complex designs where the treatment may not be binary and may not be absorbing. We first show that under no-anticipation and parallel-trends assumptions, we can identify event-study effects comparing outcomes under the actual treatment path and under the status-quo path where all units would have kept their period-one treatment throughout the panel. Those effects can be helpful to evaluate ex-post the policies that effectively took place, and once properly normalized they estimate weighted averages of marginal effects of the current and lagged treatments on the outcome. Yet, they may still be hard to interpret, and they cannot be used to evaluate the effects of other policies than the ones that were conducted. To make progress, we impose another restriction, namely a random coefficients distributed-lag linear model, where effects remain constant over time. Under this model, the usual distributed-lag two-way-fixed-effects regression may be misleading. Instead, we show that this random coefficients model can be estimated simply. We illustrate our findings by revisiting Gentzkow, Shapiro and Sinkinson (2011).

econ.EM↗

arXiv2024

Identification and Estimation of Average Causal Effects in Fixed Effects Logit Models

This paper studies identification and estimation of average causal effects, such as average marginal or treatment effects, in fixed effects logit models with short panels. Relating the identified set of these effects to an extremal moment problem, we first show how to obtain sharp bounds on such effects simply, without any optimization. We also consider even simpler outer bounds, which, contrary to the sharp bounds, do not require any first-step nonparametric estimators. We build confidence intervals based on these two approaches and show their asymptotic validity. Monte Carlo simulations suggest that both approaches work well in practice, the second being typically competitive in terms of interval length. Finally, we show that our method is also useful to measure treatment effect heterogeneity.

econ.EM↗

arXiv2024

Difference-in-Differences Estimators with Continuous Treatments and no Stayers

Many treatments or policy interventions are continuous in nature. Examples include prices, taxes or temperatures. Empirical researchers have usually relied on two-way fixed effect regressions to estimate treatment effects in such cases. However, such estimators are not robust to heterogeneous treatment effects in general; they also rely on the linearity of treatment effects. We propose estimators for continuous treatments that do not impose those restrictions, and that can be used when there are no stayers: the treatment of all units changes from one period to the next. We start by extending the nonparametric results of de Chaisemartin et al. (2023) to cases without stayers. We also present a parametric estimator, and use it to revisit Deschênes and Greenstone (2012).

econ.EM↗

arXiv2023

A Robust Permutation Test for Subvector Inference in Linear Regressions

We develop a new permutation test for inference on a subvector of coefficients in linear models. The test is exact when the regressors and the error terms are independent. Then, we show that the test is asymptotically of correct level, consistent and has power against local alternatives when the independence condition is relaxed, under two main conditions. The first is a slight reinforcement of the usual absence of correlation between the regressors and the error term. The second is that the number of strata, defined by values of the regressors not involved in the subvector test, is small compared to the sample size. The latter implies that the vector of nuisance regressors is discrete. Simulations and empirical illustrations suggest that the test has good power in practice if, indeed, the number of strata is small compared to the sample size.

econ.EM↗

arXiv2023

Partially Linear Models under Data Combination

We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics. Using recent tools from optimal transport theory, we derive a constructive characterization of the sharp identified set. We then build on this result and develop a novel inference method that exploits the specific geometric properties of the identified set. Our method exhibits good performances in finite samples, while remaining very tractable. We apply our approach to study intergenerational income mobility over the period 1850-1930 in the United States. Our method allows us to relax the exclusion restrictions used in earlier work, while delivering confidence regions that are informative.

econ.EM↗

arXiv2023

Two-way Fixed Effects and Differences-in-Differences Estimators with Several Treatments

We study two-way-fixed-effects regressions (TWFE) with several treatment variables. Under a parallel trends assumption, we show that the coefficient on each treatment identifies a weighted sum of that treatment's effect, with possibly negative weights, plus a weighted sum of the effects of the other treatments. Thus, those estimators are not robust to heterogeneous effects and may be contaminated by other treatments' effects. We further show that omitting a treatment from the regression can actually reduce the estimator's bias, unlike what would happen under constant treatment effects. We propose an alternative difference-in-differences estimator, robust to heterogeneous effects and immune to the contamination problem. In the application we consider, the TWFE regression identifies a highly non-convex combination of effects, with large contamination weights, and one of its coefficients significantly differs from our heterogeneity-robust estimator.

econ.EM↗

arXiv2022

Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey

Linear regressions with period and group fixed effects are widely used to estimate policies' effects: 26 of the 100 most cited papers published by the American Economic Review from 2015 to 2019 estimate such regressions. It has recently been shown that those regressions may produce misleading estimates, if the policy's effect is heterogeneous between groups or over time, as is often the case. This survey reviews a fast-growing literature that documents this issue, and that proposes alternative estimators robust to heterogeneous effects. We use those alternative estimators to revisit Wolfers (2006).

econ.EM↗

arXiv2020

Empirical MSE Minimization to Estimate a Scalar Parameter

We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an assumption is satisfied. We propose to use the weighted sum of the two estimators with the lowest estimated mean-squared error (MSE). We show that this third estimator dominates the other two from a minimax-regret perspective: the maximum asymptotic-MSE-gain one may incur by using this estimator rather than one of the other estimators is larger than the maximum asymptotic-MSE-loss.

math.ST↗

arXiv2020

Two-way fixed effects estimators with heterogeneous treatment effects

Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they estimate weighted sums of the average treatment effects (ATE) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression coefficient may for instance be negative while all the ATEs are positive. We propose another estimator that solves this issue. In the two applications we revisit, it is significantly different from the linear regression estimator.

econ.EM↗