Working Papers

Authors: Clément de Chaisemartin (Sciences Po Paris), Diego Ciccia (Northwestern University), Xavier D'Haulfoeuille (CREST-ENSAE Paris), Felix Knau (University of Munich)

Abstract: We consider treatment-effect estimation under a parallel trends assumption, in designs where no unit is treated at period one, all units receive a strictly positive dose at period two, and the dose varies across units. There are therefore no true control groups in such cases. First, we develop a test of the assumption that the treatment effect is mean independent of the treatment, under which the commonly-used two-way-fixed-effects estimator is consistent. When this test is rejected or lacks power, we propose alternative estimators, robust to heterogeneous effects. If there are units with a period-two treatment arbitrarily close to zero, the robust estimator is a difference-in-difference using units with a period-two treatment below a bandwidth as controls. Without such units, we propose non-parametric bounds, and an estimator relying on a parametric specification of treatment-effect heterogeneity. We use our results to revisit Pierce and Schott (2016) and Enikolopov et al. (2011).

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Authors: Laurent Davezies (CREST-ENSAE Paris), Xavier D'Haultfoeuille (CREST-ENSAE Paris), Louise Laage (Georgetown University)

Abstract: 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.

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Authors: Clément de Chaisemartin (Sciences Po Paris), Xavier D'Haultfoeuille (CREST-ENSAE Paris)

Abstract: Consider a parameter of interest, which can be consistently estimated under some conditions. Suppose also that we can at least partly test these conditions with specification tests. We consider the common practice of conducting inference on the parameter of interest conditional on not rejecting these tests. We show that if the tested conditions hold, conditional inference is valid, though possibly conservative. This holds generally, without imposing any assumption on the asymptotic dependence between the estimator of the parameter of interest and the specification test.

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Authors: Xavier D'Haultfoeuille (CREST-ENSAE Paris), Christophe Gaillac (University of Geneva), Arnaud Maurel (Duke University)

Abstract: We study best linear predictions in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Traditional approaches obtain point identification by relying, often implicitly, on exclusion restrictions. We show that without such restrictions, coefficients of interest can still be partially identified and we derive a constructive characterization of the sharp identified set. We then build on this characterization to develop computationally simple and asymptotically normal estimators of the corresponding bounds. We show that these estimators exhibit good finite sample performances.

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Authors: Marion Leroutier (CREST-ENSAE Paris), Hélène Ollivier (Paris School of Economics)

Abstract: This paper shows that even moderate air pollution levels can reduce economic activity. Using monthly firm-level data from France and exploiting variation in PM2.5 exposure driven by changes in local wind direction, we find that a 10% increase in pollution decreases firm sales by 0.4% over the following two months. Effects vary by sector and operate through reduced labor supply —with a 1% increase in sick leave— lower productivity, and demand-side responses. Our results suggest that aligning air quality with WHO guidelines could generate economic benefits comparable to the costs of regulation or the health benefits from reduced mortality.

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Authors: Bertrand Garbinti (CREST-ENSAE Paris), Cecilia Garcia-Peñalosa (Aix-Marseille University), Vladimir Pecheu (Paris School of Economics), Frédérique Savignac (Banque de France)

Abstract: Using a long administrative panel dataset for France, we analyse the dynamics and drivers of the narrowing gender gap in lifetime earnings (LTE) for cohorts born after WWII. We find that the level, trends, and distribution of gender differences in LTE contrast sharply with those observed in the US, and that these differences are more marked than when we compare cross-sectional gender gaps. We show that this reflects a specific pattern in which both men and women experienced earnings gains over the whole distribution (with the exception of the very top), in contrast with the US, where the same cohorts of men experienced earnings losses in the three bottom quartiles of the distribution. We then decompose the changing role of various factors (e.g., working (part) time, education, occupation, geographical location) in shaping the evolution of the gender LTE gap in France. The contribution of unobserved factors decreases across cohorts and increases along the distribution, remaining larger at the top, consistent with a glass ceiling effect. Meanwhile, the impact of observed factors rises, mostly due to the decline in the years worked full time by women, which has slowed gender convergence. Differences in educational attainment contribute to a lesser extent, as the gender gap in returns to education has narrowed.

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Authors: Lionel Wilner (CREST-ENSAE Paris), Philippe Choné (CREST-ENSAE Paris)

Abstract: To empirically assess how physicians respond to financial incentives, we leverage a quasi-natural experiment in France where most GPs’ fees are regulated. In 2017, a wide-scale regulatory change caused the price of a visit to increase from e23 to e25. Relying on granular claims data covering the universe of patients, doctors, and visits, we show that physician activity grew by nearly 9% after the price increase, yielding a unitary price elasticity of healthcare provision. The number of distinct patients examined increased substantially, while the provision of medical services per patient hardly changed, resulting in a slight increase in physicians’ number of days worked. Drug prescription per patient is also shown to decrease, suggesting that the policy was cost-effective and enhanced access to healthcare, with limited adverse effects. Earlycareer physicians responded strongly to these financial incentives, while later-career physicians hardly changed their labor supply behavior.

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Authors: Carole Bonnet (INED), Léa Dubreuil (CREST-ENSAE Paris), Bertrand Garbinti (CREST-ENSAE Paris), Pierre Pora (INSEE)

Abstract: Using a rich administrative dataset representative of the French population, we study the causal impact of the first childbirth on the within-couple inequality in France. We find that women’s contribution to total household income 5 years after the birth of their first child is 16% lower than what it would have been absent children. Both partners experience an income loss after childbirth, driven by a decline in working hours. However, the drop is much larger for women: 23% for women and 4% for men five years after childbirth. The drop in woman’s contribution to total household income after childbirth is more pronounced for women with a higher contribution to couple’s income before childbirth. This is both because the child penalty is higher for these women compared to others, and because their partners experience the largest increase in income following childbirth compared to other partners. Moreover, heterogeneous responses across couples reshape the entire distribution of withincouple inequality, notably through a sharp decline in the share of egalitarian couples, while the share of female-breadwinner couples slightly decreases but remains closed to its already low level.

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Authors: Stéphane Auray (CREST-ENSAI), Aurélien Eyquem (University of Lausanne), Bertrand Garbinti (CREST-ENSAE Paris), Jonathan Goupille-Lebret (CNRS-ENS Lyon)

Abstract: We study the dynamics of income and wealth inequality using a heterogeneous-agent model that combines endogenous portfolio choice, a granular representation of the tax-andtransfer system, and a reduced-form mechanism linking markups to top incomes through entrepreneurial risk. Driven by changes in taxation, markups, and asset prices, the model accounts for the observed trends in income and wealth inequality in France since 1984, up to the top 1% income and wealth shares. We combine counterfactual simulations with a simple accounting decomposition of wealth accumulation to assess the contributions of these driving forces to inequality dynamics and to identify the channels through which they operate. We identify rising markups as the primary driver of income inequality, while all three forces– taxation, markups, and asset prices– contribute significantly to wealth inequality. Our findings highlight both the mechanical impact of differential asset price movements and the central role of endogenous saving responses in shaping wealth inequality over time.

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Authors: Marco Caliendo (University of Potsdam), Deborah A. Cobb-Clark (University of Sydney), Katrin Huber (University of Potsdam), Harald Pfeifer (Federal Institute for Vocational Education and Training), Arne Uhlendorff (CREST-CNRS), Sophie Wagner (University of Potsdam)

Abstract: We examine how gender shapes managers’ decisions regarding on-the-job training using a discrete choice experiment embedded in a representative survey of German firms. While previous research on training has focused on employees’ demand for it, we make a contribution by studying firms’ supply of training. In our vignette study, 1,144 managers evaluate hypothetical candidate profiles that differ by gender, age, competence, job mobility, and training characteristics. We find that women are somewhat more likely than men to receive training offers. The exceptions are that female managers are more reluctant to choose young women for training, while male managers favor male candidates for fully employer-funded training. These patterns persist across various model specifications and remain robust when controlling for observable manager characteristics. Heterogeneity analyses reveal that female managers are more reluctant to offer training to women when they operate in competitive product markets, male-dominated industries, and firms without collective bargaining agreements. More broadly, our results highlight that managers influence not only how much training is undertaken, but also how training opportunities are distributed among employees. This has the potential to create gender disparities in early career development that may have implications for organizational equity.

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Authors: Laurent Bach (ESSEC Business School), Antoine Bozio (Paris School of Economics), Arthur Guillouzouic (AMSE), Clément Malgouyres (CREST-CNRS)

Abstract: We link French households’ tax records to the corporations they control, and build a payout-policy–neutral income measure, with corresponding tax burdens including those of "billionaires": the top 0.0002%. Def ined as such, income is more concentrated than taxable income, it better predicts rich-list membership, and persists more among billionaires. Personal taxes remain progressive until the top 0.1%, but eventually decline to 2% of income. Corporate taxes are an imperfect progressive backstop, as total tax rates fall from 45% at the 0.1% threshold to 25% for billionaires. Among these, the tax burden is global and tax-efficient pyramidal control over businesses ubiquitous.

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Authors: Matteo Mogliani (Banque de France), Anna Simoni (CREST-CNRS)

Abstract: We construct optimal macroeconomic density forecasts in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is designed for a general model which encompasses forecasting models featuring either many covariates, or unknown nonlinearities, or series sampled at different frequencies. By relying on the novel concept of bi-level sparsity in time-series econometrics, our density forecasts are based on a prior that induces sparsity both at the group level and within groups. We demonstrate the consistency of both the predictive density and the posterior distribution of the model parameter. For the posterior distribution, we show that it contracts at the minimax-optimal rate and, asymptotically, puts mass on a set that includes the support of the model. While predictors in the same group are usually characterized by strong covariation and common characteristics and patterns, our theory allows for correlation even between groups. Finite sample performance is illustrated through Monte Carlo experiments and a real-data nowcasting exercise of the US GDP growth rate.

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Authors: Marion Brouard (CREST-ENSAE Paris), Léa Dubreuil (CREST-ENSAE Paris)

Abstract: This paper investigates the respective roles of labor market constraints, childcare constraints, and maternal preferences in driving both the post-childbirth drop in mothers’ working hours and their limited responsiveness to family policies. We develop a labor supply model that incorporates preferences for maternal care and conduct a survey of 1,400 highly educated women. We find that a substantial share of the post-birth decline in hours worked reflects unconstrained choices, suggesting that the reduction in hours for this group is unlikely to be dropped by policies that solely target constraints. We show that while both labor market and childcare constraints shape mothers’ working hours, their effects are heterogeneous and, on average, offsetting, as constraints lead some women to work less than they would like, but others to work more. Consistent with the literature, we find that childcare subsidies have no net effect on hours worked, as heterogeneous constraint effects lead to varied positive and negative responses to the policy, which cancel each other out. Yet, these policies do effectively relax childcare constraints, thereby aligning actual drop in labor supply more closely with mothers’ preferences. Finally, we examine the role of social norms and beliefs and find that perceived returns to maternal care on child well-being significantly influence mothers’ preferences to stay at home.

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Authors: Pauline Rossi (CREST-École polytechnique), Yun Xiao (University of Gothenburg)

Abstract: Marriage is declining in China. Among singles, the probability to marry in 2019 was twice as low as in 1999. We estimate a Choo and Siow (2006b) model using census data to quantify the relative roles of changes in population structure and changes in marital surplus, i.e., value of marriage. We find that the increase in the supply of educated people explains half of the decline, partly due to a mismatch between educated women and less-educated men. The deterioration of female-to-male ratio, known as the marriage squeeze, explains an additional 18% for men. The decrease in surplus explains the rest.

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