Paris Econometrics

We consider the identification of matching models of the labor market in which firms and workers are ex ante heterogeneous in the presence of symmetric uncertainty and learning about worker ability and stochastic human capital acquisition by workers. We allow initial ability and acquired human capital to be general across firms to varying degrees. We establish conditions under which the primitives of these models are identified based on data on workers’ jobs and wages. We then investigate the ability of existing measures of assortativeness of matching to detect the degree of sorting implied by the class of models we consider. We propose a new measure of matching assortativeness that accounts for the evolving uncertainty about workers’ ability and workers’ accumulating human capital. Based on this measure, we assess the extent to which changes in the patterns of labor market sorting, resulting from changes in the distribution of workers’ ability, uncertainty about workers’ ability, and the returns to human capital acquisition, have accounted for the increase in wage inequality documented the United States over the past 30 years or so.

We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test statistic is a discrete analogue of a new optimal transport characterization of the sharp identified region. Both test statistic and critical values rely on simulation drawn from the distribution of latent variables and are computed using solutions to discrete optimal transport, hence linear programming problems. We also propose a fast preliminary search in the parameter space with an alternative, more conservative yet consistent test, based on a parameter free critical value.

Linear models are widely used in applied work. In this talk I explore what can be learned if some coefficients are heterogeneous and unrestricted. In a panel data setting, this corresponds to having a coefficient varying unrestrictedly across units and time periods. I mostly focus on which linear combinations of the coefficients, such as weighted averages, are identified, while also studying the identification of variances. I study three regimes, when the covariates are strictly exogenous, endogenous, and sequentially exogenous, and characterize conditions for identification in each case. I illustrate the analysis by revisiting the impact of smoking during pregnancy on the weight of children at birth.

This paper shows that kinks or discontinuities in economic incentive schemes, such as taxes or subsidies, simultaneously identify agents’ inten- sive and participation margin responses. The proposed semi-nonparametric estimator enables the evaluation of such schemes when existing kink and discontinuity methods are inapplicable due to the presence of both mar- gins. The paper applies the estimator to evaluate the German subsidy for rooftop solar panels, a cornerstone of global climate policies. Due to sizeable responses at both margins, nonlinearities in the programme only modestly increase its cost-effectiveness. The results highlight the impor- tance of simultaneously estimating both margins for optimal policy design.

I propose an approach to measure proportional treatment effects for multiplicative difference-in-differences models. TWFE (two-way fixed effect) linear estimators do not recover difference-in-differences estimates in the presence of staggered treatment. I show that this issue extends to Poisson-Pseudo Maximum Likelihood estimators. In the linear case, robust estimators exist to recover correct DiD estimates, but these approaches do not extend to PPML, as aggregation is challenging in the non-linear case. This paper develops an estimator robust to TWFE staggered bias for PPML, which recovers a quantity with a similar interpretation as in the canonical 2-by-2 model: the Ratio-of-Ratios.

We present a simulation-based inference approach for two-stage estimators, focusing on extremum estimators in the second stage. We accommodate a broad range of first-stage estimators, including extremum estimators, high-dimensional estimators, and other types of estimators such as Bayesian estimators. The key contribution of our approach lies in its ability to estimate the asymptotic distribution of two-stage estimators, even when the distributions of both the first- and second-stage estimators are non-normal and when the second-stage estimator’s bias, scaled by the square root of the sample size, does not vanish asymptotically. This enables reliable inference in situations where standard methods fail. Additionally, we propose a debiased estimator, based on the mean of the estimated distribution function, which exhibits improved finite sample properties. Unlike resampling methods, our approach avoids the need for multiple calculations of the two-stage estimator. We illustrate the effectiveness of our method in an empirical application on peer effects in adolescent fast-food consumption, where we address the issue of biased instrumental variable estimates resulting from many weak instruments.

The time at which renewable (e.g., solar or wind) energy resources produce electricity cannot generally be controlled. In many settings, however, consumers have some flexibility in their energy consumption needs, and there is growing interest in demand-response programs that leverage this flexibility to shift energy consumption to better match renewable production — thus enabling more efficient utilization of these resources. We study optimal demand response in a setting where consumers use home energy management systems (HEMS) to autonomously adjust their electricity consumption. Our core assumption is that HEMS operationalize flexibility by querying the consumer for their preferences and computing the “indifference set” of all energy consumption profiles that can be used to satisfy these preferences. Then, given an indifference set, HEMS can respond to grid signals while guaranteeing user-defined comfort and functionality; e.g., if a consumer sets a temperature range, a HEMS can precool and preheat to align with peak renewable production, thus improving efficiency without sacrificing comfort. We show that while price-based mechanisms are not generally optimal for demand response, they become asymptotically optimal in large markets under a mean-field limit. Furthermore, we show that optimal dynamic prices can be efficiently computed in large markets by only querying HEMS about their planned consumption under different price signals. Using an OpenDSS-powered grid simulation for Phoenix, Arizona, we demonstrate that our approach enables meaningful demand response without creating grid instability.

This paper considers nonparametric identification and estimation of the regression function when a covariate is mismeasured. The measurement error need not be classical. Employing the small measurement error approximation, we establish nonparametric identification under weak and easy-to-interpret conditions on the instrumental variable. The paper also provides nonparametric estimators of the regression function and derives their rates of convergence.

Standard errors become irrelevant for quantifying estimation precision of unbiased estimators with infinite variance. I study a distinct condition that implies certain unbiased estimators can only have infinite variance. I analyse model overspecifications that arise in empirical economic studies and satisfy this condition, such as modelling self-selection, endogenous switching, or skewness, without knowing that these are not characteristics of the unknown population. I describe a non-standard confidence interval to quantify estimation precision in these models.