arXiv subjects

Jean-Pierre Florens

Publications and source records attributed to Jean-Pierre Florens.

17 recordsLinked to original sources

arXiv2026

Identification and Estimation of Consumers' Preferences from Repeated Observations under Nonlinear Pricing

We develop a nonparametric approach to identify and estimate consumer preferences and unobserved heterogeneity under nonlinear price schedules. Leveraging variation across multiple price schedules, we show that both the utility function and the distribution of preference types can be nonparametrically identified. The quantile function of unobserved types becomes solution of a functional equation, and we derive conditions ensuring identification. We propose an iterative approach for estimation, in which the regularization bias decays exponentially in the number of iterations while the variance grows only polynomially, yielding a near-parametric convergence rate. We propose a valid bootstrap procedure for finite-sample inference and extend the framework to accommodate potential endogeneity of prices and additional observed heterogeneity. Monte Carlo simulations and an empirical application to data from a European mail carrier demonstrate how we can recover the utility functions and preference distributions in finite samples.

econ.EM↗

arXiv2025

Tests of exogeneity in duration models with censored data

Consider the setting in which a researcher is interested in the causal effect of a treatment $Z$ on a duration time $T$, which is subject to right censoring. We assume that $T=\varphi(X,Z,U)$, where $X$ is a vector of baseline covariates, $\varphi(X,Z,U)$ is strictly increasing in the error term $U$ for each $(X,Z)$ and $U\sim \mathcal{U}[0,1]$. Therefore, the model is nonparametric and nonseparable. We propose nonparametric tests for the hypothesis that $Z$ is exogenous, meaning that $Z$ is independent of $U$ given $X$. The test statistics rely on an instrumental variable $W$ that is independent of $U$ given $X$. We assume that $X,W$ and $Z$ are all categorical. Test statistics are constructed for the hypothesis that the conditional rank $V_T= F_{T \mid X,Z}(T \mid X,Z)$ is independent of $(X,W)$ jointly. Under an identifiability condition on $\varphi$, this hypothesis is equivalent to $Z$ being exogenous. However, note that $V_T$ is censored by $V_C =F_{T \mid X,Z}(C \mid X,Z)$, which complicates the construction of the test statistics significantly. We derive the limiting distributions of the proposed tests and prove that our estimator of the distribution of $V_T$ converges to the uniform distribution at a rate faster than the usual parametric $n^{-1/2}$-rate. We demonstrate that the test statistics and bootstrap approximations for the critical values have a good finite sample performance in various Monte Carlo settings. Finally, we illustrate the tests with an empirical application to the National Job Training Partnership Act (JTPA) Study.

econ.EM↗

arXiv2025

Panel data models with randomly generated groups

We develop a structural framework for modeling and inferring unobserved heterogeneity in dynamic panel-data models. Unlike methods treating clustering as a descriptive device, we model heterogeneity as arising from a latent clustering mechanism, where the number of clusters is unknown and estimated. Building on the mixture of finite mixtures (MFM) approach, our method avoids the clustering inconsistency issues of Dirichlet process mixtures and provides an interpretable representation of the population clustering structure. We extend the Telescoping Sampler of Fruhwirth-Schnatter et al. (2021) to dynamic panels with covariates, yielding an efficient MCMC algorithm that delivers full Bayesian inference and credible sets. We show that asymptotically the posterior distribution of the mixing measure contracts around the truth at parametric rates in Wasserstein distance, ensuring recovery of clustering and structural parameters. Simulations demonstrate strong finite-sample performance. Finally, an application to the income-democracy relationship reveals latent heterogeneity only when controlling for additional covariates.

econ.EM↗

arXiv2024

Iterative Estimation of Nonparametric Regressions with Continuous Endogenous Variables and Discrete Instruments

We consider a nonparametric regression model with continuous endogenous independent variables when only discrete instruments are available that are independent of the error term. Although this framework is very relevant for applied research, its implementation is challenging, as the regression function becomes the solution to a nonlinear integral equation. We propose a simple iterative procedure to estimate such models and showcase some of its asymptotic properties. In a simulation experiment, we detail its implementation in the case when the instrumental variable is binary. We conclude with an empirical application to returns to education.

econ.EM↗

arXiv2024

Debiasing Machine Learning Models by Using Weakly Supervised Learning

We tackle the problem of bias mitigation of algorithmic decisions in a setting where both the output of the algorithm and the sensitive variable are continuous. Most of prior work deals with discrete sensitive variables, meaning that the biases are measured for subgroups of persons defined by a label, leaving out important algorithmic bias cases, where the sensitive variable is continuous. Typical examples are unfair decisions made with respect to the age or the financial status. In our work, we then propose a bias mitigation strategy for continuous sensitive variables, based on the notion of endogeneity which comes from the field of econometrics. In addition to solve this new problem, our bias mitigation strategy is a weakly supervised learning method which requires that a small portion of the data can be measured in a fair manner. It is model agnostic, in the sense that it does not make any hypothesis on the prediction model. It also makes use of a reasonably large amount of input observations and their corresponding predictions. Only a small fraction of the true output predictions should be known. This therefore limits the need for expert interventions. Results obtained on synthetic data show the effectiveness of our approach for examples as close as possible to real-life applications in econometrics.

cs.LG↗

arXiv2023

Partly Linear Instrumental Variables Regressions without Smoothing on the Instruments

We consider a semiparametric partly linear model identified by instrumental variables. We propose an estimation method that does not smooth on the instruments and we extend the Landweber-Fridman regularization scheme to the estimation of this semiparametric model. We then show the asymptotic normality of the parametric estimator and obtain the convergence rate for the nonparametric estimator. Our estimator that does not smooth on the instruments coincides with a typical estimator that does smooth on the instruments but keeps the respective bandwidth fixed as the sample size increases. We propose a data driven method for the selection of the regularization parameter, and in a simulation study we show the attractive performance of our estimators.

econ.EM↗

arXiv2023

Testing for homogeneous treatment effects in linear and nonparametric instrumental variable models

The hypothesis of homogeneous treatment effects is central to the instrumental variables literature. This assumption signifies that treatment effects are constant across all subjects. It allows to interpret instrumental variable estimates as average treatment effects over the whole population of the study. When this assumption does not hold, the bias of instrumental variable estimators can be larger than that of naive estimators ignoring endogeneity. This paper develops two tests for the assumption of homogeneous treatment effects when the treatment is endogenous and an instrumental variable is available. The tests leverage a covariable that is (jointly with the error terms) independent of a coordinate of the instrument. This covariate does not need to be exogenous. The first test assumes that the potential outcomes are linear in the regressors and is computationally simple. The second test is nonparametric and relies on Tikhonov regularization. The treatment can be either discrete or continuous. We show that the tests have asymptotically correct level and asymptotic power equal to one against a range of alternatives. Simulations demonstrate that the proposed tests attain excellent finite sample performances. The methodology is also applied to the evaluation of returns to schooling and the effect of price on demand in a fish market.

econ.EM↗

arXiv2022

Instrumental variable estimation of dynamic treatment effects on a duration outcome

This paper considers identification and estimation of the causal effect of the time Z until a subject is treated on a survival outcome T. The treatment is not randomly assigned, T is randomly right censored by a random variable C and the time to treatment Z is right censored by min(T,C). The endogeneity issue is treated using an instrumental variable explaining Z and independent of the error term of the model. We study identification in a fully nonparametric framework. We show that our specification generates an integral equation, of which the regression function of interest is a solution. We provide identification conditions that rely on this identification equation. For estimation purposes, we assume that the regression function follows a parametric model. We propose an estimation procedure and give conditions under which the estimator is asymptotically normal. The estimators exhibit good finite sample properties in simulations. Our methodology is applied to find evidence supporting the efficacy of a therapy for burn-out.

math.ST↗

arXiv2022

Fairness constraint in Structural Econometrics and Application to fair estimation using Instrumental Variables

A supervised machine learning algorithm determines a model from a learning sample that will be used to predict new observations. To this end, it aggregates individual characteristics of the observations of the learning sample. But this information aggregation does not consider any potential selection on unobservables and any status-quo biases which may be contained in the training sample. The latter bias has raised concerns around the so-called \textit{fairness} of machine learning algorithms, especially towards disadvantaged groups. In this chapter, we review the issue of fairness in machine learning through the lenses of structural econometrics models in which the unknown index is the solution of a functional equation and issues of endogeneity are explicitly accounted for. We model fairness as a linear operator whose null space contains the set of strictly {\it fair} indexes. A {\it fair} solution is obtained by projecting the unconstrained index into the null space of this operator or by directly finding the closest solution of the functional equation into this null space. We also acknowledge that policymakers may incur a cost when moving away from the status quo. Achieving \textit{approximate fairness} is obtained by introducing a fairness penalty in the learning procedure and balancing more or less heavily the influence between the status quo and a full fair solution.

econ.EM↗

arXiv2021

Revisiting identification concepts in Bayesian analysis

This paper studies the role played by identification in the Bayesian analysis of statistical and econometric models. First, for unidentified models we demonstrate that there are situations where the introduction of a non-degenerate prior distribution can make a parameter that is nonidentified in frequentist theory identified in Bayesian theory. In other situations, it is preferable to work with the unidentified model and construct a Markov Chain Monte Carlo (MCMC) algorithms for it instead of introducing identifying assumptions. Second, for partially identified models we demonstrate how to construct the prior and posterior distributions for the identified set parameter and how to conduct Bayesian analysis. Finally, for models that contain some parameters that are identified and others that are not we show that marginalizing out the identified parameter from the likelihood with respect to its conditional prior, given the nonidentified parameter, allows the data to be informative about the nonidentified and partially identified parameter. The paper provides examples and simulations that illustrate how to implement our techniques.

econ.EM↗

arXiv2021

A nonparametric instrumental approach to endogeneity in competing risks models

This paper discusses endogenous treatment models with duration outcomes, competing risks and random right censoring. The endogeneity issue is solved using a discrete instrumental variable. We show that the competing risks model generates a non-parametric quantile instrumental regression problem. The cause-specific cumulative incidence, the cause-specific hazard and the subdistribution hazard can be recovered from the regression function. A distinguishing feature of the model is that censoring and competing risks prevent identification at some quantiles. We characterize the set of quantiles for which exact identification is possible and give partial identification results for other quantiles. We outline an estimation procedure and discuss its properties. The finite sample performance of the estimator is evaluated through simulations. We apply the proposed method to the Health Insurance Plan of Greater New York experiment.

stat.ME↗

arXiv2021

Are Unobservables Separable?

It is common to assume in empirical research that observables and unobservables are additively separable, especially, when the former are endogenous. This is done because it is widely recognized that identification and estimation challenges arise when interactions between the two are allowed for. Starting from a nonseparable IV model, where the instrumental variable is independent of unobservables, we develop a novel nonparametric test of separability of unobservables. The large-sample distribution of the test statistics is nonstandard and relies on a novel Donsker-type central limit theorem for the empirical distribution of nonparametric IV residuals, which may be of independent interest. Using a dataset drawn from the 2015 US Consumer Expenditure Survey, we find that the test rejects the separability in Engel curves for most of the commodities.

math.ST↗

arXiv2019

Gaussian processes and Bayesian moment estimation

Given a set of moment restrictions (MRs) that overidentify a parameter $θ$, we investigate a semiparametric Bayesian approach for inference on $θ$ that does not restrict the data distribution $F$ apart from the MRs. As main contribution, we construct a degenerate Gaussian process prior that, conditionally on $θ$, restricts the $F$ generated by this prior to satisfy the MRs with probability one. Our prior works even in the more involved case where the number of MRs is larger than the dimension of $θ$. We demonstrate that the corresponding posterior for $θ$ is computationally convenient. Moreover, we show that there exists a link between our procedure, the Generalized Empirical Likelihood with quadratic criterion and the limited information likelihood-based procedures. We provide a frequentist validation of our procedure by showing consistency and asymptotic normality of the posterior distribution of $θ$. The finite sample properties of our method are illustrated through Monte Carlo experiments and we provide an application to demand estimation in the airline market.

math.ST↗

arXiv2019

Overt and covert paths for sound in the auditory system of mammals

Current scientific consensus holds that sound is transmitted, solely mechanically, from the tympanum to the cochlea via ossicles. But this theory does not explain the hearing extreme quality regarding high frequencies in mammals. So, we propose a bioelectronic pathway (the covert path) that is complementary to the overt path.. We demonstrate experimentally that the tympanum produces piezoelectric potentials isochronous to acoustic vibrations thanks to its collagen fibers and that their amplitude increases along with the frequency and level of the vibrations. This finding supports the existence of an electrical pathway, specialized in transmitting high-frequency sounds, that works in unison with the mechanical pathway. A bio-organic triode, similar to a field effect transistor, is the key mechanism of our hypothesized pathway. We present evidence that any deficiency along this pathway produces hearing impairment. By augmenting the classical theory of sound transmission, our discovery offers new perspectives for research into both normal and pathological audition and may contribute to an understanding of genetic and physiological problems of hearing.

q-bio.TO↗

arXiv2017

Is completeness necessary? Estimation in nonidentified linear models

Modern data analysis depends increasingly on estimating models via flexible high-dimensional or nonparametric machine learning methods, where the identification of structural parameters is often challenging and untestable. In linear settings, this identification hinges on the completeness condition, which requires the nonsingularity of a high-dimensional matrix or operator and may fail for finite samples or even at the population level. Regularized estimators provide a solution by enabling consistent estimation of structural or average structural functions, sometimes even under identification failure. We show that the asymptotic distribution in these cases can be nonstandard. We develop a comprehensive theory of regularized estimators, which include methods such as high-dimensional ridge regularization, gradient descent, and principal component analysis (PCA). The results are illustrated for high-dimensional and nonparametric instrumental variable regressions and are supported through simulation experiments.

math.ST↗

arXiv2013

Iterative Estimation of Solutions to Noisy Nonlinear Operator Equations in Nonparametric Instrumental Regression

This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model. This is illustrated in computed examples with simulated data.

math.NA↗

arXiv2010

Frontier estimation and extreme value theory

In this paper, we investigate the problem of nonparametric monotone frontier estimation from the perspective of extreme value theory. This enables us to revisit the asymptotic theory of the popular free disposal hull estimator in a more general setting, to derive new and asymptotically Gaussian estimators and to provide useful asymptotic confidence bands for the monotone boundary function. The finite-sample behavior of the suggested estimators is explored via Monte Carlo experiments. We also apply our approach to a real data set based on the production activity of the French postal services.

math.ST↗