A Nonparametric Finite Mixture Approach to Difference-in-Difference Estimation, with an Application to On-the-job Training and Wages (with Oliver Cassagneau-Francis, Robert Gary-Bobo and Julie Pernaudet). December 2024.
We develop a finite-mixture framework for nonparametric difference-in-differences analysis with unobserved heterogeneity correlating treatment and outcome. Our framework includes an instrumental variable for the treatment, and we prove non- parametric identification. We can thus relax the single index and stationarity as- sumptions of Athey and Imbens (2006) at the cost of adding slightly more structure on unobserved heterogeneity. We apply our framework to evaluate the effect of on-the-job training on wages, using novel French linked employee-employer data. Estimating a parametric version of our model with the help of an EM-algorithm, we find small ATEs and ATTs on hourly wages, around 4% in the year of training, falling to under 2% in the following year.
Culture and marriage: Lessons from German reunification (with Marion Goussé and Nicolas Jacquemet). Novembre 2023
In this paper, we compare and contrast East and West Germany after reunification in 1989 in terms of marriage sorting by education, wages and cultural preferences, and in terms of male and female time uses (wage work, leisure and housework). Recent work by Lippman et al. (2020) shows that female labor supply drops rapidly when the wife earns more than the husband in the West, but not in the East. In this paper, we try to understand what factors explain this fact, and whether there is a family norm in the West that prevents couples where the wife earns more than the husband to form and last, which is absent in the East. To this end, we develop a search-matching/Nash bargaining model of marriage formation and divorce, and intra-household resource allocation. The model parameters are independent of the region of Germany, conditional on individual wages, education, and cultural preferences (attitudes, activities and religion), whose distributions are assumed to be exogenous and gender- and region-specific. We estimate 4 independent models in four 7-year periods (1992-1998, 1999-2005, 2006-2012, 2013-2019) using the GSOEP. The model fits the data very well. We then use the estimated model to measure how much of the observed differences between East and West (time uses and marriage sorting) are due to differences and changes in education, wages and cultural identity. Cultural identity is found to be the main factor before education and wages. It explains half of differences in time uses and marriage sorting on observables between East and West. Identity also interacts with education and wages (another 50% reduction).
Ridge Estimation of High Dimensional Two-Way Fixed Effect Regression (with Junnan He). February 2025 Online appendix
We study a ridge estimator for the high-dimensional two-way fixed effect regression model. We show in simulations that it performs much better than OLS, and possibly also, when the network is very sparse, than the usual bias corrections for second order moments. We then develop an asymptotic theory that helps understand why it is so. We develop concentration inequalities showing that when the ridge parameters increase as the log of the network size, the bias and the variance-covariance matrix of the vector of estimated fixed effects converge to deterministic equivalents that depend only on the expected network.
Individual Wage Dynamics, Continuous Firm Types and Path Dependence (With Richard Blundell, Thomas Breda and Marc Chan). February 2025
We use French matched employer-employee data to estimate a semi-structural model of wage dynamics. Adding further frictions to the sequential auction model, we find that job-to-job mobility is predominantly inefficient. That is moves are not purely in response to a financial surplus. Allowing for between job-to-job moves that should have occurred (higher surplus with an external firm) but did not, and moves that did occur but should not have (lower surplus in destination firm), we estimate that the proportion of employees whose last state change is inefficient is about 35%. We also find that there is strong worker-firm sorting, but this does not show up in wages. We investigate in detail the role of the dynamics of match specific wage shocks and examine the decomposition of the variance of wages and of the match surplus. We find that the match output, reflecting firm effects and worker-firm complementarities, is small while the match-specific effect dominates.
Labor Market Matching, Wages, and Amenities (with Thibaut Lamadon, Jeremy Lise and Costas Meghir) Appendix. July 2024
This paper develops the nonparametric identification of models with production complementarities, worker-firm specific disutility of labor and search frictions. Mobility in the model is subject to preference shocks, and we assume that firms can write wage contracts. We develop a constructive proof for the nonparametric identification of the model primitives from matched employer-employee data. We use the estimated model to decompose the sources of wage dispersion into worker heterogeneity, compensating differentials, and search frictions that generate between-firm and within-firm dispersion. We find that compensating differentials are substantial on average, but the contribution differs greatly between the lowest and highest types of workers. Finally, we use the model to provide an economic interpretation of several empirical regularities.
A Hidden Markov Model of Wages and Employment Mobility with Worker and Firm Heterogeneity: Evidence from Danish and Italian Register Data (with Long Hong and Rasmus Lentz). February 2025
In this paper we formulate a model of joint wage and mobility outcomes with two-sided heterogeneity. The paper extends the finite mixture approaches of Bonhomme, Lamadon, and Manresa (2019) and Lentz, Piyapromdee, and Robin (2023) to identify worker type dynamics to follow a hidden Markov model. Furthermore, the analysis applies a variational expectation maximization (VEM) algorithm to the firm classification that ensures that both worker and firm latent type identifications are informed by the full likelihood of the wage and mobility data. The paper documents significant classification improvements over existing methods. The hidden Markov model allows the analysis to flexibly identify models where the worker’s current type is at least in part affected by the workers’ employment history. In particular, this includes models with human capital dynamics, where these dynamics can depend on the current employment status and the type of the employer. The type dynamics also contribute to the understanding of sorting by allowing that the type dynamics of a match need not require worker reallocation, but rather that the worker’s type can change. The model is identified on Danish and Italian register data.
Wage Bargaining and Wage Posting Firms (with Kerstin Holtzheu)
This paper characterizes wage bargaining and wage posting firms. Using a theoretically derived likelihood-based estimation and clustering algorithm, we classify firms into either wage-bargaining or wage-posting types. Empirically, we leverage survey data from Germany and administrative data from Austria and find strikingly similar characterizations of both firm types. We find that wage-bargaining firms, which account for about 43% of Austrian firms and 43% of German firms, exhibit higher productivity and within-firm wage variation. Our model explains job-to-job mobility with wage decreases as workers trade current wages at posting firms for potential future gains at bargaining firms. Ensuing inefficient mobility accounts for 11–17% of worker transitions and about 1-2% of output losses.
Career Progression, Economic Downturns and Skills (with Jérôme Adda, Christian Dustmann and Costas Meghir). February 2013.
How Did Unemployment Fall in Germany After 2005? (with Carlos Carillo-Tudela and Andrey Launov). March 2018. This earlier version does more on mini-jobs, moonlighting and earnings inequality.