Stéphane Bonhomme

The Cycle of Earnings Inequality: Evidence from Spanish Social Security Data

We use detailed information on labor earnings and employment from social security records to document the evolution of earnings inequality in Spain from 1988 to 2010. Male earnings inequality was strongly countercyclical: it increased around the 1993 recession, showed a substantial decrease during the 1997-2007 expansion, and then a sharp increase during the recent recession. This evolution was partly driven by the cyclicality of employment and earnings in the lower-middle part of the distribution. We emphasize the importance of the housing boom and subsequent housing bust, and show that demand shocks in the construction sector had large effects on aggregate labor market outcomes.

Grouped Patterns of Heterogeneity in Panel Data

This paper introduces time‐varying grouped patterns of heterogeneity in linear panel data models. A distinctive feature of our approach is that group membership is left unrestricted. We estimate the parameters of the model using a “grouped fixed‐effects” estimator that minimizes a least squares criterion with respect to all possible groupings of the cross‐sectional units. Recent advances in the clustering literature allow for fast and efficient computation. We provide conditions under which our estimator is consistent as both dimensions of the panel tend to infinity, and we develop inference methods. Finally, we allow for grouped patterns of unobserved heterogeneity in the study of the link between income and democracy across countries.

Robust Priors in Nonlinear Panel Data Models

Many approaches to estimation of panel models are based on an average or integrated likelihood that assigns weights to different values of the individual effects. Fixed effects, random effects, and Bayesian approaches all fall in this category. We provide a characterization of the class of weights (or priors) that produce estimators that are firstorder unbiased. We show that such bias-reducing weights must depend on the data unless an orthogonal reparameterization or an essentially equivalent condition is available. Two intuitively appealing weighting schemes are discussed. We argue that asymptotically valid confidence intervals can be read from the posterior distribution of the common parameters when N and T grow at the same rate. Finally, we show that random effects estimators are not bias reducing in general and discuss important exceptions. Three examples and some Monte Carlo experiments illustrate the results.

Estimating multivariate latent-structure models

A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same non-orthogonal basis. An estimator of the latent-structure model may then be based on a sample version of this simultaneous-diagonalization problem. Simple algorithms are available for computation. Asymptotic theory is derived for this joint approximate-diagonalization estimator.

Nonlinear panel data estimation via quantile regressions

We introduce a class of quantile regression estimators for short panels. Our framework covers static and dynamic autoregressive models, models with general predetermined regressors, and models with multiple individual effects. We use quantile regression as a flexible tool to model the relationships between outcomes, covariates, and heterogeneity. We develop an iterative simulation-based approach for estimation, which exploits the computational simplicity of ordinary quantile regression in each iteration step. Finally, an application to measure the effect of smoking during pregnancy on children’s birthweights completes the paper.

Earnings inequality in Spain: new evidence using tax data

We use tax files from 2004 to 2010 to document the recent evolution of earnings inequality in Spain. We find that inequality went in parallel with the evolution of the unemployment rate during the period. This evolution is consistent with the evidence from Social Security records recently documented in Bonhomme and Hospido (2012). Quantitatively, the 90/10 percentile ratio of daily earnings experienced a 10% increase between 2007 and 2010, which is partly but not fully explained by changes in labour force composition. We also use the tax data to study the evolution of the gender earnings gap, and find that it has decreased throughout the distribution during the period. Lastly, we tentatively exploit the panel dimension of the data to explore the permanent and temporary dimensions of Spanish inequality.

Modeling Individual Earnings Trajectories Using Copulas: France, 1990-2002

Abstract We use copulas to construct a flexible dynamic model of individual earnings allowing for both observed and unobserved heterogeneity. We show that the dynamics of earnings ranks is best modeled using Placketts (1965) parametric copula. We use discrete mixtures to model unobserved heterogeneity. For estimation, we develop a sequential EM algorithm, which is shown to be root-N consistent and asymptotically normal. This algorithm is simple to implement and fast enough to converge for bootstrapping to be a recommendable procedure to estimate standard errors. We estimate this model using the 1990–2002 French Labour Force Survey data.

Sample Selection in Quantile Regression: A Survey

Nonrandom sample selection is a pervasive issue in applied work. In additive models, a number of techniques are available for consistent selection correction. However, progress in the development of non-additive selection corrections has been slower. In this survey we review recent proposals dealing with sample selection in quantile models.

Discretizing unobserved heterogeneity

We develop two-step and iterative panel data estimators based on a discretization of unobserved heterogeneity. We view discrete estimators as approximations, and study their properties in environments where population heterogeneity is individual-specific and un- restricted, letting the number of types grow with the sample size. Bias reduction methods can improve the performance of discrete estimators. We also show that discrete estimation may strictly dominate fixed-effects approaches when unobservables are high-dimensional, provided their underlying dimension is low. We study two applications: a structural dy- namic discrete choice model of migration, and a model of wage determination with worker and firm heterogeneity. These applications to settings with continuous heterogeneity sug- gest computational and statistical advantages of the discrete methods that we advocate.