The Special Issue on Econometrics of Heterogeneity (which arose out of the invited presentations given in The Econometrics Journal Special Session at the Royal Economic Society Annual Conference held 3-5 April 2013 at Royal Holloway University of London) has now been published.
During the conference, papers were presented by Yuichi Kitamura (Yale) and Stéphane Bonhomme (CEMFI). To view the original presentations please visit
The published article accompanying the presentation by Stéphane Bonhomme co-authored with Manuel Arellano, introduces a class of possibly nonlinear quantile specifications for short panels providing a rich description of heterogeneous responses of outcomes to variations in covariates. The framework is sufficiently general to include both static and dynamic models, allows for multiple individual effects and models with general predetermined regressors. Finite-dimensional approximations based on interpolating splines detail the interactions at various quantiles between covariates and heterogeneity. Imputed values for heterogeneity are obtained via an iterative procedure as draws from the posterior distribution of the heterogeneity components conditional on the data. These values are then used to update the quantile parameter estimates. The algorithm is a variant of the expectation-maximization algorithm, sometimes referred to as stochastic expectation maximisation, but where parameters are updated in each iteration using quantile regressions rather than maximum likelihood. The estimator is then applied in a study to assess the effect of smoking during pregnancy on a child’s birthweight.
The published paper that arises from the presentation by Yuichi Kitamura, co-authored with Giovanni Compiani, discusses mixture models which are a device commonly employed in econometrics to describe unobserved heterogeneity. Particular attention is given to semiparametric and nonparametric treatments that incorporate mixture distributions thereby relaxing the traditional parametric assumptions of correct specification of the unobserved heterogeneity distribution. This greater flexibility often reduces identifying power so allowing only partial identification results for the parameters of interest to be obtained with, in particular, significant differences between finite and continuous mixtures in terms of model identifiability. The assumptions of how component and/or the mixing distributions depend on covariates are key for parameter identification. Applications of mixture models are presented addressing various problems in econometrics including unobserved heterogeneity and multiple equilibria. Some new nonparametric identification results are obtained for finite mixture models and models with possibly infinite mixtures, in particular, panel data models, random coefficient models and random utility models are considered.
Of course, because of the time constraint imposed by the Special Session, the specific topics considered are necessarily restrictive but hopefully they do provide an impression of a few of the current frontiers pertaining to the econometrics of heterogeneity.
Previous Published Special Issue Papers are available on
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