Co-auteur
  • DHAENE Geert (7)
  • ROBIN Jean-Marc (5)
  • BONHOMME Stéphane (5)
  • DHAENE Geert (4)
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  • Working paper (20)
  • Article (12)
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We derive bias-corrected least-squares estimators of panel vector autoregressions with fixed effects. The correction is straightforward to implement and yields an estimator that is asymptotically unbiased under asymptotics where the number of time series observations grows at the same rate as the number of cross-sectional observations. This makes the estimator well suited for most macroeconomic data sets. Simulation results show that the estimator yields substantial improvements over within-group least-squares estimation. We illustrate the bias correction in a study of the relation between the unemployment rate and the economic growth rate at the U.S. state level.

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We consider point estimation and inference based on modifications of the profile likelihood in models for dyadic interactions between agents featuring n agent-specific parameters. This setup covers the b-model of network formation and generalizations thereof. The maximum-likelihood estimator of such models has bias and standard deviation of O(n−1) and so is asymptotically biased. Estimation based on modified likelihoods leads to estimators that are asymptotically unbiased and likelihood-ratio tests that exhibit correct size. We apply the modifications to versions of the b-model for network formation and of the Bradley-Terry model for paired comparisons.

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We consider a statistical model for network formation that features both node-specific heterogeneity parameters and common parameters that reflect homophily among nodes. The goal is to perform statistical inference on the homophily parameters while allowing the distribution of the node heterogeneity to be unrestricted, that is, by treating the node-specific parameters as fixed effects. Jointly estimating all the parameters leads to asymptotic bias that renders conventional confidence intervals incorrectly centered. As an alternative, we develop an approach based on a sufficient statistic that separates inference on the homophily parameters from estimation of the fixed effects. This estimator is easy to compute and is shown to have desirable asymptotic properties. In numerical experiments we find that the asymptotic results provide a good approximation to the small-sample behavior of the estimator. As an empirical illustration, the technique is applied to explain the import and export patterns in a cross-section of countries.

Publié en 2011-03-15
DHAENE Geert
JOCHMANS Koen
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Maximum-likelihood estimates of nonlinear panel data models with fixed effects are generally not consistent as the number of units, N, grows large while the number of time periods, T, stays fixed. The inconsistency can be viewed as a consequence of the bias of the score function, where the unit-specific parameters have been profiled out. We investigate ways of adjusting the profile score so as to make it unbiased or approximately unbiased. This leads to estimators, solving an adjusted profile score equation, that are fixed-T consistent or have less asymptotic bias, as T ! 1, than maximum likelihood. One approach to adjusting the profile score is to subtract its bias, evaluated at maximum- likelihood estimates of the fixed effects. When this bias does not depend on the incidental parameters, the adjustment is exact. Otherwise, it does not eliminate the bias entirely but reduces its order (in T), and it can be iterated, reducing the bias order further. We examine a range of nonlinear models with additive fixed effects. In many of these, an exact bias adjustment of the profile score is possible. In others, suitably adjusted profile scores exhibit much less bias than without the adjustment, even for very small T.

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We calculate the bias of the profile score for the regression coefficients in a multistratum autoregressive model with stratum-specific intercepts. The bias is free of incidental parameters. Centering the profile score delivers an unbiased estimating equation and, upon integration, an adjusted profile likelihood. A variety of other approaches to constructing modified profile likelihoods are shown to yield equivalent results. However, the global maximizer of the adjusted likelihood lies at infinity for any sample size, and the adjusted profile score has multiple zeros. We argue that the parameters are local maximizers inside or on an ellipsoid centered at the maximum likelihood estimator.

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In this note it is shown that the index coefficients and location parameters in the standard triangular binary-choice model are identifed under an assumption of symmetry on the joint density of the latent disturbances. Identifcation of average effects follows. The implied restrictions suggest semiparametric rank estimators that are consistent and asymptotically normal under standard conditions.

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We propose a scheme of iterative adjustments to the profile score to deal with incidental-parameter bias in models for stratified data with few observations on a large number of strata. The first-order adjustment is based on a calculation of the profile-score bias and evaluation of this bias at maximum-likelihood estimates of the incidental parameters. If the bias does not depend on the incidental parameters, the first-order adjusted profile score is fully recentered, solving the incidental-parameter problem. Otherwise, it is approximately recentered, alleviating the incidental-parameter problem. In the latter case, the adjustment can be iterated to give higher-order adjustments, possibly until convergence. The adjustments are generally applicable (e.g., not requiring parameter orthogonality) and lead to estimates that generally improve on maximum likelihood. We examine a range of nonlinear models with covariates. In many of them, we obtain an adjusted profile score that is exactly unbiased. In the others, we obtain approximate bias adjustments that yield much improved estimates, relative to maximum likelihood, even when there are only two observations per stratum.

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This note shows that the asymptotic variance of Chen’s [Chen, S., 2002. Rank estimation of transformation models. Econometrica 70 (4) 1683–1697] two-step estimator of the link function in a linear transformation model depends on the first-step estimator of the index coefficients.

in Annals of Statistics Publié en 2016
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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 joint-diagonalization problem. Algorithms are available for computation and we derive distribution theory. We further develop asymptotic theory for orthogonal-series estimators of component densities in mixture models and emission densities in hidden Markov models.

Publié en 2015-04
HENRY Marc
SALANIÉ Bernard
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Many econometric models can be analyzed as finite mixtures. We focus on two-component mixtures and we show that they are nonparametrically point identified by a combination of an exclusion restriction and tail restrictions. Our identification analysis suggests simple closed-form estimators of the component distributions and mixing proportions. We derive their asymptotic properties using results on tail empirical processes and we present a simulation study that documents their finite-sample performance.

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