Sciences Pohttp://spire.sciencespo.fr:80/dissemination/atom-publications-by-author.xml?hdl=2441/eu4vqp9ompqllr09i4kp004rnlist of publications for an author2019-04-18T14:24:54Zhttp://spire.sciencespo.fr/hdl:/2441/lpag9391598uoauqu4u9opq76We propose a two-step method to nonparametrically estimate multivariate models in which the observed outcomes are independent conditional on a discrete latent variable. Applications include microeconometric models with unobserved types of agents, regime-switching models, and models with misclassification error. In the first step, we estimate weights that transform moments of the marginal distribution of the data into moments of the conditional distribution of the data for given values of the latent variable. In the second step, these conditional moments are estimated as weighted sample averages. We illustrate the method by estimating a model of wages with unobserved heterogeneity on PSID data.Nonparametric estimation of non-exchangeable latent-variable models2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/1mc4dip81d9t8r0t57fe1h8lapWe 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. Consistent parameter estimates are obtained as local maximizers inside or on an ellipsoid centered at the maximum likelihood estimator.Likelihood Inference in an Autoregression with Fixed Effects2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/7si2u15cul9u5a44sevcgkbaa9We derive a bias-corrected least-squares estimator for panel vector autoregressions with fixed effects. The estimator is straightforward to implement and is asymptotically unbiased under asymptotics where the number of time series observations and the number of cross-sectional observations grow at the same rate. This makes the estimator particularly well suited for most macroeconomic data sets.
Bias-corrected estimation of panel vector autoregressions2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/5l8aj0dpmg9pbahnt8a4k2fcrhWe 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.Modified-likelihood estimation of the b-model2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/dpido2upv86tqc7td18fd2mnaWe 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.Semiparametric Analysis of Network Formation2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/etefo8s8r89oamhnhiclqr530A 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.Estimating Multivariate Latent-Structure Models2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/3hiheaog1g8c7bm7kuf5usjk6rEmpirical models for dyadic interactions between n agents often feature agent-specific parameters. Fixed-effect estimators of such models generally have bias of order n−1, which is non-negligible relative to their standard error. Therefore, confidence sets based on the asymptotic distribution have incorrect coverage. This paper looks at models with multiplicative unobservables and fixed effects. We derive moment conditions that are free of fixed effects and use them to set up estimators that are n-consistent, asymptotically normally-distributed, and asymptotically unbiased. We provide Monte Carlo evidence for a range of models. We estimate a gravity equation as an empirical illustration.Two-Way Models for Gravity2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/2t7dgrpjh58e9a93hqot3nu9k3Consider estimating the slope coefficients of a fixed-effect binary-choice model from two-period panel data. Two approaches to semiparametric estimation at the regular parametric rate have been proposed. One is based on a sufficient statistic, the other is based on a conditional-median restriction. We show that, under standard assumptions, both approaches are equivalent.A note on sufficiency in binary panel models 2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/2etjsneok98utpcm5s44jn4dlhEmpirical models for dyadic interactions between n agents often feature agent-specific parameters. Fixed-effect estimators of such models generally have bias of order n−1,which is non-negligible relative to their standard error. Therefore, confidence sets based on the asymptotic distribution have incorrect coverage. This paper looks at models with multiplicative unobservables and fixed effects. We first derive moment conditions that are free of fixed effects. We next use these moment conditions to set up estimators that are n-consistent, asymptotically normally-distributed, and asymptotically unbiased. We provide Monte Carlo evidence for a range of models and we estimate a gravity equation with multilateral resistance terms as an empirical illustration.Two-way models for gravity2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/4ect7tfnam9poo2tioundd7pb3We 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.Bias-corrected estimation of panel vector autoregressions2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/27t63d33os8qmoo1h92v1tvc68We 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. Consistent parameter estimates are obtained as local maximizers inside or on an ellipsoid centered at the maximum likelihood estimator.
Likelihood inference in an autogression with fixed effects2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/f6h8764enu2lskk9p2m96cphiMany 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.Inference on Mixtures Under Tail Restrictions2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/51sosj74bo8t69726q85nn2tbqThis paper provides methods to estimate finite mixtures from data with repeated measurements non-parametrically. We present a constructive identification argument and use it to develop simple two-step estimators of the component distributions and all their functionals. We discuss a computationally efficient method for estimation and derive asymptotic theory. Simulation experiments suggest that our theory provides confidence intervals with good coverage in small samples.Nonparametric estimation of finite mixtures from repeated measurements2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/323dml6suu9mb9otmuenjljv9aWe 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.Profile-score adjustments for incidental-parameter problems2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/75dbbb2hc596np6q8flqf6i79kEmpirical models for panel data frequently feature fixed effects in both directions of the panel. Settings where this is prevalent include student-teacher interaction, the allocation of workers to firms, and the import-export flows between countries.
Estimation of such fixed-effect models is difficult. We derive moment conditions for models with multiplicative unobservables and fixed effects and use them to set up generalized method of moments estimators that have good statistical properties. We estimate a gravity equation with multilateral resistance terms as an application of our methods.Two-way models for gravity2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/48bmbf4n8o90jr41qiguaqlqg8Maximum-likelihood estimation of nonlinear models with fixed effects is subject to the incidental-parameter problem. This typically implies that point estimates suffer from large bias and confidence intervals have poor coverage. This article presents a jackknife method to reduce this bias and to obtain confidence intervals that are correctly centred under rectangular-array asymptotics. The method is explicitly designed to handle dynamics in the data, and yields estimators that are straightforward to implement and can be readily applied to a range of models and estimands. We provide distribution theory for estimators of model parameters and average effects, present validity tests for the jackknife, and consider extensions to higher-order bias correction and to two-step estimation problems. An empirical illustration relating to female labour-force participation is also provided. Split-panel jackknife estimation of fixed-effect models2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/3ehoe2k1fv8imof86c6jcu8qm6This paper presents a simple approach to deal with sample selection in models with multiplicative errors. Models for non-negative limited dependent variables such as counts fit this framework. The approach builds on a specification of the conditional mean of the outcome only and is, therefore, semiparametric in nature. GMM estimators are constructed for both cross-section data and for panel data. We derive distribution theory and present Monte Carlo evidence on the finite-sample performance of the estimators.Multiplicative-error models with sample selection2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/2i27dd3b6h94aarftq0slq652aA 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.Estimating Multivariate Latent-Structure Models2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/4s9js5v8u59j6ohm90d2e3gbsuThis note discusses a class of models for panel data that accommodate between-group heterogeneity that is allowed to exhibit positive within-group variance. Such a set-up generalizes the traditional fixed-effect paradigm in which between-group heterogeneity is limited to univariate factors that act like constants within groups. Notable members of the class of models considered are non-linear regression models with additive heterogeneity and multiplicative-error models suitable for non-negative limited dependent variables. The heterogeneity is modelled as a non-parametric nuisance function of covariates whose functional form is fixed within groups but is allowed to vary freely across groups. A simple approach to perform inference in such situations is based on local first-differencing of observations within a given group. This leads to moment conditions that, asymptotically, are free of nuisance functions. Conventional generalized method of moments procedures can then be readily applied. In particular, under suitable regularity conditions, such estimators are consistent and asymptotically normal, and asymptotically valid inference can be performed using a plug-in estimator of the asymptotic variance.First-differencing in panel data models with incidental functions2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/3vl5fe4i569nbr005tctlc8ll5This paper presents simple approaches to deal with sample selection in models with multiplicative errors. GMM estimators are constructed for both cross-section data and for panel data. These estimators build only on a specification of the conditional mean of the outcome of interest and are, therefore, semiparametric in nature. In particular, the distribution of unobservables is left unspecified. In the panel-data case, we further allow for group-specific fixed effects whose relation to covariates is left unrestricted. We derive distribution theory for both sampling situations and present Monte Carlo evidence on the finite-sample performance of the approach.Multiplicative-error models with sample selection2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/f6h8764enu2lskk9p2m9mgp8lMaximum-likelihood estimation of nonlinear models with fixed effects is subject to the incidental-parameter
problem. This typically implies that point estimates suffer from large bias and confidence intervals have
poor coverage. This paper presents a jackknife method to reduce this bias and to obtain confidence intervals that are correctly centered under rectangular-array asymptotics. The method is explicitly designed to handle dynamics in the data and yields estimators that are straightforward to implement and that can be readily applied to a range of models and estimands. We provide distribution theory for estimators of index coefficients and average effects, present validity tests for the jackknife, and consider extensions to higher-order bias correction and to two-step estimation problems. An empirical illustration on female labor-force participation is also provided.Split-Panel Jackknife Estimation of Fixed-Effect Models2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/6ggbvnr6munghes9oc1j58g85The purpose of this paper is the presentation of distribution theory for generic estimators based on the pairwise comparison of observations in problems where identification is achieved through the use of control functions. The controls can be specified semi- or non-parametrically. The criterion function may be non-smooth. The theory is applied to the estimation of the coefficients in a monotone linear-index model and to inference on the link function in a partially-linear transformation model. A number of simulation exercises serve to assess the small-sample performance of these techniques.Pairwise-comparison estimation with non-parametric controls2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/7o52iohb7k6srk09n8t4k21smThe aim of this paper is to provide simple nonparametric methods to estimate finitemixture models from data with repeated measurements. Three measurements suffice for the mixture to be fully identified and so our approach can be used even with very short panel data. We provide distribution theory for estimators of the mixing proportions and the mixture distributions, and various functionals thereof. We also discuss inference on the number of components. These estimators are found to perform well in a series of Monte Carlo exercises. We apply our techniques to document heterogeneity in log annual earnings using PSID data
spanning the period 1969–1998.
Nonparametric estimation of finite mixtures2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/dambferfb7dfprc9m052g20qhWe 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.Likelihood inference in an Autoregression with fixed effects2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/dambferfb7dfprc9m01h6f4h2The purpose of this paper is the presentation of distribution theory for generic estimators based on the pairwise comparison of observations in problems where identification is achieved through the use of control functions. The controls can be specified semi- or non-parametrically. The criterion function may be non-smooth. The theory is applied to the estimation of the coefficients in a monotone linear-index model and to inference on the link function in a partially-linear transformation model. A number of simulation exercises serve to assess the small-sample performance of these techniques.Pairwise-comparison estimation with nonparametric controls2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/3l7jsh4t299ltbst22qlc044j9This 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.The variance of a rank estimator of transformation models2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/7nu0cp0n9onjmd89j2a48543oThis note shows that the asymptotic variance of Chen’s [Econometrica, 70, 4 (2002), 1683–1697] two-step estimator of the link function in a linear transformation model depends on the first-step estimator of the index coefficients.The variance of a rank estimator of transformation models 2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/eu4vqp9ompqllr09ij4oogc0gIn 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.Identification in Bivariate binary-choice Models with elliptical innovations 2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/eu4vqp9ompqllr09ij4oge90iWe calculate the bias of the profile score for the autoregressive parameters p and covariate slopes in the linear model for N x T panel data with p lags of the dependent variable, exogenous covariates, fixed effects, and unrestricted initial observations. The bias is a vector of multivariate polynomials in p with coefficients that depend only on T. We center the profile score and, on integration, obtain an adjusted profile likelihood. When p = 1, the adjusted profile likelihood coincides with Lancaster's (2002) marginal posterior. More generally, it is an integrated likelihood, in the sense of Arellano and Bonhomme (2009), with fixed effects integrated out using a new data-independent prior. It appears that p and B are identified as the unique point where the large N adjusted profile likelihood reaches a local maximum (or a at inection point, as a limiting case) inside or on an ellipsoid centered at the maximum likelihood estimator. We prove this when p = 1 and report numerical calculations that support it when p > 1. The global maximum of the adjusted profile likelihood lies at infinity for any N.An Adjusted profile likelihood for non-stationary panel data models with fixed effects2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/eu4vqp9ompqllr09j0031f620Maximum-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.Profile-score Adjustements for Nonlinearfixed-effect Models 2019-04-04T21:03:00Zhttp://spire.sciencespo.fr/hdl:/2441/eu4vqp9ompqllr09ij4j7acrhI discuss the fixed-effect estimation of panel data models with time-varying excess heterogeneity across cross-sectional units. These latent components are not given a parametric form. A modification to traditional first-differencing is motivated which, asymptotically, removes the permanent unobserved heterogeneity from the differenced model. Conventional estimation techniques can then be readily applied. Distribution theory for a kernel-weighted GMM estimator under large-n and fixed-T asymptotics is developed. The estimator is put to work in a series of numerical experiments to static and dynamic models.First-differencing in panel data models with incidental functions2019-04-04T21:02:59Zhttp://spire.sciencespo.fr/hdl:/2441/eu4vqp9ompqllr09ij4j0h0h1We propose a jackknife for reducing the order of the bias of maximum likelihood estimates of nonlinear dynamic fixed-effect panel models. Split-panel jackknife estimation of fixed-effect models2019-04-04T21:03:00Z