{"title":"A class of indirect inference estimators: higher-order asymptotics and approximate bias correction","authors":"Stelios Arvanitis, Antonis Demos","doi":"10.1111/ectj.12045","DOIUrl":"10.1111/ectj.12045","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we define a set of indirect inference estimators based on moment approximations of the auxiliary estimators. Their introduction is motivated by reasons of analytical and computational facilitation. Their definition provides an indirect inference framework for some classical bias correction procedures. We derive higher-order asymptotic properties of these estimators. We demonstrate that under our assumption framework, and in the special case of deterministic weighting and affinity of the binding function, these are second-order unbiased. Moreover, their second-order approximate mean square errors do not depend on the cardinality of the Monte Carlo or bootstrap samples that our definition might involve. Consequently, the second-order mean square error of the auxiliary estimator is not altered. We extend this to a class of multistep indirect inference estimators that have zero higher-order bias without increasing the approximate mean square error, up to the same order. Our theoretical results are also validated by three Monte Carlo experiments.</p></div>","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"18 2","pages":"200-241"},"PeriodicalIF":1.9,"publicationDate":"2015-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12045","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75430941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Specification testing in nonstationary time series models","authors":"Jia Chen, Jiti Gao, Degui Li, Zhengyan Lin","doi":"10.1111/ectj.12044","DOIUrl":"10.1111/ectj.12044","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we consider a specification testing problem in nonlinear time series models with nonstationary regressors, and we propose using a nonparametric kernel-based test statistic. The null asymptotics for the proposed nonparametric test statistic have been well developed in the existing literature. In this paper, we study the local asymptotics of the test statistic (i.e. the asymptotic properties of the test statistic under a sequence of general nonparametric local alternatives) and show that the asymptotic distribution depends on the asymptotic behaviour of the distance function, which is the local deviation from the parametrically specified model in the null hypothesis. In order to implement the proposed test in practice, we introduce a bootstrap procedure to approximate the critical values of the test statistic and establish a new Edgeworth expansion, which is used to justify the use of such an approximation. Based on the approximate critical values, we develop a bandwidth selection method, which chooses the optimal bandwidth that maximizes the local power of the test while its size is controlled at a given significance level. The local power is defined as the power of the proposed test for a given sequence of local alternatives. Such a bandwidth selection is made feasible by an approximate expression for the local power of the test as a function of the bandwidth. A Monte Carlo simulation study is provided to illustrate the finite sample performance of the proposed test.</p></div>","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"18 1","pages":"117-136"},"PeriodicalIF":1.9,"publicationDate":"2015-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12044","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124088755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On bootstrap validity for specification tests with weak instruments","authors":"Firmin Doko Tchatoka","doi":"10.1111/ectj.12042","DOIUrl":"10.1111/ectj.12042","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the asymptotic validity of the bootstrap for Durbin–Wu–Hausman tests of exogeneity, with or without identification. We provide an analysis of the limiting distributions of the proposed bootstrap statistics under both the null hypothesis of exogeneity (size) and the alternative hypothesis of endogeneity (power). We show that when identification is strong, the bootstrap provides a high-order approximation of the null limiting distributions of the statistics and is consistent under the alternative hypothesis if the endogeneity parameter is fixed. However, the bootstrap only provides a first-order approximation when instruments are weak. Moreover, we provide the necessary and sufficient condition under which the proposed bootstrap tests exhibit power under (fixed) endogeneity and weak instruments. The latter condition may still hold over a wide range of cases as long as at least one instrument is relevant. Nevertheless, all bootstrap tests have low power when all instruments are irrelevant, a case of little interest in empirical work. We present a Monte Carlo experiment that confirms our theoretical findings.</p></div>","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"18 1","pages":"137-146"},"PeriodicalIF":1.9,"publicationDate":"2014-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12042","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"95568450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust hypothesis tests for M-estimators with possibly non-differentiable estimating functions","authors":"Wei-Ming Lee, Yu-Chin Hsu, Chung-Ming Kuan","doi":"10.1111/ectj.12041","DOIUrl":"10.1111/ectj.12041","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose a new robust hypothesis test for (possibly non-linear) constraints on M-estimators with possibly non-differentiable estimating functions. The proposed test employs a random normalizing matrix computed from recursive M-estimators to eliminate the nuisance parameters arising from the asymptotic covariance matrix. It does not require consistent estimation of any nuisance parameters, in contrast with the conventional heteroscedasticity-autocorrelation consistent (HAC)-type test and the Kiefer–Vogelsang–Bunzel (KVB)-type test. Our test reduces to the KVB-type test in simple location models with ordinary least-squares estimation, so the error in the rejection probability of our test in a Gaussian location model is . We discuss robust testing in quantile regression, and censored regression models in detail. In simulation studies, we find that our test has better size control and better finite sample power than the HAC-type and KVB-type tests.</p></div>","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"18 1","pages":"95-116"},"PeriodicalIF":1.9,"publicationDate":"2014-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12041","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114756067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Specification tests for nonlinear dynamic models","authors":"Igor L. Kheifets","doi":"10.1111/ectj.12040","DOIUrl":"10.1111/ectj.12040","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any set-up where parametric conditional distribution of the data is specified and, in particular, to models involving conditional volatility, conditional higher moments, conditional quantiles, asymmetry, Value at Risk models, duration models, diffusion models, etc. Compared to other tests, the new test properly controls the nonlinear dynamic behaviour in conditional distribution and does not rely on smoothing techniques that require a choice of several tuning parameters. The test is based on a new kind of multivariate empirical process of contemporaneous and lagged probability integral transforms. We establish weak convergence of the process under parameter uncertainty and local alternatives. We justify a parametric bootstrap approximation that accounts for parameter estimation effects often ignored in practice. Monte Carlo experiments show that the test has good finite-sample size and power properties. Using the new test and graphical tools, we check the adequacy of various popular heteroscedastic models for stock exchange index data.</p></div>","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"18 1","pages":"67-94"},"PeriodicalIF":1.9,"publicationDate":"2014-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12040","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116263148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Identification and estimation of partially linear censored regression models with unknown heteroscedasticity","authors":"Zhengyu Zhang, Bing Liu","doi":"10.1111/ectj.12037","DOIUrl":"10.1111/ectj.12037","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we introduce a new identification and estimation strategy for partially linear regression models with a general form of unknown heteroscedasticity, that is, and , where ε is independent of and the functional forms of both and are left unspecified. We show that in such a model, β<sub>0</sub> and can be exactly identified while can be identified up to scale as long as permits sufficient nonlinearity in <i>X</i>. A two-stage estimation procedure motivated by the identification strategy is described and its large sample properties are formally established. Moreover, our strategy is flexible enough to allow for both fixed and random censoring in the dependent variable. Simulation results show that the proposed estimator performs reasonably well in finite samples.</p></div>","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"18 2","pages":"242-273"},"PeriodicalIF":1.9,"publicationDate":"2014-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131017468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"First-differencing in panel data models with incidental functions","authors":"Koen Jochmans","doi":"10.1111/ectj.12035","DOIUrl":"https://doi.org/10.1111/ectj.12035","url":null,"abstract":"<div>\u0000 \u0000 <p>This 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.</p></div>","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"17 3","pages":"373-382"},"PeriodicalIF":1.9,"publicationDate":"2014-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71930924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xiaohong Chen, Sokbae Lee, Oliver Linton, Elie Tamer
{"title":"Advances in Robust and Flexible Inference in Econometrics: A Special Issue in Honour of Joel L. Horowitz","authors":"Xiaohong Chen, Sokbae Lee, Oliver Linton, Elie Tamer","doi":"10.1111/ectj.12032","DOIUrl":"10.1111/ectj.12032","url":null,"abstract":"","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"17 2","pages":"Si-Sii"},"PeriodicalIF":1.9,"publicationDate":"2014-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12032","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62958037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Maximum score estimation with nonparametrically generated regressors","authors":"Le-Yu Chen, Sokbae Lee, Myung Jae Sung","doi":"10.1111/ectj.12034","DOIUrl":"https://doi.org/10.1111/ectj.12034","url":null,"abstract":"<div>\u0000 \u0000 <p>The estimation problem in this paper is motivated by the maximum score estimation of preference parameters in the binary choice model under uncertainty in which the decision rule is affected by conditional expectations. The preference parameters are estimated in two stages. We estimate conditional expectations nonparametrically in the first stage. Then, in the second stage, we estimate the preference parameters based on the maximum score estimator of Manski, using the choice data and first-stage estimates. This setting can be extended to maximum score estimation with nonparametrically generated regressors. In this paper, we establish consistency and derive the rate of convergence of the two-stage maximum score estimator. Moreover, we also provide sufficient conditions under which the two-stage estimator is asymptotically equivalent in distribution to the corresponding single-stage estimator that assumes the first-stage input is known. We also present some Monte Carlo simulation results for the finite-sample behaviour of the two-stage estimator.</p></div>","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"17 3","pages":"271-300"},"PeriodicalIF":1.9,"publicationDate":"2014-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71975643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A social interaction model with an extreme order statistic","authors":"Ji Tao, Lung-fei Lee","doi":"10.1111/ectj.12031","DOIUrl":"https://doi.org/10.1111/ectj.12031","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we introduce a social interaction econometric model with an extreme order statistic to model peer effects. We show that the model is a well-defined system of equations and that it is a static game with complete information. The social interaction model can include exogenous regressors and group effects. Instrumental variables estimators are proposed for the general model that includes exogenous regressors. We also consider distribution-free methods that use recurrence relations to generate moment conditions for estimation. For a model without exogenous regressors, the maximum likelihood approach is computationally feasible.</p></div>","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"17 3","pages":"197-240"},"PeriodicalIF":1.9,"publicationDate":"2014-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12031","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71994645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}