{"title":"What Do Kernel Density Estimators Optimize?","authors":"R. Koenker, I. Mizera, Jungmo Yoon","doi":"10.1515/2156-6674.1011","DOIUrl":"https://doi.org/10.1515/2156-6674.1011","url":null,"abstract":"Some linkages between kernel and penalty methods of density estimation are explored. It is recalled that classical Gaussian kernel density estimation can be viewed as the solution of the heat equation with initial condition given by data. We then observe that there is a direct relationship between the kernel method and a particular penalty method of density estimation. For this penalty method, solutions can be characterized as a weighted average of Gaussian kernel density estimates, the average taken with respect to the bandwidth parameter. A Laplace transform argument shows that this weighted average of Gaussian kernel estimates is equivalent to a fixed bandwidth kernel estimate using a Laplace kernel. Extensions to higher order kernels are considered and some connections to penalized likelihood density estimators are made in the concluding sections.","PeriodicalId":36727,"journal":{"name":"Journal of Econometric Methods","volume":"1 1","pages":"15 - 22"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/2156-6674.1011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66807899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Comparison of the Robustness of Several Tests of Short Memory to Autocorrelated Errors","authors":"Christine E. Amsler, P. Schmidt","doi":"10.1515/2156-6674.1002","DOIUrl":"https://doi.org/10.1515/2156-6674.1002","url":null,"abstract":"In this paper we consider the robustness to error autocorrelation of four stationarity tests. The size and power properties of these tests are investigated by simulation. Size is improved by using fixed-b critical values to account for the number of lags used in long-run variance estimation. Lo’s MR/S test is not very robust. Choi’s LM test has excellent robustness properties but this comes at some cost in power; it is not as powerful as the KPSS test or the rescaled variance (V/S) test.","PeriodicalId":36727,"journal":{"name":"Journal of Econometric Methods","volume":"1 1","pages":"56 - 66"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/2156-6674.1002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66807776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sule Alan, Bo E. Honoré, Luojia Hu, Søren Leth-Petersen
{"title":"Estimation of Panel Data Regression Models with Two-Sided Censoring or Truncation","authors":"Sule Alan, Bo E. Honoré, Luojia Hu, Søren Leth-Petersen","doi":"10.2139/ssrn.1961703","DOIUrl":"https://doi.org/10.2139/ssrn.1961703","url":null,"abstract":"Abstract This paper constructs estimators for panel data regression models with individual specific heterogeneity and two-sided censoring and truncation. Following Powell the estimation strategy is based on moment conditions constructed from re-censored or re-truncated residuals. While these moment conditions do not identify the parameter of interest, they can be used to motivate objective functions that do. We apply one of the estimators to study the effect of a Danish tax reform on household portfolio choice. The idea behind the estimators can also be used in a cross sectional setting.","PeriodicalId":36727,"journal":{"name":"Journal of Econometric Methods","volume":"3 1","pages":"1 - 20"},"PeriodicalIF":0.0,"publicationDate":"2011-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2139/ssrn.1961703","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67814192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Implications of Essential Heterogeneity for Estimating Causal Impacts Using Social Experiments","authors":"M. Ravallion","doi":"10.1515/jem-2013-0009","DOIUrl":"https://doi.org/10.1515/jem-2013-0009","url":null,"abstract":"Abstract The standard model of essential heterogeneity, whereby program take up depends on unobserved costs and benefits of take up, is generalized to allow the source of latent heterogeneity to influence counterfactual outcomes. The standard instrumental variables (IV) estimator is shown to still be preferable to the naïve, ordinary least squares (OLS), estimator for mean impact on the treated. However, under certain conditions, the IV estimate of the overall mean impact will be even more biased than OLS. Examples are given for stylized training, insurance and microcredit schemes.","PeriodicalId":36727,"journal":{"name":"Journal of Econometric Methods","volume":"4 1","pages":"145 - 151"},"PeriodicalIF":0.0,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jem-2013-0009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66939637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantile Uncorrelation and Instrumental Regressions","authors":"T. Komarova, T. Severini, E. Tamer","doi":"10.1515/2156-6674.1001","DOIUrl":"https://doi.org/10.1515/2156-6674.1001","url":null,"abstract":"Abstract We introduce a notion of median uncorrelation that is a natural extension of mean (linear) uncorrelation. A scalar random variable Y is median uncorrelated with a k-dimensional random vector X if and only if the slope from an LAD regression of Y on X is zero. Using this simple definition, we characterize properties of median uncorrelated random variables, and introduce a notion of multivariate median uncorrelation. We provide measures of median uncorrelation that are similar to the linear correlation coefficient and the coefficient of determination. We also extend this median uncorrelation to other loss functions. As two stage least squares exploits mean uncorrelation between an instrument vector and the error to derive consistent estimators for parameters in linear regressions with endogenous regressors, the main result of this paper shows how a median uncorrelation assumption between an instrument vector and the error can similarly be used to derive consistent estimators in these linear models with endogenous regressors. We also show how median uncorrelation can be used in linear panel models with quantile restrictions and in linear models with measurement errors.","PeriodicalId":36727,"journal":{"name":"Journal of Econometric Methods","volume":"1 1","pages":"14 - 2"},"PeriodicalIF":0.0,"publicationDate":"2010-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/2156-6674.1001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66807697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Score Based Approach to Wild Bootstrap Inference","authors":"Patrick M. Kline, Andrés Santos","doi":"10.1515/2156-6674.1006","DOIUrl":"https://doi.org/10.1515/2156-6674.1006","url":null,"abstract":"Abstract We propose a generalization of the wild bootstrap of Wu (1986) and Liu (1988) based upon perturbing the scores of M-estimators. This \"score bootstrap\" procedure avoids recomputing the estimator in each bootstrap iteration, making it substantially less costly to compute than the conventional nonparametric bootstrap, particularly in complex nonlinear models. Despite this computational advantage, in the linear model, the score bootstrap studentized test statistic is equivalent to that of the conventional wild bootstrap up to order Op(n-1). We establish the consistency of the procedure for Wald and Lagrange Multiplier type tests and tests of moment restrictions for a wide class of M-estimators under clustering and potential misspecification. In an extensive series of Monte Carlo experiments, we find that the performance of the score bootstrap is comparable to competing approaches despite its computational savings.","PeriodicalId":36727,"journal":{"name":"Journal of Econometric Methods","volume":"1 1","pages":"23 - 41"},"PeriodicalIF":0.0,"publicationDate":"2010-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/2156-6674.1006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66807818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonparametric Instrumental Variable Estimation in Practice","authors":"P. Shaw, Michael Andrew Cohen, Tao Chen","doi":"10.1515/jem-2013-0002","DOIUrl":"https://doi.org/10.1515/jem-2013-0002","url":null,"abstract":"Abstract This paper investigates recent developments in the literature on nonparametric instrumental variables estimation and considers the practical importance of the features of these estimators in the context of typically applied econometric models. Our primary focus is on the estimation of econometric models with endogenous regressors, and their marginal effects, without a known functional form. We develop an estimator for the marginal effects and investigate its finite sample performance. We show that when instruments are weak, in the classic sense, the nonparametric estimates of the marginal effect outperforms the classic two-stage least squares estimator, even when the model is correctly specified. When the instruments are strong, we show that the nonparametric estimator for the partial effects is still effective compared to the two-stage least squares estimator even as the number of IVs increases. We also investigate bandwidth choice and find that a rule-of-thumb bandwidth performs relatively well. Whereas cross-validation leads to a better fit when the number of instruments is small, as the number of instruments increases the rule-of-thumb standard actually results in better model fit. In an empirical application we estimate the work-horse aggregate logit demand model, discuss the required nonparametric identification properties, and document the differences between nonparametric and parametric specifications on the estimation of demand elasticities.","PeriodicalId":36727,"journal":{"name":"Journal of Econometric Methods","volume":"7 1","pages":"153 - 177"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jem-2013-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66939556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimation of Panel Data Models with Parameter Heterogeneity when Group Membership is Unknown","authors":"Chang‐Ching Lin, Serena Ng","doi":"10.1515/2156-6674.1000","DOIUrl":"https://doi.org/10.1515/2156-6674.1000","url":null,"abstract":"Abstract This paper proposes two methods for estimating panel data models with group specific parameters when group membership is not known. The first method uses the individual level time series estimates of the parameters to form threshold variables. The problem of parameter heterogeneity is turned into estimation of a panel threshold model with an unknown threshold value. The second method modifies the K-means algorithm to perform conditional clustering. Units are clustered based on the deviations between the individual and the group conditional means. The two approaches are used to analyze growth across countries and housing market dynamics across the states in the U.S.","PeriodicalId":36727,"journal":{"name":"Journal of Econometric Methods","volume":"1 1","pages":"42 - 55"},"PeriodicalIF":0.0,"publicationDate":"2007-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/2156-6674.1000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66808146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}