{"title":"On Bootstrapping Tests of Equal Forecast Accuracy for Nested Models","authors":"F. Doko Tchatoka, Qazi Haque","doi":"10.2139/ssrn.3556974","DOIUrl":"https://doi.org/10.2139/ssrn.3556974","url":null,"abstract":"The asymptotic distributions of the recursive out-of-sample forecast accuracy test statistics depend on stochastic integrals of Brownian motion when the models under comparison are nested. This often complicates their implementation in practice because the computation of their asymptotic critical values is costly. Hansen and Timmermann (2015, Econometrica) propose a Wald approximation of the commonly used recursive F-statistic and provide a simple characterization of the exact density of its asymptotic distribution. However, this characterization holds only when the larger model has one extra predictor or the forecast errors are homoscedastic. No such closed-form characterization is readily available when the nesting involves more than one predictor and heteroskedasticity is present. We first show both the recursive F-test and its Wald approximation have poor finite-sample properties, especially when the forecast horizon is greater than one. We then propose an hybrid bootstrap method consisting of a block moving bootstrap (which is nonparametric) and a residual based bootstrap for both statistics, and establish its validity. Simulations show that our hybrid bootstrap has good finite-sample performance, even in multi-step ahead forecasts with heteroscedastic or autocorrelated errors, and more than one predictor. The bootstrap method is illustrated on forecasting core inflation and GDP growth.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82495629","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 Note on Adaptive Group Lasso for Structural Break Time Series","authors":"Simon Behrendt, Karsten Schweikert","doi":"10.2139/ssrn.3486104","DOIUrl":"https://doi.org/10.2139/ssrn.3486104","url":null,"abstract":"Abstract Considering structural break autoregressive (SBAR) processes and following recent literature, the problem of estimating the unknown number of change-points is cast as a model selection problem. The adaptive group Lasso is used to select the number of change-points for which parameter estimation consistency, model selection consistency, and asymptotic normality are proven. It is shown in simulation experiments that adaptive group Lasso performs comparably to a state-of-the-art two-step group Lasso procedure with backward elimination and other leading-edge approaches. Moreover, comparing the forecasting performance of both group Lasso procedures in an empirical application to realized variance dynamics, adaptive group Lasso is found to date change-points with equal accuracy. Thus, in practice, adaptive group Lasso can provide an alternative way to consistently select change-points in related applications.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84792461","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":"An Alternative Approach for Demand Estimation","authors":"Sizhong Sun","doi":"10.2139/ssrn.3550415","DOIUrl":"https://doi.org/10.2139/ssrn.3550415","url":null,"abstract":"This paper develops an alternative approach for demand estimation. Taking willingness to pay as model primitive, it establishes a general and yet analytically simple demand function, and proposes an estimation procedure that uses survey to solicit consumers' willingness to pay with which the underlying demand function can be consistently estimated using the ordinary least square estimator. Monte Carlo simulations find the estimation procedure works well in identifying the demand function. This approach can be applied both within and outside academic arenas, for example in economics teaching and for a business to launch new products.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"258 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77058152","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":"The Determinants of Redistribution Around the World","authors":"M. Jäntti, Jukka Pirttilä, Risto Rönkkö","doi":"10.1111/roiw.12406","DOIUrl":"https://doi.org/10.1111/roiw.12406","url":null,"abstract":"This paper reexamines the determinants of redistribution in light of improved data and methods relative to earlier literature. In particular, we use the latest version of the UNU‐WIDER’s Income Inequality Database to have the best available estimates of both pre‐ and post‐redistribution inequality for the largest set of countries and periods. We tackle head‐on problems related to model specification that risk generating large biases in estimates because of mechanical associations between the dependent and explanatory variables. The results suggest that the bias in the earlier work can be substantial. The descriptive analysis highlights, in addition, how scarce the data are when it comes to information about the extent of redistribution in developing countries.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"47 2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72613424","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":"Reasonable Doubt: Experimental Detection of Job-Level Employment Discrimination","authors":"Patrick M. Kline, Christopher R. Walters","doi":"10.3386/w26861","DOIUrl":"https://doi.org/10.3386/w26861","url":null,"abstract":"This paper develops methods for detecting discrimination by individual employers using correspondence experiments that send fictitious resumes to real job openings. We establish identification of higher moments of the distribution of job‐level callback rates as a function of the number of resumes sent to each job and propose shape‐constrained estimators of these moments. Applying our methods to three experimental data sets, we find striking job‐level heterogeneity in the extent to which callback probabilities differ by race or sex. Estimates of higher moments reveal that while most jobs barely discriminate, a few discriminate heavily. These moment estimates are then used to bound the share of jobs that discriminate and the posterior probability that each individual job is engaged in discrimination. In a recent experiment manipulating racially distinctive names, we find that at least 85% of jobs that contact both of two white applications and neither of two black applications are engaged in discrimination. To assess the potential value of our methods for regulators, we consider the accuracy of decision rules for investigating suspicious callback behavior in various experimental designs under a simple two‐type model that rationalizes the experimental data. Though we estimate that only 17% of employers discriminate on the basis of race, we find that an experiment sending 10 applications to each job would enable detection of 7–10% of discriminatory jobs while yielding Type I error rates below 0.2%. A minimax decision rule acknowledging partial identification of the distribution of callback rates yields only slightly fewer investigations than a Bayes decision rule based on the two‐type model. These findings suggest illegal labor market discrimination can be reliably monitored with relatively small modifications to existing correspondence designs.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85367863","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":"(Structural) VAR Models with Ignored Changes in Mean and Volatility","authors":"M. Demetrescu, Nazarii Salish","doi":"10.2139/ssrn.3544676","DOIUrl":"https://doi.org/10.2139/ssrn.3544676","url":null,"abstract":"We discuss estimation of so-called long vector autoregressions for multivariate series exhibiting possibly time-varying mean and (co)variances. In applied work, such changes often escape undetected, and we ask how standard tools (least squares estimation, point forecasts, and estimated impulse responses) are affected when ignoring the changes altogether. Keeping the order of the autoregression fixed is known to lead to asymptotic bias in autoregressive parameter estimators in the presence of ignored changes in the mean. Yet we show that allowing the complexity of the model to increase with the sample size leads to consistent estimators of the AR coefficient matrices individually. The fitted long VAR models appear to have unit root behavior, in spite of the absence of any stochastic trend in the model, and may even mimic cointegration; but, in spite of the structural change in the data generating process, out-of-sample forecasts based on long VARs are consistent. These findings hold under constant as well as under time-varying covariances. In what concerns estimated impulse responses, their sampling behavior depends primarily on whether the residual covariance matrix is employed for identification of the structural shocks or not. While MA coefficient matrices obtained by inversion of the fitted long VAR model are consistent for the true coefficients under mild additional restrictions even under time-varying error (co)variances, the residual covariance matrix estimator converges to an \"average\" covariance matrix, such that localized estimators may be more suitable for a precise identification. Monte Carlo simulations and empirical illustration support our theoretical findings. Empirical relevance of the theory is illustrated through two illustrations: (i) international dynamics of inflation and (ii) uncertainty and economics activity.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73503353","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":"Testing Stochastic Dominance with Many Conditioning Variables","authors":"O. Linton, M. Seo, Yoon-Jae Whang","doi":"10.2139/ssrn.3535723","DOIUrl":"https://doi.org/10.2139/ssrn.3535723","url":null,"abstract":"We propose a test of the hypothesis of conditional stochastic dominance in the presence of many conditioning variables (whose dimension may grow to infinity as the sample size diverges). Our approach builds on a semiparametric location scale model in the sense that the conditional distribution of the outcome given the covariates is characterized by a nonparametric mean function and a nonparametric skedastic function with an independent innovation whose distribution is unknown. We propose to estimate the nonparametric mean and skedastic regression functions by the `1-penalized nonparametric series estimation with thresholding. Under the sparsity assumption, where the number of truly relevant series terms are relatively small (but their identities are unknown), we develop the estimation error bounds for the regression functions and series coefficients estimates allowing for the time series dependence. We derive the asymptotic distribution of the test statistic, which is not pivotal asymptotically, and introduce the smooth stationary bootstrap to approximate its sample distribution. We investigate the finite sample performance of the bootstrap critical values by a set of Monte Carlo simulations. Finally, our method is illustrated by an application to stochastic dominance among portfolio returns given all the past information.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81794442","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":"Minimum Relative Entropy Inference for Normal and Monte Carlo Distributions","authors":"Marcello Colasante, A. Meucci","doi":"10.2139/ssrn.3479693","DOIUrl":"https://doi.org/10.2139/ssrn.3479693","url":null,"abstract":"We represent affine sub-manifolds of exponential family distributions as minimum relative entropy sub-manifolds. With such representation we derive analytical formulas for the inference from partial information on expectations and covariances of multivariate normal distributions; and we improve the numerical implementation via Monte Carlo simulations for the inference from partial information of generalized expectation type.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84347317","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":"Shrinkage Estimation of Large Covariance Matrices: Keep it Simple, Statistician?","authors":"Olivier Ledoit, Michael Wolf","doi":"10.2139/ssrn.3421503","DOIUrl":"https://doi.org/10.2139/ssrn.3421503","url":null,"abstract":"Under rotation-equivariant decision theory, sample covariance matrix eigenvalues can be optimally shrunk by recombining sample eigenvectors with a (potentially nonlinear) function of the unobservable population covariance matrix. The optimal shape of this function reflects the loss/risk that is to be minimized. We solve the problem of optimal covariance matrix estimation under a variety of loss functions motivated by statistical precedent, probability theory, and differential geometry. A key ingredient of our nonlinear shrinkage methodology is a new estimator of the angle between sample and population eigenvectors, without making strong assumptions on the population eigenvalues. We also introduce a broad family of covariance matrix estimators that can handle all regular functional transformations of the population covariance matrix under large-dimensional asymptotics. In addition, we compare via Monte Carlo simulations our methodology to two simpler ones from the literature, linear shrinkage and shrinkage based on the spiked covariance model.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74827266","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}