A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions. The new statistic can be explained as a posterior version of Wald test and have several nice properties. First, it is well-defi ned under improper prior distributions. Second, it avoids Jeffreys-Lindley's paradox. Third, under the null hypothesis and repeated sampling, it follows a x2 distribution asymptotically, offering an asymptotically pivotal test. Fourth, it only requires inverting the posterior covariance for the parameters of interest. Fifth and perhaps most importantly, when a random sample from the posterior distribution (such as an MCMC output) is available, the proposed statistic can be easily obtained as a by-product of posterior simulation. In addition, the numerical standard error of the estimated proposed statistic can be computed based on the random sample. The finite sample performance of the statistic is examined in Monte Carlo studies. The method is applied to two latent variable models used in microeconometrics and financial econometrics.
{"title":"A Posterior-Based Wald-Type Statistic for Hypothesis Testing","authors":"Yong Li, Xiaobin Liu, T. Zeng, Jun Yu","doi":"10.2139/ssrn.3184330","DOIUrl":"https://doi.org/10.2139/ssrn.3184330","url":null,"abstract":"A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions. The new statistic can be explained as a posterior version of Wald test and have several nice properties. First, it is well-defi ned under improper prior distributions. Second, it avoids Jeffreys-Lindley's paradox. Third, under the null hypothesis and repeated sampling, it follows a x2 distribution asymptotically, offering an asymptotically pivotal test. Fourth, it only requires inverting the posterior covariance for the parameters of interest. Fifth and perhaps most importantly, when a random sample from the posterior distribution (such as an MCMC output) is available, the proposed statistic can be easily obtained as a by-product of posterior simulation. In addition, the numerical standard error of the estimated proposed statistic can be computed based on the random sample. The finite sample performance of the statistic is examined in Monte Carlo studies. The method is applied to two latent variable models used in microeconometrics and financial econometrics.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122703915","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}
Spanish Abstract: Bootstrapping y permutación son ejemplos de métodos de aleatorización utilizados para estimar distribuciones de probabilidad y realizar pruebas de hipótesis. English Abstract: Boostrapping and permutation are examples of randomization methods used to estimate distribution functions and perform hypothesis testing.
[Abstract: Bootstrapping排列方法的实例是aleatorización用来估计概率分布和测试的假设。English Abstract: Boostrapping and permutation are《随机化方法用来判断分销职能和区域hypothesis检测。
{"title":"Bootstrapping Y Permutación (Boostrapping and Permutation)","authors":"A. Montenegro","doi":"10.2139/ssrn.3006745","DOIUrl":"https://doi.org/10.2139/ssrn.3006745","url":null,"abstract":"<b>Spanish Abstract:</b> Bootstrapping y permutación son ejemplos de métodos de aleatorización utilizados para estimar distribuciones de probabilidad y realizar pruebas de hipótesis. <b>English Abstract:</b> Boostrapping and permutation are examples of randomization methods used to estimate distribution functions and perform hypothesis testing.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133316796","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}
In the presence of heteroskedastic errors, regression using Feasible Generalized Least Squares (FGLS) offers potential efficiency gains over Ordinary Least Squares (OLS). However, FGLS adoption remains limited, in part because the form of heteroskedasticity may be misspecified. We investigate machine learning methods to address this concern, focusing on Support Vector Regression. Monte Carlo results indicate the resulting estimator and an accompanying standard error correction offer substantially improved precision, nominal coverage rates, and shorter confidence intervals than OLS with heteroskedasticity-consistent (HC3) standard errors. Reductions in root mean squared error are over 90% of those achievable when the form of heteroskedasticity is known.
{"title":"Feasible Generalized Least Squares Using Machine Learning","authors":"Steve Miller, R. Startz","doi":"10.2139/ssrn.2966194","DOIUrl":"https://doi.org/10.2139/ssrn.2966194","url":null,"abstract":"In the presence of heteroskedastic errors, regression using Feasible Generalized Least Squares (FGLS) offers potential efficiency gains over Ordinary Least Squares (OLS). However, FGLS adoption remains limited, in part because the form of heteroskedasticity may be misspecified. We investigate machine learning methods to address this concern, focusing on Support Vector Regression. Monte Carlo results indicate the resulting estimator and an accompanying standard error correction offer substantially improved precision, nominal coverage rates, and shorter confidence intervals than OLS with heteroskedasticity-consistent (HC3) standard errors. Reductions in root mean squared error are over 90% of those achievable when the form of heteroskedasticity is known.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125912428","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}
The paper provides a review of the literature that connects Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology, and discusses research issues that are related to the various disciplines. Academics could develop theoretical models and subsequent econometric and statistical models to estimate the parameters in the associated models, as well as conduct simulation to examine whether the estimators in their theories on estimation and hypothesis testing have good size and high power. Thereafter, academics and practitioners could apply theory to analyse some interesting issues in the seven disciplines and cognate areas.
{"title":"Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections","authors":"Chia‐Lin Chang, M. McAleer, W. Wong","doi":"10.2139/ssrn.3117386","DOIUrl":"https://doi.org/10.2139/ssrn.3117386","url":null,"abstract":"The paper provides a review of the literature that connects Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology, and discusses research issues that are related to the various disciplines. Academics could develop theoretical models and subsequent econometric and statistical models to estimate the parameters in the associated models, as well as conduct simulation to examine whether the estimators in their theories on estimation and hypothesis testing have good size and high power. Thereafter, academics and practitioners could apply theory to analyse some interesting issues in the seven disciplines and cognate areas.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130228821","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}
We analyze an empirically important issue with the recursive right-tailed unit root tests for bubbles in asset prices. First, we show that serially correlated innovations, which is a feature that is present in most financial series used to test for bubbles, can lead to severe size distortions when using either fixed or automatic (based on information criteria) lag-length selection in the auxiliary regressions underlying the test. Second, we propose a sieve-bootstrap version of these tests and show that this results in more or less perfectly sized test statistics even in the presence of highly autocorrelated innovations. We also find that these improvements in size come at a relatively low cost for the power of the tests. Finally, we apply the bootstrap tests on the housing market of OECD countries, and generally find less strong evidence of bubbles compared to existing evidence.
{"title":"Testing for Explosive Bubbles in the Presence of Autocorrelated Innovations","authors":"Thomas Q. Pedersen, Erik Christian Montes Schütte","doi":"10.2139/ssrn.2916616","DOIUrl":"https://doi.org/10.2139/ssrn.2916616","url":null,"abstract":"We analyze an empirically important issue with the recursive right-tailed unit root tests for bubbles in asset prices. First, we show that serially correlated innovations, which is a feature that is present in most financial series used to test for bubbles, can lead to severe size distortions when using either fixed or automatic (based on information criteria) lag-length selection in the auxiliary regressions underlying the test. Second, we propose a sieve-bootstrap version of these tests and show that this results in more or less perfectly sized test statistics even in the presence of highly autocorrelated innovations. We also find that these improvements in size come at a relatively low cost for the power of the tests. Finally, we apply the bootstrap tests on the housing market of OECD countries, and generally find less strong evidence of bubbles compared to existing evidence.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125425487","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}
This research note deals with how to test for and evaluate interdependence among control elements that are jointly determined (a system) using structural equation modeling (SEM). Empirical research on the levers of control (LOC) frame work is used as example. In LOC-research a path model approach to interdependence has been developed. The appropriateness of this method is evaluated and in the article I instead develop SEM models that implement seemingly unrelated regression (SUR) and test them on a data set of 120 SBUs in Sweden. The empirical results suggest that modeling interdependence among control practices in a system as paths, instead of residual correlations, evidently underestimates the strength of interdependence.
{"title":"Testing for Control System Interdependence with Structural Equation Modeling: A Research Note with the Levers of Control (LOC) Framework As Example","authors":"T. Johansson","doi":"10.2139/ssrn.2908711","DOIUrl":"https://doi.org/10.2139/ssrn.2908711","url":null,"abstract":"This research note deals with how to test for and evaluate interdependence among control elements that are jointly determined (a system) using structural equation modeling (SEM). Empirical research on the levers of control (LOC) frame work is used as example. In LOC-research a path model approach to interdependence has been developed. The appropriateness of this method is evaluated and in the article I instead develop SEM models that implement seemingly unrelated regression (SUR) and test them on a data set of 120 SBUs in Sweden. The empirical results suggest that modeling interdependence among control practices in a system as paths, instead of residual correlations, evidently underestimates the strength of interdependence.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114684038","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}
type="main"> This paper advocates abandoning null hypothesis statistical tests (NHST) in favour of reporting confidence intervals. The case against NHST, which has been made repeatedly in multiple disciplines and is growing in awareness and acceptance, is introduced and discussed. Accounting as an empirical research discipline appears to be the last of the research communities to face up to the inherent problems of significance test use and abuse. The paper encourages adoption of a meta-analysis approach which allows for the inclusion of replication studies in the assessment of evidence. This approach requires abandoning the typical NHST process and its reliance on p-values. However, given that NHST has deep roots and wide ‘social acceptance’ in the empirical testing community, modifications to NHST are suggested so as to partly counter the weakness of this statistical testing method.
{"title":"Significance Testing: We Can Do Better","authors":"T. Dyckman","doi":"10.1111/abac.12078","DOIUrl":"https://doi.org/10.1111/abac.12078","url":null,"abstract":"type=\"main\"> This paper advocates abandoning null hypothesis statistical tests (NHST) in favour of reporting confidence intervals. The case against NHST, which has been made repeatedly in multiple disciplines and is growing in awareness and acceptance, is introduced and discussed. Accounting as an empirical research discipline appears to be the last of the research communities to face up to the inherent problems of significance test use and abuse. The paper encourages adoption of a meta-analysis approach which allows for the inclusion of replication studies in the assessment of evidence. This approach requires abandoning the typical NHST process and its reliance on p-values. However, given that NHST has deep roots and wide ‘social acceptance’ in the empirical testing community, modifications to NHST are suggested so as to partly counter the weakness of this statistical testing method.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126015891","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}
We explore the in- and out- of sample robustness of tests for consumer choice inconsistencies based on parameter restrictions in parametric models, with a focus on tests proposed by Ketcham, Kuminoff and Powers (2015). We start by arguing that non-parametric alternatives are inherently conservative with respect to detecting mistakes (and one specific test proposed by KKP is incorrect). We then consider several proposed robustness checks of parametric models and argue that they do not separately identify misspecification and choice inconsistencies. We also show that, when implemented using a comprehensive goodness of fit measure, the Keane and Wolpin (2007) test of out of sample forecasting demonstrates that a model allowing for choice inconsistencies forecasts substantially better than one that does not. Finally, we explore the robustness of our 2011 results to alternative normative assumptions.
{"title":"The Robustness of Tests for Consumer Choice Inconsistencies","authors":"Jason Abaluck, J. Gruber","doi":"10.3386/w21617","DOIUrl":"https://doi.org/10.3386/w21617","url":null,"abstract":"We explore the in- and out- of sample robustness of tests for consumer choice inconsistencies based on parameter restrictions in parametric models, with a focus on tests proposed by Ketcham, Kuminoff and Powers (2015). We start by arguing that non-parametric alternatives are inherently conservative with respect to detecting mistakes (and one specific test proposed by KKP is incorrect). We then consider several proposed robustness checks of parametric models and argue that they do not separately identify misspecification and choice inconsistencies. We also show that, when implemented using a comprehensive goodness of fit measure, the Keane and Wolpin (2007) test of out of sample forecasting demonstrates that a model allowing for choice inconsistencies forecasts substantially better than one that does not. Finally, we explore the robustness of our 2011 results to alternative normative assumptions.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114098868","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}
I. G. Becheri, F. C. Drost, Ramon Van den Akker, Oliver Wichert
We derive the power envelope for panel unit root tests where heterogeneous alternatives are modeled via zero-expectation random perturbations. We obtain an asymptotically UMP test and discuss how to proceed when one is agnostic about the expectation of the perturbations.
{"title":"The Power Envelope of Panel Unit Root Tests in Case Stationary Alternatives Offset Explosive Ones","authors":"I. G. Becheri, F. C. Drost, Ramon Van den Akker, Oliver Wichert","doi":"10.2139/ssrn.2664447","DOIUrl":"https://doi.org/10.2139/ssrn.2664447","url":null,"abstract":"We derive the power envelope for panel unit root tests where heterogeneous alternatives are modeled via zero-expectation random perturbations. We obtain an asymptotically UMP test and discuss how to proceed when one is agnostic about the expectation of the perturbations.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"501 1-2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123434797","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}
We consider treatment effect estimation via a difference-in-difference approach for data with local spatial interaction such that the outcome of observed units depends on their own treatment as well as on the treatment status of proximate neighbors. We show that under standard assumptions (common trend and ignorability) a straightforward spatially explicit version of the benchmark difference-in-differences regression is capable of identifying both direct and indirect treatment effects. We demonstrate the finite sample performance of our spatial estimator via Monte Carlo simulations.
{"title":"Difference-in-Differences Techniques for Spatial Data: Local Autocorrelation and Spatial Interaction","authors":"M. Delgado, R. Florax","doi":"10.2139/ssrn.2637764","DOIUrl":"https://doi.org/10.2139/ssrn.2637764","url":null,"abstract":"We consider treatment effect estimation via a difference-in-difference approach for data with local spatial interaction such that the outcome of observed units depends on their own treatment as well as on the treatment status of proximate neighbors. We show that under standard assumptions (common trend and ignorability) a straightforward spatially explicit version of the benchmark difference-in-differences regression is capable of identifying both direct and indirect treatment effects. We demonstrate the finite sample performance of our spatial estimator via Monte Carlo simulations.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128532204","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}
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