This paper proposes a new model-averaging method, called the Heteroskedasticity-Robust Cp (HRCp) method, for linear regression models with heteroskedastic errors. We provide a feasible form of the Mallows’ Cp-like criterion for choosing the weighting vector for averaging. Under some regularity conditions, we show that the HRCp method has asymptotic optimality. The simulation results show that our method works well and performs better than alternative methods in finite samples when the number of candidate models is large and/or the population coefficient of determination is not small.
{"title":"Heteroscedasticity�?Robust C Model Averaging","authors":"Qingfeng Liu, R. Okui","doi":"10.1111/ectj.12009","DOIUrl":"https://doi.org/10.1111/ectj.12009","url":null,"abstract":"This paper proposes a new model-averaging method, called the Heteroskedasticity-Robust Cp (HRCp) method, for linear regression models with heteroskedastic errors. We provide a feasible form of the Mallows’ Cp-like criterion for choosing the weighting vector for averaging. Under some regularity conditions, we show that the HRCp method has asymptotic optimality. The simulation results show that our method works well and performs better than alternative methods in finite samples when the number of candidate models is large and/or the population coefficient of determination is not small.","PeriodicalId":175689,"journal":{"name":"Wiley-Blackwell: Econometrics Journal","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"118056281","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}
Pub Date : 2008-04-01DOI: 10.1111/j.1368-423X.2008.00249.x
Teruko Takada
Motivated by finance applications, we assessed the performance of several univariate density estimation methods, focusing on their ability to deal with heavy-tailed target densities. Four approaches, a fixed bandwidth kernel estimator, an adaptive bandwidth kernel estimator, the Hermite series (SNP) estimator of Gallant and Nychka, and the logspline estimator of Kooperberg and Stone, are compared. We conclude that the logspline and adaptive kernel methods provide superior performance, and the convergence rate of the SNP estimator is remarkably slow compared with the other methods. The Hellinger convergence rate of the SNP estimator is derived as a function of tail heaviness. These findings are confirmed in Monte Carlo experiments. Qualitative assessment reveals the possibility that side lobes in the tails of the fixed kernel and SNP estimates are artefacts of the fitting method. Copyright The Author(s). Journal compilation Royal Economic Society 2008
{"title":"Asymptotic and Qualitative Performance of Non-Parametric Density Estimators: A Comparative Study","authors":"Teruko Takada","doi":"10.1111/j.1368-423X.2008.00249.x","DOIUrl":"https://doi.org/10.1111/j.1368-423X.2008.00249.x","url":null,"abstract":"Motivated by finance applications, we assessed the performance of several univariate density estimation methods, focusing on their ability to deal with heavy-tailed target densities. Four approaches, a fixed bandwidth kernel estimator, an adaptive bandwidth kernel estimator, the Hermite series (SNP) estimator of Gallant and Nychka, and the logspline estimator of Kooperberg and Stone, are compared. We conclude that the logspline and adaptive kernel methods provide superior performance, and the convergence rate of the SNP estimator is remarkably slow compared with the other methods. The Hellinger convergence rate of the SNP estimator is derived as a function of tail heaviness. These findings are confirmed in Monte Carlo experiments. Qualitative assessment reveals the possibility that side lobes in the tails of the fixed kernel and SNP estimates are artefacts of the fitting method. Copyright The Author(s). Journal compilation Royal Economic Society 2008","PeriodicalId":175689,"journal":{"name":"Wiley-Blackwell: Econometrics Journal","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120687115","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}
Pub Date : 2007-07-01DOI: 10.1111/j.1368-423X.2007.00222.x
B. Rossi
Many rational expectations models state that an economic variable is determined as the present value of future variables. These restrictions have traditionally been tested on VARs where variables appear either in levels (or cointegrating relationships) or first differences. When variables are highly persistent, commonly used test statistics may lead to overrejections in small samples. Copyright Royal Economic Society 2007
{"title":"Expectations Hypotheses Tests at Long Horizons","authors":"B. Rossi","doi":"10.1111/j.1368-423X.2007.00222.x","DOIUrl":"https://doi.org/10.1111/j.1368-423X.2007.00222.x","url":null,"abstract":"Many rational expectations models state that an economic variable is determined as the present value of future variables. These restrictions have traditionally been tested on VARs where variables appear either in levels (or cointegrating relationships) or first differences. When variables are highly persistent, commonly used test statistics may lead to overrejections in small samples. Copyright Royal Economic Society 2007","PeriodicalId":175689,"journal":{"name":"Wiley-Blackwell: Econometrics Journal","volume":"56 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117478839","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}
Pub Date : 2007-03-01DOI: 10.1111/j.1368-423X.2007.00197.x
K. Kim
This paper studies the uniform convergence rate of the truncated seminonparametric (SNP) density estimator. Using the uniform convergence rate result we obtain, we propose a test statistic testing the equivalence of two unknown densities where two densities are estimated using the SNP estimator and supports of densities are possibly unbounded. Copyright Royal Economic Society 2007
{"title":"Uniform Convergence Rate of the Seminonparametric Density Estimator and Testing for Similarity of Two Unknown Densities","authors":"K. Kim","doi":"10.1111/j.1368-423X.2007.00197.x","DOIUrl":"https://doi.org/10.1111/j.1368-423X.2007.00197.x","url":null,"abstract":"This paper studies the uniform convergence rate of the truncated seminonparametric (SNP) density estimator. Using the uniform convergence rate result we obtain, we propose a test statistic testing the equivalence of two unknown densities where two densities are estimated using the SNP estimator and supports of densities are possibly unbounded. Copyright Royal Economic Society 2007","PeriodicalId":175689,"journal":{"name":"Wiley-Blackwell: Econometrics Journal","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"119122219","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}
Pub Date : 2004-12-01DOI: 10.1111/J.1368-423X.2004.00142.X
Jonathan K. Ohn, L. W. Taylor, A. Pagan
In this paper, we discuss discrete-time tests for duration dependence. Two of our test statistics are new to the econometrics literature, and we make an important distinction between the discrete and continuous time frameworks. We then test for duration dependence in business and stock market cycles, and compare our results for business cycles with those of Diebold and Rudebusch (1990, 1991) . Our null hypothesis is that once an expansion or contraction has exceeded some minimum duration, the probability of a turning point is independent of its age--a proposition that dates back to Fisher (1925) and McCulloch (1975) . Copyright Royal Economic Socciety 2004
{"title":"Testing for Duration Dependence in Economic Cycles","authors":"Jonathan K. Ohn, L. W. Taylor, A. Pagan","doi":"10.1111/J.1368-423X.2004.00142.X","DOIUrl":"https://doi.org/10.1111/J.1368-423X.2004.00142.X","url":null,"abstract":"In this paper, we discuss discrete-time tests for duration dependence. Two of our test statistics are new to the econometrics literature, and we make an important distinction between the discrete and continuous time frameworks. We then test for duration dependence in business and stock market cycles, and compare our results for business cycles with those of Diebold and Rudebusch (1990, 1991) . Our null hypothesis is that once an expansion or contraction has exceeded some minimum duration, the probability of a turning point is independent of its age--a proposition that dates back to Fisher (1925) and McCulloch (1975) . Copyright Royal Economic Socciety 2004","PeriodicalId":175689,"journal":{"name":"Wiley-Blackwell: Econometrics Journal","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"119198894","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}
Discrete choice models are usually derived from the assumption of random utility maximization. We consider the reverse problem, whether choice probabilities are consistent with maximization of random utilities. This leads to tests that consider the variation of these choice probabilities with the average utilities of the alternatives. By restricting the range of the average utilities we obtain a sequence of tests with fewer maintained assumptions. In an empirical application, even the test with the fewest maintained assumptions rejects the hypothesis of random utility maximization.
{"title":"Discrete Choice and Stochastic Utility Maximization","authors":"R. Koning, G. Ridder","doi":"10.2139/ssrn.325080","DOIUrl":"https://doi.org/10.2139/ssrn.325080","url":null,"abstract":"Discrete choice models are usually derived from the assumption of random utility maximization. We consider the reverse problem, whether choice probabilities are consistent with maximization of random utilities. This leads to tests that consider the variation of these choice probabilities with the average utilities of the alternatives. By restricting the range of the average utilities we obtain a sequence of tests with fewer maintained assumptions. In an empirical application, even the test with the fewest maintained assumptions rejects the hypothesis of random utility maximization.","PeriodicalId":175689,"journal":{"name":"Wiley-Blackwell: Econometrics Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130356934","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 paper provides cumulative distribution functions, densities, and finite sample critical values for the single-equation error correction statistic for testing cointegration. Graphs and response surfaces summarize extensive Monte Carlo simulations and highlight simple dependencies of the statistic's quantiles on the number of variables in the error correction model, the choice of deterministic components, and the estimation sample size. The response surfaces provide a convenient way for calculating finite sample critical values at standard levels; and a computer program, freely available over the Internet, can be used to calculate both critical values and p-values. Three empirical examples illustrate these tools.
{"title":"Distributions of Error Correction Tests for Cointegration","authors":"Neil R. Ericsson, J. MacKinnon","doi":"10.2139/ssrn.224994","DOIUrl":"https://doi.org/10.2139/ssrn.224994","url":null,"abstract":"This paper provides cumulative distribution functions, densities, and finite sample critical values for the single-equation error correction statistic for testing cointegration. Graphs and response surfaces summarize extensive Monte Carlo simulations and highlight simple dependencies of the statistic's quantiles on the number of variables in the error correction model, the choice of deterministic components, and the estimation sample size. The response surfaces provide a convenient way for calculating finite sample critical values at standard levels; and a computer program, freely available over the Internet, can be used to calculate both critical values and p-values. Three empirical examples illustrate these tools.","PeriodicalId":175689,"journal":{"name":"Wiley-Blackwell: Econometrics Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116835616","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}
Pub Date : 1900-01-01DOI: 10.1111/j.1368-423X.2008.00262.x
C. Manski, J. Pepper
Econometric analyses of treatment response often use instrumental variable (IV) assumptions to identify treatment effects. The traditional IV assum ption holds that mean response is constant acros s the subpopulations of persons with different values of an observed covariate. Manski and Pepper (2000) introduced monotone instrumental variable (MIV) assumptions, which replace equalities with weak inequalities. This paper presents further ana lysis of the MIV idea. We use an e xplicit response m odel to en hance understanding of the content of MIV and traditional IV assumptions. We study the identifying power of MIV assumptions when combined with the homogeneous linear response assumption maintained in many studies of treatment response. We also consider estimation of MIV bounds, with particular attention to finite-sample bias. This paper was prepared for the tenth anniversary issue of the Econometric Journal. Our research on monotone in strumental variables (MIVs) was first circulated in 1998, th e y ear that the journal beg an publication. We are grateful for this opportunity to report further findings on MIVs and, in doing so, to mark the tenth anniversary of both the journal and the subject. We have benefitted from the comments of a referee. Manski’s research was supported in part by NSF Grant SES-0549544.
{"title":"More on Monotone Instrumental Variables","authors":"C. Manski, J. Pepper","doi":"10.1111/j.1368-423X.2008.00262.x","DOIUrl":"https://doi.org/10.1111/j.1368-423X.2008.00262.x","url":null,"abstract":"Econometric analyses of treatment response often use instrumental variable (IV) assumptions to identify treatment effects. The traditional IV assum ption holds that mean response is constant acros s the subpopulations of persons with different values of an observed covariate. Manski and Pepper (2000) introduced monotone instrumental variable (MIV) assumptions, which replace equalities with weak inequalities. This paper presents further ana lysis of the MIV idea. We use an e xplicit response m odel to en hance understanding of the content of MIV and traditional IV assumptions. We study the identifying power of MIV assumptions when combined with the homogeneous linear response assumption maintained in many studies of treatment response. We also consider estimation of MIV bounds, with particular attention to finite-sample bias. This paper was prepared for the tenth anniversary issue of the Econometric Journal. Our research on monotone in strumental variables (MIVs) was first circulated in 1998, th e y ear that the journal beg an publication. We are grateful for this opportunity to report further findings on MIVs and, in doing so, to mark the tenth anniversary of both the journal and the subject. We have benefitted from the comments of a referee. Manski’s research was supported in part by NSF Grant SES-0549544.","PeriodicalId":175689,"journal":{"name":"Wiley-Blackwell: Econometrics Journal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"119066214","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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