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dc.contributor.authorLoretan, Michael Stanislausen_US
dc.contributor.authorKurz-Kim, Jeong-Ryeolen_US
dc.date.accessioned2009-01-28T16:02:00Z-
dc.date.available2009-01-28T16:02:00Z-
dc.date.issued2007en_US
dc.identifier.urihttp://hdl.handle.net/10419/19687-
dc.description.abstractSince Mandelbrot's seminal work (1963), alpha-stable distributions with infinite variance have been regarded as a more realistic distributional assumption than the normal distribution for some economic variables, especially financial data. After providing a brief survey of theoretical results on estimation and hypothesis testing in regression models with infinite-variance variables, we examine the statistical properties of the coefficient of determination in regression models with infinite-variance variables. These properties differ in several important aspects from those in the well-known finite variance case. In the infinite-variance case when the regressor and error term share the same index of stability, the coefficient of determination has a nondegenerate asymptotic distribution on the entire [0,1] interval, and the probability density function of this distribution is unbounded at 0 and 1. We provide closedform expressions for the cumulative distribution function and probability density function of this limit random variable. In an empirical application, we revisit the Fama-MacBeth two-stage regression and show that in the infinite variance case the coefficient of determination of the second-stage regression converges to zero asymptotically.en_US
dc.language.isoengen_US
dc.relation.ispartofseriesDiscussion paper Series 1 / Volkswirtschaftliches Forschungszentrum der Deutschen Bundesbank 2007,10en_US
dc.subject.jelC13en_US
dc.subject.jelC21en_US
dc.subject.jelG12en_US
dc.subject.jelC12en_US
dc.subject.ddc330en_US
dc.subject.keywordRegression modelsen_US
dc.subject.keywordalpha-stable distributionsen_US
dc.subject.keywordinfinite varianceen_US
dc.subject.keywordcoefficient of determinationen_US
dc.subject.keywordFama-MacBeth regressionen_US
dc.subject.keywordMonte Carlo simulationen_US
dc.subject.stwRegressionen_US
dc.subject.stwSch├Ątztheorieen_US
dc.subject.stwStatistische Verteilungen_US
dc.subject.stwCapital Asset Pricing Modelen_US
dc.subject.stwTheorieen_US
dc.titleA note on the coefficient of determination in regression models with infinite-variance variablesen_US
dc.typeWorking Paperen_US
dc.identifier.ppn529232138en_US
dc.rightshttp://www.econstor.eu/dspace/Nutzungsbedingungen-
dc.identifier.repecRePEc:zbw:bubdp1:5574-
Appears in Collections:Discussion Paper Series 1: Economic Studies, Deutsche Bundesbank

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