Testing for a common latent variable in a linear regression: Or how to "fix" a bad variable by adding multiple proxies for it

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dc.creatorWittenberg, Martin
dc.date2013-10-11T12:30:45Z
dc.date2013-10-11T12:30:45Z
dc.date2005-10
dc.date.accessioned2015-05-28T10:06:28Z
dc.date.available2015-05-28T10:06:28Z
dc.date.issued2015-05-28
dc.descriptionWe analyse models in which additional “controls” or proxies are included in a regression. This might occur intentionally if there is significant measurement error in a key regressor or if a key variable is not measured at all. We develop a test of the hypothesis that a subset of the regressors are all proxying for the same latent variable and we show how an estimate of the structural coefficient might be obtained more efficiently than is available in the current literature. We apply the procedure to the determinants of sleep among young South Africans. We show that the income variable in the time use survey is badly measured. Nevertheless the measured impact of income on sleep is significant and amounts to 35 minutes per day between children with the median income and those in the topmost income bracket. Including a variety of asset proxies increases the estimated size of the coefficient enormously. The specification tests indicate that some of the asset proxies, however, have independent effects. Access to electricity, in particular, is not simply proxying for income. Instead it seems to be capturing access to various forms of entertainment, such as television. Even when this independent effect is properly accounted for, the size of the income coefficient is still 40% to 100% larger than in the specifications without the proxies.
dc.identifier1-77011-067-4
dc.identifierhttp://hdl.handle.net/11090/661
dc.identifier.ris TY - Working Paper DA - 2015-05-28 DB - OpenUCT DP - University of Cape Town KW - Latent variable KW - Econometrics KW - Regression KW - Linear regression KW - Control variables KW - Proxy variables KW - Income KW - Sleep KW - Specification test KW - Income coefficient KW - Measurement error LK - https://open.uct.ac.za PB - University of Cape Town PY - 2015 T1 - Testing for a common latent variable in a linear regression: Or how to "fix" a bad variable by adding multiple proxies for it TI - Testing for a common latent variable in a linear regression: Or how to "fix" a bad variable by adding multiple proxies for it UR - http://hdl.handle.net/11090/661 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11090/661
dc.languageen
dc.publisherCSSR and SALDRU
dc.publisher.departmentSALDRUen_ZA
dc.publisher.facultyFaculty of Commerceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.relationCSSR/SALDRU Working Papers;132
dc.subjectLatent variable
dc.subjectEconometrics
dc.subjectRegression
dc.subjectLinear regression
dc.subjectControl variables
dc.subjectProxy variables
dc.subjectIncome
dc.subjectSleep
dc.subjectSpecification test
dc.subjectIncome coefficient
dc.subjectMeasurement error
dc.titleTesting for a common latent variable in a linear regression: Or how to "fix" a bad variable by adding multiple proxies for it
dc.typeWorking Paper
uct.type.publicationResearchen_ZA
uct.type.resourceWorking Paperen_ZA
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