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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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  • Martin Wittenberg

    ()
    (School of Economics, University of Cape Town)

Abstract

We 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.

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Bibliographic Info

Paper provided by Southern Africa Labour and Development Research Unit, University of Cape Town in its series SALDRU/CSSR Working Papers with number 132.

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Date of creation: 2005
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Handle: RePEc:ldr:cssrwp:132

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  1. Darren Lubotsky & Martin Wittenberg, 2001. "Interpretation of Regressions with Multiple Proxies," Working Papers, Princeton University, Department of Economics, Industrial Relations Section. 836, Princeton University, Department of Economics, Industrial Relations Section..
  2. Martin Browning & S¯ren Leth-Petersen, 2003. "Imputing consumption from income and wealth information," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 113(488), pages F282-F301, 06.
  3. Biddle, Jeff E & Hamermesh, Daniel S, 1990. "Sleep and the Allocation of Time," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 98(5), pages 922-43, October.
  4. Filmer, Deon & Pritchett, Lant, 1998. "Estimating wealth effects without expenditure data - or tears : with an application to educational enrollments in states of India," Policy Research Working Paper Series 1994, The World Bank.
  5. Martin Wittenberg, 2005. "The school day in South Africa," SALDRU/CSSR Working Papers, Southern Africa Labour and Development Research Unit, University of Cape Town 113, Southern Africa Labour and Development Research Unit, University of Cape Town.
  6. Roland G. Fryer & Paul S. Heaton & Steven D. Levitt & Kevin M. Murphy, 2005. "Measuring the Impact of Crack Cocaine," NBER Working Papers 11318, National Bureau of Economic Research, Inc.
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