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Testing for a common latent variable in a linear regression

Author

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  • Wittenberg, Martin

Abstract

We present a test of the hypothesis that a subset of the regressors are all proxying for the same latent variable. This issue will be of interest in cases where there are several correlated measures of elusive concepts such as misgovernance or corruption; in analyses where key variables such as income are not measured at all and one is forced to rely on various proxies; and where the key regressors are badly measured and one is trying to extract a stronger signal from the regression by adding additional proxies as suggested by Lubotsky and Wittenberg (2006). We apply this test in three contexts, each characterised by a different estimation challenge arising from data limitations. We reexamine Mauro's (1995) use of three institutional quality measures in his study of corruption and growth. Here several variables, each potentially measured with error, may all be proxies for a single factor: the quality of governance. Our test suggests that the latent variable is driven primarily by the “red tape” measure, rather than the “corruption” variable on which Mauro focuses. Secondly, we look at the correlates of body mass among black South African women. The key variable of interest, namely “wealth” is not measured at all. Consequently we construct an index from a series of asset variables as suggested by Filmer and Pritchett (2001). Our test shows that some assets have independent impacts on the dependent variable. Once this is recognised the “asset index” comes apart. Finally we analyse the determinants of sleep among young South Africans. The income variable in the survey is badly measured and we supplement it with asset proxies. The test again suggests that some assets are not proxying for the badly measured income variable. We can nevertheless get a substantially stronger signal on the income variable.

Suggested Citation

  • Wittenberg, Martin, 2007. "Testing for a common latent variable in a linear regression," MPRA Paper 2550, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:2550
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    File URL: https://mpra.ub.uni-muenchen.de/2550/1/MPRA_paper_2550.pdf
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    References listed on IDEAS

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    1. repec:pri:cheawb:case_deaton_healthwealth is not listed on IDEAS
    2. Darren Lubotsky & Martin Wittenberg, 2006. "Interpretation of Regressions with Multiple Proxies," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 549-562, August.
    3. repec:pri:rpdevs:case_deaton_healthwealth is not listed on IDEAS
    4. Anne Case & Angus Deaton, 2005. "Health and Wealth among the Poor: India and South Africa Compared," American Economic Review, American Economic Association, vol. 95(2), pages 229-233, May.
    5. repec:pri:rpdevs:case_deaton_healthwealth.pdf is not listed on IDEAS
    6. repec:pri:cheawb:case_deaton_healthwealth.pdf is not listed on IDEAS
    7. Szalontai, Gabor, 2006. "The demand for sleep: A South African study," Economic Modelling, Elsevier, vol. 23(5), pages 854-874, September.
    8. Fedderke, Johannes & Klitgaard, Robert, 1998. "Economic Growth and Social Indicators: An Exploratory Analysis," Economic Development and Cultural Change, University of Chicago Press, vol. 46(3), pages 455-489, April.
    9. Daron Acemoglu & Simon Johnson & James A. Robinson, 2001. "The Colonial Origins of Comparative Development: An Empirical Investigation," American Economic Review, American Economic Association, vol. 91(5), pages 1369-1401, December.
    10. Biddle, Jeff E & Hamermesh, Daniel S, 1990. "Sleep and the Allocation of Time," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 922-943, October.
    11. 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.
    12. Barry P. Bosworth & Susan M. Collins, 2003. "The Empirics of Growth: An Update," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 34(2), pages 113-206.
    13. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    14. Paolo Mauro, 1995. "Corruption and Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 681-712.
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    Cited by:

    1. Wittenberg, Martin, 2011. "Estimating expenditure impacts without expenditure data using asset proxies," Economics Letters, Elsevier, vol. 110(2), pages 122-125, February.
    2. Martin Wittenberg, 2009. "Weighing the value of Asset Proxies: The case of the Body Mass Index in South Africa," SALDRU Working Papers 39, Southern Africa Labour and Development Research Unit, University of Cape Town.
    3. Bollinger Christopher R. & Minier Jenny, 2015. "On the Robustness of Coefficient Estimates to the Inclusion of Proxy Variables," Journal of Econometric Methods, De Gruyter, vol. 4(1), pages 1-22, January.

    More about this item

    Keywords

    measurement error; proxy variables; specification test; asset index;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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