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Regression with Imputed Covariates:a Generalized Missing Indicator Approach

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Abstract

A common problem in applied regression analysis is that covariate values may be missing for some observations but imputed values may be available. This situation generates a trade-off between bias and precision: the complete cases are often disarmingly few, but replacing the missing observations with the imputed values to gain precision may lead to bias. In this paper we formalize this trade-off by showing that one can augment the regression model with a set of auxiliary variables so as to obtain, under weak assumptions about the imputations, the same unbiased estimator of the parameters of interest as complete-case analysis. Given this augmented model, the bias-precision trade-off may then be tackled by either model reduction procedures or model averaging methods. We illustrate our approach by considering the problem of estimating the relation between income and the body mass index (BMI) using survey data affected by item non-response, where the missing values on the main covariates are filled in by imputations.

Suggested Citation

  • Valentino Dardanoni & Salvatore Modica & Franco Peracchi, 2009. "Regression with Imputed Covariates:a Generalized Missing Indicator Approach," CEIS Research Paper 150, Tor Vergata University, CEIS, revised 08 Oct 2009.
  • Handle: RePEc:rtv:ceisrp:150
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    1. Horton, Nicholas J. & Kleinman, Ken P., 2007. "Much Ado About Nothing: A Comparison of Missing Data Methods and Software to Fit Incomplete Data Regression Models," The American Statistician, American Statistical Association, vol. 61, pages 79-90, February.
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    5. John Cawley & John Moran & Kosali Simon, 2010. "The impact of income on the weight of elderly Americans," Health Economics, John Wiley & Sons, Ltd., vol. 19(8), pages 979-993, August.
    6. Anna Sanz De Galdeano, 2005. "The Obesity Epidemic in Europe," CSEF Working Papers 143, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    7. Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
    8. Tomas Philipson & Richard Posner, 2008. "Is the Obesity Epidemic a Public Health Problem? A Decade of Research on the Economics of Obesity," NBER Working Papers 14010, National Bureau of Economic Research, Inc.
    9. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
    10. Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
    11. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
    12. Julia Campos & Neil R. Ericsson & David F. Hendry, 2005. "General-to-specific modeling: an overview and selected bibliography," International Finance Discussion Papers 838, Board of Governors of the Federal Reserve System (U.S.).
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    1. Gli esperti di valutazione all’italiana
      by Alberto Baccini in ROARS - Return on Academic Research on 2011-12-16 21:45:50

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    Cited by:

    1. Djavad Salehi-Isfahani & Nadia Hassine & Ragui Assaad, 2014. "Equality of opportunity in educational achievement in the Middle East and North Africa," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(4), pages 489-515, December.
    2. repec:eee:econom:v:199:y:2017:i:2:p:141-155 is not listed on IDEAS
    3. Aedın Doris & Donal O’Neill & Olive Sweetman, 2011. "GMM estimation of the covariance structure of longitudinal data on earnings," Stata Journal, StataCorp LP, vol. 11(3), pages 439-459, September.
    4. Giuseppe De Luca & Jan R. Magnus, 2011. "Bayesian model averaging and weighted-average least squares: Equivariance, stability, and numerical issues," Stata Journal, StataCorp LP, vol. 11(4), pages 518-544, December.
    5. Valentino Dardanoni & Giuseppe De Luca & Salvatore Modica & Franco Peracchi, 2012. "A generalized missing-indicator approach to regression with imputed covariates," Stata Journal, StataCorp LP, vol. 12(4), pages 575-604, December.
    6. Valentino Dardanoni & Giuseppe De Luca & Salvatore Modica & Franco Peracchi, 2013. "Bayesian Model Averaging for Generalized Linear Models with Missing Covariates," EIEF Working Papers Series 1311, Einaudi Institute for Economics and Finance (EIEF), revised May 2013.
    7. Laszlo Goerke & Sabrina Jeworrek & Markus Pannenberg, 2015. "Trade union membership and paid vacation in Germany," IZA Journal of Labor Economics, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 4(1), pages 1-26, December.
    8. McDonough, Ian K. & Millimet, Daniel L., 2017. "Missing data, imputation, and endogeneity," Journal of Econometrics, Elsevier, vol. 199(2), pages 141-155.
    9. World Bank, 2015. "Tanzania Poverty Assessment," World Bank Other Operational Studies 21871, The World Bank.
    10. Dardanoni, Valentino & De Luca, Giuseppe & Modica, Salvatore & Peracchi, Franco, 2015. "Model averaging estimation of generalized linear models with imputed covariates," Journal of Econometrics, Elsevier, vol. 184(2), pages 452-463.
    11. Jiti Gao & Bin Peng & Zhao Ren & Xiaohui Zhang, 2015. "Variable Selection for a Categorical Varying-Coefficient Model with Identifications for Determinants of Body Mass Index," Monash Econometrics and Business Statistics Working Papers 21/15, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    Missing covariates; Imputations; Bias-precision trade-off; Model reduction; Model averaging; BMI and income.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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