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Regression with imputed covariates: A generalized missing-indicator approach

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  • Dardanoni, Valentino
  • Modica, Salvatore
  • Peracchi, Franco

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 162 (2011)
Issue (Month): 2 (June)
Pages: 362-368

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Handle: RePEc:eee:econom:v:162:y:2011:i:2:p:362-368

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Web page: http://www.elsevier.com/locate/jeconom

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

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References

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  1. 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.
  2. 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.
  3. John Cawley & John R. Moran & Kosali I. Simon, 2008. "The Impact of Income on the Weight of Elderly Americans," NBER Working Papers 14104, National Bureau of Economic Research, Inc.
  4. Gernot Doppelhofer & Ronald I. Miller & Xavier Sala-i-Martin, 2000. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (Bace) Approach," OECD Economics Department Working Papers 266, OECD Publishing.
  5. García Villar, Jaume & Quintana-Domeque, Climent, 2009. "Income and body mass index in Europe," Economics & Human Biology, Elsevier, vol. 7(1), pages 73-83, March.
  6. David M. Cutler & Edward L. Glaeser & Jesse M. Shapiro, 2003. "Why Have Americans Become More Obese?," Journal of Economic Perspectives, American Economic Association, vol. 17(3), pages 93-118, Summer.
  7. 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.
  8. 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.).
  9. 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.
  10. 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.
  11. Cutler, David & Shapiro, Jesse & Glaeser, Edward, 2003. "Why Have Americans Become More Obese," Scholarly Articles 2640583, Harvard University Department of Economics.
  12. 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.
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As found by EconAcademics.org, the blog aggregator for Economics research:
  1. Gli esperti di valutazione all’italiana
    by Alberto Baccini in ROARS - Return on Academic Research on 2011-12-16 15:45:50
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Cited by:
  1. Zhang, Xinyu, 2013. "Model averaging with covariates that are missing completely at random," Economics Letters, Elsevier, vol. 121(3), pages 360-363.
  2. Valentino Dardanoni & Giuseppe De Luca & Salvatore Modica & Franco Peracchi, 2011. "A Generalized Missing-Indicator Approach to Regression with Imputed Covariates," EIEF Working Papers Series 1111, Einaudi Institute for Economics and Finance (EIEF), revised May 2011.
  3. 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.
  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.

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