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Regression with imputed covariates: A generalized missing-indicator approach

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

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Sanz-de-Galdeano, Anna, 2005. "The Obesity Epidemic in Europe," IZA Discussion Papers 1814, Institute for the Study of Labor (IZA).
  2. David M. Cutler & Edward L. Glaeser & Jesse M. Shapiro, 2003. "Why Have Americans Become More Obese?," Harvard Institute of Economic Research Working Papers 1994, Harvard - Institute of Economic Research.
  3. 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.
  4. 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.
  5. 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.).
  6. 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.
  7. 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.
  8. 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.
  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. repec:dgr:kubcen:200839 is not listed on IDEAS
  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. 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.
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