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Modelling with Discretized Variables

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  • Felix Chan
  • Laszlo Matyas
  • Agoston Reguly

Abstract

This paper deals with econometric models in which the dependent variable, some explanatory variables, or both are observed as censored interval data. This discretization often happens due to confidentiality of sensitive variables like income. Models using these variables cannot point identify regression parameters as the conditional moments are unknown, which led the literature to use interval estimates. Here, we propose a discretization method through which the regression parameters can be point identified while preserving data confidentiality. We demonstrate the asymptotic properties of the OLS estimator for the parameters in multivariate linear regressions for cross-sectional data. The theoretical findings are supported by Monte Carlo experiments and illustrated with an application to the Australian gender wage gap.

Suggested Citation

  • Felix Chan & Laszlo Matyas & Agoston Reguly, 2024. "Modelling with Discretized Variables," Papers 2403.15220, arXiv.org.
    • Handle: RePEc:arx:papers:2403.15220
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    References listed on IDEAS

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    1. Klevmarken, Anders, 1982. "Missing Variables and Two-Stage Least-Squares Estimation from More than One Data Set," Working Paper Series 62, Research Institute of Industrial Economics.
    2. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    3. John Micklewright & Sylke V. Schnepf, 2010. "How reliable are income data collected with a single question?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(2), pages 409-429, April.
    4. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    5. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    6. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    7. Juan D. Barón & Deborah A. Cobb‐Clark, 2010. "Occupational Segregation and the Gender Wage Gap in Private‐ and Public‐Sector Employment: A Distributional Analysis," The Economic Record, The Economic Society of Australia, vol. 86(273), pages 227-246, June.
    8. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    9. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    10. Steffen Andersen & Glenn W. Harrison & Morten I. Lau & E. Elisabet Rutström, 2008. "Eliciting Risk and Time Preferences," Econometrica, Econometric Society, vol. 76(3), pages 583-618, May.
    11. Regina Riphahn & Oliver Serfling, 2005. "Item non-response on income and wealth questions," Empirical Economics, Springer, vol. 30(2), pages 521-538, September.
    12. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    13. Paul Fisher, 2019. "Does Repeated Measurement Improve Income Data Quality?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(5), pages 989-1011, October.
    14. Jason Abrevaya & Chris Muris, 2020. "Interval censored regression with fixed effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(2), pages 198-216, March.
    15. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    16. Peter A. Diamond & Jerry A. Hausman, 1994. "Contingent Valuation: Is Some Number Better than No Number?," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 45-64, Fall.
    17. Xi Wang & Songnian Chen, 2022. "Partial Identification and Estimation of Semiparametric Ordered Response Models with Interval Regressor Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(4), pages 830-849, August.
    18. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    19. David Pacini, 2019. "The two‐sample linear regression model with interval‐censored covariates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(1), pages 66-81, January.
    20. Steffen Andersen & Glenn Harrison & Morten Lau & E. Rutström, 2009. "Elicitation using multiple price list formats," Experimental Economics, Springer;Economic Science Association, vol. 12(3), pages 365-366, September.
    21. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    22. Michael B. Coelli, 2014. "Occupational Differences and the Australian Gender Wage Gap," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 47(1), pages 44-62, March.
    23. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    24. Chi Wai Yu & Y. Jane Zhang & Sharon Xuejing Zuo, 2021. "Multiple Switching and Data Quality in the Multiple Price List," The Review of Economics and Statistics, MIT Press, vol. 103(1), pages 136-150, March.
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