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Nonparametric Errors in Variables Models with Measurement Errors on both sides of the Equation

Author

Listed:
  • Michele De Nadai

    (University of Padova)

  • Arthur Lewbel

    () (Boston College)

Abstract

Measurement errors are often correlated, as in surveys where respondents' biases or tendencies to err affect multiple reported variables. We extend Schennach (2007) to identify moments of the conditional distribution of a true Y given a true X when both are measured with error, the measurement errors in Y and X are correlated, and the true unknown model of Y given X has nonseparable model errors. We also provide a nonparametric sieve estimator of the model, and apply it to nonparametric Engel curve estimation. In our application measurement errors on the expenditures of a good Y are by construction correlated with measurement errors in total expenditures X. This feature of most consumption data sets has been ignored in almost all previous demand applications. We find accounting for this feature casts doubt on Hildenbrand's (1994) "increasing dispersion" assumption.

Suggested Citation

  • Michele De Nadai & Arthur Lewbel, 2012. "Nonparametric Errors in Variables Models with Measurement Errors on both sides of the Equation," Boston College Working Papers in Economics 790, Boston College Department of Economics, revised 01 Jul 2013.
  • Handle: RePEc:boc:bocoec:790
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    References listed on IDEAS

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    1. repec:eee:stapro:v:126:y:2017:i:c:p:219-229 is not listed on IDEAS
    2. repec:ucp:jpolec:doi:10.1086/692808 is not listed on IDEAS
    3. Arthur Lewbel & Krishna Pendakur, 2017. "Unobserved Preference Heterogeneity in Demand Using Generalized Random Coefficients," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1100-1148.

    More about this item

    Keywords

    Engel curve; errors-in-variables model; Fourier transform; generalized function; sieve estimation.;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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