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Identification and Nonparametric Estimation of a Transformed Additively Separable Model


  • David Jacho-Chavez

    (Indiana University)

  • Arthur Lewbel

    () (Boston College)

  • Oliver Linton

    (London School of Economics)


Let r(x,z) be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses identification and consistent estimation of the unknown functions H, M, G and F, where r(x, z) = H[M (x, z)] and M(x,z) = G(x) + F(z). An estimation algorithm is proposed for each of the model's unknown components when r(x, z) represents a conditional mean function. The resulting estimators use marginal integration, and are shown to have a limiting Normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives. Their small sample performance is studied in a Monte Carlo experiment. We empirically apply our results to nonparametrically estimate and test generalized homothetic production functions in four industries within the Chinese economy.

Suggested Citation

  • David Jacho-Chavez & Arthur Lewbel & Oliver Linton, 2006. "Identification and Nonparametric Estimation of a Transformed Additively Separable Model," Boston College Working Papers in Economics 652, Boston College Department of Economics, revised 26 Nov 2008.
  • Handle: RePEc:boc:bocoec:652

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    References listed on IDEAS

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    Cited by:

    1. Van Keilegom, Ingrid & Vanhems, Anne, 2016. "Estimation of a semiparametric transformation model in the presence of endogeneity," TSE Working Papers 16-654, Toulouse School of Economics (TSE).
    2. Chiappori, Pierre-André & Komunjer, Ivana & Kristensen, Dennis, 2015. "Nonparametric identification and estimation of transformation models," Journal of Econometrics, Elsevier, vol. 188(1), pages 22-39.
    3. Pierre-André Chiappori & Ivana Komunjer, 2008. "Correct Specification and Identification of Nonparametric Transformation Models," Working Papers 2009-003, Becker Friedman Institute for Research In Economics.
    4. repec:eee:jmvana:v:160:y:2017:i:c:p:10-30 is not listed on IDEAS
    5. Horowitz, Joel L. & Lee, Sokbae, 2017. "Nonparametric estimation and inference under shape restrictions," Journal of Econometrics, Elsevier, vol. 201(1), pages 108-126.
    6. Lewbel, Arthur & Lu, Xun & Su, Liangjun, 2015. "Specification testing for transformation models with an application to generalized accelerated failure-time models," Journal of Econometrics, Elsevier, vol. 184(1), pages 81-96.
    7. Benjamin Colling & Ingrid Keilegom, 2016. "Goodness-of-fit tests in semiparametric transformation models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 291-308, June.
    8. Van Keilegom, Ingrid & Vanhems, Anne, 2011. "Semiparametric transformation model with endogeneity: a control function approach," TSE Working Papers 11-243, Toulouse School of Economics (TSE).
    9. repec:eee:econom:v:201:y:2017:i:1:p:95-107 is not listed on IDEAS

    More about this item


    Partly separable models; Nonparametric regression; Dimension reduction; Generalized homothetic function; Production function.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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