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Identification and estimation of local average derivatives in non-separable models without monotonicity

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  • Stefan Hoderlein
  • Enno Mammen

Abstract

In many structural economic models there are no good arguments for additive separability of the error. Recently, this motivated intensive research on non-separable structures. For instance, in Hoderlein and Mammen (2007) a non-separable model in the single equation case was considered, and it was established that in the absence of the frequently employed monotonicity assumption local average structural derivatives (LASD) are still identified. In this paper, we introduce an estimator for the LASD. The estimator we propose is based on local polynomial fitting of conditional quantiles. We derive its large sample distribution through a Bahadur representation, and give some related results, e.g. about the asymptotic behaviour of the quantile process. Moreover, we generalize the concept of LASD to include endogeneity of regressors and discuss the case of a multivariate dependent variable. We also consider identification of structured non-separable models, including single index and additive models. We discuss specification testing, as well as testing for endogeneity and for the impact of unobserved heterogeneity. We also show that fixed censoring can easily be addressed in this framework. Finally, we apply some of the concepts to demand analysis using British Consumer Data. Copyright The Author(s). Journal compilation Royal Economic Society 2009

Suggested Citation

  • Stefan Hoderlein & Enno Mammen, 2009. "Identification and estimation of local average derivatives in non-separable models without monotonicity," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 1-25, March.
  • Handle: RePEc:ect:emjrnl:v:12:y:2009:i:1:p:1-25
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    Cited by:

    1. Lu, Xun & White, Habert, 2015. "Testing For Treatment Dependence Of Effects Of A Continuous Treatment," Econometric Theory, Cambridge University Press, vol. 31(05), pages 1016-1053, October.
    2. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Iv'an Fern'andez-Val, 2011. "Conditional Quantile Processes based on Series or Many Regressors," Papers 1105.6154, arXiv.org, revised Jul 2017.
    3. Ghanem, Dalia, 2017. "Testing identifying assumptions in nonseparable panel data models," Journal of Econometrics, Elsevier, vol. 197(2), pages 202-217.
    4. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    5. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    6. Lu, Xun & White, Halbert, 2014. "Testing for separability in structural equations," Journal of Econometrics, Elsevier, vol. 182(1), pages 14-26.
    7. Blundell, Richard & Kristensen, Dennis & Matzkin, Rosa, 2014. "Bounding quantile demand functions using revealed preference inequalities," Journal of Econometrics, Elsevier, vol. 179(2), pages 112-127.
    8. Sokbae Lee & Yoon-Jae Whang, 2009. "Nonparametric tests of conditional treatment effects," CeMMAP working papers CWP36/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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