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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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    Citations

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    Cited by:

    1. Stefan Hoderlein & Yuya Sasaki, 2013. "Outcome conditioned treatment effects," CeMMAP working papers CWP39/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Ghanem, Dalia, 2017. "Testing identifying assumptions in nonseparable panel data models," Journal of Econometrics, Elsevier, vol. 197(2), pages 202-217.
    3. 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.
    4. Sokbae (Simon) 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.
    5. Peter Reinhard Hansen & Zhuo Huang, 2016. "Exponential GARCH Modeling With Realized Measures of Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 269-287, April.
    6. Nir Billfeld & Moshe Kim, 2024. "Context-dependent Causality (the Non-Nonotonic Case)," Papers 2404.05021, arXiv.org.
    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. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    9. Lu, Xun & White, Habert, 2015. "Testing For Treatment Dependence Of Effects Of A Continuous Treatment," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1016-1053, October.
    10. Jiun-Hua Su, 2019. "Counterfactual Inference in Duration Models with Random Censoring," Papers 1902.08502, arXiv.org.
    11. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    12. Zequn Jin & Lihua Lin & Zhengyu Zhang, 2022. "Identification and Auto-debiased Machine Learning for Outcome Conditioned Average Structural Derivatives," Papers 2211.07903, arXiv.org.
    13. Mammen, Enno & Van Keilegom, Ingrid & Yu, Kyusang, 2013. "Expansion for Moments of Regression Quantiles with Applications to Nonparametric Testing," LIDAM Discussion Papers ISBA 2013027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Kasy, Maximilian, 2022. "Who wins, who loses? Identification of conditional causal effects, and the welfare impact of changing wages," Journal of Econometrics, Elsevier, vol. 226(1), pages 155-170.
    15. Chen, Songnian & Wang, Xi, 2018. "Semiparametric estimation of panel data models without monotonicity or separability," Journal of Econometrics, Elsevier, vol. 206(2), pages 515-530.
    16. Lu, Xun & White, Halbert, 2014. "Testing for separability in structural equations," Journal of Econometrics, Elsevier, vol. 182(1), pages 14-26.
    17. Hubner, Stefan, 2023. "Identification of unobserved distribution factors and preferences in the collective household model," Journal of Econometrics, Elsevier, vol. 234(1), pages 301-326.

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