IDEAS home Printed from https://ideas.repec.org/p/cor/louvrp/2442.html
   My bibliography  Save this paper

Iterative regularisation in nonparametric instrumental regression

Author

Listed:
  • JOHANNES, Jan
  • VAN BELLEGEM, Sébastien
  • VANHEMS, Anne

Abstract

We consider the nonparametric regression model with an additive error that is correlated with the explanatory variables. We suppose the existence of instrumental variables that are considered in this model for the identification and the estimation of the regression function. The nonparametric estimation by instrumental variables is an illposed linear inverse problem with an unknown but estimable operator. We provide a new estimator of the regression function using an iterative regularization method (the Landweber-Fridman method). The optimal number of iterations and the convergence of the mean square error of the resulting estimator are derived under both mild and severe degrees of ill-posedness. A Monte-Carlo exercise shows the impact of some parameters on the estimator and concludes on the reasonable finite sample performance of the new estimator.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • JOHANNES, Jan & VAN BELLEGEM, Sébastien & VANHEMS, Anne, 2013. "Iterative regularisation in nonparametric instrumental regression," LIDAM Reprints CORE 2442, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2442
    DOI: 10.1016/j.jspi.2012.07.010
    Note: In : Journal of Statistical Planning and Inference, 143(1), 24-39, 2013
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    2. Joshua D. Angrist & Alan B. Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 69-85, Fall.
    3. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011. "Convergence Rates For Ill-Posed Inverse Problems With An Unknown Operator," Econometric Theory, Cambridge University Press, vol. 27(3), pages 522-545, June.
    4. Cremer, Helmuth & Gahvari, Firouz & Pestieau, Pierre, 2011. "Fertility, human capital accumulation, and the pension system," Journal of Public Economics, Elsevier, vol. 95(11), pages 1272-1279.
    5. Pierre-Philippe Combes & Thierry Mayer & Jacques-François Thisse, 2008. "Economic Geography: The Integration of Regions and Nations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00311000, HAL.
    6. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
    7. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    8. OGGIONI, Giorgia & SMEERS, Yves, 2010. "Market coupling and the organization of counter-trading: separating energy and transmission again?," LIDAM Discussion Papers CORE 2010053, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    10. Huriot,Jean-Marie & Thisse,Jacques-François (ed.), 2009. "Economics of Cities," Cambridge Books, Cambridge University Press, number 9780521118279, September.
    11. JOHANNES, Jan & VAN BELLEGEM, Sébastien & VANHEMS, Anne, 2010. "Iterative regularization in nonparametric instrumental regression," LIDAM Discussion Papers CORE 2010055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), 2008. "High Frequency Financial Econometrics," Studies in Empirical Economics, Springer, number 978-3-7908-1992-2, September.
    13. Joshua Angrist & Alan Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Working Papers 834, Princeton University, Department of Economics, Industrial Relations Section..
    14. Yves Smeers & Giorgia Oggioni & Elisabetta Allevi & Siegfried Schaible, 2010. "Generalized Nash Equilibrium and Market Coupling in the European Power System," Working Papers EPRG 1016, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Centorrino, Samuele & Florens, Jean-Pierre, 2021. "Nonparametric Instrumental Variable Estimation of Binary Response Models with Continuous Endogenous Regressors," Econometrics and Statistics, Elsevier, vol. 17(C), pages 35-63.
    2. Emir Malikov & Shunan Zhao & Subal C. Kumbhakar, 2020. "Estimation of firm‐level productivity in the presence of exports: Evidence from China's manufacturing," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 457-480, June.
    3. Vanhems, Anne & Van Keilegom, Ingrid, 2019. "Estimation Of A Semiparametric Transformation Model In The Presence Of Endogeneity," Econometric Theory, Cambridge University Press, vol. 35(1), pages 73-110, February.
    4. Bréchet, Thierry & Jouvet, Pierre-André & Rotillon, Gilles, 2013. "Tradable pollution permits in dynamic general equilibrium: Can optimality and acceptability be reconciled?," Ecological Economics, Elsevier, vol. 91(C), pages 89-97.
    5. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2010. "Iterative Regularization in Nonparametric Instrumental Regression," TSE Working Papers 10-184, Toulouse School of Economics (TSE).
    6. Centorrino Samuele & Feve Frederique & Florens Jean-Pierre, 2017. "Additive Nonparametric Instrumental Regressions: A Guide to Implementation," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-25, January.
    7. Asin, Nicolas & Johannes, Jan, 2016. "Adaptive non-parametric instrumental regression in the presence of dependence," LIDAM Discussion Papers ISBA 2016015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Melanie Birke & Sebastien Van Bellegem & Ingrid Van Keilegom, 2017. "Semi-parametric Estimation in a Single-index Model with Endogenous Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 168-191, March.
    9. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    10. Samuele Centorrino & Jean-Pierre Florens, 2014. "Nonparametric Instrumental Variable Estimation of Binary Response Models," Department of Economics Working Papers 14-07, Stony Brook University, Department of Economics.
    11. De Monte Enrico, 2024. "Nonparametric Instrumental Regression with Two-Way Fixed Effects," Journal of Econometric Methods, De Gruyter, vol. 13(1), pages 49-66, January.
    12. Jean-Pierre Florens & Elia Lapenta, 2022. "Partly Linear Instrumental Variables Regressions without Smoothing on the Instruments," Papers 2212.11012, arXiv.org, revised Oct 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bréchet, Thierry & Jouvet, Pierre-André & Rotillon, Gilles, 2013. "Tradable pollution permits in dynamic general equilibrium: Can optimality and acceptability be reconciled?," Ecological Economics, Elsevier, vol. 91(C), pages 89-97.
    2. Cremer, Helmuth & Gahvari, Firouz & Pestieau, Pierre, 2011. "Fertility, human capital accumulation, and the pension system," Journal of Public Economics, Elsevier, vol. 95(11), pages 1272-1279.
    3. Manzi, Jorge & San Martin, Ernesto & Van Bellegem, Sébastien, 2010. "School System Evaluation By Value-Added Analysis under Endogeneity," IDEI Working Papers 631, Institut d'Économie Industrielle (IDEI), Toulouse.
    4. Florens, Jean-Pierre & Schwarz, Maik & Van Bellegem, Sébastien, 2010. "Nonparametric Frontier Estimation from Noisy Data," IDEI Working Papers 625, Institut d'Économie Industrielle (IDEI), Toulouse.
    5. Gautier, Axel & Wauthy, Xavier, 2012. "Competitively neutral universal service obligations," Information Economics and Policy, Elsevier, vol. 24(3), pages 254-261.
    6. Pierre Pestieau & Maria Racionero, 2015. "Tagging with leisure needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 687-706, December.
    7. Leroux, Marie-Louise & Ponthiere, Gregory, 2013. "Utilitarianism and unequal longevities: A remedy?," Economic Modelling, Elsevier, vol. 30(C), pages 888-899.
    8. A. Mauleon & Vincent Vannetelbosch & Cecilia Vergari, 2014. "Unions' Relative Concerns And Strikes In Wage Bargaining," Bulletin of Economic Research, Wiley Blackwell, vol. 66(4), pages 374-383, October.
    9. M.-L. Leroux & P. Pestieau, 2012. "The political economy of derived pension rights," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 19(5), pages 753-776, October.
    10. Per J. Agrell & Axel Gautier, 2017. "A Theory of Soft Capture," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(3), pages 571-596, July.
    11. Michel Le Breton & Juan Moreno-Ternero & Alexei Savvateev & Shlomo Weber, 2013. "Stability and fairness in models with a multiple membership," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 673-694, August.
    12. STEPHAN, Rüdiger, 2010. "An extension of disjunctive programming and its impact for compact tree formulations," LIDAM Discussion Papers CORE 2010045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. GILLIS, Nicolas & GLINEUR, François, 2010. "On the geometric interpretation of the nonnegative rank," LIDAM Discussion Papers CORE 2010051, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Moreno-Ternero, Juan D., 2011. "Voting over piece-wise linear tax methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 29-36, January.
    15. Rombouts, Jeroen V.K. & Stentoft, Lars, 2015. "Option pricing with asymmetric heteroskedastic normal mixture models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 635-650.
    16. AGRELL, Per & KASPERZEC, Roman, 2010. "Dynamic joint investments in supply chains under information asymmetry," LIDAM Discussion Papers CORE 2010085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. DI SUMMA, Marco & WOLSEY, Laurence, 2010. "Mixing sets linked by bidirected paths," LIDAM Discussion Papers CORE 2010063, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. LUTTENS, Roland Iwan, 2010. "Lower bounds rule!," LIDAM Discussion Papers CORE 2010069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. DENUIT, Michel & EECKHOUDT, Louis & TSETLIN, Ilia & WINKLER, Robert L., 2010. "Multivariate concave and convex stochastic dominance," LIDAM Discussion Papers CORE 2010044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. GABSZEWICZ, Jean & TAROLA, Ornella, 2010. "Product innovation and market acquisition of firms," LIDAM Discussion Papers CORE 2010078, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cor:louvrp:2442. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.