IDEAS home Printed from
   My bibliography  Save this paper

Imposing Economic Constraints in Nonparametric Regression: Survey, Implementation and Extension


  • Henderson, Daniel J.

    () (University of Alabama)

  • Parmeter, Christopher F.

    () (University of Miami)


Economic conditions such as convexity, homogeneity, homotheticity, and monotonicity are all important assumptions or consequences of assumptions of economic functionals to be estimated. Recent research has seen a renewed interest in imposing constraints in nonparametric regression. We survey the available methods in the literature, discuss the challenges that present themselves when empirically implementing these methods and extend an existing method to handle general nonlinear constraints. A heuristic discussion on the empirical implementation for methods that use sequential quadratic programming is provided for the reader and simulated and empirical evidence on the distinction between constrained and unconstrained nonparametric regression surfaces is covered.

Suggested Citation

  • Henderson, Daniel J. & Parmeter, Christopher F., 2009. "Imposing Economic Constraints in Nonparametric Regression: Survey, Implementation and Extension," IZA Discussion Papers 4103, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp4103

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Matzkin, Rosa L., 1986. "Restrictions of economic theory in nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 42, pages 2523-2558 Elsevier.
    2. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Improving estimates of monotone functions by rearrangement," CeMMAP working papers CWP09/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, May.
    4. Murphy, Kevin M & Welch, Finis, 1990. "Empirical Age-Earnings Profiles," Journal of Labor Economics, University of Chicago Press, vol. 8(2), pages 202-229, April.
    5. Matzkin, Rosa L, 1991. "Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models," Econometrica, Econometric Society, vol. 59(5), pages 1315-1327, September.
    6. S. M. Goldman & P. A. Ruud, 1993. "Nonparametric Multivariate Regression Subject to Constraint," Econometrics 9311001, EconWPA.
    7. Beresteanu, Arie, 2004. "Nonparametric Estimation of Regression Functions under Restrictions on Partieal Derivatives," Working Papers 04-06, Duke University, Department of Economics.
    8. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
    9. Wheelock, David C. & Wilson, Paul W., 2001. "New evidence on returns to scale and product mix among U.S. commercial banks," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 653-674, June.
    10. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    11. Qi Li & Jeffrey S. Racine & Jeffrey M. Wooldridge, 2008. "Estimating Average Treatment Effects with Continuous and Discrete Covariates: The Case of Swan-Ganz Catheterization," American Economic Review, American Economic Association, vol. 98(2), pages 357-362, May.
    12. Gallant, A. Ronald & Golub, Gene H., 1984. "Imposing curvature restrictions on flexible functional forms," Journal of Econometrics, Elsevier, vol. 26(3), pages 295-321, December.
    13. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
    14. Henderson, Daniel J. & List, John A. & Millimet, Daniel L. & Parmeter, Christopher F. & Price, Michael K., 2008. "Imposing Monotonicity Nonparametrically in First-Price Auctions," MPRA Paper 8769, University Library of Munich, Germany.
    15. Rosa L. Matzkin, 1988. "Nonparametric and Distribution-Free Estimation of the Binary Choice and the Threshold-Crossing Models," Cowles Foundation Discussion Papers 889, Cowles Foundation for Research in Economics, Yale University.
    16. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
    17. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    18. Gallant, A. Ronald, 1982. "Unbiased determination of production technologies," Journal of Econometrics, Elsevier, vol. 20(2), pages 285-323, November.
    19. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Lee, Tae-Hwy & Tu, Yundong & Ullah, Aman, 2014. "Nonparametric and semiparametric regressions subject to monotonicity constraints: Estimation and forecasting," Journal of Econometrics, Elsevier, vol. 182(1), pages 196-210.
    2. Michaelides, Panayotis G. & Tsionas, Efthymios G. & Vouldis, Angelos T. & Konstantakis, Konstantinos N., 2015. "Global approximation to arbitrary cost functions: A Bayesian approach with application to US banking," European Journal of Operational Research, Elsevier, vol. 241(1), pages 148-160.
    3. Henderson, Daniel J. & List, John A. & Millimet, Daniel L. & Parmeter, Christopher F. & Price, Michael K., 2012. "Empirical implementation of nonparametric first-price auction models," Journal of Econometrics, Elsevier, vol. 168(1), pages 17-28.
    4. Don Harding, 2010. "Applying shape and phase restrictions in generalized dynamic categorical models of the business cycle," Working Papers 2010.05, School of Economics, La Trobe University.
    5. Tsionas, Euthimios G. & Mamatzakis, Emmanuel C., 2017. "Adjustment costs in the technical efficiency: An application to global banking," European Journal of Operational Research, Elsevier, vol. 256(2), pages 640-649.
    6. Yu Zhang & Jingping Gu & Qi Li, 2011. "Nonparametric panel estimation of online auction price processes," Empirical Economics, Springer, vol. 40(1), pages 51-68, February.
    7. Wenchuan Liu & Yu Zhang & Qi Li, 2015. "A semiparametric varying coefficient model of monotone auction bidding processes," Empirical Economics, Springer, vol. 48(1), pages 313-335, February.
    8. Wolters, Mark A., 2012. "A particle swarm algorithm with broad applicability in shape-constrained estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2965-2975.
    9. Stefan Seifert, 2016. "Semi-Parametric Measures of Scale Characteristics of German Natural Gas-Fired Electricity Generation," Discussion Papers of DIW Berlin 1571, DIW Berlin, German Institute for Economic Research.
    10. repec:eee:ejores:v:264:y:2018:i:3:p:1172-1188 is not listed on IDEAS

    More about this item


    identification; concavity; Hessian; constraint weighted bootstrapping; earnings function;

    JEL classification:

    • J20 - Labor and Demographic Economics - - Demand and Supply of Labor - - - General
    • J30 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:iza:izadps:dp4103. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mark Fallak). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.