IDEAS home Printed from https://ideas.repec.org/p/iza/izadps/dp4103.html
   My bibliography  Save this paper

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

Author

Listed:
  • Henderson, Daniel J.

    (University of Alabama)

  • Parmeter, Christopher F.

    (University of Miami)

Abstract

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 of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp4103
    as

    Download full text from publisher

    File URL: https://docs.iza.org/dp4103.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Adonis Yatchew & Len Bos, 1997. "Nonparametric Least Squares Regression and Testing in Economic Models," Working Papers yatchew-99-01, University of Toronto, Department of Economics.
    2. Paul Ruud, "undated". "Restricted Least Squares Subject to Monotonicity and Concavity Constraints," Working Papers _007, University of California at Berkeley, Econometrics Laboratory Software Archive.
    3. 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.
    4. Beresteanu, Arie, 2004. "Nonparametric Estimation of Regression Functions under Restrictions on Partieal Derivatives," Working Papers 04-06, Duke University, Department of Economics.
    5. 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.
    6. 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.
    7. 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.
    8. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
    9. 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.
    10. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Improving Estimates Of Monotone Functions By Rearrangement," Boston University - Department of Economics - Working Papers Series WP2007-012, Boston University - Department of Economics.
    11. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-270, March.
    12. 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.
    13. Goldman, Steven M., 1993. "Nonparametric Multivariate Regression Subject to Constraint," Department of Economics, Working Paper Series qt7r623607, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    14. 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.
    15. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, October.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. Gallant, A. Ronald, 1982. "Unbiased determination of production technologies," Journal of Econometrics, Elsevier, vol. 20(2), pages 285-323, November.
    22. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    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. Esteve, Miriam & Aparicio, Juan & Rodriguez-Sala, Jesus J. & Zhu, Joe, 2023. "Random Forests and the measurement of super-efficiency in the context of Free Disposal Hull," European Journal of Operational Research, Elsevier, vol. 304(2), pages 729-744.
    2. 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.
    3. Jun Ma & Vadim Marmer & Artyom Shneyerov & Pai Xu, 2021. "Monotonicity-constrained nonparametric estimation and inference for first-price auctions," Econometric Reviews, Taylor & Francis Journals, vol. 40(10), pages 944-982, November.
    4. 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.
    5. 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.
    6. Christopher Parmeter & Kai Sun & Daniel Henderson & Subal Kumbhakar, 2014. "Estimation and inference under economic restrictions," Journal of Productivity Analysis, Springer, vol. 41(1), pages 111-129, February.
    7. 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.
    8. Zheng Li & Guannan Liu & Qi Li, 2017. "Nonparametric Knn estimation with monotone constraints," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 988-1006, October.
    9. 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.
    10. Olesen, O.B. & Ruggiero, J., 2022. "The hinging hyperplanes: An alternative nonparametric representation of a production function," European Journal of Operational Research, Elsevier, vol. 296(1), pages 254-266.
    11. 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.
    12. Artem Prokhorov & Kien C. Tran & Mike G. Tsionas, 2021. "Estimation of semi- and nonparametric stochastic frontier models with endogenous regressors," Empirical Economics, Springer, vol. 60(6), pages 3043-3068, June.
    13. 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.
    14. 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.
    15. 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.
    16. Valero-Carreras, Daniel & Aparicio, Juan & Guerrero, Nadia M., 2021. "Support vector frontiers: A new approach for estimating production functions through support vector machines," Omega, Elsevier, vol. 104(C).
    17. Olesen, O.B. & Ruggiero, J., 2018. "An improved Afriat–Diewert–Parkan nonparametric production function estimator," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1172-1188.

    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. Pang Du & Christopher F. Parmeter & Jeffrey S. Racine, 2012. "Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints," Department of Economics Working Papers 2012-08, McMaster University.
    2. Paul W. Wilson & Kathleen Carey, 2004. "Nonparametric analysis of returns to scale in the US hospital industry," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(4), pages 505-524.
    3. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    4. Das, Sonali & Racine, Jeffrey S., 2018. "Interactive nonparametric analysis of nonlinear systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 290-301.
    5. Steffen Andersen & Glenn Harrison & Arne Hole & Morten Lau & E. Rutström, 2012. "Non-linear mixed logit," Theory and Decision, Springer, vol. 73(1), pages 77-96, July.
    6. Gad Allon & Michael Beenstock & Steven Hackman & Ury Passy & Alexander Shapiro, 2007. "Nonparametric estimation of concave production technologies by entropic methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 795-816.
    7. David C. Wheelock & Paul W. Wilson, 2011. "Are Credit Unions Too Small?," The Review of Economics and Statistics, MIT Press, vol. 93(4), pages 1343-1359, November.
    8. Simar, Leopold & Zelenyuk, Valentin, 2011. "To Smooth or Not to Smooth? The Case of Discrete Variables in Nonparametric Regressions," LIDAM Discussion Papers ISBA 2011042, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Ye Chen & Liangjun Su & Aman Ullah, 2009. "Functional Coefficient Estimation with Both Categorical and Continuous Data," Working Papers 200909, University of California at Riverside, Department of Economics, revised Jun 2009.
    10. Leora Friedberg & Steven Stern, 2014. "Marriage, Divorce, And Asymmetric Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(4), pages 1155-1199, November.
    11. David C. Wheelock & Paul W. Wilson, 2009. "Are U.S. banks too large?," Working Papers 2009-054, Federal Reserve Bank of St. Louis.
    12. 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.
    13. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    14. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    15. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2017. "Nonparametric estimation of dynamic discrete choice models for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 97-120.
    16. Michael S. Delgado & Daniel J. Henderson & Christopher F. Parmeter, 2014. "Does Education Matter for Economic Growth?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 334-359, June.
    17. Nolwenn Roudaut & Anne Vanhems, 2012. "Explaining firms efficiency in the Ivorian manufacturing sector: a robust nonparametric approach," Journal of Productivity Analysis, Springer, vol. 37(2), pages 155-169, April.
    18. Daniel J. Henderson & Alexandre Olbrecht & Solomon W. Polachek, 2006. "Do Former College Athletes Earn More at Work?: A Nonparametric Assessment," Journal of Human Resources, University of Wisconsin Press, vol. 41(3).
    19. Hsiao, Cheng & Li, Qi & Racine, Jeffrey S., 2007. "A consistent model specification test with mixed discrete and continuous data," Journal of Econometrics, Elsevier, vol. 140(2), pages 802-826, October.
    20. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.

    More about this item

    Keywords

    identification; concavity; Hessian; constraint weighted bootstrapping; earnings function;
    All these keywords.

    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:

    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:iza:izadps:dp4103. 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: Holger Hinte (email available below). General contact details of provider: https://edirc.repec.org/data/izaaade.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.