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Imposing Curvature and Monotonicity on Flexible Functional Forms: An Efficient Regional Approach


  • Hendrik Wolff


  • Thomas Heckelei
  • Ron Mittelhammer


Abstract In many areas of economic analysis, economic theory restricts the shape as well as other characteristics of functions used to represent economic constructs. Obvious examples are the monotonicity and curvature conditions that apply to utility, profit, and cost functions. Commonly, these regularity conditions are imposed either locally or globally. Here we extend and improve upon currently available estimation methods for imposing regularity conditions by imposing regularity on a connected subset of the regressor space. This method offers important advantages over the local approach by imposing theoretical consistency not only locally, at a given evaluation point but also within the whole empirically relevant region of the domain associated with the function being estimated. The method also provides benefits relative to the global approach, through higher flexibility, which generally leads to a better model fit to the sample data compared to the global imposition of regularity. Specific contributions of this paper are (a) to increase the computational speed and tractability of imposing regularity conditions in estimation, (b) to provide regularity preserving point estimates, (c) to avoid biases existent in previous applications, and (d) to illustrate the benefits of the regional approach via numerical simulation results
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  • Hendrik Wolff & Thomas Heckelei & Ron Mittelhammer, 2010. "Imposing Curvature and Monotonicity on Flexible Functional Forms: An Efficient Regional Approach," Computational Economics, Springer;Society for Computational Economics, vol. 36(4), pages 309-339, December.
  • Handle: RePEc:kap:compec:v:36:y:2010:i:4:p:309-339 DOI: 10.1007/s10614-010-9215-1

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    References listed on IDEAS

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    Cited by:

    1. Suh, Dong Hee & Moss, Charles B., 2014. "Exploring Agricultural Production Systems: Interactions between the Crop and Livestock Sectors," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170149, Agricultural and Applied Economics Association.
    2. Femenia, Fabienne & Gohin, Alexandre, 2007. "Estimating price elasticities of food trade functions: How relevant is the gravity approach?," Working Papers 7211, TRADEAG - Agricultural Trade Agreements.
    3. repec:kap:jproda:v:47:y:2017:i:3:d:10.1007_s11123-017-0496-4 is not listed on IDEAS
    4. repec:spr:empeco:v:52:y:2017:i:4:d:10.1007_s00181-016-1112-6 is not listed on IDEAS
    5. Mellah, Thuraya & Ben Amor, Tawfik, 2016. "Performance of the Tunisian Water Utility: An input-distance function approach," Utilities Policy, Elsevier, vol. 38(C), pages 18-32.

    More about this item


    Nonlinear inequality constraints; Flexible functional forms; Metropolis-Hastings; Accept–Reject algorithm; Cost function; Regularity conditions; C51; D21; C11;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General


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