IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/199814.html
   My bibliography  Save this paper

Nonparametric estimation and testing of interaction in additive models

Author

Listed:
  • Sperlich, Stefan
  • Tjøstheim, Dag
  • Yang, Lijian

Abstract

We consider an additive model with second order interaction terms. It is shown how the components of this model can be estimated using marginal integration, and the asymptotic distribution of the estimators is derived. Moreover, two test statistics for testing the presence of interactions are proposed. Asymptotics for the test functions are obtained, but in this case the asymptotics produce inaccurate results unless the number of observations is very large. For small or moderate sample sizes a bootstrap procedure is suggested and is shown to work well on a simulated example. Finally, our methods are illustrated on a five-dimensional production function for a set of Wisconsin farm data. In particular, the separability hypothesis for the production function is discussed.

Suggested Citation

  • Sperlich, Stefan & Tjøstheim, Dag & Yang, Lijian, 1998. "Nonparametric estimation and testing of interaction in additive models," SFB 373 Discussion Papers 1998,14, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199814
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/61263/1/721139124.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    2. Fuss, Melvyn & McFadden, Daniel & Mundlak, Yair, 1978. "A Survey of Functional Forms in the Economic Analysis of Production," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.),Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 4, McMaster University Archive for the History of Economic Thought.
    3. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    4. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762.
    5. Fan, J. & Härdle, Wolfgang & Mammen, Enno, 1996. "Direct estimation of low dimensional components in additive models," SFB 373 Discussion Papers 1996,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    7. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
    8. Härdle, Wolfgang & Linton, O., 1995. "Nonparametric Regression," SFB 373 Discussion Papers 1995,29, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
    10. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    11. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    12. Masry, E. & Tjostheim, D., 1996. "Additive nonlinear ARX time series and projection estimates," SFB 373 Discussion Papers 1996,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    13. Ernst R. Berndt & Laurits R. Christensen, 1973. "The Internal Structure of Functional Relationships: Separability, Substitution, and Aggregation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 403-410.
    14. Denny, Michael & Fuss, Melvyn A, 1977. "The Use of Approximation Analysis to Test for Separability and the Existence of Consistent Aggregates," American Economic Review, American Economic Association, vol. 67(3), pages 404-418, June.
    Full references (including those not matched with items on IDEAS)

    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. Stefan Profit & Stefan Sperlich, 2004. "Non-uniformity of job-matching in a transition economy - A nonparametric analysis for the Czech Republic," Applied Economics, Taylor & Francis Journals, vol. 36(7), pages 695-714.
    2. Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2004. "Bootstrap Inference In Semiparametric Generalized Additive Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 265-300, April.
    3. Rodriguez Poo, Juan M. & Sperlich, Stefan & Vieu, Philippe, 2000. "Semiparametric estimation of weak and strong separable models," DES - Working Papers. Statistics and Econometrics. WS 10064, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Richmond, J, 2000. "Separability and Specification Tests," Economics Discussion Papers 8832, University of Essex, Department of Economics.
    5. Gloria A. Grizzle & Ann D. Witte, 1984. "Evaluating Multidimensional Performance," Evaluation Review, , vol. 8(6), pages 777-800, December.
    6. Marc Gaudry & Emile Quinet, 2009. "Track wear-and-tear cost by traffic class: Functional form, zero output levels and marginal cost pricing recovery on the French rail network," Working Papers halshs-00574977, HAL.
    7. Perekhozhuk, Oleksandr, 2007. "Marktstruktur und Preisbildung auf dem ukrainischen Markt für Rohmilch," Studies on the Agricultural and Food Sector in Transition Economies, Leibniz Institute of Agricultural Development in Transition Economies (IAMO), volume 41, number 92322.
    8. V. Vandenberghe, 2018. "The Contribution of Educated Workers to Firms’ Efficiency Gains: The Key Role of Proximity to the ‘Local’ Frontier," De Economist, Springer, vol. 166(3), pages 259-283, September.
    9. Moschini, G. & Moro, D., 1993. "A Food demand System for Canada," Papers 1-93, Gouvernement du Canada - Agriculture Canada.
    10. Huiban, Jean-Pierre & Mastromarco, Camille & Musolesi, Antonio & Simioni, Michel, 2016. "The impact of pollution abatement investments on production technology: new insights from frontier analysis," Working Papers MOISA 235162, Institut National de la recherché Agronomique (INRA), UMR MOISA : Marchés, Organisations, Institutions et Stratégies d'Acteurs : CIHEAM-IAMM, CIRAD, INRA, Montpellier SupAgro, Montpellier, France.
    11. Sauer, J., 2007. "Monotonicity and Curvature – A Bootstrapping Approach," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 42, March.
    12. Andreas Reinstaller & Werner Hölzl, 2004. "Complementarity constraints and induced innovation: some evidence from the first IT regime," Chapters, in: John Foster & Werner Hölzl (ed.), Applied Evolutionary Economics and Complex Systems, chapter 6, Edward Elgar Publishing.
    13. Carter, Michael R., 1986. "Peasant Productivity And Differentiation: A Microeconometric Analysis Of The Impact Of Small Farm Credit In Nicaragua," 1986 Annual Meeting, July 27-30, Reno, Nevada 278458, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    14. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2016. "Congestion in production correspondences," Journal of Economics, Springer, vol. 119(1), pages 65-90, September.
    15. Andrea Mantovi, 2016. "Smooth preferences, symmetries and expansion vector fields," Journal of Economics, Springer, vol. 119(2), pages 147-169, October.
    16. Wunscher, Tobias & Engel, Stefanie & Wunder, Sven, 2011. "Practical Alternatives to Estimate Opportunity Costs of Forest Conservation," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 115774, European Association of Agricultural Economists.
    17. van Groenendaal, Willem J. H., 1995. "Assessing demand when introducing a new fuel : Natural gas on Java," Energy Economics, Elsevier, vol. 17(2), pages 147-161, April.
    18. Mazzocco, Michael A. & Eales, James S., 1987. "Estimating Factor Demands for Iltinois Cash Grain Farms: Differences Between Profitable and Unprofitable Farms," 1987 Annual Meeting, August 2-5, East Lansing, Michigan 269945, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    19. Tzouvelekas, Evaggelos, 2000. "Approximation Properties and Estimation of the Translog Production Function with Panel Data," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 1(1), pages 1-16, January.
    20. McDonald, John & Snooks, G. D., 1986. "Domesday Economy: A New Approach to Anglo-Norman History," OUP Catalogue, Oxford University Press, number 9780198285243.

    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:zbw:sfb373:199814. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sfhubde.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.