Nonparametric Integration of Regression Functions







Christophe Bontemps*    Arnaud Reynaud#

January 2000 %


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Abstract:

For many problems in economics, econometricians only observe realizations of the derivative of the function they are interested in. This situation occurs each time one studies the objective function of an agent while only a first order condition resulting from an optimization problem is available. We propose a nonparametric procedure to estimate the integral of unknown, unspecified economic functions. A very simple integral estimator, built on Mack and Müller's kernel estimator (89), is suggested and analyzed. We propose plug-in and cross-validation criteria adapted to our bandwidth choice problem. A factor method developped for derivative estimators bandwidth selection is also examined ; we show how this method could be used to solve our bandwidth choice problem. An application to pollution abatement cost functions shows the potential of this procedure for many other types of economic problems.
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LEERNA and INRA, Toulouse. LEERNA is a joint research lab in the field of Environment and NAtural Resource Economics. The first author belongs to the INRA component (National Agronomical Research Institute), while the second is in the academic part (University of Social Sciences, Toulouse)
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LEERNA and GREMAQ (University of Social Sciences, Toulouse).
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We would like to thank Jean-Pierre Amigues and Alban Thomas for helpful comments on this preliminary version. Corresponding adress : LEERNA, Université des Sciences Sociales de Toulouse, 21 allée de Brienne, 31000 Toulouse, France. Email : bontemps@toulouse.inra.fr and areynaud@toulouse.inra.fr.
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