Jansson, Torbjörn: Econometric specification of constrained optimization models. - Bonn, 2007. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-11576
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-11576,
author = {{Torbjörn Jansson}},
title = {Econometric specification of constrained optimization models},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2007,
note = {This thesis provides a general estimation framework for econometric specification of constrained optimization models, with special attention to problems arising when (i) inequality constraints are present in the constrained optimization model M that is to be estimated and/or (ii) when the estimation problem is ill-posed. The approach followed here is to use the necessary and sufficient conditions for optimality of M as estimating equations in an extremum estimation setup.
When M contains inequality constraints, then the optimality conditions contain complementary slackness conditions, which are likely to make the estimation numerically difficult to solve. In that case, the estimation problem profits from being considered a bilevel programming problem, for which general solution algorithms exist.
In a theoretical chapter, the solution of the estimation problem as a bilevel programming problem is proposed for a (synthetic) transportation model, where numerical problems make the estimation problem intractable to conventional estimation techniques. Numerical simulations are used to analyse some small sample properties of the estimator, which is shown to be more efficient than a traditional calibration methods for that problem. In a subsequent empirical chapter, the estimation of trade costs, prices and regional excess demands in a spatial price equilibrium model of trade in primary crop products in the West African country Benin is formulated as a bilevel programming problem. In that way, all available information is used and errors in both quantities and prices are taken into account. The resulting estimates are compared to results of empirical studies.
Ill-posedness, or lack of identification of the paramters, is likely to occur in estimation problems such as those considered here. Common reasons for ill-posedness are the desire for a rich model structure, data scarcity/quality problems, and the occurrance of nuisance parameters due to the measurement error structure.
If changes to the the model structure are excluded, the resolution of ill-posedness requires the researcher to introduce prior information that helps distinguish between otherwise equivalent parameter sets. During the last decade, generalized maximum entropy (GME) and general cross entropy (GCE) have been frequent means to that end. In chapter four of this thesis, a Bayesian alternative to GME/GCE is introduced, which is shown to contain GME/GCE estimators as special cases. The Bayesian alternative suggests that the prior information is introduced in the form of a-priori probability distributions for the parameters, and that the estimating equations are interpreted as a (degenerate) likelihood function. Using Bayes’ theorem, the posterior density function can be formulated, and used to obtain point estimates. Several illustrative applications of the proposed estimators are worked out in detail. Chapter five of the thesis contains an empirical application of a Bayesian estimator to the estimation of behavioural parameters of a large scale non-linear model of agricultural production in the European Union. Parameters governing the supply response of 23 crops in 165 regions are estimates using time series data. The estimator proves to deliver robust results that compare well to other empirical studies of agricultural supply response.},

url = {https://hdl.handle.net/20.500.11811/2728}

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