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Empirical Economics
Erschienen in: Empirical Economics 2/2014

01.09.2014

Estimating SUR system with random coefficients: the unbalanced panel data case

verfasst von: Erik Biørn

Erschienen in: Empirical Economics | Ausgabe 2/2014

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Abstract

A system of regression equations for analyzing panel data with random heterogeneity in intercepts and coefficients, and unbalanced panel data is considered. A maximum likelihood (ML) procedure for joint estimation of all parameters is described. Since its implementation for numerical computation is complicated, simplified procedures are presented. The simplifications essentially concern the estimation of the covariance matrices of the random coefficients. The application and ‘anatomy’ of the proposed algorithm for modified ML estimation are illustrated by using panel data for output, inputs and costs for 111 manufacturing firms observed up to 22 years.
Vorheriger Artikel On the choice of regularization parameters in specification testing: a critical discussion
Nächster Artikel The last fifteen years of stagnation in Italy: a business cycle accounting perspective

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Fußnoten
1
Subscripts denoting the calendar period may be attached. This may be convenient for data documentation and in formulating dynamic models, but will not be necessary for the static model considered here. For example, in a dataset with \(P\!=\!20\), from the years 1981–2000, some units in the \(p\!=\!18\) group may be observed in the years 1981–1998, some in 1982–1999, some in 1981–1990 and 1992–1999, etc.
 
2
For notational simplicity, the conditioning on \(({\varvec{X}}_{g(ip)},{\varvec{X}}_{h(ip)})\) is suppressed.
 
3
We here neglect possible cross-equational coefficient restrictions.
 
4
This estimator is positive definite and consistent if both \(p\) and \(N_p\) go to infinity. It is not, however, unbiased in finite samples. Modified estimators for similar balanced situations are considered in (Hsiao 2003, pp. 146–147).
 
5
Note that while \(\widehat{{\varvec{\Omega }}}_{(ip)}^{}\) is constructed from observations from all units, \(\widehat{{\varvec{\Sigma }}}_{}^{\,u}\) and \(\widehat{{\varvec{\Sigma }}}_{}^{\,\delta }\) are constructed from observations from units observed at least \(q\) times.
 
6
The data are from virtually the same source as that of (Biørn et al. 2002).
 
7
Technical change is, for simplicity, disregarded. The underlying total cost also includes energy cost, which is not modelled in the example. Neither capital cost nor capital input is represented in the model. Hence, we have no ‘full’ cost function represented.
 
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Metadaten
Titel
Estimating SUR system with random coefficients: the unbalanced panel data case
verfasst von
Erik Biørn
Publikationsdatum
01.09.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Empirical Economics / Ausgabe 2/2014
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI
https://doi.org/10.1007/s00181-013-0753-y

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