SFB 303 Discussion Paper No. B-301

Author: Werner, Hans Joachim, and Cemil Yapar

Title: More on partitioned possibly restricted linear regression
Abstract: This paper deals with the general partitioned linear regression model where the regressor matrix $X=\pmatrix{X_1 & X_2\cr}$ may be deficient in column rank, the dispersion matrix $V$ is possibly singular, $\beta^t=\pmatrix{\beta_1^t & \beta_2^t\cr}$ - being partitioned according to $X$ - is the vector of unknown regression coefficients, and $\beta_2$ is possibly subject to consistent linear equality or inequality restrictions. In particular, we are interested in the set of {\it generalized least squares (GLS) selections} for $\beta_2$. Inspired by Aigner and Balestra [1], as well as by Nurhonen and Puntanen [2], we also consider a specific reduced model and describe a scenario under which the set of GLS selections for $\beta_2$ under the reduced model equals the set of GLS selections for $\beta_2$ under the original full model. The results obtained in [2] and [1] for the unrestricted {\it standard} (full rank) regression model are reobtained as special cases.
Keywords: Gauss-Markov model, singular model, perfect multicollinearity, partitioned linear regression, linear equality constraints, linear inequality constraints, constrained generalized least squares selections, oblique projectors, generalized inverses.
JEL-Classification-Number: C20
Creation-Date: 1994
URL: ../1994/b/bonnsfb301.pdf

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