Fully restricted linear regression: A pedagogical note

This paper presents a comprehensive approach to estimation and hypothesis testing under a set of full restrictions, some of these arising from adding-up conditions on the endogenous variable. In contrast to the existing statistical literature, this paper uses an argumentation style familiar from classical econometric textbooks, to provide an insightful, straightforward, and nevertheless rigorous exposition of this topic.Restricted least squares Adding-up Singularity Wald-Test SUR.

Consistency of nonlinear regression quantiles under Type I censoring weak dependence and general covariate design

For both deterministic or stochastic regressors, as well as parametric nonlinear or linear regression functions, we prove the weak consistency of the coefficient estimators for the Type I censored quantile regression model under different censoring mechanisms with censoring points depending on the observation index (in a nonstochastic manner) and a weakly dependent error process. Our argumentation is based on an exposition of the connection between the residuals of the economically relevant model at the outset of the censored regression problem, and the residuals which are subject to the corresponding optimization process of censored quantile regression. In dieser Arbeit wird die schwache Konsistenz der Koeffizientenschätzer für das zensierte (Typ I) Quantilsregressionsmodell unter sehr allgemeinen Bedingungen -- lineare und nichtlineare Regressionsfunktionen, deterministische und stochastische Regressoren, Zensierungsgrenzen die (in nichtstochastischer Weise) vom Beobachtungsindex abhängen sowie schwach abhängige Fehlerterme -- bewiesen. Die Argumentation basiert dabei auf dem Zusammenhang zwischen den ökonomischen relevanten Residuen des Ausgangsmodells und den Residuen die Gegenstand der Zielfunktion des Optimierungskalküls der zensierten Quantilsregression sind.Quantil ; Nichtlineare Regression; Typ I Zensierung; Quantile regression ; nonlinear regression ; Type I censoring

Modelling Fertility: A Semi-Parametric Approach

This article presents a categorical model of fertility based on the statistical theory of the Generalised Linear Model (GLM). Focussing on the individual probability of giving birth to a child, we derive distributions which can be embedded in a GLM framework. A major advance of that methodology is the knowledge of the distribution of the random variable, which leads to a Maximum Likelihood estimation procedure. The approach takes into account the smooth shapes of parameter development over the age of the mother as well as over time. The estimation of this semi-parametric approach is done using the Local-Likelihood-method. The presented method provides stable results of the fertility, especially for smaller populations. This is illustrated by using a data set which consists of less than 100,000 inhabitants. Dieser Aufsatz stellt ein kategorielles Modell der Geburtenhäufigkeit auf Basis der statistischen Theorie des Verallgemeinerten Linearen Modells (VLM) vor. Ausgehend von individuellen Gebär-Wahrscheinlichkeiten leiten wir Verteilungen ab, welche in einen VLM-Rahmen eingebettet werden können. Ein besonderer Vorteil dieser Methode ist das Wissen um die Verteilung der Zufallsvariablen, welches ein Maximum-Likelihood Schätzverfahren ermöglicht. Der Ansatz berücksichtigt den gleichmäßigen Verlauf der Parameter-Entwicklung über das Alter der Mutter und über die Zeit. Die Schätzung dieses semi-parametrischen Ansatzes erfolgt mit Hilfe der Local-Likelihood-Methode. Die vorgestellte Methode liefert solide Ergebnisse zur Geburtenhäufigkeit, insbesondere bei kleineren Bevölkerungszahlen. Dies wird anhand eines Datensatzes mit weniger als 100.000 Einwohnern gezeigt.Geburtenentwicklung ; Semiparametrische Schätzung ; Verallgemeinertes lineares Modell; ;

On autoregressive errors in singular systems of equations

Dhrymes (1994, Econometric Theory, 10, 254-285) demonstrates the arising identification and estimation problems in singular equation systems when the error vector obeys an autoregressive scheme, as an extension of restricted least squares. Unfortunately, his main theorem concerning the identification of such systems, does not hold in general, though.identification

Prior Information: The Mixed Prediction Approach

This paper addresses the combination of incomplete prior and sample information. In difference to the mixed estimation approach developed by H. Theil and A.S. Goldberger, dealing with prior knowledge of regression coefficients, we consider prior information on future observations of the dependent variable(s). This prior information could be given in the form of experts' expectations, or from estimations and/or projections of additional models. A framework for the incorporation of this prior knowledge in least squares estimation and prediction is developed. The approach is particularly useful when only aggregated information on the endogenous variables is available, as is often the case with regional level data.

Estimation of Constrained Singular Seemingly Unrelated Regression Models

The topic of this paper is the problem of a singular disturbance covariance matrix in (seemingly unrelated) systems of linear regression equations. This singularity is considered as being caused by exact linear restrictions on the endogenous variables, adding-up to a predetermined aggregate. It is well known, that the estimation of such systems require the substitution of one equation by the "adding up condition" as proposed by Barten (1969), or, as alternatively proposed by Theil (1971), a modification of the GLS estimator. The consequently occuring question of the invariance of the parameter estimates to the choice of which equation is deleted has been discussed exhaustively by Powell (1969) for GLS and Barten (1969) for ML estimation. Dhrymes and Schwarz (1987a,b) pointed out the parallels between the different procedings and argued that the estimator of Theil (1971) fails to exist in most of the practically relevant constellations. The rank conditions given by Theil (1971) and the corresponding objections of Dhrymes and Schwarz (1987a,b) are substantially simplified and generalized. In the second section of this paper we introduce a general model, where we discuss all necessary preliminaries, assumptions and constraints and consider relevant model alternatives. Estimation topics are discussed in section three. In section four we derive less restrictive rank conditions than postulated by Theil (1971) in a more general framework as in the corresponding considerations of Dhrymes and Schwarz (1987a,b). The special case of identical regressors in every equation of the system and homoscedasticity is considererd in section five. Section six deals with the problem of the deletion choice. Strongly related to the work of Powell (1969) and Barten (1969) we show, that under consideration of the constraints, the estimator is invariant to the deletion choice and equivalent to the modified GLS estimator. In section seven we briefly discuss starting conditions for feasible GLS estimation.

Studienabbruchsquote und Typologie der Studienabbrecher und Hochschulwechsler

Berechnung einer statistisch validen Studienabbruchquote für die Wirtschaftswissenschaftliche Fakultät der Universität Regensburg für das Hochschuljahr 1999 / 2000. Calculation of a statistically valid quota of students that didn't finish their studies for the faculty of business and economics at the university Regensburg in 1999 / 2000.Studienabbruch ; Drop-out; Studienabbruchquote ; Drop-out-Quote;

Bubbles and Information: An Experiment

We study whether information about imminent future dividends can abate bubbles in experimental asset markets. Using the seminal design of Smith et al. (1988) we find that markets where traders are asymmetrically informed about future dividends have smaller, and shorter, bubbles than markets with symmetrically informed or uninformed traders. Hence, fundamental values are better reflected in market prices - implying higher market efficiency - when some traders know more than others about the future prospects of an asset. We also find that asymmetric information has a similar abating impact on bubbles as when uninformed traders accumulate experience, though for different reasons