The Linear Regression Model Under Test
Published on 29. August 1986
Book
Hardback
X, 190 pages
978-3-7908-0356-3 (ISBN)
Description
This monograph grew out of joint work with various dedicated colleagues and students at the Vienna Institute for Advanced Studies. We would probably never have begun without the impetus of Johann Maurer, who for some time was the spiritus rector behind the Institute's macromodel of the Austrian economy. Manfred Deistler provided sustained stimulation for our research through many discussions in his econometric research seminar. Similar credits are due to Adrian Pagan, Roberto Mariano and Garry Phillips, the econometrics guest professors at the Institute in the 1982 - 1984 period, who through their lectures and advice have contributed greatly to our effort. Hans SchneeweiB offered helpful comments on an earlier version of the manuscript, and Benedikt Poetscher was always willing to lend a helping . hand when we had trouble with the mathematics of the tests. Needless to say that any errors are our own. Much of the programming for the tests and for the Monte Carlo experiments was done by Petr Havlik, Karl Kontrus and Raimund Alt. Without their assistance, our research project would have been impossible. Petr Havlik and Karl Kontrus in addition. read and criticized portions of the manuscript, and were of great help in reducing our error rate. Many of the more theoretical results in this monograph would never have come to light without the mathematical expertise of Werner Ploberger, who provided most of the statistical background of the chapter on testing for structural change . .
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W. Kraemer | H. Sonnberger
The Linear Regression Model Under Test
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Content
1. Introduction.- 2. Technical Preliminaries.- a) The Linear Regression Model.- Notation and assumptions.- Regression residuals.- b) LR-, Wald- and LM-Tests.- Basic principles.- A simple example.- Estimating the information matrix.- c) Miscellaneous Terminology.- 3. Testing Disturbances.- a) Autocorrelation.- The Durbin-Watson test.- The power of the Durbin-Watson test.- The DW inconclusive region.- Relationship to the LM principle.- Dynamic regressions.- Simultaneous equations.- Other alternatives to the DW test.- b) Heteroskedasticity.- Comparing empirical variances.- A general LM test.- Testing for arbitrary heteroskedasticity.- c) Normality.- Comparing moments.- Residuals vs. true disturbances.- 4. Testing Regressors.- a) Structural Change.- The Chow test and related methods.- Testing subsets of the regression coefficients.- Coefficient stability vs. stability of the variance.- Shift point unknown.- The CUSUM and CUSUM of squares tests.- The CUSUM and CUSUM of squares tests with dummy exogenous variables.- Alternatives to the CUSUM and CUSUM of squares tests.- The Fluctuation test.- Local power.- A Monte Carlo comparison of the CUSUM and Fluctuation tests.- Dynamic models.- A modification of the CUSUM test.- A modification of the CUSUM of squares test.- b) Functional Form.- Ramsey's RESET.- The Rainbow test.- Convex or concave alternatives.- Linear vs. log-linear functional form.- Outliers.- c) General Misspecification.- Hausman-type specification tests.- Errors in variables.- Computing the Hausman test.- Exogeneity.- A Hausman test with trending data.- Hausman tests versus classical tests.- The differencing test.- First differences as an IV estimator.- The information matrix test.- 5. Unifying Themes.- a) Variable Transformation.- Linear transformations.- Examples.- Relationship to IV estimation.- b) Variable Addition.- Data transformation tests as RESETs.- Hausman tests as RESETs.- Power comparisons.- Asymptotic independence.- 6. Diagnostic Checking in Practice.- a) Empirical Results.- Demand for money.- Currency substitution.- Bond yield.- Growth of money supply.- The Value of stocks.- Wages.- Unemployment.- Discussion.- b) Issues in Multiple Testing.- Controlling the size.- Rüger's test.- Global vs. multiple significance level.- Holm's procedure.- Robustness.- Further reading.- a) Sample Data.- b) The IAS-SYSTEM.- References.- Author Index.