By Werner Ploberger, Walter Krämer, Raimund Alt (auth.), Walter Krämer (eds.)
Econometric types are made from assumptions which by no means precisely fit fact. one of the so much contested ones is the requirement that the coefficients of an econometric version stay reliable over the years. contemporary years have accordingly visible a variety of makes an attempt to check for it or to version attainable structural switch while it could not be missed. This choice of papers from Empirical Economics mirrors a part of this improvement. the purpose of departure of such a lot reviews during this quantity is the normal linear regression version Yt = x;fJt + U (t = I, ... , 1), t the place notation is apparent and the place the index t emphasises the truth that structural swap is usually mentioned and encountered in a time sequence context. it really is less of an issue for pass part information, even though many checks follow there to boot. The null speculation of such a lot checks for structural switch is that fJt = fJo for all t, i.e. that an analogous regression applies to all time classes within the pattern and that the disturbances u are good behaved. the well-known Chow try out for example assumes t that there's a unmarried structural shift at a recognized time limit, i.e. that fJt = fJo (t< t*), and fJt = fJo + t1fJ (t"?:. t*), the place t* is known.
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Extra info for Econometrics of Structural Change
The problem of testing w 2 = is seen to be invariant under the transformation (4) and so the Locally Best Invariant test follows from (5) and is given by ° y'XVXyjy'y. (9) Under normality, the exact distribution of (9) may be calculated via Imhofs method. Section 4 gives the asymptotic distribution when y is allowed to be a-mlxmg. When fJo is unknown, and hence is a nuisance parameter as well, we note that the testing problem is invariant under (6) and the Locally Best Invariant test c'(XVX)cj c' c follows from (8).
How should one compute v? Observe that Var (p]z) = rrP]Mp] = rrlm so that p]Z - N(O, (72Im). This implies that v can be regarded as a linear unbiased with scalar covariance matrix (LUS) residual vector divided by its norm. For any given regression model there are an infinite number of LUS residual vectors. Some of the best known are Theil's (1965, 1968) BLUS residuals and recursive residuals. These and other LUS residuals are reviewed by King (1987). When testing for structural change, we recommend the use of recursive residuals.
Also, Bacon/Watts (1971), Tsurumi (1980) and Katayama/Ohtani/Toyoda (1987) considered the switching regression model when the change in regression coefficients occurs gradually. I We thank Professor S. Katayama for his help in another related project. , Toshihisa Toyoda, Department of Economics, University of Essex, Wivenhoe Park, Colchester C04 3SQ, England, and Faculty of Economics, Kobe University, Nada-ku, Kobe 657, Japan. ) Kazuhiro Ohtani, Faculty of Economics, Kobe University, Nada-ku, Kobe 657, Japan.