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The MODEL Procedure |
The Chow test is used to test for break points or structural changes in a model. The problem is posed as a partitioning of the data into two parts of size n_{1} and n_{2}. The null hypothesis to be tested is
where is estimated using the first part of the data and is estimated using the second part.
The test is performed as follows (refer to Davidson and MacKinnon 1993, p. 380).
Chow's test is not applicable if min(n_{1},n_{2}) < p, since one of the two subsamples does not contain enough data to estimate .In this instance, the predictive Chow test can be used. The predictive Chow test is defined as
You can select the Chow test and the predictive Chow test by specifying the CHOW=arg and the PCHOW=arg options in the FIT statement, where arg is either the number of observations in the first sample or a parenthesized list of first sample sizes. If the sizes for the second or the first group are less than the number of parameters, then a PCHOW test is automatically used. These tests statistics are not produced for GMM and FIML estimations.
The following is an example of the use of the Chow test.
data exp; x=0; do time=1 to 100; if time=50 then x=1; y = 35 * exp( 0.01 * time ) + rannor( 123 ) + x * 5; output; end; run; proc model data=exp; parm zo 35 b; dert.z = b * z; y=z; fit y init=(z=zo) / chow =(40 50 60) pchow=90; run;The data set introduced an artificial structural change into the model (the structural change effects the intercept parameter). The output from the requested Chow tests are shown in Figure 14.46.
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