I am modeling a production function based on a time series data for 40
periods. I have Capital and Labor inputs so I used a cobb-douglas
function. I cannot use CES because it is difficult if not impossible
to find rent and wage data. I would like to perform a Chow test in SAS
to examine the data to see if the results are meaningful. I know how
to do an autoregression in SAS and use the Chow option. The problem is
that I don't know how to interpret the results.

How do I interpret the results of a Chow test?

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Clarification of Question by permanent_student-ga on 28 May 2006 12:45 PDT

Below is the output from SAS using proc autoreg /chow.



                                            The SAS System            
 12:37 Sunday, May 28, 2006   1

                                        The AUTOREG Procedure

                                   Dependent Variable    logoutput


                                   Ordinary Least Squares Estimates

                    SSE                 0.03573462    DFE                       36
                    MSE                  0.0009926    Root MSE             0.03151
                    SBC                 -151.14479    AIC               -156.13547
                    Regress R-Square        0.5388    Total R-Square        0.5388
                    Durbin-Watson           1.5906                                


                                        Structural Change Test
 
                                       Break
                 Test                  Point    Num DF    Den DF    F
Value    Pr > F

                 Chow                     20         3        33      
3.39    0.0295


                                                     Standard         
       Approx
                 Variable        DF     Estimate        Error    t
Value    Pr > |t|

                 Intercept        1     -11.0368       5.2099     
-2.12      0.0411
                 logcows          1       2.1147       0.3272      
6.46      <.0001
                 loglabor         1       0.2484       0.0891       2.79      0.0084

Very first, Chow test is a application of F test.
If you know how to interpret F test, you should be able to interpret Chow test.

F test hypothesis looks like
H_0 : X1=0,X2=1,X3=3
H_1 : H_0 is false
So F statistics tests... how untruthful is the null hypothesis. It is
one tailed test. (If I remember correctly, I never got confused of
one-tail test or two-tail test to operate. The F-table only refers two
degrees of freedom - SAS apparently gives Num DF and DEN DF.)

It is really difficult to see because the output you pasted was
wrapped. But SAS gave you this result:
                 Break
Test             Point    Num DF    Den DF    F Value    Pr > F

Chow                20         3        33       3.39    0.0295
It says: "Test was selected to be 'Chow Test'. (I don't know what
Break Point refers) Numerator Degrees of Freedom is 3. Denominator
Degrees of Freedom is 33. F Value of the test was 3.39. Thus the
probability, Pr(F>3.39)~0.0295." So, depending on your significance
level, you will find the test reject or fail to reject the null
hypothesis.

In the beginning, there is some descriptive statistics about errors,
thus goodness of fit. The last thing I suppose is the testing of
significance of each variable you tested in Chow Test...