Chow test in Seemingly Unrelated Regression

[Martin B]

Hi at all!

I have a time sample 1 to T1 (1/2006 to 6/2007) and a second time sample T1 + 1 to T2 (7/2007 to 12/2008)

I estimate the following as a system of seemingly unrelated regressions:
Sub-Sample from 1 to T1: (error terms denoted by u)

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y_1t = a + b_1*x_t + c*z_1t + u_1t y_2t = a + b_2*x_t + c*z_2t + u_2t

Sub-Sample from T1+1 to T2: (error terms denoted by v)

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y_1t = d + f_1*x_t + g*z_1t + v_1t y_2t = d + f_2*x_t + g*z_2t + v_2t

Hereby, the coefficient a in the first period is denoted d in the second, the same is true for b and f and for c and g.

Now what I am interested in: I want to now if the coefficient c is significantly different from g. Thus, if the variable z is priced different in the two sub-periods.

I know that in a normal regression this can be done by a Chow-Test. Is there a possibility to conduct a Chow-Test in a system of seemingly unrelated regressions?

I thank you very much.

Kind regards

M

[EViews Gareth]

EViews doesn't have a Chow test for SUR built in, but it is relatively simple enough to do one yourself - just estimate over both time periods (i.e. 1 to T2) and include dummy variables for the T2 period.

[Martin B]

Hi Gareth

Thank you for your reply.

So you are suggesting that I estimate a SUR model over the whole time period.

But how exactly can I then conduct the Chow-Test? I mean, if I have two regressions in the system, I have two error terms and two sums of squared errors. I am not quite sure how I can built the test statistics.

Sorry to bother with so many questions...

Kind regards

M

[startz]

Hi Gareth

Thank you for your reply.

So you are suggesting that I estimate a SUR model over the whole time period.

But how exactly can I then conduct the Chow-Test? I mean, if I have two regressions in the system, I have two error terms and two sums of squared errors. I am not quite sure how I can built the test statistics.

Sorry to bother with so many questions...

Kind regards

M

A Chow test is just a test that the coefficients are equal across periods. You can use View/Coefficient tests/Wald to test that the coefficients from the first period equal those from the second period.

[EViews Gareth]

Create a dummy variable that is equal to 1 during T1+1 : T2 and 0 during 1:T1. Lets call this dummy DUM.

Then run the following SUR over 1:T2:

y_1t = a + d1*DUM + b_1*x_t + c*z_1t + u_1t
y_2t = a + d1*DUM + b_2*x_t + c*z_2t + u_2t


The t-test on the DUM coefficient (d1) will be a Chow test for the intercept. If you want to do a Chow test on all coefficients, then you'd do:

y_1t = a + d1*DUM + b_1*x_t + d2*DUM*x_t + c*z_1t + d3*DUM*z_1t + u_1t
y_2t = a + d1*DUM + b_2*x_t + d2*DUM*x_t + c*z_2t + d3*DUM*z_2t + u_2t

The Wald test on d1=d2=d3=0 is then a Chow test on all coefficients.

[Martin B]

Ok, thanks very much.

So if I want to test if the coefficient on the variable z_t is different in the first period than in the second period, I would do:

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y_1t = a + b_1*x_t + c*z_1t + d3*DUM*z_1t + u_1t y_2t = a + b_2*x_t + c*z_2t + d3*DUM*z_2t + u_2t

Is this correct?

Question: say, the coefficient d3 proves to be significantly larger than zero (t-statistics). How can I interpret this result? Is it true that in this case the coefficient on z is larger in the second period than in the first period?

Again, thanks...

[EViews Gareth]

Right. In fact the coefficient d3 is an estimate of how much bigger the coefficient on Z is in the second period.

[Martin B]

I thank you very, very much for your most helpful advice!

Kind regards

M