Suppose you are given a sample of n observations and the following structure is

ID: 1198674 • Letter: S

Question

Suppose you are given a sample of n observations and the following structure is hypothesized to generate the observed regressions:

Yi = 1 + 1 Xi + 1 Wi + 1 Zi + Ui for i = 1,..., n1

Yi = 2 + 2 Xi + 2 Wi + 2 Zi + Ui for i = n1+1,..., n1+n2

Yi = 3 + 3 Xi + 3 Wi + 3 Zi + Ui for i = n1+n2+1,...n

You wish to test the null hypothesis: Ho: 1 = 2 = 3 and 1 = 2 = 3. Develop the appropriate test to test Ho. Include in your development

(i) the assumptions you need;

(ii) the regression(s) you would run;

(iii) the statistic(s) you would compute;

(iv) the distributions of the computed statistic(s);

(v) the conditions under you would reject Ho.

v) the conditions under you would reject H0

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