Question

1. Three equations for the course average of ECON3210 are estimated as follows. The first equation is for men, and the second equation is for women. The third equation combines men and women. ym 20.52 13.60x1 + 0.670x2 (3.72) (0.94) n 406, R2 0.4025, SSR = 38,781.38 (0.150) n 408, R2 0.3666, SSR = 48,029.82 13.79+ 11.89x1 + 1.03x2 yw (4.11) |(1.09) (0.18) n 814, R2 0.3946, SSR = 87,128.96 y 15.603.17m + 12.82x1 + 0.838x2 (0.72) (0.116) (2.80) (0.73) Where course average for men, yw= course average for women, X1 = overall GPA, x2 = ACT score, 1 for men, etc. ym m You are to conduct Chow test that the regression equations are same for men and women: 1) State the hypotheses. a. 2) Compute the test statistic 3) Based on the computed value above, draw your conclusion (show your educated guess without the table) b. With the third equation, test if the dummy variable is significant. With the two tests conducted above, do you find any inconsistency? If yes, how can you interpret this outcome? Discuss C.

Answer 1

a)

1)

The null hypothesis for the test is define as there is no break point such that,

Ho aa, b b2, c1 C

2)

The test statistic is obtained using the formula,

(RSS RSS1- RSS2)/k CHOWF statistic (RSS1RSS2)/(n1+n2 2k)

Where,

RSS = Residual sum of square for combined model = 87,128.96

RSS₁ = Residual sum of square for model 1 = 38,781.38

RSS₂ = Residual sum of square for model 2 = 48,029.82

k = number of predictor = 3

n1 = 406

n2 = 408

48029.82)/3 (87128.95 38781.38 (38781.38 48029.82)/(406408 2 x 3) CHOWF statistic

CHOWF statistic = 0.985825

3)

Critical value

The critical value for F statistic is obtained from F distribution table for degree of freedom for numerator = k = 3 and degree of freedom for denominator = n1+n2-2k = 406+408-6=808 and significance level = 0.05.

dfdf2.a-0.05lower critical value 0.117

dfdf2.a-0.05 upper critical value = 2.6159

Decision Rule:

Rejection Region: Reject H if 0.1172> F-statistic > 2.6159

Since  F-statistic = 0.985825 < F critical value = 2.6159 , the null hypothesis is not rejected. hence we can conclude that both the equation are same.

b)

The significance of dummy variable is tested by calculating the t statistic as follow,

3.17 Slope t Standard error 4.34 SE 0.73

The critical t value is obtained from t distribution table for degree of freedom for numerator = n-k =814-3=811 and significance level = 0.05

teritical = 1.963

Since t-statistic > t critical value, the null hypothesis is rejected. Hence there is significant effect of dummy variable on model.

c)

There is a added dummy variable (which is significant in model) in combined model while ignored in individual model which means the ignored variable can take any value and create inconsistency.