1. Consider the wage equation where the explanatory variables are years of educa
ID: 3374950 • Letter: 1
Question
1. Consider the wage equation where the explanatory variables are years of education, years of experience and hours worked per week. Estimation results for this equation, and for modified versions of it obtained by dropping some of the variables, are displayed in Table 6.4. These results are from the 1000 observations in the file cps4c small.dat. (a) Suppose you wish to test the hypothesis that a year of education has the same effect on In (WAGE) as a year of experience. What null and alternative hypoth- eses would you set up? (b) What is the restricted model, assuming that the null hypothesis is true? (c) Given that the sum of squared errors from the restricted model is SSER 254.1726, test the hypothesis in (a). For SSEu use the relevant value from Table 6.4. The sample size is N 1,000.)Explanation / Answer
Sol:
a) Ho: B2 = B4 (here B represents beta)
H1: B2 not equal to B4
If education and experience have same effect that means their coefficients should be equal.
b) If the null hypothesis is true then we need to restrict model by removing either experience or education. Restricted model will have 1 less variables.
c) Use F statistic to test the hypothesis.
F = [(SSEu - SSEr)/r] / [SSEu/(N-k)]
SSEu = SSE of unrestricted model
SSEr= SSE of restricted model
r= no. of restrictions
k=no. of coeffcients
F = SSEu - (254.1726)/1] / [SSEu/(1000-6)]
If the calculated value is greater than crictical value 2 (approx as n is very large), then null hypothesis is rejected.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.