Consider the wage equation ln(WAGE) = beta_1 + beta_2 EDUC + beta_3 EDUC^2 + bet
ID: 3290608 • Letter: C
Question
Consider the wage equation ln(WAGE) = beta_1 + beta_2 EDUC + beta_3 EDUC^2 + beta_4 EXPER + beta_5 EXPER^2 + beta_6 (EDUC times EXPER) + beta_7 HRSWK + e (a) Using an approximate 5% critical value of t_c = 2 what coefficient estimates are not significantly different from zero? (b) What restriction on the coefficients of Eqn (A) gives Eqn (B)? Use an F-test to test this restriction. Show how the same result can be obtained using a t-test? (c) What restrictions on the coefficients of Eqn (A) give Eqn (C)? Use an F-test to test these restrictions. What question would you be trying to answer by performing this test? (d) What restrictions on the coefficients of Eqn (B) give Eqn (D)? Use an F-test to test these restrictions. What question would you be trying to answer by performing this test? (e) What restrictions on the coefficients of Eqn (A) give Eqn (E)? Use an F-test to test these restrictions. What question would you be trying to answer by performing this test? (f) Based on your answers to parts (a) to (e), which model would you prefer? Why? Consider the wage equation ln (WAGE) =beta_1 + beta_2 EDUC + beta_3 EDUC^2 + beta_4 EXPER + beta_5 EXPER^2 + beta_6 HRSWK + e (a) Suppose you wish to test the hypothesis that a year of education has the same effect on ln(WAGE) as a year of experience. What null and alternative hypotheses 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 SSE_R = 254.1726, test the hypothesis in (a). The sample size is N = 1000Explanation / Answer
(a) Variable EDUC & EDUC2 are insignificant. Reason:
formula:
(b) The restriction imposed is coefficient for variable EXPER X EDUC=0
(C) The restriction imposed is coefficient for variable EXPER, EXPER2 and EXPER X EDUC=0
PE SE t 1.055 0.266 3.966165 0.0498 0.0397 1.254408 insignificant 0.00319 0.00169 1.887574 insignificant 0.0373 0.0081 4.604938 -0.00049 0.00009 -5.38889 -0.00051 0.000482 -1.05809 0.01145 0.00137 8.357664