Consider this regression model (1) : Yt = β0 + β1 Ut + β2 Vt + β3 Wt + β4 Xt + εt ; where t= 1, ..., 75. We use OLS to estimate the parameters, producing the following model: Ŷt = 1.115 + 0.790 Ut − 0.327 Vt + 0.763 Wt + 0.456 Xt (0.405) (0.178) (0.088) (0.274) (0.017) Given that: R2 = 0.941; Durbin Watson stat DW = 1.907; RSS = 0.0757. (To answer the question, use the 5% level of significance, state clearly H0 and H1 that are tested, the test statistics that are used, and interpret the decisions.) (a) Describe the concepts of unbiasedness and efficiency. State the conditions required of regression (1) in order that the OLS estimators of the model parameters possess these properties. (b) Perform the following tests on the parameters of regression (1): (i) test whether the parameters β1, β2, β3 and β4 are individually statistically significant; (ii) test the overall significance of the regression model; (iii) test whether β4 is statistically equal to 0.5 against whether it is less than 0.5. (c) Suppose you wish to test whether the economic variables U and W have the same impact on Y or if they have different impacts on Y . Express this in terms of an appropriate null and alternative hypothesis and show that if the impacts were the same then the regression model would become: Yt = β0 + β1 Zt + β2 Vt + β4 Xt + εt , (2) where Zt = (Ut + Wt). Perform the test, using the information in the following OLS estimated regression: Ŷt = 1.225 + 0.782 Zt − 0.403 Vt + 0.412 Xt (0.361) (0.147) (0.151) (0.081) where the RSS = 0.0781 and the DW = 2.043. (d) What are the consequences of autocorrelated errors on OLS estimators? For the model that you have chosen as a result of the test in part (c), perform a test for autocorrelation of the error term.
Hello, please help me to solve the question (c) and (d) below.
Consider this regression model (1) : Yt = β0 + β1 Ut + β2 Vt + β3 Wt + β4 Xt + εt ; where t= 1, ..., 75.
We use OLS to estimate the parameters, producing the following model:
Ŷt = 1.115 + 0.790 Ut − 0.327 Vt + 0.763 Wt + 0.456 Xt
(0.405) (0.178) (0.088) (0.274) (0.017)
Given that:
R2 = 0.941; Durbin Watson stat DW = 1.907; RSS = 0.0757.
(To answer the question, use the 5% level of significance, state clearly H0 and H1 that are tested, the test statistics that are used, and interpret the decisions.)
(a) Describe the concepts of unbiasedness and efficiency. State the conditions required of regression (1) in order that the OLS estimators of the model parameters possess these properties.
(b) Perform the following tests on the parameters of regression (1): (i) test whether the parameters β1, β2, β3 and β4 are individually statistically significant; (ii) test the overall significance of the regression model; (iii) test whether β4 is statistically equal to 0.5 against whether it is less than 0.5.
(c) Suppose you wish to test whether the economic variables U and W have the same impact on Y or if they have different impacts on Y . Express this in terms of an appropriate null and alternative hypothesis and show that if the impacts were the same then the regression model would become:
Yt = β0 + β1 Zt + β2 Vt + β4 Xt + εt , (2)
where Zt = (Ut + Wt). Perform the test, using the information in the following OLS estimated regression:
Ŷt = 1.225 + 0.782 Zt − 0.403 Vt + 0.412 Xt
(0.361) (0.147) (0.151) (0.081)
where the RSS = 0.0781 and the DW = 2.043.
(d) What are the consequences of autocorrelated errors on OLS estimators? For the model that you have chosen as a result of the test in part (c), perform a test for autocorrelation of the error term.
Step by step
Solved in 5 steps
