Economics 400;

1. Given the following estimated model (standard errors in parentheses): Y = 2.67 +.71* X2; +7.00* X3 -1.44* X.; tu; (1.03) (.12) (3.00) (6.31) N =17, RZ =.38, RSS = 189 (a) Form the t-statistic to test the hypothesis that the coefficient on X, equals 1.0, i.e. Ho : By =1.0 versus H, : B; #1.0. Find the t-statistic in the attached table (use a 5% level of significance), and conduct the test. (b) In the model Y = B, + B,X, +B,XB + B.Xiatu; describe in detail how to test the hypothesis that Ho : B, = B, = 2.0 versus H, : at least one not equal to 2.0. 2. (a) What are the consequences of estimating a heteroskedastic model with OLS? (b) Suppose that Y, = B, + B,X2 + B,Xsi + u; and that you suspect heteroskedasticity of the form: o , = d, +a,X,+a, X ,(b) Describe how to conduct an LM test for the presence of heteroskedasticity and, if heteroskedasticity is present, how to correct the problem. 3. (a) What is the difference between bias and consistency? (b) Explain the consequences of estimating the following model with OLS: Y, = aY_ _ + B, + B,X2 + ByXystu,, 1, = pulte, (c) Explain why the Durbin-Watson test fails for this model. What test should be used instead of the Durbin-Watson?4. (a) Describe White's test for heteroskedasticity. (b) Give a step by step description of how to conduct a Breusch-Pagan test for higher order serial correlation in the following model: Y, = B + ByX2 + ByAy, tly, U, = Pill, + Palli_2 + Pyll,3 + PAllite, 5. For the following errors in variable model, show that the OLS estimate of B, is biased and inconsistent: Y, = B, + BV, +u; , where Xi = Vitei In this model, V is unobservable. However, X; is observable and it is used instead of V; in the OLS regression. Assume that all random variables in the model, i.e. up and et, are independent