1. Using n = 97 observations on the rate of wage inflation (DW), the rate of price inflation (DP) and the unemployment rate (U₁), the following regression results are obtained by ordinary least squares; the dependent variable is DW₁, t= 1,2,...,n. Variable Coefficient SE HCSE HACSE constant 0.0242 0.0081 0.0103 0.0062 0.0177 0.0836 0.1505 0.0968 -0.9536 0.1430 0.2085 0.2044 0.6359 0.0837 0.1221 0.0758 U₁-1 DU DP-1 R² = 0.5248 SSR = 0.1285 RESET 1.4605 [0.2299] WH=13.727 [0.0000] BG=5.8774 [0.0040] DU₁ = U₁ - U₁-1 is the change in the unemployment rate; SE is ordinary estimated standard error; HCSE is heteroskedasticity consistent standard error; HACSE is heteroskedasticity and autocorrelation consistent standard error; SSR is the sum of squared residuals; R² is the coefficient of determination; RESET is Ramsey's regression specification error test; WH is White's heteroskedasticity test; BG is the Breusch-Godfrey test for second-order autocorrelation; figures in brackets are the p-values of tests. (a) For each of the three diagnostic tests, RESET, WH and BG, what does the outcome of the test mean? (b) In light of your answer in (a), which is your preferred choice among SE, HCSE and HACSE, and why? (e) In light of your answers in (a) and (b), test the null hypothesis that the coef- ficient on DP-1 is equal to 1 against the alternative that it is less than 1 at significance level 10% (the critical value for the test is -1.2907). State clearly what the distribution of your test statistic is under the null hypothesis. (d) In light of your answers in (a) and (b), compute a 90% confidence interval for the coefficient on U₁-1 (the 0.05 quantiles that are needed for the interval are 1.6614). Given this confidence interval, would you say that U₁-1 has a significant effect on DW,? Explain. (e) Use a conventional F-statistic to test whether the slope coefficients are jointly equal to zero at significance level 10% (the critical value for the test is 2.1436). State clearly what the distribution of the test statistic is under the null hy- pothesis. In light of your answers in (a) and (b), is this test reliable?