use eviews

Questions
1. Consider the following aggregate production function for the U.S. manufacturing sector Yt = K1 t L2 t E3 t M4 t expf”tg where “t~N(0;2), Yt is gross output at time t, Kt is capital, Lt is labor, Et is energy, and Mt denotes other intermediate materials. The data underlying these variables are given in index form in the le q1.wf1.
(a) Show how to nd a transform regression that enables you to estimate the original production function using the Least Squares method. (5 marks)
(b) Report (in a table) the Least Squares estimates of the unknown parameters of the original production function, their standard deviations, the corresponding t statistics and the p-values. (6 marks)
(c) Do your results above suggest labour plays a role in nal goods production at the 5% signicance level? How about at the 10% level? (6 marks)
(d) Explain what a p-value is; then use your results in part (b) to illustrate in a gure the area implied by the reported p-value for the estimated capital elasticity. (You mayrstdrawthegureonanadditionalpieceofpaper, thenscanandcopy/paste it to your work for part (d) ) (6 marks)
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(e) Now, suppose the data are time-series data and crises occurred in periods 1, 2, 3, 4, 5, 21, 22, 23 and 24 (thus, there were two major crisis episodes). Estimate and report the impact of crisison output production and test for its signicance at the 5% signicance level. How does the inclusion of the intercept dummy change the signicance of other variables? (7 marks)
2. In the le q2.wf1 there are 56 time-series observations on total cost (Ct) and output (Qt) for two clothing manufacturing rms. It is hypothesized that both rmscost functions are cubic and can be written as: rm1: C1t = + 1Q1t + 2Q2 1t + 3Q3 1t + “1t rm2: C2t = + 1Q2t + 2Q2 2t + 3Q3 2t + “2t where E(“1t) = E(“2t) = 0, V ar(“1t) = 2 1 and V ar(“2t) = 2 2. Also, “1t and “2t are independent of each other and over time.
(a) Pool the data as if there is no di⁄erence between the rms and estimate the cost function for the whole industry using the OLS method. Report the estimated cost function, then plot the residual series using a line chart. Does the residual series display any sign of Heterskedasticity? (8 marks)
(b) Estimate the cost function for each rm separately; then, at the 5% signicance level, use the Goldfeld-Quandt test to formally test for Heteroskedasticity. (8 marks) *Hint: the test will be built on your estimation results. You will also set up your hypotheses and need to consider whether it is a one-tail or two-tail test*
(c) Based on your estimation results in part (b), re-estimate the cost function for the whole industry using the method of Generalized Least Squares and report your results (the estimated coe¢ cients and their standard errors only). (10 marks) *Hint: you should show your transformed variables and the transformed regressions*
(d) What would be the consequence if one estimates a regression using the OLS method, instead of the GLS method, when heteroskedasticity exists? (10 marks)
3. To investigate the relationship between job vacancies (JVt) and the unemployment rate (Ut), a researcher sets up the model: ln(JVt) = + ln(Ut) + “t and assumes that “t~N(0;2 “) is the random error.
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(a) Using the data in le q3.wf1, nd the Least Squares estimates of and ; then, construct the residual series and use the LM test to test for Autocorrelation at the 10% signicance level. (8 marks) *Hint: you will show your hypothesis, the auxiliary equation, and the relevant test statistics*
(b) Re-estimate the model, assuming that the random error follows an AR(1) process, and report the estimation results (only the estimated coe¢ cients and their standard deviations). Then, show how to derive the transformed regression that Eviews actually estimated in the background. (10 marks)
(c) Use the OLS method to estimate the following regression: ln(JVt) = + 1 ln(Ut) + 2 ln(Ut1) + ln(JVt1) + vt; then, at the 10% signicance level, test the hypothesis H0:2 = 1 against the alternative hypothesis H1:2 6= 1. (8 marks)
(d) Compare your answers in part (b) and part (c). Comment briey on the models specication in relation to the problem of Autocorrelation. (8 marks