@ solve this please
4. A model of the number of light trucks sold in the United States from 1990 through 2014 produced the following results (standard errors in parentheses): C , = 3738 - 28.0P, + 10.0Y, + 6.0 InA, - 360.0R. (12.0) (2.0) (2.0) (120.0) R 2 =.85 DW = 1.96 n = 25 (annual) where: C = thousands of trucks sold in year t P. = price index for domestic trucks in year t Y. = disposable income (billions of dollars) in year t A = millions of dollars of truck industry advertising expenditures in year t R = the interest rate in year t a. Do any econometric problems appear to be present in this equation? Why? b. Suppose you were told that the simple correlation coefficients between P, A, and Y were all between .88 and .94 and that a Breusch-Pagan test produced an insignificant chi-squared result. Would your answer to part a above change? Why or why not? How would it change? c. Assuming (whether indicated by the equation and statistics as reported above or not) that autocorrelation is a problem and had been corrected by performing GLS, what would likely happen to the resulting t statistics?It is postulated that a reasonable demand-supply model for the wine industry in Australia, under market clearing assumption, would be given by Qt = ontop" +azpi tash toA tu demand Qt = Po+ BIP"" + ByS + the supply where Q: = real per capita consumption of wine, Po = price of wine relative to CPI, Ph = price of beer relative to CPI, Y, = real per capita disposable income, A, = real per capital advertising expenditure, and S, = storage cost. CPI is the Consumer Price Index. The endogenous variables in this model are @ and P", and the exogenous variables are p, Y, A and S. The variance of wt and t are, respectively on, and of, and Cov(us, ") = Our # 0. The errors do not exhibit any correlation over time. (a) (5 marks) Provide the reduced form for Pu. (b) (5 marks) The OLS estimation of the demand function, based on annual data from 1955-1975 (7 = 20), gave the following results (all variables are in logs and figures in parentheses are t-ratios). Q+ = -23.651 + 1.158PM -0.275 P +3.212 Y, -0.603 At (-6.04) (4.0) (-0.45) (4.5) (-1.3) All the coefficients except that of Y have the wrong signs. The coefficient of P" (price elasticity of demand, o) not only has the wrong sign but also appears significant. Explain why the OLS parameter estimator may give rise to these counter-intuitive results. You are expected to use your results in answer (a) to support your answer.(iii) Assume that government spending G is 10, the representative consumer receivm the prots that you calculated above and earns hourly wage to = 10. Calculate how many hours of work the representative con- sumer would like to supply in the market. (11] marks] (iv) In the economy described above, (i) the government budget is balanced, (ii) the representative consumer maximizes lifetime utility given the budget constraint and w, and (iii) the rm maximises prots given the production function and to. Is this a competitive equilibrium? Why or why not?l (05 marks) A researcher has data on class size (CS) and average test scores from 100 econometrics classes (TS). He estimates the OLS regression and obtains the following regression line: TS = 520.4-5.82 x CS reg (20.4) (2.21) where the R2 = 0.08, SER = 11.5, and the standard errors of each coefficient is in parentheses underneath. inf a) What are Bo and B1, and what are their standard errors? 51 b) Interpret the R for this regression. c) A classroom has 22 students. What is the regression's prediction for that classroom's average test score? d) Last year a classroom had 19 students and this year it has 23 students. What is the regression's prediction for the change in the classroom average test score? (Hint: A change of 1 unit of X induces a change of B 1 units in Y, so a change in 4 units of X will induce what change in Y?) e) The sample average class size across the 100 classrooms is 21.4. What is the sample average of test scores across the 100 classrooms? (Hint: The estimated regression line (above) gives you the average relationship between Y and X!) f) Is Bi significant at the 5% significance level (i.e. can you reject the null that B 1 = 0)? (Hint: Same procedure as 4b where the critical value is now for 98 degrees of freedom at the 5% level-see Table 2) . g) Construct a 95% confidence interval for 1, the regression slope coefficient.3. An economics department at a large state university keeps track of its majors' starting salaries. Does taking econometrics affect starting salary? Let SAL = salary in dollars, GPA = grade point average on a 4.0 scale, METRICS = 1 if student took econometrics, and METRICS = 0 otherwise. Using the data file metrics.dat, which contains information on 50 recent graduates, we obtain the estimated regression SAL = 24200 + 1643GPA + 5033METRICS R= = 0.74 (se ) (1078) (352) (456) (a) Interpret the estimated equation. (b) How would you modify the equation to see whether women had lower starting salaries than men? (Hint: Define an indicator variable FEMALE = 1, if female; zero otherwise.) (c) How would you modify the equation to see if the value of econometrics was the same for men and women?
