With good explanations please...
Problem 2: (20 points) The following tables give results for an annual data set for 162 farms overs the years 1993 to 1998. The variables are: MILK: milk output in liters per year COWS: number of cows LAND: land area, constant for each farm FEED: feed input Table 1 gives output of a pooled regression of log(MILK) on an intercept (C), log(COWS), log(LAND) and log(FEED). Table 2 gives output from a fixed effects regression where the estimated fixed effects are not reported, and Table 3 gives results from a random effects estimation: Table 1: Pooled Estimation Dep. Variable: LOG(MILK) Method: Least Squares Sample (adjusted): 1 972 Included observations: 972 after adjusting endpoints variable Coefficient Std. Error t-Statistics Prob. C 6,976457 0,040584 171,9009 0,0000 LOG(COWS) 0,600228 0,023564 25,49150 0,0000 LOG(LAND) 0,020668 0,014120 1,463763 0,1436 LOG(FEED) 0,455605 0,013712 33,22704 0,0000 R-squared 0,956152 Mean dep. var. 11,71364 Adjusted R-squared 0,956017 S.D. dep. var. 0,607083 S.E. of regression 0,127319 Sum squared resid 15,69139 F-statistics 7036,159 Durbin-Watson stat 0,573676 Table 2: Fixed Effects Estimation Dep. Variable: LOG(MILK) Econometrics - Exam Method: Pooled Least Squares Sample: 1993 1998 Included Observations: 6 Number of cross-sections used: 162 Total panel (balanced) observations: 972 variable Coefficient Std. Error t-Statistics Prob. LOG(COWS) 0,674705 0,032031 21,06433 0,0000 LOG(FEED) 0,396393 0,014944 26,52504 0,0000 fixed effects R-squared 0.986294 Mean dep. var. 11,71364 Adjusted R-squared 0,983529 S.D. dep. var. 0,607083 S.E. of regression 0,077914 Sum squared resid 4,905013 F-statistics 58142,43 Durbin-Watson stat 1,717733Econometrics - Exam Method: Pooled Least Squares Sample: 1993 1998 Included Observations: 6 Number of cross-sections used: 162 Total panel (balanced) observations: 972 variable Coefficient Std. Error t-Statistics Prob. LOG(COWS) 0,674705 0,032031 21,06433 0,0000 LOG(FEED) 0,396393 0,014944 26,52504 0,0000 fixed effects R-squared 0,986294 Mean dep. var. 11,71364 Adjusted R-squared 0,983529 S.D. dep. var. 0,607083 S.E. of regression 0,077914 Sum squared resid 4,905013 F-statistics 58142,43 Durbin-Watson stat 1,717733 Table 3: Random Effect Estimation Dep. Variable: LOG(MILK) Method: GLS (Variance Component) Sample: 1993 1998 Included Observations: 6 Number of cross-sections used: 162 Total panel (balanced) observations: 972 variable Coefficient Std. Error t-Statistics Prob. C 7,086916 0,057206 123,8852 0,0000 LOG(COWS) 0,657466 0,027075 24,28350 0,0000 LOG(LAND) 0,020818 0,023718 0.877749 0,3830 LOG(FEED) 0,410013 0,013630 30,08170 0.0000 GLS Transformed Regression Econometrics - Exam 5 R-squared 0,983509 Mean dep. var. 11,71364 Adjusted R-squared 0,983458 S.D. dep. var. 0,607083 S.E. of regression 0,078080 Sum squared resid 5,901458 Durbin-Watson stat 1,445803 Unweighted Statistics including Random Effects R-squared 0,986028 Mean dep. var. 11,71364 Adjusted R-squared 0,985985 S.D. dep. var. 0,607083 S.E. of regression 0,071870 Sum squared resid 5,000071 Durbin-Watson stat 1,706445 1. Test the hypothesis that log(LAND) has no significant effect on milk production. Describe which model you use, what is the null hypothe sis, the test statistics and its distribution. Explain how you used the displayed output to form your conclusion.Econometrics - Exam 7 Problem 3: (10 points) Suppose that the joint distribution of the two random variables r and y is f(x, y) = de-(8+0)w (By)2 I! where 3, 0 > 0, y 2 0, x = 0, 1,2, ... and a! denotes 1 . 2 . ... . I. 1. (8 points) Find the maximum likelihood estimators for B and 0. 2. (2 points) Find the maximum likelihood estimator of @/(3 + 0).Econometrics - Exam 8 Problem 4: (10 points) Consider the stochastic processes given below, where &, is a normally distri- buted white noise. For each process determine whether it is covariance sta- tionary, strictly covariance stationary, or integrated of order one lie. / (1)]. or neither of these: 1. Xt = 0.7X-1+ et Covariance stationary and strictly covariance stationary. 2. Xi = X-1+ + 861-1 Integrated of order one. 3. X, = 0.3X _, + 8, for To
