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Question 8: 15 points Data on the costs of 6 airlines for years 19701984 (with no year's missing observations) are analyzed. The variables are; C= cost, Q=output, in revenue passenger miles (an index number), F= fuel price, and L= load factor, the average capacity utilization of the fleet. The aim is to model the airline cost function. A random effect model with airline specific random intercept is estimated. Then, the Hausman test and Lagrange multiplier tests are performed. The results are shown below. Dependent Variable: TC Method: Panel EGLS (Cross-section random effects) Sample: 1-15 Periods included: 15 Cross-sections included: 6 Total panel (balanced) observations: 90 Swamy and Arora estimator of component variances Intercept Coefficient 107429.3 2288588 1.123591 -3084994 Sid. Error 3039862 88172.77 0.083298 5843732 Statistic 3.534251 25.95572 13.48877 -5.27915 Prob. 0.0007 0.0000 0.0000 0.0000 F Effects Specification SD Cross-section random Idiosyncratic random 1074112 210422.8 Rho 0.2067 0.7933 1 2 3 4 5 Airline 1.000000 2.000000 3.000000 4.000000 5.000000 6.000000 Effect -270615.0 -87061.32 -21338.40 187142.9 134488.9 57383.00 Chi-Sq.d.f. Correlated Random Effects-Hausman Test Equation: Untitled Test cross-section random effects Chi-Sq. Test Summary Statistic Cross-section random 49.619687 Cross-section random effects test comparisons: Variable Fixed Random Q 3319023.28 2288587.96 F 0.773071 1.123591 L -3797367.59 -3084994.0 Prob 0.0000 Var (Dir.) 21587779733 0.002532 35225469544 Prob 0.0000 0.0000 0.0000 Breusch and Pagan Lagrange Multiplier Test Chi-Sq. Statistic 0.61 Chi-Sq. d.l. Prob. 1 0.4348 a) Write down the functional form of the random effect model used in the analysis using Latin and/or Greek letters with correct pair of indices (subscript numbers and letters) standing for both time and airline. b) Repeat as in point (a) above, if a fixed effect model with dummy variables were used. i.e., write down a model with airline dummy variables, with correct indices (subscript numbers and letters). 3 What conclusion de you get from Lagrange Multiplier test? c) Question 8: 15 points Data on the costs of 6 airlines for years 19701984 (with no year's missing observations) are analyzed. The variables are; C= cost, Q=output, in revenue passenger miles (an index number), F= fuel price, and L= load factor, the average capacity utilization of the fleet. The aim is to model the airline cost function. A random effect model with airline specific random intercept is estimated. Then, the Hausman test and Lagrange multiplier tests are performed. The results are shown below. Dependent Variable: TC Method: Panel EGLS (Cross-section random effects) Sample: 1-15 Periods included: 15 Cross-sections included: 6 Total panel (balanced) observations: 90 Swamy and Arora estimator of component variances Intercept Coefficient 107429.3 2288588 1.123591 -3084994 Sid. Error 3039862 88172.77 0.083298 5843732 Statistic 3.534251 25.95572 13.48877 -5.27915 Prob. 0.0007 0.0000 0.0000 0.0000 F Effects Specification SD Cross-section random Idiosyncratic random 1074112 210422.8 Rho 0.2067 0.7933 1 2 3 4 5 Airline 1.000000 2.000000 3.000000 4.000000 5.000000 6.000000 Effect -270615.0 -87061.32 -21338.40 187142.9 134488.9 57383.00 Chi-Sq.d.f. Correlated Random Effects-Hausman Test Equation: Untitled Test cross-section random effects Chi-Sq. Test Summary Statistic Cross-section random 49.619687 Cross-section random effects test comparisons: Variable Fixed Random Q 3319023.28 2288587.96 F 0.773071 1.123591 L -3797367.59 -3084994.0 Prob 0.0000 Var (Dir.) 21587779733 0.002532 35225469544 Prob 0.0000 0.0000 0.0000 Breusch and Pagan Lagrange Multiplier Test Chi-Sq. Statistic 0.61 Chi-Sq. d.l. Prob. 1 0.4348 a) Write down the functional form of the random effect model used in the analysis using Latin and/or Greek letters with correct pair of indices (subscript numbers and letters) standing for both time and airline. b) Repeat as in point (a) above, if a fixed effect model with dummy variables were used. i.e., write down a model with airline dummy variables, with correct indices (subscript numbers and letters). 3 What conclusion de you get from Lagrange Multiplier test? c)