APPENDIX
Part A: Tables
1. The original OLS model: ROA
1.1. Test for Autocorrelation: the original OLS model - ROA
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 0.315321 Prob. F(2,200) 0.729916
Obs*R-squared 0.647520 Prob. Chi-Square(2) 0.723424
Test Equation:
Dependent Variable: RESID Method: Least Squares Date: 06/29/07 Time: 21:58 Sample: 1 206
Included observations: 206
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
IDV -0.003052 0.029478 -0.103522 0.9177 MAS 0.000829 0.026311 0.031527 0.9749 UAI 0.000886 0.023908 0.037046 0.9705 C 0.086093 3.120752 0.027587 0.9780 RESID(-1) -0.039750 0.071125 -0.558870 0.5769 RESID(-2) 0.039434 0.071879 0.548619 0.5839
R-squared 0.003143 Mean dependent var 2.33E-15
Adjusted R-squared -0.021778 S.D. dependent var 3.394879
S.E. of regression 3.431647 Akaike info criterion 5.332651
Sum squared resid 2355.241 Schwarz criterion 5.429580
Log likelihood -543.2631 F-statistic 0.126129
Durbin-Watson stat 1.993928 Prob(F-statistic) 0.986376
1.2. White Heteroskedasticity Test: the original OLS model - ROA
White Heteroskedasticity Test:
F-statistic 2.524515 Prob. F(6,199) 0.022347
Obs*R-squared 14.57083 Prob. Chi-Square(6) 0.023871
Included observations: 206
Variable Coefficient Std. Error t-Statistic Prob.
C 6.676133 29.30815 0.227791 0.8200 IDV -0.473853 0.956168 -0.495575 0.6207 IDV^2 0.005146 0.008185 0.628741 0.5302 MAS -1.327291 0.595847 -2.227570 0.0270 MAS^2 0.017085 0.006515 2.622227 0.0094 UAI 1.032702 0.911894 1.132481 0.2588 UAI^2 -0.007114 0.006806 -1.045264 0.2972
R-squared 0.070732 Mean dependent var 11.46926
Adjusted R-squared 0.042714 S.D. dependent var 15.64732
S.E. of regression 15.30949 Akaike info criterion 8.328213
Sum squared resid 46641.74 Schwarz criterion 8.441296
Log likelihood -850.8060 F-statistic 2.524515
Durbin-Watson stat 2.210226 Prob(F-statistic) 0.022347
1.3. Hausman test for correlation between the included variables and error terms: ROA
Dependent Variable: DEPENDENT_ROA Method: Least Squares
Date: 06/29/07 Time: 21:26 Sample (adjusted): 2 206
Included observations: 205 after adjustments
White Heteroskedasticity-Consistent Standard Errors & Covariance
Variable Coefficient Std. Error t-Statistic Prob.
IDV -0.331149 0.109415 -3.026533 0.0028 MAS -0.068888 0.116817 -0.589713 0.5561 UAI -0.071629 0.160934 -0.445081 0.6567 V_HAT_IDV 0.052850 0.112664 0.469088 0.6395 V_HAT_MAS 0.100542 0.119821 0.839099 0.4024 V_HAT_UAI 0.059643 0.163580 0.364609 0.7158 C 28.39351 14.39289 1.972746 0.0499
R-squared 0.362863 Mean dependent var -0.027138
Adjusted R-squared 0.343556 S.D. dependent var 4.243525
S.E. of regression 3.438157 Akaike info criterion 5.341298
Sum squared resid 2340.543 Schwarz criterion 5.454767
Log likelihood -540.4831 F-statistic 18.79418
2. The original OLS model: EBITOA
2.1. Test for Autocorrelation: the original OLS model - EBITOA
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 0.091353 Prob. F(2,200) 0.912734
Obs*R-squared 0.188015 Prob. Chi-Square(2) 0.910276
Test Equation:
Dependent Variable: RESID Method: Least Squares Date: 06/29/07 Time: 22:04 Sample: 1 206
Included observations: 206
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
IDV -0.001836 0.036767 -0.049928 0.9602 MAS 0.000845 0.032799 0.025749 0.9795 UAI 0.001283 0.030014 0.042751 0.9659 C -0.015468 3.901829 -0.003964 0.9968 RESID(-1) -0.019455 0.071294 -0.272890 0.7852 RESID(-2) 0.023752 0.072292 0.328557 0.7428
R-squared 0.000913 Mean dependent var 2.09E-15
Adjusted R-squared -0.024064 S.D. dependent var 4.232457
S.E. of regression 4.283080 Akaike info criterion 5.775915
Sum squared resid 3668.955 Schwarz criterion 5.872844
Log likelihood -588.9193 F-statistic 0.036541
Durbin-Watson stat 1.996730 Prob(F-statistic) 0.999277
2.2. White Heteroskedasticity Test: the original OLS model - EBITOA
White Heteroskedasticity Test:
F-statistic 3.886714 Prob. F(6,199) 0.001081
Obs*R-squared 21.60837 Prob. Chi-Square(6) 0.001425
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 06/29/07 Time: 22:06 Sample: 1 206
IDV -0.869454 1.465005 -0.593482 0.5535 IDV^2 0.007710 0.012541 0.614767 0.5394 MAS -3.660909 0.912935 -4.010044 0.0001 MAS^2 0.043268 0.009983 4.334348 0.0000 UAI 1.747126 1.397170 1.250475 0.2126 UAI^2 -0.011102 0.010428 -1.064553 0.2884
R-squared 0.104895 Mean dependent var 17.82673
Adjusted R-squared 0.077907 S.D. dependent var 24.42747
S.E. of regression 23.45664 Akaike info criterion 9.181574
Sum squared resid 109492.6 Schwarz criterion 9.294657
Log likelihood -938.7021 F-statistic 3.886714
Durbin-Watson stat 2.101327 Prob(F-statistic) 0.001081
2.3. Hausman test for correlation between the included variables and error terms: EBITOA
Dependent Variable: DEPENDENT_EBITOA Method: Least Squares
Date: 06/29/07 Time: 21:27 Sample (adjusted): 2 206
Included observations: 205 after adjustments
White Heteroskedasticity-Consistent Standard Errors & Covariance
Variable Coefficient Std. Error t-Statistic Prob.
IDV -0.419489 0.131527 -3.189376 0.0017 MAS -0.157839 0.146428 -1.077933 0.2824 UAI -0.053140 0.171963 -0.309019 0.7576 V_HAT_IDV 0.066525 0.129987 0.511784 0.6094 V_HAT_MAS 0.180016 0.149165 1.206820 0.2289 V_HAT_UAI 0.054080 0.175204 0.308670 0.7579 C 36.97339 16.45471 2.246979 0.0257
R-squared 0.385847 Mean dependent var -0.032388
Adjusted R-squared 0.367236 S.D. dependent var 5.380453
S.E. of regression 4.279959 Akaike info criterion 5.779314
Sum squared resid 3626.974 Schwarz criterion 5.892782
Log likelihood -585.3797 F-statistic 20.73254
Part B: Figures:
1. Test for normality test of the residuals – ROA: Fixed effect model:
Figure 1: Histogram and normality test of the residuals - ROA
0 20 40 60 80 100 120 140 -20 -15 -10 -5 0 5 10 15
Series: Standardized Residuals Sample 2000 2004 Observations 1030 Mean 2.35e-15 Median 0.108424 Maximum 14.16105 Minimum -19.81577 Std. Dev. 3.830347 Skewness -0.606872 Kurtosis 5.254506 Jarque-Bera 281.3604 Probability 0.000000
2. Test for normality test of the residuals – EBITOA: Fixed effect model:
Figure 2: Histogram and normality test of the residuals - EBITOA
0 40 80 120 160 200 240 -10 -5 0 5
3. Test for normality test of the residuals – the second step:
3.1. The original OLS model
Figure 3: Histogram and normality test of the residuals - ROA – the original OLS model
0 4 8 12 16 20 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 Series: Residuals Sample 1 206 Observations 206 Mean 2.33e-15 Median 0.019694 Maximum 7.727404 Minimum -9.393856 Std. Dev. 3.394879 Skewness -0.150765 Kurtosis 2.852235 Jarque-Bera 0.967817 Probability 0.616370
