Hello all, I am new here to use Stata. I would like to ask questions about curvilinear relationships using OLS, GMM and fixed effect regression.
bdirectorships = average number of board directorships
bdirectorships2 = average number of board directorships^2
captalexp = capital expenditure divided by total assets
lev = leverage
When I use OLS, the results indicate that it is an inverted U-shape relationship. However, when I used fixed effect panel data regression and GMM, the results indicate that it is a U-Shape relationship.
Partial Results of OLS
Since coefficient of bdirectorships is positive (1.21) and the coefficient bdirectorships2 is negative (-0.277), the curvilinear relationship is an inverted U-shape.
I ran utest after OLS results
Extreme point: 2.18
Test:
H1: Inverse U shape
Vs H0: Monotone or U shape
Overall test of presence of a U shape:
t-value = 4.81
p-value =7.98e-07
However, if I run GMM and fixed effect panel effect, the results are different.
Partial results for fixed effect panel data regression
Since coefficient of bdirectorships is negative (-0.055) and the coefficient of bdirectorships2 is positive (0.0597), the curvilinear relationship is a U-shape.
Partial results for GMM estimates
Similar to results from fixed effect panel data regression, since coefficient of bdirectorships is negative (-0.647) and the coefficient bdirectorships2 is positive (0.141), the curvilinear relationship is a U-shape.
I have also run a utest after GMM. The result is as follows:
Utest bdirectorships bdirectorships2
Extreme point: 2.34
Test:
H1: U shape
Vs H0: Monotone or Inverse U shape
Overall test of presence of a U shape:
t-value = 1.73
p-value =0.0418
May I ask which results I should use for my research (U or inverted U-shape) as there are inconsistent results?
Thank you very much.
Steven
bdirectorships = average number of board directorships
bdirectorships2 = average number of board directorships^2
captalexp = capital expenditure divided by total assets
lev = leverage
When I use OLS, the results indicate that it is an inverted U-shape relationship. However, when I used fixed effect panel data regression and GMM, the results indicate that it is a U-Shape relationship.
Partial Results of OLS
| coefficient | p-value | |
| bdirectorships | 1.21 | 0.000 |
| Bdirectorships2 | -0.277 | 0.000 |
| captalexp | 34.56 | 0.000 |
| lev | -0.15 | 0.000 |
I ran utest after OLS results
Extreme point: 2.18
Test:
H1: Inverse U shape
Vs H0: Monotone or U shape
| Lower bound | Upper bound | |
| Interval | 0 | 6.91 |
| Slope | 1.205 | -2.619 |
| t-value | 6.35 | -4.814 |
| p-value | 1.32e-10 | 7.98e-0.7 |
t-value = 4.81
p-value =7.98e-07
However, if I run GMM and fixed effect panel effect, the results are different.
Partial results for fixed effect panel data regression
| coefficient | p-value | |
| bdirectorships | -0.055 | 0.495 |
| Bdirectorships2 | 0.0597 | 0.016 |
| captalexp | 3.451 | 0.000 |
| lev | 0.0141 | 0.231 |
Partial results for GMM estimates
| coefficient | p-value | |
| bdirectorships | -0.647 | 0.054 |
| Bdirectorships2 | 0.141 | 0.052 |
| captalexp | 1.93 | 0.459 |
| lev | 0.0531 | 0.320 |
I have also run a utest after GMM. The result is as follows:
Utest bdirectorships bdirectorships2
Extreme point: 2.34
Test:
H1: U shape
Vs H0: Monotone or Inverse U shape
| Lower bound | Upper bound | |
| Interval | 0 | 6.91 |
| Slope | -0.671 | 1.313 |
| t-value | -1.82 | 1.73 |
| p-value | 0.035 | 0.041 |
t-value = 1.73
p-value =0.0418
May I ask which results I should use for my research (U or inverted U-shape) as there are inconsistent results?
Thank you very much.
Steven
