Table 1: Estimation bias of various cointegration estimators
|
Bias | ||||
|
two-stage |
FM-OLS |
DOLS |
OLS | |
|
T = |
N |
10 | ||
|
15 |
-0.1363 |
-0.4280 |
-0.4294 |
-0.4824 |
|
15 |
-0.1304 |
-0.6487 |
-0.6487 |
-0.7476 |
|
20 |
-0.0900 |
-0.5675 |
-0.5675 |
-0.6811 |
|
30 |
-0.0300 |
-0.4578 |
-0.4578 |
-0.5759 |
|
50 |
0.0124 |
-0.3233 |
-0.3233 |
-0.4390 |
|
100 |
0.0233 |
-0.1842 |
-0.1842 |
-0.2732 |
|
T = |
N= |
20 | ||
|
15 |
-0.1316 |
-0.6439 |
-0.6439 |
-0.7524 |
|
20 |
-0.0884 |
-0.5654 |
-0.5654 |
-0.6832 |
|
30 |
-0.0327 |
-0.4515 |
-0.4515 |
-0.5752 |
|
50 |
0.0091 |
-0.3158 |
-0.3158 |
-0.4362 |
|
100 |
0.0198 |
-0.1766 |
-0.1766 |
-0.2688 |
|
__________________RMSE__________________ | ||||
|
two-stage |
FM-OLS |
DOLS |
OLS | |
|
T = |
N= |
10 | ||
|
15 |
0.2100 |
0.6806 |
0.6806 |
0.7651 |
|
20 |
0.1723 |
0.5999 |
0.5999 |
0.6983 |
|
30 |
0.1227 |
0.4874 |
0.4874 |
0.5926 |
|
50 |
0.0883 |
0.3485 |
0.3485 |
0.4541 |
|
100 |
0.0650 |
0.2016 |
0.2016 |
0.2849 |
|
T = |
N = |
20 | ||
|
15 |
0.1746 |
0.6604 |
0.6604 |
0.7611 |
|
20 |
0.1355 |
0.5813 |
0.5813 |
0.6921 |
|
30 |
0.0909 |
0.4664 |
0.4664 |
0.5840 |
|
50 |
0.0633 |
0.3284 |
0.3284 |
0.4438 |
|
100 |
0.0461 |
0.1851 |
0.1851 |
0.2749 |
Note: The entries of the Table report the estimated bias and root mean
squared error (RMSE) of the cointegration parameter b based on 5000 replica-
tion of the model (16). “two-step” indicates the two-step estimator suggested
in Section 3, “FM-OLS” denotes the Fully-modified panel cointegration esti-
mator suggested by Pedroni (1996), “DOLS” is the dynamic OLS estimator of
Kao and Chiang (2000), and “OLS” indicates the ordinary least-squares esti-
mator of the pooled model, where the first variable is regressed on the second
variable.
22
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