Table 1.
Estimator |
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MIIV-2SLS |
pseudo-ML |
Kalman Filter |
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Time Series Length |
Time Series Length |
Time Series Length |
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Parameter | T = 50 | T = 100 | T = 250 | T = 500 | T = 50 | T = 100 | T = 250 | T = 500 | T = 50 | T = 100 | T = 250 | T = 500 |
Correctly Specified Model | ||||||||||||
ϕ11 | −15 | −6 | −3 | −2 | −14 | −6 | −3 | −1 | −9 | −6 | −2 | −1 |
ϕ12 | −6 | −4 | −3 | 0 | −10 | −2 | 2 | 2 | −5 | −5 | −3 | 0 |
ϕ21 | 3 | −1 | −2 | 1 | 5 | 2 | −0 | 1 | −3 | −3 | 1 | −0 |
ϕ22 | −11 | −7 | −4 | −1 | −14 | −7 | −4 | −1 | −13 | −5 | −2 | −2 |
−0 | −0 | −0 | 0 | 1 | 0 | 0 | 0 | −0 | −0 | 0 | 0 | |
−1 | 0 | 0 | 0 | 2 | 1 | −0 | 0 | −1 | 1 | 0 | 1 | |
2 | −1 | −1 | 0 | 4 | 0 | 1 | 0 | 0 | −1 | 1 | 1 | |
1 | 1 | −0 | −0 | 3 | 1 | 0 | −0 | −0 | 0 | 0 | 0 | |
0 | 1 | −1 | 0 | 2 | 2 | −0 | 0 | −1 | 1 | 0 | 0 | |
Δ Percentage of Relative Bias from Correctly Specified Model Due to Omission of | ||||||||||||
ϕ11 | 0 | 0 | 0 | 0 | 13 | 12 | 11 | 11 | 11 | 10 | 10 | 10 |
ϕ12 | 0 | 0 | 0 | 0 | −42 | −44 | −45 | −46 | −33 | −34 | −35 | −36 |
ϕ21 | 0 | 0 | 0 | 0 | 4 | 2 | 1 | 1 | −0 | −3 | −2 | −3 |
ϕ22 | 0 | 0 | 0 | 0 | −3 | −3 | −3 | −3 | −1 | −1 | −1 | −1 |
0 | 0 | 0 | 0 | 0 | −0 | −0 | 0 | −2 | −1 | −1 | −1 | |
35 | 37 | 39 | 40 | 44 | 44 | 45 | 45 | 39 | 40 | 42 | 42 | |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
0 | 0 | 0 | 0 | −0 | 0 | −0 | −0 | 0 | 0 | 0 | 0 | |
Δ Percentage of Relative Bias from Correctly Specified Model Due to Omission of ϕ12 and ϕ21 | ||||||||||||
ϕ11 | −3 | −2 | −2 | −2 | 9 | 9 | 9 | 9 | 10 | 10 | 10 | 10 |
ϕ22 | −5 | −6 | −4 | −4 | 9 | 8 | 8 | 9 | 13 | 10 | 10 | 10 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | −0 | |
0 | 0 | 0 | 0 | −0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | |
0 | 0 | 0 | 0 | −1 | −1 | −1 | −1 | −2 | −3 | −3 | −4 | |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |