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On the Identification of Misspecified Propensity Scores - School of ...

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TABLE 4: P<br />

c=0.05<br />

Proportion <strong>of</strong> Rejections<br />

1% level 5% level 10% level<br />

n=100 0.023 0.082 0.150<br />

n=200 0.074 0.169 0.232<br />

n=400 0.321 0.490 0.587<br />

n=500 0.440 0.621 0.698<br />

n=800 0.838 0.917 0.942<br />

n=1000<br />

c=0.10<br />

0.929 0.977 0.986<br />

n=100 0.037 0.076 0.134<br />

n=200 0.131 0.242 0.303<br />

n=400 0.457 0.620 0.691<br />

n=500 0.642 0.776 0.848<br />

n=800 0.935 0.969 0.980<br />

n=1000<br />

c=0.15<br />

0.986 0.997 0.997<br />

n=100 0.039 0.076 0.124<br />

n=200 0.162 0.271 0.331<br />

n=400 0.557 0.689 0.751<br />

n=500 0.707 0.825 0.877<br />

n=800 0.957 0.978 0.986<br />

n=1000 0.993 0.998 0.998<br />

DGP: D ∗ = 1 + X1 + X2 − ǫi, ǫ ∼ χ 2 1 ,<br />

Estimated model: Q(X, β) = Φ(β 0 +β 1 X1+β 2 X2)

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