Predicting binary variable for IV model

[Cristina Ortega]

I want to implement an IV model for a dummy endogenous variable following Wooldridge approach (2002) procedure 18.4.1. I have unbalanced panel data.

In the first stage, I use a bank-level probit model in which I regress a bank's participation on a program (binary variable P) on the instrument (L) and all bank controls from the main regression model. Ithen use the P binary fitted value from the first stage and use this variable as instrument for the final stage.

P = 0 (925 BANKS)
P = 1 (8445 BANKS)

However the prediction ability seems not to be the best for 0 cases (as you can see in the stat classification):

True ---	----
Classified D	~D	Total
8332	884	9216
15	16	31
Total 8347	900	9247
Classified + if predicted Pr(D)	>= .5
True D defined as PPP != 0
Sensitivity	Pr( + D)	99.82%
Specificity	Pr( -~D)	1.78%
Positive predictive value	Pr( D +)	90.41%
Negative predictive value	Pr(~D -)	51.61%
False + rate for true ~D	Pr( +~D)	98.22%
False - rate for true D	Pr( - D)	0.18%
False + rate for classified +	Pr(~D +)	9.59%
False - rate for classified -	Pr( D -)	48.39%
Correctly classified		90.28%

Looking directly at the data, it does not seem to be different pattern on the values of the predicted probabilities for each binary case:

P Phat

0 .3213659
0 .3529814
0 .3880158
0 .3913027
1 .4174738
1 .4290477
1 .429468
1 .4403449
0 .4563234
1 .4711134
0 .4754532

....


I would like to create a new dummy derived from this predicted probability...

Could you please indicate me if I'm doing something wrong or any important thing that I'm not considering here?

Thank you for your time.

[Joro Kolev]

I think what you are doing is correct, and that you are overthinking it. You cannot control the predictive power in your models, the predictive power is what it is.

[Joro Kolev]

If you go for a standard two stage least squares, this would be equivalent to doing what you do but with a fist stage linear probability model.

You can compare the IV results across these two approaches.