I am working on a project where I investigate growth in wages due to migration. I correct for the endogeneity in the decision to migrate (only those that are most likely to gain from migration will migrate) by first using a probit model to predict the probabilities of migration based on various characteristics. I then use the predicted probabilities in a second step as a proxy for migration (this in effect is an instrumental variables regression).
My problem is that I get unreasonably high estimates - wages are predicted to increase up to 200%. My concern is that since my predicted probabilities are very low (on average 3%, 25% at the 99th percentile), which is reasonable as in the sample only about 5% migrate, the results that I get come from the marginal increase of probability to migrate from 0 to 1. As far as the predicted probabilities go in my sample, an increase from 0 to 1 is very extreme. Could this be causing the huge estimates? Am I interpreting this correctly? Or should I rather look at the strength of my instruments, etc.?