I have a regression with an endogenous variable for which I have an instrument.
By computing
ivreg income (immigrants=enclave) YearDummy*
I obtain a given coefficient.

If instead i first compute the first stage and then regress the dependent variable on the exogenous fitted value of the endogenous variable I obtain a completely different result.
reg immigrants enclave YearDummy*
predict immhat, xb
reg income immhat YearDummy*

If I'm not mistaken the result shoud be the same, as a 2sls regression is computed that way. Is there a reason why this is actually not the case?