When we have binary dependent and independent variableS (and binary Instrumental variable). in STATA which command gives better estimates either ivregress 2sls or ivrprobit ?. I am not estimating any margins, I just want to identify the causal relationship between my dependent and independent variable. I am little confused on which command to use.
Siri, when you have a binary outcome, you need to assume a mapping function (the probability distribution for outcomes between 0 and 1). This needs to be assumed - you cannot test what form this underlying mapping function takes.
A practical advice that suffices for most applied work: You should use and report a probit, logit, and linear probability model, the latter being the ivregress 2sls command. Ideally, if you are not somewhere at the tails, the three models give very similar estimates (not on the absolute level of the coefficient though, but the marginal effects), as well as similar significance levels. (If not, the choice of the "right" model becomes much more difficult, because there is no "right" model cause you do not know what the true underlying mapping function is.)
Or "mostly harmless econometrics" for an introduction into the topic.