Solved – Linear first stage, non-linear second stage 2SLS regression

2slsbinary dataeconometricsinstrumental-variables

I was wondering if it's possible to perform a 2SLS regression where I first run a regression for my endogenous variable, obtain the predicted values and then use them in my second stage regression (a logit)?

Would this approach yield consistent estimators?

Best Answer

If I've understood the question correctly, you are manually performing two steps:

  1. Use OLS to regress your endogenous variable on your instrumental variable(s) and the exogenous covariates, and save the predicted values
  2. Use logit to regress your $Y$ variable on the predicted values and the exogenous covariates.

If this is the case, then there are two potential problems:

  1. 2SLS literally refers to 2 Stage (Ordinary) Least Squares regressions, not 1 OLS and then 1 logit. See section 4.8.7 here. The textbook properties of 2SLS need not carry through with 1 OLS, 1 logit. Hence, the answer to your question is that this approach may not yield a consistent estimate.
  2. Although 2SLS literally refers to 2 OLS regressions, even if you do that with your statistical software, your standard errors will be incorrect. Here is an illustration using STATA.
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