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three-stage least square (3SLS) with fixed effects and how to interpret results

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Dear all,

I am running empirical models based on 3SLS due to the potential endogeneity issue caused by simultaneity. So, I opted for 3SLS as my main analysis tool, and I am using reg3 command to analyze it. My model and STATA command are as below.

Empirical model: DV = intercept + endog_var1 + control1 + ... + control6 + i.industry + i.year + error term (In this model, I assume that there is only one endogenous variable because I am only interested in var1, and there could be potentially simultaneity bias between DV and var1 due to the unobservable that affects both, and I am planning to relieve the bias by using one instrument.)

STATA command: reg3 (DV endog_var1 control1 control2 control3 control4 control5 control6 i.industry i.Year) (endog_var1 DV instrument1 i.industry i.Year)

Actually, when I run fixed effects models that have opposite DV and endog_var1 as DV and IV, respectively, (i.e., model 1: DV = intercept + endog_var1 + control1 + ... + control6 + i.industry + i.year + error term & model 2: endog var1 = intercept + DV + control1 + ... + control6 + i.industry + i.year + error term), either way, I could find that the coefficients of DV and endog_var1 are quite statistically significant.

However, if I run the STATA command above, I could only see significant endog_var1 in the first parentheses, but DV becomes insignificant (p-value > 0.1) in the second parentheses (first-stage) in the 3SLS model.

To sum up, my questions are fourfold.

1. Should I also put all the control variables into the first stage (second parantheses in reg3 model) in 3SLS model? (However, I keep getting a warning like equation is not identified—does not meet order conditions.

2. How to interpret when DV becomes insignificant after running the 3SLS model? (endog_var1 DV instrument1 i.industry i.Year; Here, DV is not significant.)

3. If I want to add fixed effects into the model, how could I add them to the STATA command?

4. What if I set up a model like reg3 (DV endog_var1 control1 control2 control3 control4 control5 control6 i.industry i.Year) (endog_var1 instrument1 i.industry i.Year) without DV in the first stage. Does this model still cope with simultaneity bias that my model might have?

Thank you for reading this question.




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