So in my situation I have my dependent variable Log Income my Instrument Diabetes and my supposedly endogenous explanatory variable Reads Nutri. Where things start to get confusing for me is that there are two other explanatory variables in my model that should also be correlated with my instrument BMI and health related work limitations. If BMI positively effects Diabetes and Diabetes positively effects health related work limitations, than should BMI and health related work limitations also be instrumented in my 2SLS regression? how do I now go about preforming my 2SLS IV regression?
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$\begingroup$ What is your structural model? Is it $lnincome=\beta_0 + \beta_1ReadsNutri+\beta_2BMI+\beta_3Limit+\epsilon$ or should $BMI$ and $HealthLimit$ be included in the structural model as well? $\endgroup$– Marquis de CarabasCommented May 4, 2016 at 22:52
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$\begingroup$ It seems to me that a rudimentary conceptual model showing the hypothesized relationships would help clarify the question. The bigger concern is: are there other factors affecting $Diabetes$ besides $BMI$ that you need to account for in the model? Are there other factors affecting $HealthLimit$ and $lnincome$ as yet not accounted for in the model? $\endgroup$– Marquis de CarabasCommented May 4, 2016 at 23:25
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$\begingroup$ @marquisdecarabas, my model is: 'Log Income' = b0 + b1*'Black' + b2*'Male' + b3*'Highest Grade' + b4*'Health Limitations' + b5*''Height' + b6*'Reads Nutri' + b7*'Maried-ish' +b8*'Age' + b9*'Age squared' + b10*'Number of Jobs' + b11*'Experience (weeks)' + b12* 'Experience (weeks) squared' + b14'BMI' . what do you think? $\endgroup$– Noam RosenbergCommented May 5, 2016 at 14:10
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$\begingroup$ First and foremost, I'd be skeptical that BMI is a valid instrument. There's a million reasons why obesity could affect income. $\endgroup$– DurdenCommented Mar 28, 2023 at 19:45
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It is fine that your other variables of the structural equation, BMI and health-related work limitations. be correlated with the instrument. If they are not your research interest, it will even be fine for the variables to be endogenous.
Additionally, I believe you could not have more endogenous variables than instruments. So if you are performing 2SLS in STATA:
ivregress Log_Income Controls (Reads_Nutri= Diabetes), robust
where Controls are just all the controls you have.