Instrumenting an Endogenous Variable and Its Interaction Term Using ivregress

[Kleon Marenas]

Hello everyone,

I am using Stata 15 on Windows 10 and have a question about implementing an instrumental variables regression involving an endogenous variable and its interaction term.


Context:
- Dependent Variable: Y
- Endogenous Variable: X1
- Exogenous Variable: X2
- Interaction Term: X1X2 (which is X1 * X2) <- these are centered
- Instruments:
For X1: Z1
For X1X2: Z2 (constructed as Z1 * X2) <- these are centered

The stata commands I used are the following:
ivregress 2sls Y X2 (X1 X1X2 =Z1 Z2), r
estat endog, forcenonrobust
estat firststage, all forcenonrobust

Questions:
1. First-Stage Regressions:
- Will Stata produce two first-stage regression tables, one for each endogenous variable (X1 and X1X2), each including both instruments (Z1 and Z2)?
- Are my commands correct or am I missing something?

2. Significance of Instruments:
- In the first-stage regression where X1 is the dependent variable, Z1 is significant while Z2 is not.
- In the first-stage regression where X1X2 is the dependent variable, Z2 is significant while Z1 is not.
- Is this situation acceptable, or should I be concerned about the insignificance of one of the instruments in each first-stage regression?

Thank you in advance

[Andrew Musau]

ivregress supports factor variables, so do not generate any interactions by hand.

ivregress 2sls Y X2 (X1 c.X1#c.X2 =Z1 c.Z1#c.X2), r

In this specification, it all boils down to whether Z1 is a good instrument for X1. If that holds, you're fine.