IV 2SLS with different unit of analysis for first and second stage regressions

[Nitin Jain]

Hi,

My dependent variable is at the "firm" level and the endogenous variable is at the “group of other firms” level. Can I use the controls for the first stage at the “group of other firms” level, i.e., the average of the values for the firms in that group.

Any suggestions are very much welcome along with any reference to any textbook/papers on this kind of an analysis. Thanks.

[Sebastian Kripfganz]

From the perspective of spatial econometrics, this sounds like your endogenous variable is a "spatial lag" (where "space" is defined by the relationship of firms to each other within a group) and you want to use spatial lags of other controls as instruments. This sounds like a reasonable approach. You might want to have a closer look at the spatial econometrics literature.

[Nitin Jain]

From the perspective of spatial econometrics, this sounds like your endogenous variable is a "spatial lag" (where "space" is defined by the relationship of firms to each other within a group) and you want to use spatial lags of other controls as instruments. This sounds like a reasonable approach. You might want to have a closer look at the spatial econometrics literature.

Thanks, Sebastian. I have found the instrument. But I am a little unclear at what level should the controls for the first-stage be? I think they should be at the group level since the endogenous variable is also at the group level. However, my final outcome variable is at the firm level, so the controls for the second stage would be at the firm level. So I wanted to know if it is fine for the controls for the first- and second-stage to be at different levels.