Programming the statistical procedures from SAS

Interaction terms between endogenous explanatory variables

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Interaction terms between endogenous explanatory variables


I'm doing regression analysis that contains interaction terms. The equation looks something like this

y = b0 + b1*x1* + ... + bN*xN + b23*x1*x2 + epsilon.

The problem is that the variables in the interaction terms are endogeneous.

Normally, I would use 2sls (e.g. proc syslin) and use the instrumental variables approach to control for endogeneity. I am not sure whether the 2sls can be straightforwardly applied to models with interaction terms.

Can I assume that the interaction terms are just like any other variable and use, for instance, lagged interaction terms as an instrument for the interaction terms that consist of endgogenous explanatory variables. That is, can I use 2sls to estimate

y = b0 + b1*x1* + ... + bN*xN + bZ*z + epsilon,

where z=x1*x2

and conveniently "forget" that z is computed from other variables.

Any comments are welcome!

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