Question about instruments in this model

[PLM]

Hi,

Sorry in advance for this long post.

I have the following (as simplified as possible) base model:

dSALARY = LUCK + LUCK_LESS_THAN_0*LUCK + ...

Essentially, the coefficient on the second term shows how sensitive salary is to luck when luck is less than 0 ("down").

I'm trying to investigate whether a number (5) of variables affect the sensitivity when luck is down. I simply add the following terms:
.. + VARIABLE1 * LUCK_LESS_THAN_0*LUCK + VARIABLE2 * LUCK_LESS_THAN_0*LUCK + VARIABLE3 * LUCK_LESS_THAN_0*LUCK + ...

Now, the I think endogeneity might be a problem (i.e. the variables of interest and dSALARY might be jointly determined). Would finding instruments for the variables of interest and using IV regression be a decent solution?

Given the model, it just seems like it might not be a good idea for a few reasons:
- It's not actually the change and salary itself that is jointly determined, but its sensitivity when luck is down. I.e., it might be more correct to say that a certain sensitivity of luck and the variables of interest are jointly determined. In this case I think IV regression is not needed.
- Quickly throwing a few instruments for each in spits out estimations which are all not significantly different to 0. Is this due to some modelling, etc. error? The model then has quite a lot of variables and lots of instruments.

Basic econometrics tells me that IV regression makes sense but I seem a bit hesitant...

Thanks!

[startz]

It's hard to give a really good answer without knowing much more about what you're doing than is easy to convey in a post. Two points though:

(1) The fact that you don't get signficant coefficients with IV could either mean that you don't have good enough instruments or that the coefficients really aren't different from zero.

(2) What do you mean by "sensitivity?" Is it that the response fnction is actually nonlinear?

[PLM]

Thanks for the quick reply!

Let me address your first point and then try to get what I'm doing across.

- This may be possible and I'll do the standard tests for independence and exogeneity on the instruments.

Essentially, I'm looking at how sensitive a change in salary (dSalary as dependent var) is to a benchmark (luck). Without the indicator variable (luck_less_than_0), the coefficient on luck tells us how large this sensitivity is. Now, to see how this sensitivity differs between when luck is "good" (>=0) and "bad" (<0), I add the interaction term. So yes, the response function is assumed to be non-linear around 0.

Very roughly, if the coefficient on this indicator term is negative, it suggests that the CEO is able to benchmark his salary LESS when the benchmark is down (so this is bad - he probably captured the pay process or something). My research is looking at determinants of this weaker benchmarking when luck is down. This involves adding additional interaction terms of my variables of interest with luck*luck_is_down.

[startz]

If you think the error term might be correlated with the interaction term--I take it that's your worry--then, yes, instrumental varibles would be called for.