I have panel data and am interested in changes in total expenditures. I would like to consider an instrumental variable approach to deal with an endogenous regressor – the short run elasticity of income, lagged by 3 years.
There are two ways I can think to do this:
- I could calculate the elasticity using all years and then run a cross-sectional analysis.
- I could calculate the elasticity by using a moving average of the last five years and then comparing that to expenditures in time t + 3. However, this would make the instrument correlated over time. I don't think this violates the exclusion restriction in my case, but I am wondering if this violates other assumptions, such as randomness.
