I work for a company that produces retail items and I am tasked with calculating the price elasticity of demand for a subcategory that shall remain unnamed. I have 5 years of monthly market data that shows market price as well as ounces sold. My independent variables include IV estimated prices, monthly income spent on non-durables (national Fred data), ounces sold of a related subcategory, and 11 dummy variables for the 12 months of seasonality. The model is Log-Log.
My idea was to control for everything that would be a supply side factor and then use the coefficient of price as my demand curve slope. Of course, the demand curve is always changing, but in aggregate I would assume a relatively steady demand curve. It would at least be better than simply calculating dQ/dP. The problem is my coefficient for price is positive. Also, even though the R-Square is around 70% and the F-Stat is significant at the 99%+ level, my individual parameters are mostly not statistically significant.
The problem is, I am looking at monthly data for an entire subcategory. The volume sold and weighted average prices continue to rise and I am not sure how to isolate demand. Any ideas would be greatly appreciated.
Regarding the IV price estimator to remove endogeneity, I ran the stage 1 regression with the cost of raw materials as my X and price as Y. This price estimator has an R-Square of .91. The cost of raw materials has a correlation of .11 versus .32 when run against quantity.