I have a time series of units sold, and price. I'd like to calculate elasticity of demand wrt to price and a few other variables, some of them are fixed effects.
Qp = b0 + b1 * log(Price) + b2 * Location + b3 * log(Income) + b4 * log(HouseHolds)
I am using log-log regression to calculate the elasticities, and the independent variable of interest is Price. Qp is # of units sold.
My questions are
Can I use Median Income, and Households are fixed effects for the time period in log-log regression model.
Interpretation of Log - Log regression. 1% change in price changes the units sold by b1%(coefficient of price), Ceteris paribus, all else being equal.
Cross Elasticity. What I add a term for # of available substitutable units? How would I interpret the term?
Qp = b0 + b1 * Price + b2 * Location + b3 * Income + b4 * HouseHolds + b5 * substitutable units
I also have additional categorical variable, i.e type of unit sold.
type 2. Does it make sense to include that variable in the equation or fit a regression separately for each type? How would you interpret different coefficients of categorical variable?
I'd like to find the point where increasing the Price negatively affects units sold.