# Regression approximation for the rate of change in occupancy rate of residential market with respect to price

I have historical data on occupancy rates for a given neighborhood, along with characteristics and other local economic variables.

I am looking to estimate the regression equation with occupancy rates as dependent variable and price, level of supply, characteristics and economic vars as independent variables.

D(p) = Rent + Median Income + Supply + # of HH

• Median Income is time fixed effect.

My questions are:

1. How do you interpret the equilibrium price from the regression output? i.e price at which Occupancy rate is 100%. or price elasticity of demand.
2. Interaction term. Given that supply follows rental prices, add supply * rent as interaction term.
3. What other regression methods would make sense for this problem?

2. What is the level of analysis? If you have panel data (historical data for $$n$$ neighborhoods), I would suggest looking into spatial regression.
For a given neighborhood $$x$$, the occupancy rate of the surrounding neighborhoods may affect demand for housing (the negative affects of vacancy "spill over" into $$x$$). Another example, if rent is high in the neighborhoods surrounding $$x$$,a shift in the demand for housing will occur, because people are making a spatial decision regarding where they will live and take into account the housing characteristics of the neighborhoods of a given area. Therefore, to model housing demand, the occupancy rate and independent variables of surrounding neighborhoods may capture the process of housing demand in $$x$$.