# 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?

## 1 Answer

If the goal of the project is to model housing demand, I would suggest using the actual number of occupied housing units. Census data may calculate occupancy as an algebraic function of supply, that is, occupancy is derived using the supply variable. This may show up as a strong correlation in the model, but it doesn't capture the stochastic properties of housing demand.

1. If you are interested in the price elasticity of housing, just use a log-log regression. Here is a good post about equilibrium price.

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 $$x$$.

This is refereed to as spatial dependence and it can affect the model a lot. I would recommend the software Geoda and GeodaSpace to analyze and run spatial regression models.

• I like the idea of spatial regression. Are there any relevant links, papers you can share? – kms Aug 17 '20 at 5:03
• Anselin, Rey. (2014). Modern Spatial Econometrics in Practice: A Guide to GeoDa, GeoDaSpace and PySAL. That book is a mixture of statistics theory and also serves as a usuer manual for the open source software Geoda, GeodaSpace, and Pysal (a Python package). If you are interested in the heavier statistics theory I would recommend Anselin. (1988). Spatial Econometrics: Methods and Models. It basically laid the foundation for modern spatial econometrics. – Andrew Aug 17 '20 at 9:26