<p>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 <em>using</em> 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.</p>
<ol start="2">
<li><p>If you are interested in the price elasticity of housing, just use a log-log regression. Here is a good post about <a href="https://economics.stackexchange.com/questions/19077/equilibrium-price-ols-regression">equilibrium price</a>.</p>
</li>
<li><p>What is the level of analysis? If you have panel data (historical data for <span class="math-container">$n$</span> neighborhoods), I would suggest looking into spatial regression.</p>
</li>
</ol>
<p>For a given neighborhood <span class="math-container">$x$</span>, the occupancy rate of the surrounding neighborhoods may affect demand for housing (the negative affects of vacancy &quot;spill over&quot; into <span class="math-container">$x$</span>). Another example, if rent is high in the neighborhoods surrounding <span class="math-container">$x$</span>,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 <span class="math-container">$x$</span>.</p>
<p>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.</p>

CC BY-SA 4.0
2020-08-17T05:03:35.367Z
I like the idea of spatial regression. Are there any relevant links, papers you can share?
kms
CC BY-SA 4.0
2020-08-17T09:26:59.680Z
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
CC BY-SA 4.0
2020-08-17T02:23:33.830Z
2020-08-17T02:23:33.830Z
Andrew
<p>I have historical data on occupancy rates for a given neighborhood, along with characteristics and other local economic variables.</p>
<p>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.</p>
<pre><code>D(p) = Rent + Median Income + Supply + # of HH
</code></pre>
<ul>
<li>Median Income is time fixed effect.</li>
</ul>
<p>My questions are:</p>
<ol>
<li>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.</li>
<li>Interaction term. Given that supply follows rental prices, add <code>supply * rent</code> as interaction term.</li>
<li>What other regression methods would make sense for this problem?</li>
</ol>

<elasticity><regression><general-equilibrium>
Regression approximation for the rate of change in occupancy rate of residential market with respect to price
kms
# Regression approximation for the rate of change in occupancy rate of residential market with respect to price

(Asked by: username_0 on 2020-08-15)

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:

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.
Interaction term. Given that supply follows rental prices, add supply * rent as interaction term.
What other regression methods would make sense for this problem?

**Tags:** elasticity, regression, general-equilibrium

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## 1 answers

### Answer by username_1 on 2020-08-17. Score: 2

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.

2. If you are interested in the price elasticity of housing, just use a log-log regression. Here is a good post about [equilibrium price](https://economics.stackexchange.com/questions/19077/equilibrium-price-ols-regression).
3. 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.

> **Comments:**
> **username_0**: I like the idea of spatial regression. Are there any relevant links, papers you can share?  
> **username_1**: 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.  

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