ECO 311 Lecture Notes - Lecture 1: Dependent And Independent Variables, Sun Belt

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Published on 30 Jan 2018
Housing prices have been a very interesting topic this past decade in Florida. As much of the populations shifts
to the sun belt, demand for new housing has skyrocketed. Combine this with risky financial speculation and lack of
regulation, and you can get a financial crisis. Naturally, governments seek to prevent economic crises of this level
and seek to prevent fraud. Our task is to create a model that effectively determines the market value of a house in a
municipality in Florida.
This model we have created will accurately reflect the trend in housing prices for the region of Florida. By
using variables and statistical methods that show causation we have found a model that the legislature can use to
accurately use to set policy by looking at numbers of the past to regulate housing in the future. Hopefully this work
can help the Florida legislature prevent future financial crises from occurring and effectively curtail harmful
practices in the market.
3. Explanatory Variables
Dependent Variable
Explanatory Variables
The construction of correct explanatory variables is the key to this model. If we fail to correlate certain
variables or leave impactful variables out of the model any meaningful conclusion drawn will be useless. Excluding
interaction terms for now, we had fourteen explanatory variables. After cleaning up total and living sqft, we
generated two variables for that area. The average Living Sqft was significantly higher than average Nonliving Sqft
across every municipality and property type. After generating bedroom and bathroom variables it was clear that
most condos and townhouse have about 2 bedrooms and 2 baths, while single family homes ranged a little higher
with about 3 bedrooms, but still around 2 baths. Garage Spaces and pool variables were simple to find and make.
Condos had more access to pools than any other home category. Average year built for each property varied
depending mainly on municipality and ranged from mid seventies to mid two thousands, with most being built
around late eighties/mid nineties. The average property was on the market longer than seventy five days, but some
sold in as quickly as forty. Special views for golf course, ocean, intercoastal, river, and lake view all really depended
on municipality to determine whether or not they were used. These are all the generated pure explanatory variables.
Of course certain variables overlap, and that overlap can cause different effects than each variable alone.
Certain variables may affect the model more than others as well, so it is appropriate to introduce quadratic terms into
models to show the extra effect. Living sqft certainly is a major determining factor in value, so the variable
livingftsquared was created to better reflect that effect. To account for the effect of multiple special views for each
property, we created twenty three interaction variables to accurately reflect that. The final special variable we
created was daysonmarketsquared, as days on the market certainly affects the price a property can command
significantly. Explanatory variables are the key to a good model.
The Model
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A proper test for robustness compares explanatory variables in each model to see how they compare with one
another. If there is no difference between a model that is based on one location and a model based on another, then it
only makes sense to have just one model. To properly test for robustness, you should compare the coefficients for
each variable by a t test with the corresponding coefficients in the others. If any coefficient is statistically
significantly different than the same effect in another model, two models are required.
To properly check our model, we compared every explanatory variable with the dependent variable. We looked
for any and all statistically significant relationships that would show the variable should not belong in the model.
Luckily, most variables showed a strong difference from the dependent, so we included all the variables. In our
generated models for condos, single family homes, and townhouses, we didn’t see any strong similarity that would
warrant one model. Our robustness checks encouraged us to build different models for different property types.
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4. Bivariate Relationships between Dependent and Explanatory Variables
In the models that we have created, there is a relationship between the dependent and each and every
explanatory variable. These explanatory variables are what end up creating the model and determine the dependent
variable. The explanatory variables in our model are exogenous, that is: they have an effect on our dependent
variable but the dependent variable does not have a returned effect on the explanatory variables.
The dependent variable in our model is selling price, it will be determined by the explanatory variables that
we have included in each of our three models. Those models being based on type of building: a condo, a townhouse
or a single family house. In our models, the explanatory variables that we have decided to include are days on the
market, days on the market squared, the different view types (ocean view, river view, golf course view, lake view,
intercostal view, an ocean and river view, etc.), the city, if the venue has pool access, the year it was sold, number
of bedrooms, total number of baths, garage space, non-living square feet, non-living square feet squared, living
square feet, living square feet squared, the year it was built, and the type of building. Every single one of these
variables has an effect on the dependent variable but only a few have a bivariate relationship with the dependent
variable, selling price. The explanatory variables that have a bivariate relationship with the dependent variable are
the dummy variables. These dummy variables can only have values of either 1 or 0. These values will change selling
price. If the value is 1 then this variable is included, for example, if the variable pool access had a value of 1 then it
means there is pool access whereas 0 means that it does not have pool access. The dummy variables that are
included in the model and have a bivariate relationship are view type, pool access, and city.
5. Linear Model
The price of a house is dependent upon many different factors such as type of building, location, number of
bedrooms, etc. After creating the necessary dummy terms, dummy interaction terms, and quadratics that weren’t
originally in the data, the models are able to be created.
5a. Presentation of the Linear Models
Three models are necessary to measure property values as there are three different types of houses:
condominium, townhouse, and single family. For each model the only thing that is changed is the type of house. All
of the other variables apply to each type of house. Also, when the models were being run, several of the dummy
interaction terms for view type were omitted for collinearity.
Condo: Sp = CAf + €f
Townhouse: Sp = TAf + €f
Single Family: Sp = GAf + €f
Sp = Sales Price
C = Condominium
T = Townhouse
G = Single Family Home
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