An Analysis on the Influence of Mortgage Rates on Housing Prices - Final Draft

C.Goettl An Analysis of the Influence of Mortgage Rates on Housing Prices 1
Caleb Goettl
Econ 485W
Term Paper
8/30/2015
An Analysis of the Influence of Mortgage Rates on Housing Prices
Abstract
This paper analyzes the influence mortgage rates have on housing prices in the United States. If
a significant long-run relationship between mortgage rates and housing prices can be found, as
it has been in studies done in other countries, it can then be used as a tool to guide creating
policies that can positively affect the housing market. The study uses the Augmented Dickey-
Fuller(ADF) test as well as the Phillips-Perron(PP) test for unit roots in order to determine if
cointegration exists, and if there is a relationship between the variables or not. From there, an
error-correction model is used in order to capture the long and short run effects of the data. A
major emphasis is put on testing for stationary variables as it is critical to avoiding spurious
results. The study employs three variables: Housing Price(dependent), Mortgage
Rates(Independent), Gasoline Price(Independent). This study uses monthly data that ranges
from January 1973 to August 2015. After obtaining the output, the error correction model
showed that there was virtually no short run relationship between the variables. The model did
however show significant coefficients in the long run, although the impact was very small. The
findings of this study were fairly consistent with previous research done on this topic.

Introduction
Housing Prices in the United States have increased steadily over the past century, with
the exception of the housing market crash in 2007. Leaving out the housing market crash, prices
of homes have increased as expected due to the growth of the American economy as a whole.
However, there are potentially many factors that affect housing prices that are important and
useful to examine. This paper analyzes the influence that mortgage rates, as well as gasoline
prices, have on housing prices. However, the main focus is on the relationship between prices
and rates since, theoretically, that relationship makes the most sense.
It is helpful to understand the relationship between mortgage rates and housing prices for
both lenders and borrowers as well as the recent history of the U.S. housing market. To illustrate
how the variables can affect each other, it is useful to examine the housing bubble crisis that
occurred in the U.S. in the early 2000’s. First of all, a “housing bubble” can be defined as
excessive public expectations of future prices that causes actual prices to be temporarily
elevated. In the U.S. market, a housing boom began to occur in the year 2000 and continued until
about 2006. Banks were also offering historically low rates. Homebuyers were purchasing homes
they previously thought were too expensive thinking that they would be compensated by the
increase in the value or prices of their homes in the future. Doing so meant that they put much
more money into their house payments and much less money in their savings. Eventually, prices
stopped going up and people’s willingness to buy higher priced homes, as they did during the
boom, disappeared. As the demand diminished, the prices plummeted and mortgage rates
skyrocketed causing the housing bubble to burst. Since people saved less and put most of their
money into their homes prior to the bubble bursting, many people defaulted on their mortgages
and caused huge losses for banks and the investors that backed them. By the year 2008, there

was over 3 million foreclosures throughout the United States. The collapse of the housing market
in 2007 created a ripple effect and affected many other markets. In September 2008, the entire
financial system collapsed and the worst recession since World War II was in full swing. Figure
1, shown below, illustrates the rise of the housing bubble as well as the enormous drop in prices
in the housing market around 2008. Figure 1 also shows a graph of the stock market during that
time period making it is easy to see how closely related the two markets are.
Figure 1:
Depiction of housing market Depiction of stock market
*Both graphs show an upward trend until about 2006-2008. Then, they both drop off sharply, illustrating the effect the housing
bubble had on the stock market. Housing Market Graph: S&P/Case Shiller U.S. Housing Price Index, see references. Stock
Market Graph: data provided by Yahoo! Finance.
The U.S. Government implemented a credit freeze after the collapse which was intended
to slow the recession from getting worse, but it also caused high volatility in the stock market.
Although the credit freeze may have saved us from worst case outcomes, it also left large budget
deficits that could take decades to reverse.
If it can be proven that mortgage rates are an effective indicator of the movement of
housing prices, then lenders, borrowers, and the Federal Reserve Bank can use that information
to prevent another crisis from occurring. Borrowers can more effectively predict when it is the
0
400
800
1,200
1,600
2,000
2,400
1975 1980 1985 1990 1995 2000 2005 2010 2015
S&P 500 Historical Stock Market Data
*Source: Yahoo! Finance

right time to enter the housing market by using these relationships to secure a loan that allows
them to pay the lender the least amount of money. Additionally, homeowner’s can use these
relationships to gauge when it is the right time to sell so that they can obtain the highest possible
value from their home. Lenders and government can also benefit from paying attention to these
factors so that they can efficiently regulate the housing market and try to keep it from crashing as
it did in 2007.
The first objective in this study is to review past literature on this topic and identify areas
that can be improved or corrected. The second objective is to formulate an error correction model
to examine the long-run and short-run effects that mortgage rates and gasoline price have on
housing prices in the United States by using time series data. It is also important to note that
testing for cointegration is an essential part of creating a good error correction model and will be
incorporated into this study. The remainder of this study is organized into the following sections:
Literature Review, Data, Methodology, Empirical Results, and Conclusion.
Literature Review
As it is with any economic study, it is critical to carefully examine previous work on the
topic or topics closely related. Doing so can greatly help with coming up with new and improved
methodology. This section of the paper is dedicated to just that. Although many papers were
reviewed for this study, it was narrowed down to several that were related the closest to the topic
and that were of the most use in formulating a model.
When examining the housing market it, it is typical to question if the demand side or the
supply side of the market has the dominate effect. A study by Hendershott (1980) used a

neoclassical model of investment to show that an increase in mortgage rates has a negative effect
on housing demand, which would subsequently drive prices down. Additionally, it has been
shown that higher mortgage rates can also have a negative effect on the supply side. Poterba
(1984) conducted a study that used interest rates as a cost, and holding housing prices constant,
higher rates drove down the supply of housing as well. However, both of these studies used fixed
housing prices that did not allow to view the co-movements of prices and rates together.
Thinking about the co-movements theoretically leads to an assumption that mortgage
rates have an opposite effects from the demand and supply sides of the market. Holding supply
constant, higher rates will lead to a fall in demand and eventually a fall in prices. Holding
demand constant, higher rates would decrease the supply and increase prices. Essentially what
this is saying, as McGibany and Nourzad (2004) noted, higher interest rates could either lower or
raise housing prices depending upon if the demand effect or supply effect is stronger.
Many studies have found that the demand side is the more prominent effect, however the
significance of the effect varies from study to study. For example Englund and Ioannides (1997)
have found that housing prices are strongly negatively affected by an increase in mortgage rates.
Reichert (1990) proves that housing prices of new homes in the United States are also negatively
affected by increases in mortgage rates in all but 2 regions. The list could go on and on of
researchers who have shown similar results.
Another aspect of the relationship between mortgage rates and housing prices that is
critical to note is that of stationarity. McGibany and Nourzad (2004) mention that many time
series data are integrated to the order one, I(1). They also mention that not checking for
stationarity and using ordinary least squares would lead to spurious results if the variables were
indeed integrated to I(1). In order to avoid this problem, it is absolutely critical to check the order

of integration using the Augmented Dickey-Fuller and/or the Phillips-Perron tests. From there an
error correction model can be created in order to capture the short run and long run effects.
Furthermore, it may also be important to include gasoline price as a variable that is
related to Mortgage rates. Park and Budhathoki (2007) used an error correction model and the
Kalman filter technique to show that the short-run movement of gasoline price can significantly
increase the correct prediction of movements in mortgage rates. Their reasoning was that rising
gasoline prices can cause money to move in the bond market which can decrease inflation and
help bolster lower mortgage rates, at least in the short-term. Knowing this, gasoline price could
be an essential piece to add to a model that is trying to explain housing prices.
Lastly, a question remains of whether or not stronger monetary policy by the central bank
can help control or regulate the housing market more efficiently in order to avoid another
housing bubble. Shi, Jou, and Tripe (2014) conducted a study in New Zealand that examines if
interest rates can really control housing prices. They found that real interest rates are
significantly related to real housing prices. They then tested interest rates and found housing
bubbles that could have been prevented had the central bank taken notice and intervened earlier
than they actually did. This study is evidence that macroprudential policy can effectively prevent
housing bubbles from reaching the point of financial crisis.
After closely reviewing the previous literature on this topic, we can begin to form a plan
of action for analyzing the variables affecting housing price. Since it is likely that the variables
used in this study (housing price, gas price, and mortgage rates) are non-stationary, testing for
cointegration is a must. If it turns out to be true that they are integrated to the order 1, I(1), then
an error correction model would be the appropriate model to use. However, since more time has
passed since the last study conducted on housing prices, more data will be available and used in

this analysis. Also, if it can be shown that gasoline price and mortgage rates can be significant
indicators of housing price, then that information can be used to help regulate the market and
prevent a recession caused by another bursting housing bubble.
DATA
As it was noted in the study by McGibany and Nourzad (2004) there is a very large
amount of time-series data available for the variables incorporated in this study both at the
national and international levels. However, this study focuses solely on the data available for
the United States. The data was easily obtainable from various government organizations that
publish it for public use on the internet. In a time series analysis such as this one, data that is
reported more frequently leads to much better and more accurate results. The data employed
in this study is monthly from January 1973 to August 2015, which is just over 42 years-worth of
monthly observations.
The first independent variable used in the model is a form of mortgage rates. It can be
defined as the effective rate on conventional mortgages for all loans that were closed in the
United States. This data was located using the FRED tool on the Federal Reserve Bank of St.
Louis’s website. In the model, the variable is denoted as ER.
The second independent variable used in the study is Gasoline Price. This variable is
denoted GP in the model, and it can be defined as the average residential gasoline price in the
United States. This model was included due to past literature by Park and Budhathoki (2007)
that showed gas prices can predict mortgage rates in the short run.

The data collected for the dependent variable comes from the United States Census
Bureau. The data used to represent housing price is the median house price of new single
family homes sold in the United States. In the model, this variable is denoted HP.
Lastly, it could be important to note that there was originally a few more variables being
considered. However, after examining and running various tests on the data, those variables
were thrown out due to their unimportance in association with this study.
Methodology
First we start by formulating a simple regression model to show the variables in this study
that expect to affect housing price. Although this model will not be used to actually examine the
data, it is important to not to show the potential relationship between them. The simple model
representing the long-run relationship between the dependent variable, housing price, and the
two independent variables used, mortgage rate and gasoline price is stated below:
𝑯𝑷𝒕 = 𝜷 𝟎 + 𝜷 𝟏 𝑬𝑹𝒕 + 𝜷 𝟐 𝑮𝑷𝒕 (1)
The dependent variable denoted HP is housing price. The independent variable ER is the
effective mortgage rate, and the independent variable GP is gasoline price. The subscript t
denotes the time period, which is monthly in this study. As it was pointed out in the study by
McGibany and Nourzad (2004), it is important to test the stationarity of the variables when using
an error-correction model. If two or more variables are integrated to the same order, those

variables are said to be cointegrated, meaning some linear combination of the non-stationary
variables is stationary.
Equation (1) can then be re-written as a lag model that accounts for the short-run and
long-run effects of the data. Since it is likely that housing price, gasoline price, and mortgage
rates are all integrated to the order of one, I(1), we use a lag length of 1 for each variable. The
basic error correction model version of equation (1) can be written as follows:
∆𝒍𝒐𝒈( 𝑯𝑷 𝒕
) = 𝜷 𝟎 + 𝜷 𝟏∆𝑬𝑹𝒕 + 𝜷 𝟐∆𝒍𝒐𝒈(𝑮𝑷 𝒕) + 𝜷 𝟑(𝒍𝒐𝒈(𝑯𝑷 𝒕−𝟏) − 𝜷 𝟒 𝑬𝑹𝒕−𝟏 − 𝜷 𝟓 𝒍𝒐𝒈(𝑮𝑷 𝒕−𝟏)) + 𝒖𝒕 (2)
This equation (2) is the basic format of an error-correction model. Therefore, we can
interpret 𝛽1 as the short-run effect of the effective mortgage rate on housing price. 𝛽2 can be
interpreted as the short-run effect of gasoline price on housing price. We can also interpret 𝛽4
and 𝛽5 as the long-run effect of the effective mortgage rate, and the long-run effect of gasoline
price on housing price, respectively. Additionally, 𝛽3 can be interpreted as the speed of
adjustment of the residuals in the long-run cointegration process between the dependent and
independent variables.
Empirical Results
As mentioned previously, the first step in getting the error-correction model results was to
determine the order of integration of each variable. For this study, both the Augmented Dickey-
Fuller (ADF) test, as well as the Phillips-Perron (PP) test were used in determining what order of
integration each variable was. Not surprisingly, the dependent variable, housing price, was
integrated to the order of one, I(1), in both the ADF and the PP tests. Additionally, both
independent variables, mortgage rate and gasoline price, were also integrated to the order of one,
I(1), as shown by both tests. The actual results of the ADF and PP tests for each variable are

ADF Tests: Figure 5 PP Tests:
shown in Figure 5 below. The findings of these tests of stationarity are consistent with previous
research done by McGibany and Nourzad (2004) for all three variables. The findings are also
consistent with the previous research done by Park and Budhathoki (2007) for the variables
gasoline price and mortgage.
Null Hy pothesis: D(LHP) has a unit root
Exogenous: Constant, Linear Trend
Bandwidth: 23 (Newey -West automatic) using Bartlett
kernel
Adj. t-Stat Prob.*
Phillips-Perron test statistic -45.72646 0.0001
Test critical
v alues: 1% lev el -3.976153
5% lev el -3.418657
10%
lev el -3.131849
Null Hy pothesis: D(LHP) has a unit root
Lag Length: 11 (Automatic - based on SIC, maxlag=18)
t-Statistic Prob.*
Augmented Dickey -Fuller test
statistic -5.762174 0.0000
Test critical
v alues: 1% lev el -3.976554
5% lev el -3.418852
10%
lev el -3.131965
Null Hy pothesis: D(ER) has a unit root
kernel
Adj. t-Stat Prob.*
Test critical
v alues: 1% lev el -3.976153
5% lev el -3.418657
10%
lev el -3.131849
Null Hy pothesis: D(ER) has a unit root
Lag Length: 0 (Automatic - based on SIC, maxlag=18)
t-Statistic Prob.*
statistic -13.25497 0.0000
Test critical
v alues: 1% lev el -3.976153
5% lev el -3.418657
10%
lev el -3.131849
Null Hy pothesis: D(LGP) has a unit root
Lag Length: 1 (Automatic - based on SIC,
maxlag=18)
t-Statistic Prob.*
statistic -15.21383 0.0000
Test critical v alues: 1% lev el -3.976188
5% lev el -3.418674
10% lev el -3.131859
Null Hy pothesis: D(LGP) has a unit root
kernel
Adj. t-Stat Prob.*
Test critical
v alues: 1% lev el -3.976153
5% lev el -3.418657
10%
lev el -3.131849

The estimates of the equation (2) error-correction model that was obtained in the
methodology section are reported in table 1. The model was obtained using a general to specific
method that eliminated all variables and lag-lengths that were statistically insignificant and
theoretically unimportant. After testing the variables for cointegration, it was verified that it
does, indeed, exist among all 3 of the I(1) variables. For the evaluation of the output, each test
statistic was examined at the standard significance level.
Table 1: Regression Output of Error-Correction Model
(dependent variable = Δlog(𝐻𝑃𝑡))
______________________________________________________________________________
Variable Coefficient Std. Error p-value Newey-West t-
Value
Constant 0.215804 0.083721 0.0102 4.887203
∆𝐸𝑅𝑡
0.000466 0.010063 0.9631 0.062298
Δlog(𝐺𝑃𝑡) 0.001626 0.031362 0.9587 0.072107
Log(𝐻𝑃𝑡−1) -0.017161 0.006910 0.0133 -4.706971
𝐸𝑅𝑡−1
0.091361 0.038952 0.0194 5.138213
𝑙𝑜𝑔(𝐺𝑃𝑡−1) -0.496156 0.212285 0.0198 -4.235970
______________________________________________________________________________
𝑅2
= 0.01567 D.W. Stat = 3.007477 F-Stat = 0.156227
Note: Newey-West t-values are reported for better efficiency and accuracy.
According to the estimation output, the short-run effect of mortgage rates on housing prices
is insignificant at the standard significance level. Even by increasing the significance level shows
that there is still a very weak relationship between the two variables. Similarly, almost the same
can be said for gasoline price in the short-run. At the standard significance level, it is clear that

there is virtually no relationship between gasoline price and housing price in the short-run.
However, these short-run results were to be expected as similar results were shown in previous
studies done on this topic that are listed in the literature review section, such as the one conducted
by McGibany and Nourzad (2004).
On the other hand, there are some significant relationships found in the long-run, although
they are rather weak. The effective mortgage rate is significant at the 5% level, indicating it has
some merit in predicting housing price. The interpretation of this coefficient is that a 1 percentage
point increase in the effective mortgage rate leads to a -0.09percent increase in housing price. This
result is also consistent with previous studies such as the one by McGibany and Nourzad(2004) in
that it shows a negative relationship between mortgage rates and housing price, although a very
weak one at that. The negative relationship also tells us that the demand side of the market has the
dominate effect, which is explained further in the conclusion section of this paper. Also, the
relationship between gasoline price and housing price is significant at the 5% level as well. This
relationship is slightly more explanatory than the effective mortgage rate, however it is still a weak
predictor of housing price. The interpretation of the coefficient for gasoline price says that a 1
percentage point increase in gasoline price leads to a .496 percent increase in housing price. An
expectation of an increase in inflation could most definitely lead to an increase in prices in many
major markets, including the housing market. This could very well be the relationship that is
captured in the output for the long run gas price coefficient. The final thing to note is the variable
labeled Log(𝐻𝑃𝑡−1) represents the speed of adjustment of the equation. In this equation, the speed
of adjustment represents the speed at which housing price will return to the equilibrium after shock
or deviation has occurred.

Figures 2, 3, and 4 shown below are separate response graphs that show the response of the
differenced logged dependent variable, DLHP, to each differenced logged independent variable,
DLGP and DER. The inclusion of these graphs help visualize how housing price responds when
there is a shock of one standard deviation in the economy for each variable.
Focusing on the first graph, Figure 2, we can see the response of housing prices to a shock
in the market for mortgage rates, DER. The interpretation of this response says that after the shock,
housing prices respond almost immediately by increasing and peaking at about 2 months after the
shock. Then, the response of housing prices decreases before bottoming out at about 4 months.
The response then fluctuates back and forth before settling just below the line zero at about 8
months, which is another illustration of the negative relationship between housing prices and
mortgage rates.
Figure 3 shows a similar response for housing prices to a shock in the market for gasoline
price. The difference is that for this variable, the response is negative at first instead of positive.
More specifically, the response decreases right away and bottoms out about 2 months after the
shock, and then increases and peaks at about 3 months. The response then fluctuates back and forth
before settling just above the line zero at about 8 months, indicating a positive relationship that
was also shown in the regression output (Table 1).
Lastly, Figure 4 shows the response of housing prices to a shock in the market for housing
prices. The more extreme response is most likely attributed to the fact that it shows the response
of a variable to a shock in its own market. It depicts the response as peaking right away 1 month
after the shock occurs, and then sharply decreasing and bottoming out about 2 months after the
shock. Then the response fluctuates back and forth before settling just above or around the line
zero at about 11 months.

Conclusion
This paper analyzes the influence mortgage rates and gasoline price have on housing
prices in the short-run and in the long-run. The method used to examine this relationships is an
Figure 2
Figures 2, 3, & 4 show the impulse
response of the first difference logarithms
of housing prices, DLHP, to the first
difference effective mortgage rate, DER,
and to the first difference logarithm of
gasoline price, DLGP, and to itself DLHP,
respectively.
-.02
-.01
.00
.01
.02
.03
2 4 6 8 10 12 14 16 18 20 22 24
Response of DLHP to DLGP
-.02
-.01
.00
.01
.02
.03
2 4 6 8 10 12 14 16 18 20 22 24
Response of DLHP to DER
-.02
-.01
.00
.01
.02
.03
2 4 6 8 10 12 14 16 18 20 22 24
Response of DLHP to DLHP
Figure 3
Figure 4
Impulse Response Graphs

error-correction model. Since it makes the most sense that mortgage rates would affect housing
prices the most, since they are more closely related, the main focus is on the relationship between
those two variables.
The results of the estimation of the error-correction model that includes the three
previously mentioned variables, showed that all relationships tested were insignificant in the
short-run. This finding is no surprise as it has been shown in many other studies that it is nearly
impossible to predict a short-run response in a market that takes a while for shocks to play out.
However in the long-run, significant relationships were found. According to the estimation
output, there is a negative relationship between housing prices and mortgage rates, which adds to
the piles of past literature that have proven the same thing. Also consistent with past studies, this
finding suggests that the demand side has the dominate effect in the market, meaning that higher
mortgage rates reduce the price of housing because of people’s diminishing willingness to pay
the higher rates. Although, since the prediction power of those rates is so small, we cannot be
one hundred percent certain about the demand effect. Also in the long run, it was proven that
gasoline price is also a significant predictor of housing prices, although the predicting power of
this variable is also small. Since gasoline price and mortgage rates have relatively little influence
in predicting housing prices, it can be said that the United States housing market has more of an
inelastic response to changes in those two independent variables. Since that is the case, it would
be difficult for the lenders, borrows, and the central bank to use mortgage rates alone as
information in creating macro-prudential policy that can effectively keep the housing market
from crashing as it did in 2007.

References
Engle, R. F. and Granger, C. W. J. (1987) Co-integration and error correction: representation, estimation
and testing, Econometrica, 55, 251–76.
Englund, P. and Ioannides, Y. M. (1997) House price dynamics: an international empirical perspective,
Journal of Housing Economics, 6, 119–36.
Federal Reserve Bank of St. Louis. FRED Economics Database.
Hendershott, P. H. (1980) Real user costs and the demand for single-family housing, Brookings Papers on
Economic Activity, 2, 401–44.
Johansen, S. (1988) Statistical analysis of cointegration vectors, Journal of Economic Dynamics and
Control, 12, 231–54
Poterba,J. M. (1984) Tax subsidies to owner-occupied housing: an asset market approach, Quarterly
Journal of Economics, 99, 729–52.
Park, K. W., and Budhathoki, M. (2007) Gasoline Price As A Leading Indicator Of Mortgage Rate,
Minnesota State University, Mankto Faculty Research Paper
Reichert, A. K. (1990) The impact of interest rates,income, and employment upon regional housing
prices, Journal of RealEstate Finance and Economics, 3, 373–91.
Song, S., Jou, J., and Tripe, D. 2014. "Can Interest Rates Really Control Housing Prices? Effectiveness
and Implications of Macroprudential Policy." Journal of Banking & Finance 15-28.
United States Census Bureau. International Database.
US. Federal Housing Finance Agency, All-Transactions House Price Index for the United States
[USSTHPI], retrieved from FRED,Federal Reserve Bank of St. Louis
https://research.stlouisfed.org/fred2/series/USSTHPI/, November 17, 2015.
S&P Dow Jones Indices LLC, S&P/Case-Shiller U.S. National Home Price Index©[CSUSHPINSA],
retrieved from FRED, Federal Reserve Bank of St. Louis
https://research.stlouisfed.org/fred2/series/CSUSHPINSA/, November 30, 2015.

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