Download The Aggregate Demand for Housing in the U.S.

Lena Guo
Jon Heroux
Sudhir Nair
The Aggregate Demand of
Housing in the US
Introduction
• Home ownership has always been the American
dream
• There are many factors which affect the demand
for housing in the United States
• Housing markets have historically gone through
boom and bust cycles over the past several
decades
• This study uses annual data for the United States
from 1980 to 2011 to find the determinants of
home prices
Objective
• To develop an econometric model to
determine which market variables explain
aggregate demand for housing in the United
States.
• H0: Aggregate demand for housing is
influenced by various market conditions
Data
Variable
Personal Income
Source
US Dept of Commerce - Bureau of Economic Analysis
30-Year Fixed Rate Mortgage
Freddie Mac
Consumer Price Index
US Dept of Labor - Bureau of Labor Statistics
Dow Jones Industrial Average
Federal Reserve Bank of St. Louis.
Housing Price Index for US
Federal Housing Finance Agency
Median Asking Rent
US Dept of Commerce - US Census Bureau
Total Housing Inventory
US Dept of Commerce - US Census Bureau
US Population
US Dept of Commerce - US Census Bureau
US Annual GDP
Measuring Worth and US Bureau of Economic Analysis
Average Persons per Household
US Census Bureau - America’s Families and Living
Arrangements
Vacancy Rates (1, 2+ and 5+)
US Census Bureau - Housing Vacancies and
Homeownership
US Annual Inflation
World Bank
US Unemployment Rate
US Dept of Labor - Bureau of Labor Statistics
Methodology
Software: WinORS™ used to calculate best model:
• Entered time series data into spreadsheet from 1980 - 2011
• Stepwise regression used to remove variables deemed not
significant
• Ordinary least squares used (using Ten Basic steps) to
continually eliminate variables based on p-value (>0.05) & VIF
(>10) and to test data for autocorrelation, multicollinearity,
homoscedasticity, and normality
• Attempted to force House Price Index and CPI while working
through OLS
• Further tested the model using Zero intercept as well as
Multiplicative model to find the best solution
Included Variables
• Dependent variable: Total Housing Inventory
Parameter Standard t For Ho: P-Value
Variable
Estimate
Error
Intercept
109443.5
4987.102 21.945
0.00001
n/a
30-Year Fixed -1830.99
Rate Mortgage
311.426
-5.879
0.00002
2.963
Housing Price
Index for
United States
11.369
7.578
0.00001
2.963
86.15
Est = 0
(95%=0.05) VIF
Excluded Variables
• Average #
Persons/Household
•US Annual GDP
• Consumer Price Index
•US Unemployment
Rate
• Dow Jones Industrial
Average
•US Population
•Vacancy Rate
• Inflation Rate
•Vacancy Rate 1 Unit
• Median Asking Rent
•Vacancy Rate 2+ Units
• Personal Income
•Vacancy Rate 5+ Units
Exogenous vs Endogenous
Housing Price Index
Endogenous
30 Year Fixed Mortgage Rate
Endogenous
Average # Persons/Household
Exogenous
Consumer Price Index
Exogenous
Dow Jones Average
Exogenous
Inflation Rate
Exogenous
Median Asking Rent
Endogenous
Personal Income
Exogenous
US Annual GDP
Exogenous
US Population
Exogenous
US Unemployment Rate
Exogenous
Vacancy Rate
Endogenous
Vacancy Rate 1 Unit
Endogenous
Vacancy Rate 2+ Units
Endogenous
Vacancy Rate 5+ Units
Endogenous
Model
• True demand model
• Q= 109443.465 + 86.15 P -18030.993 FRM
Q= total housing inventory
P= housing price index
FRM= 30-year fixed rate mortgage
Model
Multicollinearity
• First of 4 assumptions of regression: absence of
collinearity
– The independent variables are not correlated
– Confirmed by variance inflation factor less than 10,
ideally less than 5
• Removed all variables one-by-one with VIF >10
• Average VIF= 2.963
Autocorrelation
• Durbin: 1.237
• Durbin H: n/c
• H0: Rho=0
– Rho: Pos & Neg
– Rho: Pos
– Rho: Neg
Reject
Do not reject
Reject
• Ideal value for Durbin is 2.0 and do not reject H0
• Attempted to remove autocorrelation
– First differences
– Durbin-adjusted method
– Model dissipated in both cases
Constant Variance
• White’s test: 23.835
• P-value: 0.00023 reject
• Determines homoscedascity
• Ideal value is > 0.05 and do not reject
• Attempted to correct with weighted OLS file
– Did not improve model
– Continued with original model
Constant Variance
Normality
• Correlation for Normality: 0.9708
• Approx Critical Value: 0.0720
• Ideal is correlation value > critical value
• Confirmed normal: follows and hugs line
Normality
R-squared
• R-squared: 94.384%
– Shows great explanatory power from the
independent variables
– Measures proportion of variation in dependent
variable about its mean explained by variance in
independent variables
• Adjusted R-squared: 93.997%
– Remains high and in acceptable range
F-statistic
• F-value: 243.699 p-value: 0.00001
– Ratio of explained variation:unexplained
variation
– Result indicates a statistically significant
proportion of total variation in dependent
variable is explained
– P-value is probability of rejecting null
hypothesis, confidence level of 99.99%
Elasticities
Average==>
30-Year Fixed
Mortgage Rate
-0.14944
Housing Price
Index for US
0.16311
• Estimates elasticity of independent variables
against the dependent variable
• A negative value implies an elastic relationship
and a positive value implies inelastic
relationship
Conclusions
• Tested the model with both linear additive as well as
multiplicative model, however results were similar
• Not able to conclude with this model that the aggregate
demand of housing in US is determined by the 15 market
variables tested during the time period of 1980-2011
• A key observation was the high relationship 30-year fixed
mortgage has to the housing inventory
– During all the various test runs, 30 year FMR was in the final 2 results
– Leads us to the conclusion (despite reject of Rho) that there is an
inherent relationship between 30-year FMR and the housing demand
– Rate of interest does seem to have an inherent relationship with the
aggregate housing demand, compared to other independent variables.
Conclusions
• 30 year FMR has an elastic relationship with the housing
inventory levels, while Housing Price Index has a inelastic
relationship with the housing inventory levels
• These results make sense, when the interest rates go down,
the housing inventory levels go down, which means the
demand has increased
• Likewise when the Housing Price index goes up, the inventory
levels also go up, meaning the housing demand goes down.
•
Note: This was an exploratory study to develop an econometric model to determine which
market variables explain aggregate demand for housing in the United States.
References
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Professor Gordon Dash’s Lecture Notes and website - http://www.ghdash.net/
WinOrs Software and WinOrs Help files.
Aggregate demand of Housing in US.
http://research.stlouisfed.org/fred2/series/DJIA/downloaddata?cid=32255
http://research.stlouisfed.org/fred2/series/UNRATE/downloaddata
US Annual gdp
http://wikiposit.org/w?filter=Economics/MeasuringWorth.com/GDP/
US Rate of inflation
http://inflationdata.com/Inflation/Inflation_Rate/CurrentInflation.asp
Consumer Price Index
ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt
30 Yr Conventional Mortgage Rate
http://research.stlouisfed.org/fred2/series/WRMORTG/downloaddata
Total Housing Inventory
http://www.census.gov/compendia/statab/2012/tables/12s0982.pdf
Modeling the U.S. housing bubble: an econometric analysis
by Jonathan Kohn and Sarah K. Bryant
http://www.aabri.com/manuscripts/09381.pdf