The Aggregate Demand of Housing in the US

Lena Guo

Jon Heroux

Sudhir Nair

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

DataVariable Source Personal Income 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 BankUS 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

Parameter Standard t For Ho: P-ValueVariable Estimate Error Est = 0 (95%=0.05) VIF

Intercept 109443.5 4987.102 21.945 0.00001 n/a30-Year Fixed Rate Mortgage

-1830.99 311.426 -5.879 0.00002 2.963

Housing Price Index for United States

86.15 11.369 7.578 0.00001 2.963

• Dependent variable: Total Housing Inventory

Excluded Variables

• Average # Persons/Household

• Consumer Price Index

• Dow Jones Industrial Average

• Inflation Rate

• Median Asking Rent

• Personal Income

•US Annual GDP

•US Population

•US Unemployment Rate

•Vacancy Rate

•Vacancy Rate 1 Unit

•Vacancy Rate 2+ Units

•Vacancy Rate 5+ Units

Exogenous vs EndogenousHousing 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 inventoryP= 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 Reject– Rho: Pos Do not reject– Rho: Neg 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

• Estimates elasticity of independent variables against the dependent variable

• A negative value implies an elastic relationship and a positive value implies inelastic relationship

30-Year Fixed Mortgage Rate

Housing Price Index for US

Average==> -0.14944 0.16311

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

• 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=32255http://research.stlouisfed.org/fred2/series/UNRATE/downloaddata

• US Annual gdphttp://wikiposit.org/w?filter=Economics/MeasuringWorth.com/GDP/

• US Rate of inflationhttp://inflationdata.com/Inflation/Inflation_Rate/CurrentInflation.asp

• Consumer Price Indexftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt

• 30 Yr Conventional Mortgage Ratehttp://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 analysisby Jonathan Kohn and Sarah K. Bryanthttp://www.aabri.com/manuscripts/09381.pdf