The Aggregate Demand of Housing in the US

1. Lena Guo Jon Heroux Sudhir Nair The Aggregate Demand of Housing in the US

2. 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

3. 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

4. Data

5. 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

6. Included Variables • Dependent variable: Total Housing Inventory

7. Excluded Variables • US Annual GDP • US Population • US Unemployment Rate • Vacancy Rate • Vacancy Rate 1 Unit • Vacancy Rate 2+ Units • Vacancy Rate 5+ Units • Average # Persons/Household • Consumer Price Index • Dow Jones Industrial Average • Inflation Rate • Median Asking Rent • Personal Income

8. Exogenous vs Endogenous

9. 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

10. Model

11. 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

12. 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

13. 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

14. Constant Variance

15. Normality • Correlation for Normality: 0.9708 • Approx Critical Value: 0.0720 • Ideal is correlation value > critical value • Confirmed normal: follows and hugs line

16. Normality

17. 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

18. 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%

19. Elasticities • Estimates elasticity of independent variables against the dependent variable • A negative value implies an elastic relationship and a positive value implies inelastic relationship

20. 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.

21. 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.

22. 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