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The Aggregate Demand of Housing in the US

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Lena Guo

Jon Heroux

Sudhir Nair

The Aggregate Demand of Housing in the US

- 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

- 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

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

- Dependent variable: Total Housing Inventory

- 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

- 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

- 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

- 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

- 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

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

- 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-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%

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

- 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.

- 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.

- 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