Why Can’t I Afford a Home? By: Philippe Bonnan Emelia Bragadottir Troy Dewitt Anders Graham S. Matthew Scott Lingli Tang

Organization Time Series Regression Time Series Regression United States: Ten year regression of explanatory variables against median price of a home United States: Ten year regression of explanatory variables against median price of a home

Organization Cross Section Regression Cross Section Regression 14 Different Areas for 2 separate years: 2000 and Different Areas for 2 separate years: 2000 and 2005

The Variables Median Price of a Home (dependent variable) Median Price of a Home (dependent variable) β 1 = Unemployment Rate β 1 = Unemployment Rate β 2 = Median Family Income β 2 = Median Family Income β 3 = Building Permits β 3 = Building Permits β 4 = Population β 4 = Population β 5 = Distance from the coast (Not applicable for Time-Series) β 5 = Distance from the coast (Not applicable for Time-Series) Β 6 = Mortgage Rates (Not applicable for Cross-Section) Β 6 = Mortgage Rates (Not applicable for Cross-Section)

Graphical Relationships The following graphs compare the median price of a home with each variable over a period of ten years The following graphs compare the median price of a home with each variable over a period of ten years Each variable uses 1996 as an index for comparison (For each variable, the value for 1996 is set to 1) Each variable uses 1996 as an index for comparison (For each variable, the value for 1996 is set to 1)

Unemployment Rate

Median Family Income

Building Permits

Population

Mortgage Rates

Our Hypothesis Ho: The explanatory variables in the regression don’t explain the median price of a home Ho: The explanatory variables in the regression don’t explain the median price of a home i.e. β 1 = β 2 = … =β n =0 Ha: At least one explanatory variable explains the median price of a home Ha: At least one explanatory variable explains the median price of a home i.e. β 1 ≠0 or β 2 ≠0 … or β n ≠0

Results for Time Series Analysis (U.S.)

Time Series Analysis – Correlation Matrix PRICEHOME MORTGAGE RATE INCOMEPERMITSPOPU LATION UNEMPLOYMENT RATE PRICE HOMEMORTGAGERATE INCOME PERMITS POPULATION UNEMPLOYMENTRATE

Time Series Regression Dependent Variable: PRICE Dependent Variable: PRICE Method: Least Squares Method: Least Squares Date: 12/06/06 Time: 09:38 Date: 12/06/06 Time: 09:38 Sample: 1 10 Sample: 1 10 Included observations: 10 Included observations: 10 VariableCoefficientStd. Errort-StatisticProb. VariableCoefficientStd. Errort-StatisticProb. HOMEMORTGAGERATE HOMEMORTGAGERATE INCOME INCOME PERMITS PERMITS POPULATION POPULATION UNEMPLOYMENTRATE UNEMPLOYMENTRATE C C R-squared Mean dependent var R-squared Mean dependent var Adjusted R-sq S.D. dependent var Adjusted R-sq S.D. dependent var S.E. of regression Akaike info criterion S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Log likelihood F-statistic Durbin-Watson sta Prob(F-statistic) Durbin-Watson sta Prob(F-statistic) Significant Test with 10 observations and Alpha = 0.05 Unemployment Rate is the only significant variable Therefore we reject the null hypothesis because unemployment is Therefore we reject the null hypothesis because unemployment isSignificant.

Explanation of results for time series analysis T-stats for coefficients of the explanatory variables are not significant (except unemployment) but coefficient of determination, R-squared, is high. T-stats for coefficients of the explanatory variables are not significant (except unemployment) but coefficient of determination, R-squared, is high. This means that the explanatory variables are highly correlated. This means that the explanatory variables are highly correlated. This is explained in the correlation matrix on a previous slide. This is explained in the correlation matrix on a previous slide. This is an example of multicollinearity. This is an example of multicollinearity. Therefore we decided to drop out one of the explanatory variables in order to erase the multicollinearity. Therefore we decided to drop out one of the explanatory variables in order to erase the multicollinearity.

Drop Mortgage Rate Dependent Variable: PRICE Dependent Variable: PRICE Method: Least Squares Method: Least Squares Date: 12/06/06 Time: 19:25 Date: 12/06/06 Time: 19:25 Sample: 1 10 Sample: 1 10 Included observations: 10 Included observations: 10 VariableCoefficientStd. Errort-StatisticProb. VariableCoefficientStd. Errort-StatisticProb. INCOME INCOME PERMITS PERMITS POPULATION POPULATION UNEMPLOYMENTRATE UNEMPLOYMENTRATE C C R-squared Mean dependent var R-squared Mean dependent var Adjusted R-squared S.D. dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion S.E. of regression Akaike info criterion Sum squared resid 1.42E+08 Schwarz criterion Sum squared resid 1.42E+08 Schwarz criterion Log likelihood F-statistic Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Durbin-Watson stat Prob(F-statistic) Significant Test with 10 observations and Alpha = 0.05 Significant Test with 10 observations and Alpha = 0.05 Population is the only significant variable Population is the only significant variable Unemployment now becomes insignificant Unemployment now becomes insignificant

Drop Permits Dependent Variable: PRICE Dependent Variable: PRICE Method: Least Squares Method: Least Squares Date: 12/06/06 Time: 19:27 Date: 12/06/06 Time: 19:27 Sample: 1 10 Sample: 1 10 Included observations: 10 Included observations: 10 VariableCoefficientStd. Errort-StatisticProb. VariableCoefficientStd. Errort-StatisticProb. HOMEMORTGAGERATE HOMEMORTGAGERATE INCOME INCOME POPULATION POPULATION UNEMPLOYMENTRATE UNEMPLOYMENTRATE C C R-squared Mean dependent var R-squared Mean dependent var Adjusted R-squared S.D. dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion S.E. of regression Akaike info criterion Sum squared resid 1.58E+08 Schwarz criterion Sum squared resid 1.58E+08 Schwarz criterion Log likelihood F-statistic Log likelihood F-statistic Durbin-Watson sta Prob(F-statistic) Durbin-Watson sta Prob(F-statistic) Both Income and Population are now significant explanatory variables Both Income and Population are now significant explanatory variables

Drop Population Dependent Variable: PRICE Dependent Variable: PRICE Method: Least Squares Method: Least Squares Date: 12/06/06 Time: 19:28 Date: 12/06/06 Time: 19:28 Sample: 1 10 Sample: 1 10 Included observations: 10 Included observations: 10 Variable CoefficientStd. Errort-StatisticProb. Variable CoefficientStd. Errort-StatisticProb. HOMEMORTGAGERATE HOMEMORTGAGERATE INCOME INCOME PERMITS PERMITS UNEMPLOYMENTRATE UNEMPLOYMENTRATE C C R-squared Mean dependent var R-squared Mean dependent var Adjusted R-squared S.D. dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion S.E. of regression Akaike info criterion Sum squared resid 1.33E+08 Schwarz criterion Sum squared resid 1.33E+08 Schwarz criterion Log likelihood F-statistic Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Durbin-Watson stat Prob(F-statistic) When we drop Population, all our explanatory variables now become significant When we drop Population, all our explanatory variables now become significant

Drop Unemployment Rate Dependent Variable: PRICE Dependent Variable: PRICE Method: Least Squares Method: Least Squares Date: 12/06/06 Time: 19:29 Date: 12/06/06 Time: 19:29 Sample: 1 10 Sample: 1 10 Included observations: 10 Included observations: 10 VariableCoefficientStd. Errort-StatisticProb. VariableCoefficientStd. Errort-StatisticProb. HOMEMORTGAGERATE HOMEMORTGAGERATE INCOME INCOME PERMITS PERMITS POPULATION POPULATION C C R-squared Mean dependent var R-squared Mean dependent var Adjusted R-square S.D. dependent var Adjusted R-square S.D. dependent var S.E. of regression Akaike info criterion S.E. of regression Akaike info criterion Sum squared resid 2.92E+08 Schwarz criterion Sum squared resid 2.92E+08 Schwarz criterion Log likelihood F-statistic Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Durbin-Watson stat Prob(F-statistic) We have no significant explanatory variables when we drop Unemployment Rate We have no significant explanatory variables when we drop Unemployment Rate

DROP INCOME Dependent Variable: PRICE Dependent Variable: PRICE Method: Least Squares Method: Least Squares Date: 12/06/06 Time: 09:42 Date: 12/06/06 Time: 09:42 Sample: 1 10 Sample: 1 10 Included observations: 10 Included observations: 10 VariableCoefficientStd. Errort-StatisticProb. VariableCoefficientStd. Errort-StatisticProb. HOMEMORTGAGERATE HOMEMORTGAGERATE PERMITS PERMITS POPULATION POPULATION UNEMPLOYMENTRATE UNEMPLOYMENTRATE C C R-squared Mean dependent var R-squared Mean dependent var Adjusted R-sq S.D. dependent var Adjusted R-sq S.D. dependent var S.E. of regression Akaike info criterion S.E. of regression Akaike info criterion Sum squared resid 1.16E+08 Schwarz criterion Sum squared resid 1.16E+08 Schwarz criterion Log likelihood F-statistic Log likelihood F-statistic Durbin-Watson sta Prob(F-statistic) Durbin-Watson sta Prob(F-statistic) All our explanatory variables are significant. All our explanatory variables are significant. This is the best result because the probability of the F-statistic is the lowest. This is the best result because the probability of the F-statistic is the lowest.

Observations of Time- Series Regression Analysis After the original regression, dropping the variables with the lowest t-statistic optimized the regression results. After the original regression, dropping the variables with the lowest t-statistic optimized the regression results. Ex: Population and Income  Dropping the variable with the highest t-stat made the regression analysis less optimal Ex: Unemployment Rate

Results for Cross Section Analysis

Organization Cross Section Regression Cross Section Regression 14 Different Areas for 2 separate years: 2000 and Different Areas for 2 separate years: 2000 and 2005

Relationship between Location, Income and House Price

The Variables Median Price of a Home (dependent variable) Median Price of a Home (dependent variable) β 1 = Unemployment Rate β 1 = Unemployment Rate β 2 = Median Family Income β 2 = Median Family Income β 3 = Building Permits β 3 = Building Permits β 4 = Population β 4 = Population β 5 = Distance from the coast β 5 = Distance from the coast

2000 and 2005 COAST OR NOT COAST OR NOT DUMMY VARIABLE DUMMY VARIABLE IF COAST 1 IF COAST 1 IF NOT 0 IF NOT 0

Relationship between Location and House Price

Explanation of Relationship Two different trends explained by dummy = 1 (coastal) and dummy = 0 (not coastal) Two different trends explained by dummy = 1 (coastal) and dummy = 0 (not coastal) Those cities close to the coast experience a higher median house price Those cities close to the coast experience a higher median house price Is this relationship significant? Is this relationship significant?

Results for Cross Section Analysis (14 Metropolitan Statistical Areas)

Cross Section Analysis Correlation Matrix HOUSE PRICE DUMMY COAST INCOMEPERMITSPOPULAT ION UNEMPLOYMENT RATE HOUSEPRICE DUMMYCOAST INCOME PERMITS POPULATION UNEMPLOYMENTRATE

Cross-Section Regression 2005 Dependent Variable: HOUSEPRICE Dependent Variable: HOUSEPRICE Method: Least Squares Method: Least Squares Date: 12/06/06 Time: 00:11 Date: 12/06/06 Time: 00:11 Sample: 1 14 Sample: 1 14 Included observations: 14 Included observations: 14 Variable CoefficientStd. Errort-StatisticProb. Variable CoefficientStd. Errort-StatisticProb. DUMMYCOAST DUMMYCOAST INCOME INCOME PERMITS PERMITS POPULATION POPULATION UNEMPLOYMENTRATE UNEMPLOYMENTRATE C C R-squared Mean dependent var R-squared Mean dependent var Adjusted R-squared S.D. dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion S.E. of regression Akaike info criterion Sum squared resid1.02E+11 Schwarz criterion Sum squared resid1.02E+11 Schwarz criterion Log likelihood F-statistic Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Durbin-Watson stat Prob(F-statistic) DummyCoast only variable that is significant

Drop all insignificant variables (2005) Dependent Variable: HOUSEPRICE Dependent Variable: HOUSEPRICE Method: Least Squares Method: Least Squares Date: 12/06/06 Time: 00:18 Date: 12/06/06 Time: 00:18 Sample: 1 14 Sample: 1 14 Included observations: 14 Included observations: 14 VariableCoefficientStd. Errort-StatisticProb. VariableCoefficientStd. Errort-StatisticProb. DUMMYCOAST DUMMYCOAST C C R-squared Mean dependent var R-squared Mean dependent var Adjusted R-squared S.D. dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion S.E. of regression Akaike info criterion Sum squared resid1.39E+11 Schwarz criterion Sum squared resid1.39E+11 Schwarz criterion Log likelihood F-statistic Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Durbin-Watson stat Prob(F-statistic)

Cross Section Regression 2000 Dependent Variable: HOUSEPRICE Dependent Variable: HOUSEPRICE Method: Least Squares Method: Least Squares Date: 12/06/06 Time: 00:28 Date: 12/06/06 Time: 00:28 Sample: 1 14 Sample: 1 14 Included observations: 14 Included observations: 14 Variable CoefficientStd. Errort-StatisticProb. Variable CoefficientStd. Errort-StatisticProb. INCOME INCOME DUMMYCOAST DUMMYCOAST POPULATION POPULATION UNEMPLOYMENTRATE UNEMPLOYMENTRATE C C R-squared Mean dependent var R-squared Mean dependent var Adjusted R-squared S.D. dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion S.E. of regression Akaike info criterion Sum squared resid5.71E+10 Schwarz criterion Sum squared resid5.71E+10 Schwarz criterion Log likelihood F-statistic Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Durbin-Watson stat Prob(F-statistic) DummyCoast variable is very significant but not as significant as in 2005

Drop all insignificant variables (2000) Dependent Variable: HOUSEPRICE Dependent Variable: HOUSEPRICE Method: Least Squares Method: Least Squares Date: 12/06/06 Time: 00:29 Date: 12/06/06 Time: 00:29 Sample: 1 14 Sample: 1 14 Included observations: 14 Included observations: 14 VariableCoefficientStd. Errort-StatisticProb. VariableCoefficientStd. Errort-StatisticProb. DUMMYCOAST DUMMYCOAST C C R-squared Mean dependent var R-squared Mean dependent var Adjusted R-squared S.D. dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion S.E. of regression Akaike info criterion Sum squared resid7.05E+10 Schwarz criterion Sum squared resid7.05E+10 Schwarz criterion Log likelihood F-statistic Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Durbin-Watson stat Prob(F-statistic)

Conclusion With time series we ran into multicollinearity issues, and as a result of this we were forced to drop one explanatory variable With time series we ran into multicollinearity issues, and as a result of this we were forced to drop one explanatory variable By dropping one explanatory variable we erased the multicollinearity issue and found that all of our variables can be significant (best results by dropping median family income) By dropping one explanatory variable we erased the multicollinearity issue and found that all of our variables can be significant (best results by dropping median family income) In the cross section analysis, none of these same variables were significant In the cross section analysis, none of these same variables were significant So we introduced one more variable (DummyCoast) and found it to be very significant So we introduced one more variable (DummyCoast) and found it to be very significant Conc - Due to the variability of the housing market, it is difficult to predict housing price over a period of time (difficult to determine the most significant explanatory variable when there is multicollinearity). Conc - Due to the variability of the housing market, it is difficult to predict housing price over a period of time (difficult to determine the most significant explanatory variable when there is multicollinearity). Since that is the case with all our explanatory variables, the best is the variable that does not change with time (i.e. location) Since that is the case with all our explanatory variables, the best is the variable that does not change with time (i.e. location)

References US Census Bureau US Census Bureau US Department of Housing and Urban Development US Department of Housing and Urban Development Real Estate Center at Texas A&M University Real Estate Center at Texas A&M University National Association of Realtors National Association of Realtors Keller – Statistics for Management and Economics Keller – Statistics for Management and Economics US Council of Economic Advisors US Council of Economic Advisors Bureau of Labor Statistics Bureau of Labor Statistics Maryland Association of Realtors Maryland Association of Realtors