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Why Can’t I Afford a Home?

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 United States: Ten year regression of explanatory variables against median price of a home. Organization.

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Why Can’t I Afford a Home?

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

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

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

  4. The Variables • Median Price of a Home (dependent variable) • β1= Unemployment Rate • β2= Median Family Income • β3= Building Permits • β4= Population • β5= Distance from the coast (Not applicable for Time-Series) • Β6= Mortgage Rates (Not applicable for Cross-Section)

  5. Graphical Relationships • 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)

  6. Unemployment Rate

  7. Median Family Income

  8. Building Permits

  9. Population

  10. Mortgage Rates

  11. Our Hypothesis • Ho: The explanatory variables in the regression don’t explain the median price of a home i.e. β1= β2= … =βn=0 • Ha: At least one explanatory variable explains the median price of a home i.e. β1≠0 or β2≠0 … or βn≠0

  12. Results for Time Series Analysis (U.S.)

  13. Time Series Analysis – Correlation Matrix

  14. Time Series Regression • Dependent Variable: PRICE • Method: Least Squares • Date: 12/06/06 Time: 09:38 • Sample: 1 10 • Included observations: 10 • Variable Coefficient Std. Error t-Statistic Prob. • HOMEMORTGAGERATE 632665. 1151196. 1.418234 0.2291 • INCOME -6.116375 6.401278 -0.955493 0.3934 • PERMITS 0.092208 0.056354 1.636246 0.1771 • POPULATION 0.006230 0.004887 1.274867 0.2714 • UNEMPLOYMENTRATE 1033710. 358705.7 2.881777 0.0449 • C -1622644. 933044.8 -1.739085 0.1570 • R-squared 0.990920 Mean dependent var 153950.0 • Adjusted R-sq. 0.979571 S.D. dependent var 34063.41 • S.E. of regression 4868.733 Akaike info criterion 20.10276 • Sum squared resid 94818259 Schwarz criterion 20.28432 • Log likelihood -94.51382 F-statistic 87.30830 • Durbin-Watson sta 3.279181 Prob(F-statistic) 0.000357 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 Significant.

  15. 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. • This means that the explanatory variables are highly correlated. • This is explained in the correlation matrix on a previous slide. • This is an example of multicollinearity. • Therefore we decided to drop out one of the explanatory variables in order to erase the multicollinearity.

  16. Drop Mortgage Rate • Dependent Variable: PRICE • Method: Least Squares • Date: 12/06/06 Time: 19:25 • Sample: 1 10 • Included observations: 10 • Variable Coefficient Std. Error t-Statistic Prob. • INCOME -12.22777 5.190382 -2.355851 0.0651 • PERMITS 0.027076 0.035811 0.756096 0.4837 • POPULATION 0.010664 0.004118 2.589475 0.0489 • UNEMPLOYMENTRATE 824150.2 358395.3 2.299557 0.0698 • C -2334912. 862220.4 -2.708022 0.0424 • R-squared 0.986355 Mean dependent var 153950.0 • Adjusted R-squared0.975438 S.D. dependent var 34063.41 • S.E. of regression 5338.490 Akaike info criterion 20.31013 • Sum squared resid 1.42E+08 Schwarz criterion 20.46142 • Log likelihood -96.55063 F-statistic 90.35561 • Durbin-Watson stat 2.343565 Prob(F-statistic) 0.000075 • Significant Test with 10 observations and Alpha = 0.05 • Population is the only significant variable • Unemployment now becomes insignificant

  17. Drop Permits • Dependent Variable: PRICE • Method: Least Squares • Date: 12/06/06 Time: 19:27 • Sample: 1 10 • Included observations: 10 • Variable Coefficient Std. Error t-Statistic Prob. • HOMEMORTGAGERATE 97613.97 770997.7 0.126607 0.9042 • INCOME -15.51536 3.264526 -4.752713 0.0051 • POPULATION 0.013532 0.002301 5.880010 0.0020 • UNEMPLOYMENTRATE 998640.4 413787.3 2.413415 0.0606 • C -2949376. 533483.0 -5.528529 0.0027 • R-squared 0.984843 Mean dependent var 153950.0 • Adjusted R-squared 0.972717 S.D. dependent var 34063.41 • S.E. of regression 5626.411 Akaike info criterion 20.41518 • Sum squared resid 1.58E+08 Schwarz criterion 20.56648 • Log likelihood -97.07592 F-statistic 81.21998 • Durbin-Watson sta 2.325004 Prob(F-statistic) 0.000098 • Both Income and Population are now significant explanatory variables

  18. Drop Population • Dependent Variable: PRICE • Method: Least Squares • Date: 12/06/06 Time: 19:28 • Sample: 1 10 • Included observations: 10 • Variable Coefficient Std. Error t-Statistic Prob. • HOMEMORTGAGERATE 2571603. 938466.0 2.740220 0.0408 • INCOME 1.992947 0.761256 2.617971 0.0472 • PERMITS 0.157815 0.024359 6.478855 0.0013 • UNEMPLOYMENTRATE 967915.6 376516.0 2.570715 0.0500 • C -442695.1 125212.2 -3.535560 0.0166 • R-squared 0.987231 Mean dependent var 153950.0 • Adjusted R-squared0.977016 S.D. dependent var 34063.41 • S.E. of regression 5164.203 Akaike info criterion 20.24374 • Sum squared resid 1.33E+08 Schwarz criterion 20.39503 • Log likelihood -96.21871 F-statistic 96.64315 • Durbin-Watson stat3.147208 Prob(F-statistic) 0.000064 • When we drop Population, all our explanatory variables now become significant

  19. Drop Unemployment Rate • Dependent Variable: PRICE • Method: Least Squares • Date: 12/06/06 Time: 19:29 • Sample: 1 10 • Included observations: 10 • Variable Coefficient Std. Error t-Statistic Prob. • HOMEMORTGAGERATE 266099.7 1645584. 0.161705 0.8779 • INCOME -3.839510 9.965120 -0.385295 0.7159 • PERMITS 0.082505 0.088246 0.934945 0.3927 • POPULATION 0.004204 0.007586 0.554139 0.6034 • C -1002577. 1424248. -0.703935 0.5129 • R-squared 0.972069 Mean dependent var 153950.0 • Adjusted R-square 0.949725 S.D. dependent var 34063.41 • S.E. of regression 7637.749 Akaike info criterion 21.02645 • Sum squared resid 2.92E+08 Schwarz criterion 21.17774 • Log likelihood -100.1322 F-statistic 43.50361 • Durbin-Watson stat1.359493 Prob(F-statistic) 0.000447 • We have no significant explanatory variables when we drop Unemployment Rate

  20. DROP INCOME • Dependent Variable: PRICE • Method: Least Squares • Date: 12/06/06 Time: 09:42 • Sample: 1 10 • Included observations: 10 • Variable Coefficient Std. Error t-Statistic Prob. • HOMEMORTGAGERATE 2373126. 843852.1 2.812254 0.0374 • PERMITS 0.140527 0.024652 5.700503 0.0023 • POPULATION 0.001590 0.000543 2.927870 0.0327 • UNEMPLOYMENTRATE 991406.2 352851.3 2.809700 0.0376 • C -749970.5 189154.5 -3.964858 0.0107 • R-squared 0.988848 Mean dependent var 153950.0 • Adjusted R-sq 0.979926 S.D. dependent var 34063.41 • S.E. of regression 4826.173 Akaike info criterion 20.10835 • Sum squared resid 1.16E+08 Schwarz criterion 20.25964 • Log likelihood -95.54174 F-statistic 110.8364 • Durbin-Watson sta 3.205994 Prob(F-statistic) 0.000046 • All our explanatory variables are significant. • This is the best result because the probability of the F-statistic is the lowest.

  21. Observations of Time-Series Regression Analysis • 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

  22. Results for Cross Section Analysis

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

  24. Relationship between Location, Income and House Price

  25. The Variables • Median Price of a Home (dependent variable) • β1= Unemployment Rate • β2= Median Family Income • β3= Building Permits • β4= Population • β5= Distance from the coast

  26. 2000 and 2005 • COAST OR NOT • DUMMY VARIABLE • IF COAST 1 • IF NOT 0

  27. Relationship between Location and House Price

  28. Explanation of Relationship • 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 • Is this relationship significant?

  29. Results for Cross Section Analysis (14 Metropolitan Statistical Areas)

  30. Cross Section Analysis Correlation Matrix - 2005

  31. Cross-Section Regression 2005 • Dependent Variable: HOUSEPRICE • Method: Least Squares • Date: 12/06/06 Time: 00:11 • Sample: 1 14 • Included observations: 14 • Variable Coefficient Std. Error t-Statistic Prob.   • DUMMYCOAST 323679.4 84887.58 3.813036 0.0051 • INCOME 3.798266 3.436786 1.105180 0.3012 • PERMITS -2.459958 3.160409 -0.778367 0.4588 • POPULATION 0.006328 0.014042 0.450617 0.6642 • UNEMPLOYMENTRATE 1141333. 2298304. 0.496598 0.6328 • C -112592.2 321611.0 -0.350088 0.7353 • R-squared 0.828896     Mean dependent var 339964.3 • Adjusted R-squared 0.721956     S.D. dependent var 214654.6 • S.E. of regression 113187.2     Akaike info criterion 26.40900 • Sum squared resid 1.02E+11     Schwarz criterion 26.68288 • Log likelihood -178.8630     F-statistic 7.751030 • Durbin-Watson stat 2.377582     Prob(F-statistic) 0.006204 DummyCoast only variable that is significant

  32. Drop all insignificant variables (2005) • Dependent Variable: HOUSEPRICE • Method: Least Squares • Date: 12/06/06 Time: 00:18 • Sample: 1 14 • Included observations: 14 • Variable Coefficient Std. Error t-Statistic Prob.   • DUMMYCOAST 362557.1 57513.80 6.303829 0.0000 • C 158685.7 40668.40 3.901942 0.0021 • R-squared 0.768063     Mean dependent var 339964.3 • Adjusted R-squared0.748735     S.D. dependent var 214654.6 • S.E. of regression 107598.5     Akaike info criterion 26.14176 • Sum squared resid 1.39E+11     Schwarz criterion 26.23306 • Log likelihood -180.9923     F-statistic 39.73826 • Durbin-Watson stat1.652406     Prob(F-statistic) 0.000039

  33. Cross Section Regression 2000 • Dependent Variable: HOUSEPRICE • Method: Least Squares • Date: 12/06/06 Time: 00:28 • Sample: 1 14 • Included observations: 14 • Variable Coefficient Std. Error t-Statistic Prob.   • INCOME 2.993843 2.888653 1.036415 0.3271 • DUMMYCOAST 134588.0 47862.77 2.811957 0.0203 • POPULATION -0.002972 0.005146 -0.577589 0.5777 • UNEMPLOYMENTRATE 400794.1 2795135. 0.143390 0.8891 • C -47469.59 248491.1 -0.191031 0.8527 • R-squared 0.623754     Mean dependent var 195085.7 • Adjusted R-squared 0.456534     S.D. dependent var 108047.6 • S.E. of regression 79652.92     Akaike info criterion 25.68120 • Sum squared resid 5.71E+10     Schwarz criterion 25.90943 • Log likelihood -174.7684     F-statistic 3.730130 • Durbin-Watson stat 1.866677     Prob(F-statistic) 0.046794 DummyCoast variable is very significant but not as significant as in 2005

  34. Drop all insignificant variables (2000) • Dependent Variable: HOUSEPRICE • Method: Least Squares • Date: 12/06/06 Time: 00:29 • Sample: 1 14 • Included observations: 14 • Variable Coefficient Std. Error t-Statistic Prob.   • DUMMYCOAST 152342.9 40981.01 3.717401 0.0029 • C 118914.3 28977.95 4.103613 0.0015 • R-squared 0.535227     Mean dependent var 195085.7 • Adjusted R-squared0.496496     S.D. dependent var 108047.6 • S.E. of regression 76668.45     Akaike info criterion 25.46393 • Sum squared resid 7.05E+10     Schwarz criterion 25.55523 • Log likelihood -176.2475     F-statistic 13.81907 • Durbin-Watson stat1.843468     Prob(F-statistic) 0.002941

  35. Conclusion • 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) • 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 • 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)

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

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