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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? 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 • Cross Section Regression • 14 Different Areas for 2 separate years: 2000 and 2005
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)
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)
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
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.
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.
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
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
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
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
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.
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
Organization • Cross Section Regression • 14 Different Areas for 2 separate years: 2000 and 2005
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
2000 and 2005 • COAST OR NOT • DUMMY VARIABLE • IF COAST 1 • IF NOT 0
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?
Results for Cross Section Analysis (14 Metropolitan Statistical Areas)
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
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
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
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
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)
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