Transcript Why Can’t I Afford a House?

Why Can’t I Afford a
Home?
By:
Philippe Bonnan
Emelia Bragadottir
Troy Dewitt
Anders Graham
S. Matthew Scott
Lingli Tang
Organization
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Time Series Regression
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United States: Ten year regression
of explanatory variables against
median price of a home
Organization
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Cross Section Regression
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14 Different Areas for 2 separate years: 2000
and 2005
Metropolitan Statistical Area
Santa Barbara, CA MSA
San Diego, CA MSA
Dallas-Fort Worth, TX MSA
El Paso, TX MSA
Colorado Springs, CO MSA
Washington-Arlington-Alexandria DC-MD-VA-WV MSA
Chicago-Naperville-Joliet,IL MSA
Boston-Cambridge-Quincy, MA MSA
NY-Northern New Jersey-Long Island, NY MSA
Columbus, OH MSA
Omaha, NE MSA
Miami-Fort Lauderdale-Miami Beach, FL MSA
Cumberland, MD-VA MSA
San Francisco, CA MSA
The Variables
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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)
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Unemployment Rate
2.00
1.50
1.00
0.50
0.00
1996
1997 1998
1999
2000 2001
Median Price
2002
2003 2004
Unemployment Rate
2005
Median Family Income
2.0
1.5
1.0
0.5
0.0
1996
1997
1998
1999
2000
Median Family Income
2001
2002
2003
Median Price
2004
2005
Building Permits
2.00
1.50
1.00
0.50
0.00
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Building Permits
Median Price
Population
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
1996
1997
1998
1999
2000
Median Price
2001
2002
2003
Population
2004
2005
Mortgage Rates
2.00
1.50
1.00
0.50
0.00
1996 1997 1998 1999 2000
Median Price
2001 2002 2003 2004 2005
Home Mortgage Rates
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
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Results for Time
Series Analysis (U.S.)
Time Series Analysis –
Correlation Matrix
PRICE
HOME
MORTGAGE
RATE
INCOME
PERMITS
POPU
LATION
UNEMPLOYMENT
RATE
PRICE
1
-0.908548
0.923769
0.978469
0.952524
0.436929
HOMEMORTGAGERATE
-0.90855
1
-0.91219
-0.93725
-0.91575
-0.573675
INCOME
0.923769
-0.912188
1
0.905082
0.994486
0.413594
PERMITS
0.978469
-0.937248
0.905082
1
0.93711
0.385133
POPULATION
0.952524
-0.915753
0.994486
0.93711
1
0.382568
UNEMPLOYMENTRATE
0.436929
-0.573675
0.413594
0.385133
0.382568
1
Time Series Regression
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Dependent Variable: PRICE
Method: Least Squares
Date: 12/06/06 Time: 09:38
Sample: 1 10
Included observations: 10
Variable
HOMEMORTGAGERATE
INCOME
PERMITS
POPULATION
UNEMPLOYMENTRATE
C
R-squared
0.990920
Adjusted R-sq.
0.979571
S.E. of regression 4868.733
Sum squared resid 94818259
Log likelihood
-94.51382
Durbin-Watson sta 3.279181
Coefficient Std. Error t-Statistic Prob.
632665.
1151196. 1.418234 0.2291
-6.116375 6.401278 -0.955493 0.3934
0.092208 0.056354 1.636246 0.1771
0.006230 0.004887 1.274867 0.2714
1033710. 358705.7 2.881777 0.0449
-1622644. 933044.8 -1.739085 0.1570
Mean dependent var
153950.0
S.D. dependent var
34063.41
Akaike info criterion
20.10276
Schwarz criterion
20.28432
F-statistic
87.30830
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.
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Explanation of results for
time series analysis
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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
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Dependent Variable: PRICE
Method: Least Squares
Date: 12/06/06 Time: 19:25
Sample: 1 10
Included observations: 10
Variable
INCOME
PERMITS
POPULATION
UNEMPLOYMENTRATE
C
R-squared
0.986355
Adjusted R-squared0.975438
S.E. of regression 5338.490
Sum squared resid 1.42E+08
Log likelihood
-96.55063
Durbin-Watson stat 2.343565
Coefficient Std. Error t-Statistic Prob.
-12.22777 5.190382 -2.355851 0.0651
0.027076 0.035811 0.756096 0.4837
0.010664 0.004118 2.589475 0.0489
824150.2 358395.3 2.299557 0.0698
-2334912. 862220.4 -2.708022 0.0424
Mean dependent var
153950.0
S.D. dependent var
34063.41
Akaike info criterion
20.31013
Schwarz criterion
20.46142
F-statistic
90.35561
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
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Dependent Variable: PRICE
Method: Least Squares
Date: 12/06/06 Time: 19:27
Sample: 1 10
Included observations: 10
Variable
HOMEMORTGAGERATE
INCOME
POPULATION
UNEMPLOYMENTRATE
C
R-squared
0.984843
Adjusted R-squared 0.972717
S.E. of regression 5626.411
Sum squared resid 1.58E+08
Log likelihood
-97.07592
Durbin-Watson sta 2.325004
Coefficient Std. Error t-Statistic Prob.
97613.97 770997.7 0.126607 0.9042
-15.51536 3.264526 -4.752713 0.0051
0.013532 0.002301 5.880010 0.0020
998640.4 413787.3 2.413415 0.0606
-2949376. 533483.0 -5.528529 0.0027
Mean dependent var
153950.0
S.D. dependent var
34063.41
Akaike info criterion
20.41518
Schwarz criterion
20.56648
F-statistic
81.21998
Prob(F-statistic)
0.000098
Both Income and Population are now significant explanatory
variables
Drop Population
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Dependent Variable: PRICE
Method: Least Squares
Date: 12/06/06 Time: 19:28
Sample: 1 10
Included observations: 10
Variable
HOMEMORTGAGERATE
INCOME
PERMITS
UNEMPLOYMENTRATE
C
R-squared
0.987231
Adjusted R-squared0.977016
S.E. of regression 5164.203
Sum squared resid 1.33E+08
Log likelihood
-96.21871
Durbin-Watson stat3.147208
Coefficient Std. Error t-Statistic Prob.
2571603. 938466.0 2.740220 0.0408
1.992947
0.761256 2.617971 0.0472
0.157815 0.024359 6.478855 0.0013
967915.6 376516.0 2.570715 0.0500
-442695.1 125212.2 -3.535560 0.0166
Mean dependent var
153950.0
S.D. dependent var
34063.41
Akaike info criterion
20.24374
Schwarz criterion
20.39503
F-statistic
96.64315
Prob(F-statistic)
0.000064
When we drop Population, all our explanatory variables now
become significant
Drop Unemployment Rate
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Dependent Variable: PRICE
Method: Least Squares
Date: 12/06/06 Time: 19:29
Sample: 1 10
Included observations: 10
Variable
HOMEMORTGAGERATE
INCOME
PERMITS
POPULATION
C
R-squared
0.972069
Adjusted R-square 0.949725
S.E. of regression 7637.749
Sum squared resid 2.92E+08
Log likelihood
-100.1322
Durbin-Watson stat1.359493
Coefficient Std. Error t-Statistic Prob.
266099.7 1645584. 0.161705 0.8779
-3.839510 9.965120 -0.385295 0.7159
0.082505
0.088246 0.934945 0.3927
0.004204
0.007586 0.554139 0.6034
-1002577. 1424248. -0.703935 0.5129
Mean dependent var
153950.0
S.D. dependent var
34063.41
Akaike info criterion
21.02645
Schwarz criterion
21.17774
F-statistic
43.50361
Prob(F-statistic)
0.000447
We have no significant explanatory variables when we drop
Unemployment Rate
DROP INCOME
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Dependent Variable: PRICE
Method: Least Squares
Date: 12/06/06 Time: 09:42
Sample: 1 10
Included observations: 10
Variable
HOMEMORTGAGERATE
PERMITS
POPULATION
UNEMPLOYMENTRATE
C
R-squared
0.988848
Adjusted R-sq
0.979926
S.E. of regression 4826.173
Sum squared resid 1.16E+08
Log likelihood
-95.54174
Durbin-Watson sta 3.205994
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All our explanatory variables are significant.
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This is the best result because the probability of the F-statistic is
the lowest.
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Coefficient Std. Error t-Statistic Prob.
2373126. 843852.1 2.812254 0.0374
0.140527
0.024652 5.700503 0.0023
0.001590
0.000543 2.927870 0.0327
991406.2 352851.3 2.809700 0.0376
-749970.5 189154.5 -3.964858 0.0107
Mean dependent var
153950.0
S.D. dependent var
34063.41
Akaike info criterion
20.10835
Schwarz criterion
20.25964
F-statistic
110.8364
Prob(F-statistic)
0.000046
Observations of TimeSeries 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
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Results for Cross
Section Analysis
Organization
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Cross Section Regression
•
14 Different Areas for 2 separate years: 2000
and 2005
Metropolitan Statistical Area
Santa Barbara, CA MSA
San Diego, CA MSA
Dallas-Fort Worth, TX MSA
El Paso, TX MSA
Colorado Springs, CO MSA
Washington-Arlington-Alexandria DC-MD-VA-WV MSA
Chicago-Naperville-Joliet,IL MSA
Boston-Cambridge-Quincy, MA MSA
NY-Northern New Jersey-Long Island, NY MSA
Columbus, OH MSA
Omaha, NE MSA
Miami-Fort Lauderdale-Miami Beach, FL MSA
Cumberland, MD-VA MSA
San Francisco, CA MSA
Relationship between Location,
Income and House Price
House Price and Income
$800,000
$95,000
$700,000
$64,700
$63,400
$600,000
House Price
$500,000
$54,400
$82,600
$400,000
$89,300
$52,725
$300,000
$69,700
$63,400
$200,000
$65,100
$64,000
$65,250
$38,250
$100,000
$47,450
$0
$0
$10,000
$20,000
$30,000
$40,000
$50,000
Incom e
$60,000
$70,000
$80,000
$90,000
$100,000
The Variables
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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
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Relationship between
Location and House Price
Dummy Coast and House Price
1.4
y = 2E-06x - 0.2202
R2 = 0.7681
1.2
1.0
Dummy
0.8
0.6
0.4
0.2
0.0
$0
$100,000
$200,000
$300,000
$400,000
-0.2
House Price
$500,000
$600,000
$700,000
$800,000
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?
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Results for Cross Section
Analysis (14 Metropolitan
Statistical Areas)
Cross Section Analysis
Correlation Matrix - 2005
HOUSE
PRICE
DUMMY
COAST
INCOME
PERMITS
POPULAT
ION
UNEMPLOYMENT
RATE
HOUSEPRICE
1
0.876392
0.537036
0.152616
0.240021
-0.005214
DUMMYCOAST
0.876392
1
0.426185
0.342507
0.382309
0.063996
INCOME
0.537036
0.426185
1
0.032389
0.058681
-0.637418
PERMITS
0.152616
0.342507
0.032389
1
0.883983
-0.034606
POPULATION
0.240021
0.382309
0.058681
0.883983
1
-0.001086
UNEMPLOYMENTRATE
-0.00521
0.063996
-0.63742
-0.03461
-0.00109
1
800000
700000
HOUSEPRICE
600000
500000
400000
300000
200000
100000
0
1.0
DUMMYCOAST
0.8
0.6
0.4
0.2
0.0
100000
90000
INCOME
80000
70000
60000
50000
40000
30000
70000
60000
PERMITS
50000
40000
30000
20000
10000
0
2.00E+ 07
1.20E+ 07
8.00E+ 06
4.00E+ 06
0.00E+ 00
.11
.10
UNEMPLOYMENTRATE
POPULATION
1.60E+ 07
.09
.08
.07
.06
.05
.04
.03
.02
0
200000
400000
600000
HO USEPRICE
8000000.0
0.2
0.4
0.6
DUMMYCO AST
0.8
1.0 30000
50000
70000
INCO ME
90000
0
10000
30000
PERMITS
50000
70000
0.00E+ 00
1.00E+ 07
POPULATION
2.00E+ 07
.02
.04
.06
.08
.10
UNEMPLO YMENTRAT E
.12
Cross-Section Regression
2005
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Dependent Variable: HOUSEPRICE
Method: Least Squares
Date: 12/06/06 Time: 00:11
Sample: 1 14
Included observations: 14
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Variable
Coefficient
Std. Error
t-Statistic
Prob.
DUMMYCOAST
323679.4
INCOME
3.798266
PERMITS
-2.459958
POPULATION
0.006328
UNEMPLOYMENTRATE 1141333.
C
-112592.2
84887.58
3.436786
3.160409
0.014042
2298304.
321611.0
3.813036
1.105180
-0.778367
0.450617
0.496598
-0.350088
0.0051
0.3012
0.4588
0.6642
0.6328
0.7353
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R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.828896
0.721956
113187.2
1.02E+11
-178.8630
2.377582
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
DummyCoast only variable that is significant
339964.3
214654.6
26.40900
26.68288
7.751030
0.006204
Drop all insignificant
variables (2005)
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Dependent Variable: HOUSEPRICE
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Method: Least Squares
Date: 12/06/06 Time: 00:18
Sample: 1 14
Included observations: 14
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Variable
Coefficient Std. Error
t-Statistic
Prob.
DUMMYCOAST
C
362557.1
158685.7
6.303829
3.901942
0.0000
0.0021
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57513.80
40668.40
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R-squared
0.768063
Adjusted R-squared0.748735
S.E. of regression 107598.5
Sum squared resid 1.39E+11
Log likelihood
-180.9923
Durbin-Watson stat1.652406
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
339964.3
214654.6
26.14176
26.23306
39.73826
0.000039
Cross Section Regression
2000
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Dependent Variable: HOUSEPRICE
Method: Least Squares
Date: 12/06/06 Time: 00:28
Sample: 1 14
Included observations: 14
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Variable
Coefficient
Std. Error
t-Statistic
Prob.
INCOME
DUMMYCOAST
POPULATION
UNEMPLOYMENTRATE
C
2.993843
134588.0
-0.002972
400794.1
-47469.59
2.888653
47862.77
0.005146
2795135.
248491.1
1.036415
2.811957
-0.577589
0.143390
-0.191031
0.3271
0.0203
0.5777
0.8891
0.8527
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.623754
0.456534
79652.92
5.71E+10
-174.7684
1.866677
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Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
195085.7
108047.6
25.68120
25.90943
3.730130
0.046794
DummyCoast variable is very significant but not as significant as in
2005
Drop all insignificant
variables (2000)
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Dependent Variable: HOUSEPRICE
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Method: Least Squares
Date: 12/06/06 Time: 00:29
Sample: 1 14
Included observations: 14
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Variable
Coefficient Std. Error
t-Statistic
Prob.
DUMMYCOAST
C
152342.9
118914.3
3.717401
4.103613
0.0029
0.0015
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40981.01
28977.95
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R-squared
0.535227
Adjusted R-squared0.496496
S.E. of regression 76668.45
Sum squared resid 7.05E+10
Log likelihood
-176.2475
Durbin-Watson stat1.843468
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
195085.7
108047.6
25.46393
25.55523
13.81907
0.002941
Conclusion
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With time series we ran into multicollinearity issues,
and as a result of this we were forced to drop one
explanatory variable
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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
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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