Do Borrowers Tend to Overborrow?
Joshua Bates
Econ 4355
December 3, 2009
I. Introduction and Review of Previous Literature
Since the beginning of the current recession, blame has been laid at the feet of either pushy loan sharks or unreliable borrowers, depending on who was unpopular at the time. This study aims at finding the true culprit by isolating the borrowers, and studying their borrowing habits. By examining how much money the borrowers attempt to get based on their ability to pay, it is possible to get into the mindset of the consumers.
Certainly something clearly went wrong in the loan market. The FDIC is running a complete program designed to help both borrowers and lenders in need, as required by the federal government. Although the current program is aimed at lenders, the FDIC proposed another program for borrowers specifically, “based on the approach that the FDIC implemented in connection with its operation of IndyMac Bank, FSB (IndyMac) after it failed on July 11, 2008, which, as of November 20, 2008, resulted in more than 5,300 modifications. The Program was required to be used by Citigroup, Inc., in connection with the recent government intervention and loss sharing arrangement with that company.”(Mierzewski, DeSimone and Hochberg 2009, 15) The sample from this study takes place in normal times and the expected result is that, “the equilibrium amount of the loan is positively linked to household net wealth and income profile, as the theory predicts.”(Magri 2006, 403-404) It also seems the case that,” low-risk borrowers receive a larger loan than under full information and put up more collateral than high-risk borrowers.”(Khalil, et al. 1998) These behaviors are expected, and have been tested, but perhaps there is more to learn from further study.
II. Specification of the Model
This model uses the amount of time employed, as well as yearly and monthly income, and education level to determine how financially able a loan applicant thinks they are. It also uses credit history and the lender’s request for private mortgage insurance as further indicators of fiscal responsibility. The impacts the latter factors have on loan acceptance are not as well known to the borrower as employment or income. Certainly a clean credit history is helpful, but the mathematical calculation behind this is not obvious to the average consumer. The dependent variable is the amount the borrower asks of the lender.
Here y is the loan amount, Beta 1 is the constant, X2 is how long the applicant has been employed in the same industry, X3 is the number of lines of credit on the applicant’s credit report, X4 is the applicant’s monthly income, X5 is the applicant’s yearly income, X6 is a dummy variable equal to one if the applicant has more than 12 years of schooling, X7 is a dummy variable equal to one if the lender requests private mortgage insurance, X8 is a dummy variable equal to one if the applicant has never missed a payment, X9 is a dummy variable equal to one if the applicant has only missed one or two payments and X10 is a dummy variable equal to one if the applicant has missed more than two payments.
It would be expected that higher income and long employment would increase the loan size, and that poor credit would reduce loan size. A cosigner could go either way, increasing the loan size since a cosigner better guarantees application acceptance, or decreasing it since most people who are well off do not require a cosigner. It seems intuitive that higher income and employment would substantially increase loan size since these are known variables to the borrower and the borrower would know exactly how much he or she could afford. Since credit history, its effects, and the effect of a request for private mortgage insurance is less known, these variables would be expected to be a little smaller, if expected to be helpful and a little bigger if expected to be hurtful, due to the uncertainty.
III. Data Description
The data are taken from a study of cultural affinity in the loan approval process, obtained via the University of Texas at Dallas’s elearning website. Mary Beth Walker and William C. Hunter describe the data in their paper, “The Cultural Affinity Hypothesis and Mortgage Lending Decisions:”
The data used in this study were taken from the augmented 1990 HMDA data collected by the Federal Reserve Bank of Boston. Augmentation of the HMDA data was necessary because applicant and loan characteristics collected under HMDA are severely limited. The Boston Fed, with the support of other supervisory agencies, obtained additional information on the borrowers and loan applications included in the 1990 HMDA report from the Boston Metropolitan Statistical Area. The Boston Fed data file included a random sample of 3,300conventional applications made by whites and 722 conventional applications made by blacks and Hispanics (Hunter and Walker 1996, 59-60).
An examination of the summary statistics reveals a fairly wealthy group of applicants, particularly for the year the data was collected, with an average income of $84,677.73, and median income of $64,000. Most have not been in their jobs very long, if employed at all, with the 75th percentile housing the first applicant employed for a full year. Monthly income was included because in many cases, it differed from yearly income, perhaps due to either rounding or bonuses not counted as monthly income. The average number of lines on the credit reports is greatly skewed by one entry being six digits when every other entry is two. It is an educated group with 77% attending some form of school after high school, and fairly reliable group with only 20% requiring private mortgage insurance. 33% have never been late on a payment before, and 64% have never even made a payment before; that statistic, coupled with the employment numbers indicate that this is potentially a young group of applicants or at least one new to both loans and employment.
IV. Results
The first model calculated was heteroskedastic, so the reported model uses White heteroskedastic robust standard errors. As formulated, the model has a coefficient of determination of 0.3745
(4.399) (1.325) (.00001) (.001) (.04) (2.686)
(2.744) (3.752) (13.829) (25.11)
The error term on mort4 is particularly large, as well as the P-value of .461 and the insignificant t-statistic of -0.74; similar results were gleaned from mort3, with a P-value of .566 and a t-statistic of 0.57. However, it made sense in the context, and when tested jointly with mort1 and mort 3, both proved to be significant. Mort1, mort3 and mort4 were chosen over mort2 because after running multiple auxiliary regressions, it was found that mort 2 had a collinear relationship with the other three that they did not share with each other. Two variables that seem to behave in a quadratic fashion are emp and appinc.
(1.877) (6.073) (.813)
Predicting the values of loanamt and graphing the predicted values on the x axis and
(3.25) (.045) (.00006)
Using the same prediction and graphing methods above, this looked like an upside down parabola with a maximum of 353.5.
Since different people use different loans for different reasons, it is useful to get a percent value of each variable.
(.026) (.012) (1.05e-07) (4.69e-06) (.00021)
(.022) (.019) (.023) (.067) (.127)
Once again, White robust errors were used, and mort3 and mort4 were only significant if tested together with mort1. This time, emp was not significant to the 95th percentile, with a P-value of .073, which still leaves it in the 90th percentile. The results of this variable in this format were not used in the analysis.
V. Discussion
The biggest surprise is the employment coefficient; being negative means that the longer people are employed, the smaller their loans. This seems to be in direct violation of both common sense, and the fact that income grows the size of loans taken. However, the coefficients on both income variables are so small that they make very little difference. This clearly supports the theory that the sample, if not the population get big loans early in their careers. The downward trend of employment’s effect on loan size appears to bottom out at 4.6 years on the job, before it rebounds. This seems to indicate that people get large loans either prior to employment, such as student loans, or in the early years of their employment. The former hypothesis seems to be confirmed by the large number of people who have more than twelve years of schooling; perhaps a large number of those are getting student loans.
Income has a much smaller effect on loan size than seems intuitive. It seems that people only want to spend $144 more dollars on loans than each additional thousand dollars they make. When stated in this fashion, this statistic makes more sense. The maximum effect that income seems to have on loan size is $353,500. Once income passes this threshold, the need for a loan seems to decrease, as more money can be put towards the down payment, and more things can be bought without needing to borrow.
Another oddity is the sign on the coefficient for applicants requested to get private mortgage insurance; this would seem like an indication that the applicant cannot afford more loan. However, this coefficient not only positively affects loan size it has one of the larger effects in this model. Research into the nature of private mortgage insurance reveals that it is mostly required when making a small down payment on a home. The San Francisco Fed describes it as “extra insurance that lenders require from most homebuyers who obtain loans that are more than 80 percent of their new home's value. In other words, buyers with less than a 20 percent down payment are normally required to pay PMI.”(Federal Reserve Bank of San Francisco) This would indicate that loans requiring this insurance would be bigger, regardless of the applicant’s financial responsibility.
Not surprisingly, borrowers who pay their bills on time are more likely to borrow more in the future; this has the largest effect of any single factor in this model. People able to pay on time will try to borrow an additional 11.33%. Even people who missed one or two payments will attempt to borrow an additional 5.33%. Only those who chronically miss payments must cut back, and even then, they only borrow 3.62% less. Apparently, missing payments does not cause people to want to borrow less. Perhaps those most predisposed to missing payments are also those most predisposed to borrowing more.
Also not tremendously surprising is the fact that the number of credit lines on the credit report has a negative impact on loan size. This impact seems to be negligible, but is likely skewed by one absurdly large observation six digits long when all of the others have only two digits. Additional schooling boosts loan values by 12.9%; however, this could be for student loans. People who have had an education also tend to make more money and spend fewer years in their field, and both of these traits appear to be conducive to larger loans. Perhaps those schooled are more likely to use the capital gained using a loan, or they learn ways to manipulate the loan process to their advantage. This could probably use some study.
VI. Conclusions
The only real issue with the data is the fact that the sample was so willing to repay its loans. This may not be an accurate portrayal of the loan market. Even if it was an accurate in the 1990’s, it may not be accurate currently. Furthermore, there was one entry that seems like it must have been a typographical error. Future studies using this data should be cautious, and find out if this entry is correct. This particular data set was created for the purpose of testing for racial bias in the loan approval process and future studies should probably use data collected for the purpose.
This small study appears to show that people do not tend to get into loans they cannot repay. The affect income has is smaller than would seem intuitive, which paints a picture of people who hold on to their hard earned money, and do not rush into debt. This sample seemed to do well repaying loans on time in most cases, and seemed to know when to stop taking out large loans. This study also paints a picture of a forgiving, perhaps too forgiving, market, perceived by their customers as willing to shrug off one or two missing payments to get borrowers into bigger loans, and only modestly discouraging people when their repayment history exceeded two missed payments. This conclusion seems correct given the events of 2008.
VII. References
Federal Reserve Bank of San Francisco. Private Mortgage Insurance (PMI) New Law Requires Lenders to Cancel PMI. Federal Reserve Bank of San Francisco. http://www.frbsf.org/publications/consumer/pmi.html
Hunter, William C., and Mary Beth Walker. 1996. "The Cultural Affinity Hypothesis and Mortgage Lending Decisions." Journal of Real Estate Finance and Economics 13, no. 1: 57-70. EconLit, EBSCOhost (accessed December 3, 2009).
Khalil, Fahad, and Bruno M. Parigi. 1998. "Loan size as a commitment device*." International Economic Review 39, no. 1: 135. Business Source Complete, EBSCOhost (accessed December 3, 2009).
Magri, Silvia. 2007. "Italian households’ debt: the participation to the debt market and the size of the loan." Empirical Economics 33, no. 3: 401-426. Business Source Complete, EBSCOhost (accessed December 3, 2009).
Mierzewski, Michael B., Beth S. DeSimone, and Jeremy W. Hochberg. 2009. "FDIC'S Loan Modification Program and Loss Sharing Proposal." Real Estate Finance (Aspen Publishers Inc.) 25, no. 5: 15-18. Business Source Complete, EBSCOhost (accessed December 3, 2009).
Variable Names and Descriptions
Variable Name | Description |
loanamt | Loan amount in thousands of dollars |
emp | Years employed in current field |
atotinc | Total monthly income |
lines | Number of credit lines on report |
appinc | Applicant's income in thousands |
inss | Equals 1 if private mortgage insurance is sought |
sch | Equals 1 if the applicant has more than twelve years of education. |
mort1 | Equals 1 if applicant has never missed a payment |
mort2 | Equals 1 if applicant has never made a payment |
mort3 | Equals 1 if applicant has missed one or two payments |
mort4 | Equals 1 if applicant has missed more than two payments |
Summary Statistics
Variable | Obs | Mean | Std. Dev. | Min | Max |
loanamt | 1989 | 143.2453 | 80.52041 | 2 | 980 |
emp | 1989 | 0.209653 | 1.00391 | 0 | 9 |
atotinc | 1989 | 5195.55 | 5269.056 | 0 | 81000 |
lines | 1989 | 516.3617 | 22422.11 | 0 | 999999.4 |
appinc | 1989 | 84.67773 | 87.05834 | 0 | 972 |
inss | 1989 | 0.200101 | 0.400176 | 0 | 1 |
sch | 1989 | 0.771745 | 0.419814 | 0 | 1 |
mort1 | 1989 | 0.331825 | 0.470987 | 0 | 1 |
mort2 | 1989 | 0.638512 | 0.480552 | 0 | 1 |
mort3 | 1989 | 0.019105 | 0.136929 | 0 | 1 |
mort4 | 1989 | 0.010558 | 0.102234 | 0 | 1 |
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------
name: <unnamed>
log: C:\Users\mitthrawnuruodo\Desktop\Econometrics\Econometrics Project\loanapp.log
log type: text
opened on: 3 Dec 2009, 17:33:58
. set more off
. g mort1 = (mortg <= 1)
. g mort2 = (mortg >1 & mortg <3)
. g mort3 = (mortg >2 & mortg <4)
. g mort4 = (mortg >= 4 & mortg !=.)
. summ loanamt emp atotinc lines appinc inss sch mort1 mort2 mort3 mort4
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
loanamt | 1989 143.2453 80.52041 2 980
emp | 1989 .2096531 1.00391 0 9
atotinc | 1989 5195.55 5269.056 0 81000
lines | 1989 516.3617 22422.11 0 999999.4
appinc | 1989 84.67773 87.05834 0 972
-------------+--------------------------------------------------------
inss | 1989 .2001006 .400176 0 1
sch | 1989 .7717446 .4198136 0 1
mort1 | 1989 .331825 .470987 0 1
mort2 | 1989 .6385118 .4805524 0 1
mort3 | 1989 .0191051 .1369288 0 1
-------------+--------------------------------------------------------
mort4 | 1989 .0105581 .1022343 0 1
. summ loanamt emp atotinc lines appinc inss sch mort1 mort2 mort3 mort4, detail
loan amt in thousands
-------------------------------------------------------------
Percentiles Smallest
1% 30 2
5% 57 9
10% 71 17 Obs 1989
25% 100 20 Sum of Wgt. 1989
50% 126 Mean 143.2453
Largest Std. Dev. 80.52041
75% 165 732
90% 224 750 Variance 6483.536
95% 280 800 Skewness 3.128007
99% 484 980 Kurtosis 20.36366
years employed in line of work
-------------------------------------------------------------
Percentiles Smallest
1% 0 0
5% 0 0
10% 0 0 Obs 1989
25% 0 0 Sum of Wgt. 1989
50% 0 Mean .2096531
Largest Std. Dev. 1.00391
75% 0 9
90% 0 9 Variance 1.007834
95% 1 9 Skewness 6.687797
99% 6 9 Kurtosis 50.56875
total monthly income
-------------------------------------------------------------
Percentiles Smallest
1% 1141 0
5% 1894 0
10% 2235 0 Obs 1989
25% 2876 0 Sum of Wgt. 1989
50% 3813 Mean 5195.55
Largest Std. Dev. 5269.056
75% 5596 63337
90% 8881 67000 Variance 2.78e+07
95% 12841 72529 Skewness 6.360304
99% 26000 81000 Kurtosis 65.3365
no. of credit lines on reports
-------------------------------------------------------------
Percentiles Smallest
1% 0 0
5% 2 0
10% 3 0 Obs 1989
25% 7 0 Sum of Wgt. 1989
50% 12 Mean 516.3617
Largest Std. Dev. 22422.11
75% 19 48
90% 27 50 Variance 5.03e+08
95% 32 55 Skewness 44.56455
99% 41 999999.4 Kurtosis 1987
applicant income, $1000s
-------------------------------------------------------------
Percentiles Smallest
1% 24 0
5% 32 4
10% 38 5 Obs 1989
25% 48 10 Sum of Wgt. 1989
50% 64 Mean 84.67773
Largest Std. Dev. 87.05834
75% 88 732
90% 131 796 Variance 7579.154
95% 189 870 Skewness 5.263864
99% 666 972 Kurtosis 36.70095
PMI sought
-------------------------------------------------------------
Percentiles Smallest
1% 0 0
5% 0 0
10% 0 0 Obs 1989
25% 0 0 Sum of Wgt. 1989
50% 0 Mean .2001006
Largest Std. Dev. .400176
75% 0 1
90% 1 1 Variance .1601408
95% 1 1 Skewness 1.499215
99% 1 1 Kurtosis 3.247645
=1 if > 12 years schooling
-------------------------------------------------------------
Percentiles Smallest
1% 0 0
5% 0 0
10% 0 0 Obs 1989
25% 1 0 Sum of Wgt. 1989
50% 1 Mean .7717446
Largest Std. Dev. .4198136
75% 1 1
90% 1 1 Variance .1762435
95% 1 1 Skewness -1.294922
99% 1 1 Kurtosis 2.676823
mort1
-------------------------------------------------------------
Percentiles Smallest
1% 0 0
5% 0 0
10% 0 0 Obs 1989
25% 0 0 Sum of Wgt. 1989
50% 0 Mean .331825
Largest Std. Dev. .470987
75% 1 1
90% 1 1 Variance .2218287
95% 1 1 Skewness .7143181
99% 1 1 Kurtosis 1.51025
mort2
-------------------------------------------------------------
Percentiles Smallest
1% 0 0
5% 0 0
10% 0 0 Obs 1989
25% 0 0 Sum of Wgt. 1989
50% 1 Mean .6385118
Largest Std. Dev. .4805524
75% 1 1
90% 1 1 Variance .2309306
95% 1 1 Skewness -.5766141
99% 1 1 Kurtosis 1.332484
mort3
-------------------------------------------------------------
Percentiles Smallest
1% 0 0
5% 0 0
10% 0 0 Obs 1989
25% 0 0 Sum of Wgt. 1989
50% 0 Mean .0191051
Largest Std. Dev. .1369288
75% 0 1
90% 0 1 Variance .0187495
95% 0 1 Skewness 7.02578
99% 1 1 Kurtosis 50.36158
mort4
-------------------------------------------------------------
Percentiles Smallest
1% 0 0
5% 0 0
10% 0 0 Obs 1989
25% 0 0 Sum of Wgt. 1989
50% 0 Mean .0105581
Largest Std. Dev. .1022343
75% 0 1
90% 0 1 Variance .0104519
95% 0 1 Skewness 9.577315
99% 1 1 Kurtosis 92.72496
. regress mort1 mort2 mort3
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) =20523.28
Model | 420.643052 2 210.321526 Prob > F = 0.0000
Residual | 20.3524229 1986 .010247947 R-squared = 0.9538
-------------+------------------------------ Adj R-squared = 0.9538
Total | 440.995475 1988 .22182871 Root MSE = .10123
------------------------------------------------------------------------------
mort1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort2 | -.969163 .0048081 -201.57 0.000 -.9785924 -.9597336
mort3 | -.969163 .016874 -57.44 0.000 -1.002256 -.9360704
_cons | .969163 .0038792 249.83 0.000 .9615552 .9767708
------------------------------------------------------------------------------
. scalar r1 = e(r2)
. regress mort2 mort3 mort1
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) =21074.36
Model | 438.431591 2 219.215795 Prob > F = 0.0000
Residual | 20.6584043 1986 .010402016 R-squared = 0.9550
-------------+------------------------------ Adj R-squared = 0.9550
Total | 459.089995 1988 .230930581 Root MSE = .10199
------------------------------------------------------------------------------
mort2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort3 | -.9837335 .0167867 -58.60 0.000 -1.016655 -.9508121
mort1 | -.9837335 .0048804 -201.57 0.000 -.9933047 -.9741624
_cons | .9837335 .0028385 346.56 0.000 .9781667 .9893004
------------------------------------------------------------------------------
. scalar r2 = e(r2)
. regress mort3 mort1 mort2
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) = 1743.56
Model | 23.7485833 2 11.8742917 Prob > F = 0.0000
Residual | 13.5254237 1986 .006810385 R-squared = 0.6371
-------------+------------------------------ Adj R-squared = 0.6368
Total | 37.274007 1988 .018749501 Root MSE = .08253
------------------------------------------------------------------------------
mort3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort1 | -.6440678 .0112138 -57.44 0.000 -.6660598 -.6220758
mort2 | -.6440678 .0109906 -58.60 0.000 -.6656221 -.6225135
_cons | .6440678 .0107438 59.95 0.000 .6229974 .6651382
------------------------------------------------------------------------------
. scalar r3 = e(r2)
. regress mort1 mort2 mort4
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) =11194.41
Model | 405.064243 2 202.532122 Prob > F = 0.0000
Residual | 35.9312321 1986 .018092262 R-squared = 0.9185
-------------+------------------------------ Adj R-squared = 0.9184
Total | 440.995475 1988 .22182871 Root MSE = .13451
------------------------------------------------------------------------------
mort1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort2 | -.9455587 .0063377 -149.20 0.000 -.9579879 -.9331296
mort4 | -.9455587 .0297902 -31.74 0.000 -1.003982 -.8871354
_cons | .9455587 .0050912 185.72 0.000 .9355741 .9555434
------------------------------------------------------------------------------
. scalar r4 = e(r2)
. regress mort1 mort3 mort4
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) = 15.31
Model | 6.69495698 2 3.34747849 Prob > F = 0.0000
Residual | 434.300518 1986 .218681026 R-squared = 0.0152
-------------+------------------------------ Adj R-squared = 0.0142
Total | 440.995475 1988 .22182871 Root MSE = .46763
------------------------------------------------------------------------------
mort1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort3 | -.3419689 .0766033 -4.46 0.000 -.4922002 -.1917376
mort4 | -.3419689 .1025997 -3.33 0.001 -.5431832 -.1407547
_cons | .3419689 .0106445 32.13 0.000 .3210933 .3628445
------------------------------------------------------------------------------
. scalar r5 = e(r2)
. regress mort2 mort3 mort4
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) = 56.68
Model | 24.7894768 2 12.3947384 Prob > F = 0.0000
Residual | 434.300518 1986 .218681026 R-squared = 0.0540
-------------+------------------------------ Adj R-squared = 0.0530
Total | 459.089995 1988 .230930581 Root MSE = .46763
------------------------------------------------------------------------------
mort2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort3 | -.6580311 .0766033 -8.59 0.000 -.8082624 -.5077998
mort4 | -.6580311 .1025997 -6.41 0.000 -.8592453 -.4568168
_cons | .6580311 .0106445 61.82 0.000 .6371555 .6789067
------------------------------------------------------------------------------
. scalar r6 = e(r2)
. regress mort2 mort1 mort4
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) =11362.70
Model | 422.193971 2 211.096985 Prob > F = 0.0000
Residual | 36.8960245 1986 .018578059 R-squared = 0.9196
-------------+------------------------------ Adj R-squared = 0.9196
Total | 459.089995 1988 .230930581 Root MSE = .1363
------------------------------------------------------------------------------
mort2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort1 | -.970948 .0065078 -149.20 0.000 -.9837109 -.9581851
mort4 | -.970948 .0299812 -32.39 0.000 -1.029746 -.9121501
_cons | .970948 .0037687 257.63 0.000 .9635569 .9783391
------------------------------------------------------------------------------
. scalar r7 = e(r2)
. regress mort3 mort2 mort4
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) = 37.11
Model | 1.34277495 2 .671387474 Prob > F = 0.0000
Residual | 35.9312321 1986 .018092262 R-squared = 0.0360
-------------+------------------------------ Adj R-squared = 0.0351
Total | 37.274007 1988 .018749501 Root MSE = .13451
------------------------------------------------------------------------------
mort3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort2 | -.0544413 .0063377 -8.59 0.000 -.0668704 -.0420121
mort4 | -.0544413 .0297902 -1.83 0.068 -.1128646 .0039821
_cons | .0544413 .0050912 10.69 0.000 .0444566 .0644259
------------------------------------------------------------------------------
. scalar r8 = e(r2)
. regress mort3 mort1 mort4
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) = 10.17
Model | .377982574 2 .188991287 Prob > F = 0.0000
Residual | 36.8960245 1986 .018578059 R-squared = 0.0101
-------------+------------------------------ Adj R-squared = 0.0091
Total | 37.274007 1988 .018749501 Root MSE = .1363
------------------------------------------------------------------------------
mort3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort1 | -.029052 .0065078 -4.46 0.000 -.0418149 -.0162891
mort4 | -.029052 .0299812 -0.97 0.333 -.0878499 .0297459
_cons | .029052 .0037687 7.71 0.000 .0216609 .0364431
------------------------------------------------------------------------------
. scalar r9 = e(r2)
. regress mort4 mort1 mort2
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) = 532.49
Model | 7.25285681 2 3.62642841 Prob > F = 0.0000
Residual | 13.5254237 1986 .006810385 R-squared = 0.3491
-------------+------------------------------ Adj R-squared = 0.3484
Total | 20.7782805 1988 .010451851 Root MSE = .08253
------------------------------------------------------------------------------
mort4 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort1 | -.3559322 .0112138 -31.74 0.000 -.3779242 -.3339402
mort2 | -.3559322 .0109906 -32.39 0.000 -.3774865 -.3343779
_cons | .3559322 .0107438 33.13 0.000 .3348618 .3770026
------------------------------------------------------------------------------
. scalar r10 = e(r2)
. regress mort4 mort2 mort3
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) = 20.78
Model | .425857635 2 .212928818 Prob > F = 0.0000
Residual | 20.3524229 1986 .010247947 R-squared = 0.0205
-------------+------------------------------ Adj R-squared = 0.0195
Total | 20.7782805 1988 .010451851 Root MSE = .10123
------------------------------------------------------------------------------
mort4 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort2 | -.030837 .0048081 -6.41 0.000 -.0402664 -.0214076
mort3 | -.030837 .016874 -1.83 0.068 -.0639296 .0022556
_cons | .030837 .0038792 7.95 0.000 .0232292 .0384448
------------------------------------------------------------------------------
. scalar r11 = e(r2)
. regress mort4 mort1 mort3
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) = 5.76
Model | .119876205 2 .059938103 Prob > F = 0.0032
Residual | 20.6584043 1986 .010402016 R-squared = 0.0058
-------------+------------------------------ Adj R-squared = 0.0048
Total | 20.7782805 1988 .010451851 Root MSE = .10199
------------------------------------------------------------------------------
mort4 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mort1 | -.0162665 .0048804 -3.33 0.001 -.0258376 -.0066953
mort3 | -.0162665 .0167867 -0.97 0.333 -.0491879 .016655
_cons | .0162665 .0028385 5.73 0.000 .0106996 .0218333
------------------------------------------------------------------------------
. scalar r12 = e(r2)
. scalar list r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
r1 = .95384891
r2 = .95500141
r3 = .63713524
r4 = .91852245
r5 = .01518146
r6 = .05399699
r7 = .91963226
r8 = .03602443
r9 = .01014065
r10 = .34905953
r11 = .02049533
r12 = .0057693
. reg loanamt emp lines atotinc appinc inss sch mort1 mort3 mort4
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 9, 1979) = 131.65
Model | 4827080.2 9 536342.245 Prob > F = 0.0000
Residual | 8062190.06 1979 4073.87067 R-squared = 0.3745
-------------+------------------------------ Adj R-squared = 0.3717
Total | 12889270.3 1988 6483.53635 Root MSE = 63.827
------------------------------------------------------------------------------
loanamt | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
emp | -2.99535 1.457862 -2.05 0.040 -5.854455 -.1362448
lines | -.0001118 .0000652 -1.72 0.086 -.0002396 .0000159
atotinc | .007104 .0003396 20.92 0.000 .0064381 .0077699
appinc | .1443049 .0199717 7.23 0.000 .1051372 .1834725
inss | 15.90966 3.668758 4.34 0.000 8.714623 23.10469
sch | 16.60709 3.464125 4.79 0.000 9.813379 23.40081
mort1 | 19.26968 3.177624 6.06 0.000 13.03784 25.50152
mort3 | 7.929083 10.54598 0.75 0.452 -12.75331 28.61148
mort4 | -18.50448 14.28428 -1.30 0.195 -46.51829 9.509326
_cons | 72.45234 3.513822 20.62 0.000 65.56116 79.34351
------------------------------------------------------------------------------
. estat imtest, white
White's test for Ho: homoskedasticity
against Ha: unrestricted heteroskedasticity
chi2(45) = 497.21
Prob > chi2 = 0.0000
Cameron & Trivedi's decomposition of IM-test
---------------------------------------------------
Source | chi2 df p
---------------------+-----------------------------
Heteroskedasticity | 497.21 45 0.0000
Skewness | 22.54 9 0.0073
Kurtosis | 3.48 1 0.0620
---------------------+-----------------------------
Total | 523.24 55 0.0000
---------------------------------------------------
. reg loanamt emp lines atotinc appinc inss sch mort1 mort3 mort4
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 9, 1979) = 131.65
Model | 4827080.2 9 536342.245 Prob > F = 0.0000
Residual | 8062190.06 1979 4073.87067 R-squared = 0.3745
-------------+------------------------------ Adj R-squared = 0.3717
Total | 12889270.3 1988 6483.53635 Root MSE = 63.827
------------------------------------------------------------------------------
loanamt | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
emp | -2.99535 1.457862 -2.05 0.040 -5.854455 -.1362448
lines | -.0001118 .0000652 -1.72 0.086 -.0002396 .0000159
atotinc | .007104 .0003396 20.92 0.000 .0064381 .0077699
appinc | .1443049 .0199717 7.23 0.000 .1051372 .1834725
inss | 15.90966 3.668758 4.34 0.000 8.714623 23.10469
sch | 16.60709 3.464125 4.79 0.000 9.813379 23.40081
mort1 | 19.26968 3.177624 6.06 0.000 13.03784 25.50152
mort3 | 7.929083 10.54598 0.75 0.452 -12.75331 28.61148
mort4 | -18.50448 14.28428 -1.30 0.195 -46.51829 9.509326
_cons | 72.45234 3.513822 20.62 0.000 65.56116 79.34351
------------------------------------------------------------------------------
. test mort1 mort3 mort4
( 1) mort1 = 0
( 2) mort3 = 0
( 3) mort4 = 0
F( 3, 1979) = 13.60
Prob > F = 0.0000
. g emp2 = (emp^2)
. reg loanamt emp emp2
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) = 3.63
Model | 46913.3683 2 23456.6842 Prob > F = 0.0268
Residual | 12842356.9 1986 6466.44356 R-squared = 0.0036
-------------+------------------------------ Adj R-squared = 0.0026
Total | 12889270.3 1988 6483.53635 Root MSE = 80.414
------------------------------------------------------------------------------
loanamt | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
emp | -14.57729 6.072924 -2.40 0.016 -26.48726 -2.66732
emp2 | 1.571137 .8134426 1.93 0.054 -.0241532 3.166428
_cons | 144.6498 1.877054 77.06 0.000 140.9686 148.331
------------------------------------------------------------------------------
. predict ehat, xb
. twoway (line ehat emp2, sort)
. g appinc2 = (appinc^2)
. reg loanamt appinc appinc2
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 2, 1986) = 589.03
Model | 4799018.99 2 2399509.49 Prob > F = 0.0000
Residual | 8090251.28 1986 4073.64113 R-squared = 0.3723
-------------+------------------------------ Adj R-squared = 0.3717
Total | 12889270.3 1988 6483.53635 Root MSE = 63.825
------------------------------------------------------------------------------
loanamt | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
appinc | 1.413947 .0450402 31.39 0.000 1.325616 1.502278
appinc2 | -.0016145 .0000668 -24.16 0.000 -.0017455 -.0014834
_cons | 47.32212 3.250778 14.56 0.000 40.94682 53.69741
------------------------------------------------------------------------------
. predict yhat, xb
. twoway (line yhat appinc2, sort)
. g lnloanamt = log(loanamt)
. reg lnloanamt emp lines atotinc appinc sch inss mort1 mort3 mort4
Source | SS df MS Number of obs = 1989
-------------+------------------------------ F( 9, 1979) = 77.11
Model | 122.61196 9 13.6235512 Prob > F = 0.0000
Residual | 349.623459 1979 .17666673 R-squared = 0.2596
-------------+------------------------------ Adj R-squared = 0.2563
Total | 472.235419 1988 .237542968 Root MSE = .42032
------------------------------------------------------------------------------
lnloanamt | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
emp | -.0207538 .0096004 -2.16 0.031 -.0395818 -.0019259
lines | -1.54e-06 4.29e-07 -3.60 0.000 -2.39e-06 -7.03e-07
atotinc | .0000325 2.24e-06 14.53 0.000 .0000281 .0000369
appinc | .0007854 .0001315 5.97 0.000 .0005275 .0010434
sch | .1288713 .0228122 5.65 0.000 .0841329 .1736098
inss | .1532152 .0241598 6.34 0.000 .1058339 .2005965
mort1 | .1097318 .0209255 5.24 0.000 .0686934 .1507702
mort3 | .0391587 .0694482 0.56 0.573 -.0970405 .1753579
mort4 | -.0491878 .0940659 -0.52 0.601 -.2336664 .1352907
_cons | 4.449036 .0231395 192.27 0.000 4.403656 4.494416
------------------------------------------------------------------------------
. set more on
. log close
name: <unnamed>
log: C:\Users\mitthrawnuruodo\Desktop\Econometrics\Econometrics Project\loanapp.log
log type: text
closed on: 3 Dec 2009, 17:34:02
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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