Dinh & Kleimeier (2007) A Credit Scoring Model for Vietnam’s Retail Banking Market. International Review of Financial[r]
Trang 1LOGIT AND PROBIT
MODEL
Trang 2OLS AND RELATIONSHIP BETWEEN VARIABLES
When increases by 1 unit, increases by units
y x
y
x
Trang 3BINARY DEPENDENT VARIABLE
3
Sometimes the dep var under consideration is
binary:
Trang 4OLS WITH BINARY DEP VAR:
THE LINEAR PROBABILITY MODEL
4
then the model is called Linear Probability Model (LPM)
y
Trang 5Example: probability of default
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Problem: how individual and loan characteristics affect the probability of loan default
Data: 1.810 customers (borrowers) of a bank in VN
Dep var: default (= 1 if there is one time (or more)
during the loan duration, the borrower is unable to
repay the installment within 90 days after due date,
otherwise 0)
Dep vars:
Income ( income )
Ratio of collateral/loan amount ( coltoloan )
Data file: default.dta
Trang 7sort default
Trang 9LINEAR PROBABILITY MODEL
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_cons 2595005 .0163538 15.87 0.000 2274262 .2915748 coltoloan -.0075866 .0040737 -1.86 0.063 -.0155763 000403 income -.0011562 .0004898 -2.36 0.018 -.0021167 -.0001956 default Coef Std Err t P>|t| [95% Conf Interval]
Total 308.798343 1809 170701129 Root MSE = 41224 Adj R-squared = 0.0044 Residual 307.089262 1807 169944251 R-squared = 0.0055 Model 1.70908036 2 854540178 Prob > F = 0.0066 F( 2, 1807) = 5.03 Source SS df MS Number of obs = 1810 reg default income coltoloan
Trang 10LINEAR PROBABILITY MODEL
Trang 11DISADVANTAGES OF LPM
11
regardless the initial value of
distributed
has unequal variance, resulting in
unreliability of hypothesis testing
1
X X
1
Trang 12THE LOGIT MODEL
The probability of default is then:
If this probability is symmetric, then :
i i
i X u
I *
) (
) 0 (
) 0 (
) 1 ( Y i P I i * P X i u i P u i X i
) (
) 1
Trang 13THE LOGIT MODEL
i X u
i
Z i
Trang 14THE LOGIT MODEL
14
The odd ratio in this case is the ratio between
probability of default and probability of non-default:
Taking log of both sides, we otain the logit:
LPM assumes P i linearly correlates with X i , the Logit
model assumes the logit linearly correlates with X i
i i
i
Z Z
i i
optional
Trang 15PROPERTIES OF LOGIT MODEL
Trang 16Z
Trang 17ESTIMATE LOGIT MODEL IN STATA
17
_cons -1.019157 .097014 -10.51 0.000 -1.209301 -.8290129 coltoloan -.0547242 .0307794 -1.78 0.075 -.1150508 .0056024 income -.0071093 .003187 -2.23 0.026 -.0133557 -.0008628 default Coef Std Err z P>|z| [95% Conf Interval]
Log likelihood = -944.24413 Pseudo R2 = 0.0057 Prob > chi2 = 0.0045
LR chi2(2) = 10.79Logistic regression Number of obs = 1810
Iteration 3: log likelihood = -944.24413
Iteration 2: log likelihood = -944.24414
Iteration 1: log likelihood = -944.28455
Iteration 0: log likelihood = -949.63676
logit default income coltoloan
Trang 18INTERPRETATION OF COEFFICIENT
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Coefficient
Coefficient only indicates the direction of the effect
of on It says nothing about the magnitude of the effect
i i
i
Z i
Z
Trang 19MARGINAL EFFECTS
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then how much changes (marginal effect)
varies with
X P
Trang 20MARGINAL EFFECTS IN STATA
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coltol~n -.0092774 .0052 -1.78 0.075 -.019476 000921 1.76776 income -.0012052 00054 -2.24 0.025 -.002261 -.000149 24.094 variable dy/dx Std Err z P>|z| [ 95% C.I ] X = 21632929
y = Pr(default) (predict)
Marginal effects after logit
mfx
coltol~n -.0091914 .0055 -1.67 0.095 -.019971 001588 0 income -.0011941 00049 -2.42 0.015 -.002161 -.000228 40 variable dy/dx Std Err z P>|z| [ 95% C.I ] X = .2135719
y = Pr(default) (predict)
Marginal effects after logit
mfx, at(income = 40 coltoloan = 0)
Marginal effects at mean of X
Marginal effects at income
of 40 mil VND and no collateral
Trang 21HYPOTHESIS TESTING
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default simultaneously
Prob > chi2 = 0.0257 chi2( 1) = 4.98 ( 1) [default]income = 0
test income
Prob > chi2 = 0.0067 chi2( 2) = 10.02
( 2) [default]coltoloan = 0 ( 1) [default]income = 0 test income coltoloan
Trang 22THE PROBIT MODEL
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In the Logit model, u follows logistic distribution
In the Probit model, u follows normal distribution
Trang 23PROBIT MODEL IN STATA
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_cons -.6222283 .0573382 -10.85 0.000 -.7346092 -.5098474 coltoloan -.0339395 .0179847 -1.89 0.059 -.0691889 .0013098 income -.0042379 .0018321 -2.31 0.021 -.0078288 -.0006471 default Coef Std Err z P>|z| [95% Conf Interval]
Log likelihood = -943.93571 Pseudo R2 = 0.0060 Prob > chi2 = 0.0033
LR chi2(2) = 11.40Probit regression Number of obs = 1810
Iteration 3: log likelihood = -943.93571
Iteration 2: log likelihood = -943.93572
Iteration 1: log likelihood = -943.96949
Iteration 0: log likelihood = -949.63676
probit default income coltoloan
Trang 24LOGIT OR PROBIT
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compared to the Probit model
two models
computing the marginal effects
Trang 25APPLICATION OF LOGIT/PROBIT
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Dinh & Kleimeier (2007) A Credit Scoring Model for Vietnam’s
Retail Banking Market International Review of Financial
Analysis 16: 471-95
case presented in this lecture
Trang 26APPLICATION OF LOGIT/PROBIT
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Dymski & Mohanty (1999) Credit and Banking Structure: Asian
and African-American Experience in LA American Economic
Review 89(2): 362-6
purchasing loan application
purchasing loan) is approved (1) or not (0)
income, accommodation, distance to bank
Trang 27APPLICATION OF LOGIT/PROBIT
27
Fernandez-Perez et al (2014) The Term Structure of Interest
Rates as a Predictor of Stock Returns: Evidence for the IBEX35
during a Bear Market International Review of Economics and
Finance 31: 21-33
market)
and financial indicators