Bài 9: Mô hình Ordered Probit

constraint higher than large firms by 5.1 percentage points.  Medium firms has probability of severe financial[r]

ORDERED PROBIT MODEL

Ordinal discrete variable

2

 Many discrete outcomes have natural ordering

 credit rating

 self-reported financial constraint [likert scale - 5]  financial management practice [poor/good/better]

 the degree to which customer agree with a statement

[totally disagree/disagree/neutral/agree/totally agree]  What if these are our dependent variable?

 OLS: the variable has no quantitative meaning

A Case Study

3

 dependent variable: financial constraint of firms [f_con]

 1 = no obstacle  2 = minor obstacle

 3 = moderate obstacle  4 = major obstacle

 5 = severe obstacle

 independent variable:

Financial Constraint

4

Total 59,856 100.00

6,834 11.42 100.00 10,518 17.57 88.58 13,865 23.16 71.01 10,924 18.25 47.85 17,715 29.60 29.60 Freq Percent Cum. range to

The Ordered Probit model

5

 Let

 Higher indicates higher constraint

 Let be the categories of financial

constraint

 Decision rule

yi=1 if yi* ≤ u1

yi=2 if u1 < yi* ≤ u2 yi=3 if u2 < yi* ≤ u3 yi=4 if u3 < yi* ≤ u4 yi=5 if yi* > u4

*

an indicator of financial constraint

y 

*

y

1, 2, 3, 4, 5

y 

*

The Ordered Probit model

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 Assume is a function of X and error terms

 and critical values will be

estimated by the model

*

y

*

0 1 1 k k

y     x    x   X  

The Ordered Probit model

7

 Similar to logit and probit, whether the model is

ordered logit orprobit depends on the assumption on the distribution of the error terms

 logistic: ordered logit model  normal: ordered probit model

 Probit is more popular

The probability

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 Consider the case of Pr(yi=1)

   * 

1

Pr yi  1 Pr yi  u

   1

Pr yi  1 Pr xi  i u

   1 

Pr yi  1 Pr i  u xi

   1

Pr yi    1 1 xi  u

The probability

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 Now consider the case of Pr(yi=5)

   * 

4

Pr yi  5  Pr yi  u

   4 

Pr yi  5  Pr xi  i u

   4 

Pr yi  5  Pr i  u  xi

   4   4 

Probability of y=3

10

   * 

2 3

Pr yi  3  Pr u  yi  u

 *   * 

3 2

Pr yi u Pr yi u

   

 3   2 

Pr xi i u Pr xi i u

     

 3   2 

Pr i u xi Pr i u xi

     

u3 xi  u2 xi 

     

 3   2 

1 xi u 1 xi u

       

 xi u2  xi u3 

The probabilities

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









   1

Pr yi    1 1 xi  u

   4 

Pr yi  5   xi  u

   2   3 

Pr yi  3   xi  u   xi  u

   1  2 

Pr yi  2   xi  u   xi  u

   3   4 

Likelihood function

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

 

ln Pr

k i

i k

LL  Y  y  k 

1 0

i k

if y k

Y

if otherwise

Financial Constraint

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Total 59,856 100.00

6,834 11.42 100.00 10,518 17.57 88.58 13,865 23.16 71.01 10,924 18.25 47.85 17,715 29.60 29.60 Freq Percent Cum. range to

The case study: summary stat

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fsize_l 50890 .1976223 .3982096 1

fsize_m 50890 .3147966 .4644394 1

fsize_s 50890 .4875811 .4998507 1

f_par 55997 .3555369 47868 1

Bivariate analysis

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100.00 100.00 100.00 Total 49,705 6,095 55,800 36.39 28.42 35.52 18,088 1,732 19,820 63.61 71.58 64.48 31,617 4,363 35,980 ion Total participat foreign ownerhsip

female

Bivariate analysis

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100.00 100.00 100.00 100.00 100.00 100.00 Total 16,194 9,929 12,400 8,796 5,630 52,949 36.23 35.02 36.50 36.89 35.65 36.11 5,867 3,477 4,526 3,245 2,007 19,122 63.77 64.98 63.50 63.11 64.35 63.89 10,327 6,452 7,874 5,551 3,623 33,827 ion Total participat financial constraint; range to

female

ORDERED PROBIT IN STATA

oprobit f_con own_f0 f_par fsize_s fsize_m fsize_l

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/cut4 1.359213 .0144248 1.330941 1.387485 /cut3 7180097 .0134373 .691673 .7443463 /cut2 1126264 .013135 0868823 .1383705 /cut1 -.3725456 .0132426 -.3985006 -.3465907 fsize_l (omitted)

Hypothesis testing

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 Likelihood ratio tests is applied in oprobit and

ologit

Prob > chi2 = 0.0000 chi2( 2) = 381.59 ( 2) [f_con]fsize_m = 0

Interpreting the coefficients

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 For y = 5

 For y = 3

   4   

4

Pr 5 

           i i i i i

y x u

x u x x

     

3 4

Pr i 3

i i

i

y

x u x u x     

 

 

     

Marginal effects

mfx compute, predict(outcome(5))

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(*) dy/dx is for discrete change of dummy variable from to

fsize_m* .0256648 00299 8.59 0.000 .019807 031523 .320061 fsize_s* .0510257 00275 18.56 0.000 .045637 056414 .468961 f_par* -.0017725 00206 -0.86 0.389 -.005803 002258 .366149 own_f0* -.0347317 00263 -13.20 0.000 -.039889 -.029575 .117813 variable dy/dx Std Err z P>|z| [ 95% C.I ] X = 11131648

Interpreting the marginal effects

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 Foreign owned firms has probability of severe financial

constraint lower by 3.4 percentage points.

 Firms owned by female and male have now difference

in probability of severe financial constraint.

 Small firms has probability of severe financial

constraint higher than large firms by 5.1 percentage points.

 Medium firms has probability of severe financial

constraint higher than large firms by 2.6 percentage points.

Marginal effects at a value point

mfx compute, predict(outcome(5)) at(own_f0=0 f_par=1)

22

(*) dy/dx is for discrete change of dummy variable from to

fsize_m* .0262124 00305 8.59 0.000 .02023 032195 .320061 fsize_s* .0521237 00283 18.45 0.000 .046585 057662 .468961 f_par* -.0018241 00212 -0.86 0.389 -.005972 002324 own_f0* -.0344659 00261 -13.19 0.000 -.039587 -.029345 variable dy/dx Std Err z P>|z| [ 95% C.I ] X = .1147311

Application of Ordered Probit Model

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Bendig&Arun (2011) Microfinance Services and Risk

Management: Evidence from Sri Lanka J of Economic Development 36(4): 97-126.

 Data: 330 households in Sri Lanka 2008

 dependent variable: number of financial services used [0,

1, 2, 3]

 the services include saving, loan, and insurance  independent variables

 attitude toward risk

 economic conditions variables  natural disasters and risk

Application of Ordered Probit Model

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Gogas et al (2014) Forecasting Bank Credit Ratings J

of Risk Finance 15(2):185-209

 forecast US banks’ credit ratings [Fitch] using

publicly available information

 dependent variable: the rating  independent variables:

 assets and liabilities  income and expenses  performance

Application of Ordered Probit Model

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Hogarth&Anguelov (2004) Are Families who use E-banking Better Financial Managers? Financial Counseling &

Planning 15(2):61-77.

 Data: US Survey of Consumer Finances 2001, 4449 HHs  dependent variables: Financial management practice,

generated from

 use of banking services

 spending and saving behaviors  credit behaviors

 planning behavior

 consumer skills in credit/borrowing/investment

Application of Ordered Probit Model

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 independent variables

 e-banking products and services  socioeconomic characteristics

Application of Ordered Probit Model

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Asiedu et al (2013) Assess to Credits by Firms in Sub-Saharan Africa: How Relevant is Gender? American Economic

Review 103(3): 293-7.

 data: 34,000 firms from 90 developing countries  dependent variable: financial constraint

 1) no obstacle  2) minor obstacle

 3) moderate obstacle  4) major obstacle

 5) severe obstacle

 dependent variable: