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

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 Many discrete outcomes have natural ordering

 credit rating

 self-reported financial constraint [likert scale 1 - 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

 MNL: appropriate for non-ordinal discrete variable

 ORDERED PROBIT MODEL

 foreign ownership [own_f0]

 female participation [f_par]

 dummy for small firm [fsize_s]

 dummy for medium firm [fsize_m]

 dummy for large firm [fsize_l]

Financial Constraint

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Total 59,856 100.00

4 Freq Percent Cum range 0 to

constraint;

financial tab f_con

The Ordered Probit model

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 Let

 Higher indicates higher constraint

The Ordered Probit model

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 Assume is a function of X and error terms

estimated by the model

The Ordered Probit model

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 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



i k

Financial Constraint

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Total 59,856 100.00

4 Freq Percent Cum range 0 to

constraint;

financial tab f_con

The case study: summary stat

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fsize_l 50890 .1976223 .3982096 0 1

fsize_m 50890 .3147966 .4644394 0 1

fsize_s 50890 .4875811 .4998507 0 1

f_par 55997 .3555369 47868 0 1

own_f0 62289 .1224293 .3277836 0 1

Variable Obs Mean Std Dev Min Max sum own_f0 f_par fsize_s fsize_m fsize_l

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

1 18,088 1,732 19,820 63.61 71.58 64.48

0 31,617 4,363 35,980 ion 0 1 Totalparticipat foreign ownerhsip

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

1 5,867 3,477 4,526 3,245 2,007 19,122 63.77 64.98 63.50 63.11 64.35 63.89

0 10,327 6,452 7,874 5,551 3,623 33,827 ion 1 2 3 4 5 Totalparticipat financial constraint; range 0 to 4

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 0 (omitted)

fsize_m 1314779 .0148557 8.85 0.000 1023613 .1605944 fsize_s 2660076 .0140379 18.95 0.000 2384939 .2935213 f_par -.0093605 .0108761 -0.86 0.389 -.0306773 .0119563 own_f0 -.2015443 .0168015 -12.00 0.000 -.2344746 -.168614 f_con Coef Std Err z P>|z| [95% Conf Interval]

Log likelihood = -64297.123 Pseudo R2 = 0.0049 Prob > chi2 = 0.0000

LR chi2(4) = 628.23Ordered probit regression Number of obs = 41464

( 2) [f_con]fsize_m = 0 ( 1) [f_con]fsize_s = 0 test fsize_s fsize_m

Interpreting the coefficients

y = Pr(f_con==5) (predict, outcome(5))

Marginal effects after oprobit

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.

at mean

Marginal effects at a value point

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

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(*) dy/dx is for discrete change of dummy variable from 0 to 1

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 1 own_f0* -.0344659 00261 -13.19 0.000 -.039587 -.029345 0 variable dy/dx Std Err z P>|z| [ 95% C.I ] X = .1147311

y = Pr(f_con==5) (predict, outcome(5))

Marginal effects after oprobit

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

 individual characteristics

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

 conditions

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

to generate a 3-order dependent variable [fair/good/better]

Application of Ordered Probit Model

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