Bài 12: Nội sinh và biến công cụ

 contract’s characteristics (prices, collateral, loan terms)  relationship (bank-firm years of relationship).  bank’s characteristics[r]

ENDOGENEITY AND

INSTRUMENTAL VARIABLE REGRESSION

Endogeneity  OLS assumption

 When :

Endogeneity problem

 | X  0

    2

V  | X  

 | X  0 or   X 0

Reasons for Endogeneity  errors in variables

Consequences of endogeneity

 If we use OLS in a regression with endogeneity:

BIASED AND INCONSISTENT ESTIMATES

x y

ε

y

x x

 

 

 

 

Endogeneity: errors in variables  Consider a regression

 We can’t observe , but  Then the regression becomes

y   x 

 y x,  y x*, *

*

y  y  v

*

x  x  u

 

* ˆ * ˆ ˆ

y   x   y   x    v u

*

Endogeneity: Endogenous variables

 Consider a (market) demand equation

is not exogenous by theory

 Instead, it should be the supply-demand system

1 2

d d

q   p  y u

1 2

d d

q   p  y u p

1

s s

q   p u

s d

q  q

2

1 1 1 1

d s

u u

p  y

   



 

 

  2

1 1

0

d

u d

u p 

 

  

Endogeneity: Omitted variables  Suppose the true model is

 If we regress

0 1 1 2 2

y     x   x 

0 1 1 omitted variable: 2

y     x   x

2 2

then   x 

 1  1 2 

Solution to Endogeneity: Instruments

 Instrumental variables (instruments) Z must satisfy

 exogeneity (uncorrelated with or )  relevance (correlated with )

u y

Identification problem

 If is the number of endogenous variables, and is the number of instruments, then

 If the model is unidentified  If the model is just-identified  If the model is over-identified

k

h

IV Estimation

 If is the number of endogenous variables, and is the number of instruments, then

 If find the instrument!!!

 If use IV estimator

 If use 2SLS or GMM

k

h

Two-Stage Least Square (2SLS)  Consider a regression

where is endogenous

 if is used as instruments Then the procedure is

 Step 1: Regress each endogenous variable on

and

 Step 2: Compute the fitted values

 Step 3: Regress

1 2 y    X   X  X Z X X Z

2 1

x    X  Z v

2 ˆ0 ˆ1 ˆ2 ˆx    X  Z

1 ˆ2

The wage equation

 ed: education

 X: other control variables

 Endogeneity: missing important variable of ability

 ability is believed to be correlated with ed.

 

Summary statistics

year 20306 2001.088 1.61576 1999 2003

h 20306 2022.203 706.4409 5508

married 20306 660002 .4737198 1

nch 20306 .9591746 1.137898 8

race 20306 1.410618 .6499018 3

mo_ed 20306 1.844726 .6290755 3

fa_ed 20306 1.83857 .6961686 3

ed 20306 13.4512 2.488962 17

union 20306 .1518763 .3589098 1

tenure 20306 6.359746 7.725706 42

wage 20306 20.08589 19.17634 491

age 20306 39.01532 9.901983 21 59

OLS Regression

Testing for endogeneity

 regress ed on X and IV variables

 predict error terms e

 regress with e included

 endogeneity if e is statistically significant

 

ln wage  f ed X,  

 var, 

ed  f IV X  e

 

Testing for endogeneity

 quietly regress ed age age2 tenure union nch married

white black fa_ed1 fa_ed2 mo_ed1 mo_ed2 year2001 year2003

 predict ed_hat, xb /* find the fitted value of ed*/

 predict r, resid /* find the error variance of the

model*/

 regress lnwage ed age age2 tenure union nch married

Testing for endogeneity

_cons -.2893795 .0781816 -3.70 0.000 -.4426218 -.1361372 r -.0745455 .0048828 -15.27 0.000 -.0841163 -.0649748 year2003 -.0092245 .0092467 -1.00 0.318 -.0273487 .0088997 year2001 -.000035 .0092487 -0.00 0.997 -.0181632 .0180932 black -.1986132 .0159947 -12.42 0.000 -.229964 -.1672624 white -.0707782 .0163623 -4.33 0.000 -.1028496 -.0387068 married 0142878 .008775 1.63 0.103 -.002912 .0314876 nch 0253419 .0038428 6.59 0.000 0178097 .0328742 union 1061971 .0107717 9.86 0.000 0850837 .1273104 tenure 011755 .0005423 21.68 0.000 0106921 .0128179 age2 -.0004601 .0000409 -11.26 0.000 -.0005401 -.00038 age 0444652 .0032132 13.84 0.000 038167 .0507634 ed 1527935 .0045929 33.27 0.000 143791 161796 lnwage Coef Std Err t P>|t| [95% Conf Interval]

Prob > F = 0.0000 F( 1, 20293) = 233.08 ( 1) r = 0

2SLS IV Regression [Manually]

Testing for good instruments  quietly regress ed age age2 tenure union nch

married white black fa_ed1 fa_ed2 mo_ed1

mo_ed2 year2001 year2003

Prob > F = 0.0000 F( 4, 20291) = 660.56 ( 4) mo_ed2 = 0

( 3) mo_ed1 = 0 ( 2) fa_ed2 = 0 ( 1) fa_ed1 = 0

Implement IV reg in Stata

 ivreg lnwage age age2 tenure union nch married white black year2001 year2003 (ed = fa_ed1

Implement IV reg in Stata

_cons 10.03607 .2575517 38.97 0.000 9.531245 10.54089 mo_ed2 1.221048 .0654893 18.65 0.000 1.092684 1.349412 mo_ed1 5029502 .0450191 11.17 0.000 4147092 .5911912 fa_ed2 1.833566 .0582525 31.48 0.000 1.719386 1.947746 fa_ed1 6310663 .0429161 14.70 0.000 5469473 .7151854 year2003 -.0024599 .0391737 -0.06 0.950 -.0792435 .0743237 year2001 -.0107218 .0391791 -0.27 0.784 -.0875159 .0660724 black 8421189 .0659016 12.78 0.000 7129464 .9712914 white 1.072611 .0633436 16.93 0.000 9484524 1.19677 married 3649581 .0366104 9.97 0.000 2931988 .4367174 nch -.2159402 .0156491 -13.80 0.000 -.2466137 -.1852667 union 074779 .0456544 1.64 0.101 -.0147073 .1642652 tenure 0054745 .0022971 2.38 0.017 0009721 009977 age2 -.0004542 .0001726 -2.63 0.009 -.0007926 -.0001158 age 053069 .0135771 3.91 0.000 0264568 .0796812 ed Coef Std Err t P>|t| [95% Conf Interval]

Implement IV reg in Stata

SECOND STAGE

Hausman test OLS agaisnt IV  regress lnwage ed age age2 tenure union nch

married white black year2001 year2003  est store OLS

 ivreg lnwage age age2 tenure union nch married white black year2001 year2003 (ed = fa_ed1

fa_ed2 mo_ed1 mo_ed2), first  est store IV

Hausman test OLS agaisnt IV

year2003 -.0092245 -.006866 -.0023585 .0027505

year2001 -.000035 0009202 -.0009552 .0027474 black -.1986132 -.1106727 -.0879405 .0074915 white -.0707782 0655964 -.1363746 .0102137 married 0142878 0362749 -.0219871 .0029815 nch 0253419 010029 .0153129 .0015232 union 1061971 1102531 -.004056 .0032101 tenure .011755 0120222 -.0002671 000162 age2 -.0004601 -.0005048 .0000447 .0000125 age 0444652 047922 -.0034568 .0009811 ed 1527935 0868367 .0659568 004554

IV OLS Difference S.E

(b) (B) (b-B) sqrt(diag(V_b-V_B)) Coefficients

hausman IV OLS /*note the order of IV and OLS*/

Prob>chi2 = 0.0000 = 209.77

OLS vs IV – the contribution of ed

Relationship and credit limit

Chakraborty et al (2010) The Importance of Being Known: Relationship Banking and Credit Limits

Quarterly J of Finance and Accounting 49(2) 27-48.

 Objective: investigate the effect of relationship on credit limits given to firms

Relationship and credit limit Chakraborty et al (2010)

 Indep var:

 contract’s characteristics (prices, collateral, loan terms)  relationship (bank-firm years of relationship)

 bank’s characteristics

 Endogeneity: credit limit (dep var) and contract’s

characteristics are determined simultaneously

 Istrumented vars: contract’s characteristics (interest rate

and collateral)

Bank loan and trade credit Du et al (2012) Bank Loan vs Trade Credit –

Evidence from China Economics of Transition 20(3): 457-80

 Objective: effects of bank loan and trade credit on firm performance and growth

Bank loan and trade credit  Dep var:

 labor productivity: output per worker [in log]  ROA

 change in employment [in log]

 reinvestment rate [share of profit reinvested]

 Indep var

 bank loan [ratio of bank loan to total asset]

 trade credit [% purchased with credit of two main

inputs]

Bank loan and trade credit

 Instrumented variables: bank loan and trade credit  Endogeneity:

 reverse causality  spurious correlation

 Instrumental variables:

 for trade credit: relationship [dummy, if the two main inputs are supplied by relatives or friends]

 previous studies showed that suppliers are more likely to offer trade

credit when customers are in the same network

 for bank loan: British administration [dummy, if the located city is administered by GB in the Qing dynasty]

 reason: GB during their administration develop their own bank

Incentive Contracts and Bank Performance

Li et al (2007) Incentive Contracts and Bank Performance – Evidence from Rural China

Economics of Transition 15(1): 109-24.

 Objective: the effect of incentive to bank’s manager to bank performance.

 Data: bank branches in rural China  Dep var:

 deposit growth

Incentive Contracts and Bank Performance

 Indep var:

 the amount of money given to manager per

performance point

 branch size [asset value]

 town’s industrial development [per capita industrial

output]

Incentive Contracts and Bank Performance

 Endogeneity: omitted variables, such as manager’s ability

 Instrumented variable: incentive