Tải bản đầy đủ (.pdf) (35 trang)

Bài 12: Nội sinh và biến công cụ

Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (714.95 KB, 35 trang )

(1)

ENDOGENEITY AND



INSTRUMENTAL VARIABLE


REGRESSION




(2)

Endogeneity


OLS assumption



When

:



Endogeneity problem



|

X

0



2



V

| X



|

X

0 or

 

X

0




(3)

Reasons for Endogeneity


errors in variables




(4)

Consequences of endogeneity



If we use OLS in a regression with endogeneity:



BIASED AND INCONSISTENT ESTIMATES



x

y




ε



y



x

x








 






(5)

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



*




(6)

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



 






(7)

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




(8)

Solution to Endogeneity:


Instruments



Instrumental variables (instruments) Z must satisfy



exogeneity (uncorrelated with or )


relevance (correlated with )



u

y




(9)

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





(10)

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




(11)

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 1 2 2

y

 

 

X

X


2

X


Z


2

X


1

X

Z



2 0 1 1 2


x

X

Z

v



2

ˆ

0

ˆ

1 1

ˆ

2

ˆx

X

Z



1 1 2

ˆ

2



(12)

(13)

The wage equation



ed: education



X: other control variables



Endogeneity: missing important variable of

ability



ability is believed to be correlated with ed.







(14)

Summary statistics



year 20306 2001.088 1.61576 1999 2003



h 20306 2022.203 706.4409 1 5508



married 20306 .660002 .4737198 0 1




nch 20306 .9591746 1.137898 0 8



race 20306 1.410618 .6499018 1 3



mo_ed 20306 1.844726 .6290755 1 3



fa_ed 20306 1.83857 .6961686 1 3



ed 20306 13.4512 2.488962 0 17




union 20306 .1518763 .3589098 0 1



tenure 20306 6.359746 7.725706 0 42



wage 20306 20.08589 19.17634 5 491



age 20306 39.01532 9.901983 21 59





(15)

OLS Regression




(16)

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






(17)

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




(18)

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





(19)

2SLS IV Regression [Manually]




(20)

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




(21)

Implement IV reg in Stata



. ivreg lnwage age age2 tenure union nch married


white black year2001 year2003 (ed = fa_ed1




(22)

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]



(23)

Implement IV reg in Stata



SECOND STAGE




(24)

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





(25)

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



(26)

OLS vs. IV – the contribution of ed





(27)

(28)

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




(29)

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)




(30)

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




(31)

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]




(32)

Bank loan and trade credit



Instrumented variables: bank loan and trade credit


Endogeneity:




reverse causality


spurious correlation



Instrumental variables:



for trade credit: relationship [dummy, 1 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, 1 if the located


city is administered by GB in the Qing dynasty]



reason: GB during their administration develop their own bank




(33)

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




(34)

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]




(35)

Incentive Contracts and Bank


Performance



Endogeneity: omitted variables, such as manager’s


ability



Instrumented variable: incentive






×