Microsoft Word - EC655 Practice Questions.docx
EC655 Practice Questions
Fall 2020
1) In an influential paper relating log weekly wages (LWKLYWGE) to years of schooling (EDUC),
Angrist and Krueger XXXXXXXXXXinstrumented years of schooling with a person’s quarter of birth.
The idea behind the instrument is that people born in first quarter of the year will have fewer
years of total schooling because they reach the legal school exit age before students born later
in the year. As the excluded instruments in the regression, the authors created three quarter of
irth dummy variables (QTR1, QTR2, QTR3) and then interacted them with a set of dummy
variables for a person’s year of birth (Y20, Y21, …, Y29), for a total of 30 excluded instruments
(the uninteracted year dummy variables are included instruments).
A replication of their two-stage least squares results is below, which includes the first stage,
second stage, and several additional statistics. Comment on their results.
. ivreg2 LWKLYWGE YR20-YR28 (EDUC = QTR120-QTR129 QTR220-QTR229 QTR320-QTR329), ffirst
obust first
First-stage regressions
-----------------------
First-stage regression of EDUC:
Statistics robust to heteroskedasticity
Number of obs = XXXXXXXXXX329509
------------------------------------------------------------------------------
| XXXXXXXXXXRobust
XXXXXXXXXXEDUC | Coef. Std. E
. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
QTR120 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR121 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR122 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR123 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR124 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR125 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR126 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR127 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR128 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR129 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR220 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR221 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR222 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR223 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR224 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR225 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR226 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR227 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR228 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR229 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR320 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR321 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR322 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR323 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR324 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR325 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR326 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR327 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR328 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
QTR329 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXYR20 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXYR21 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXYR22 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXYR23 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXYR24 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXYR25 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXYR26 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXYR27 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXXYR28 | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
_cons | XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
------------------------------------------------------------------------------
F test of excluded instruments:
F( 30,329469) = XXXXXXXXXX
Prob > F = XXXXXXXXXX
Sanderson-Windmeijer multivariate F test of excluded instruments:
F( 30,329469) = XXXXXXXXXX
Prob > F = XXXXXXXXXX
Summary results for first-stage regressions
-------------------------------------------
XXXXXXXXXXUnderid XXXXXXXXXXWeak id)
Variable | F( 30, XXXXXXXXXXP-val | SW Chi-sq( 30) P-val | SW F( 30,329469)
EDUC | XXXXXXXXXX0000 | XXXXXXXXXX0000 | XXXXXXXXXX
NB: first-stage test statistics heteroskedasticity-robust
Stock-Yogo weak ID F test critical values for single endogenous regressor: