Title: Instrumental Variables IV
1????????? / ?????????????? ????? ???
Instrumental Variables (IV)
2????????? - ??????? ??????
?? ?? ??? (?? "????" ???) ??????? ??? ?- X??
???? ??????? ???????, ??? ?????? ? - OLS ?? ?????
?????? ??????.
3??? ??? ?-X ???? ??????? ???????
- ?????? ????????
- ????? ??????
- ??????? ??????????
- ?? ???? ???, ???? ????? ???? ??????
- ????? ?????, ???? ?"?????? ?????" ?-X
4 Errors in Variables "?????? ?????"
x ??? ?????? ??????, ?? ??? ????? ????, ??????
?????? ?? x . ??????, x "?????" (?? ???
?????), ?? x ???? ????? ???????, ??????? ???,
y.
5?????? ????? ????? ?????
6?????? ????? ????? ????? - ????
7????? - ????
- ?????, ????? ???? ?????? ????, ????? ??? ?- su2
???? ???? ???? ? sx2 ????? ????? ????? ????
????. - ?? ??? ????? ????? ??????? ????? ??????
???????? ?? u. ????? ??? - bias (coefficient of omitted on included 1)
times (coefficient of omitted -beta) -beta
- ???? ??????? ?? ????? ?? ???? ???????????
?????, ???? ?? su2 ??? ??? ???? ???.
8???? ?- IV ????? ????? ?? "?????? ?????"
y ????? x - ????? ??????, ??? ???? ?? ??????
????? (?? ??????? ?? ?? ??????) x ????? ??????
???? ????? ????? z, ?????? ?? x ?? ?? ?? u
(??? ?? e ). ????? ?- z ???? ????? ?????? ?"?
????.
9???? IV
10IV ???? ?????
??? ??,
??? bols ?? ????,
11????? ????? IV
???? ?????? ?? ????? ??? Z (???? ?- Z?? ?????
?- X??), ?? ?-
???? ?? ????? IV ?????? ??? Z,
12????? IV ????
??? ????? ??? ? X?? ? Z ?? ??? ????, ???? ???, ??
????? ???? ???? (??? ???? ?- (ZX!
13????? ?????? ??????????? ?? ????? IV
??? ? X ? Z ??????? ??? ????, ?????? ??"? ?????
???? ????. ?????? ?? ????? ????? ???, ????
??????? ?? ??????!
14Endogeneity Simultaneity Bias
????? ??????? ?????? ????? ???? ??????? ???
???????? ?? ???? ????? ?? "?????" ?? ???? ???,
??? ???? ????? (???? ?????? 6). ????? ??????
?-IO, ?????? ????? ??????? ???????, ???? PCs ??
????????. ????
si ??? ??? ?? ?- brand ?- i ???? ??????? ??????
x , ?????? ??????? ?? ????? ??????? ? ei
?????, PCs ???? ????? ???? ????? ???? ????
????? ????), ??? ?? ????? ?? ?????? ?????? ?? ??
?????
15???? ??? ????? ?? ????
S
P
P
??? ?? ???? ??? ??? P ? e) ????? ?? ?????? ???
????), ??? ????? ????? ?????? ????? ? a (????
?? ???? ????? ?????!).
16????? IVs ????? ??
???? ?????? ????? ??????? ?? ????? ?? ?? ??
?????? ??? ???? (??? ??????? ??????). ???? ?????
?-PC ????? ???? ???????
F frontier (latest technology) B brand
(e.g. IBM, HP, Compaq) N no (e.g. NB no
brand clone)
17IVs ??????? ?? ????, ?? ?? ??????? ?? ?????
- ???? ??????? ?? ????? ??????, ??? ????? ???????
?????? ???? ????? ???? (?? ???? ??????). - ??"? ???? ? - Xs ?? ?????? ??? ??????? ??????
?? ??????? ????, ?? ????? ????. - ??? ????? ??????? ?? ?? ????? ???? ?? ????? ???,
?? ????? ????. - ??"? ???? ? - Xs ?? ?????? ??? ??????? ??????
?? ????? ?????? ????, ?? ????? ????.
18IV ?????? ?? ???? - ????
?????? ????? ????? ????? IV ?????? ??????, ????
??? ?????! ?? ????? panel, ?? ???? ???????
(entry) ???? ?? ????? ??????? ??? ????? (???????
??????), ??? ?? ???? ?? X?? ????????.
19??????? ??????????
- ????? ?? ??????? ????????
- ?????? ????????? ?????????
- ?????? ???? ????? ?????? ????? ????????
Structural equations vs. reduced form
??????? ????? ?????? ?? ????? ?????
20????? ????????
21?????????? ????? ??????
- ???? ????? ?? P ??? ??????? ?? ed ??? es, ??? ??
?? ?????? ?? ??? ???????? ????? ???? ???? ??????
????? ??? ??????. - ?? ???? ?????? (????? ??????) .
- ??? ????? ?? ????? ???? IV ?????? ?? (ILS, TSLS)
- ?? exactly identified, ??? ILS ??? ? IV. ?????
???? ????? ?? ??????? ?? ??????? ????? ??????
????? ????????.
22????? ????? - ????
- ????? ????? ?- TSLS
- ??? ???? ?????? ?? ?? ????? ???? (????
X?? ??????? ?????) - ?? ?????? ?? ??????? ??????????
Limited Information ?? ?????? ????. Full
Information ???? ??? 3SLS - ????? ????? - ????
????? ??? ????????? ?? over identified.
23Hausman Test ???? ??????????? (???? ???? Wu)
???? ??? ???? ?? ????? ?????
?? ?????? ?? ???? ????? (?? ?????), ?? ????
?????? ?????? ????? ???????? ???? p (?? ????
???? q)
24???? Hausman - ????
?? ??? ??????????, ??? ??? "??? ???", ??
????? ?? ??????, ??? ?? ???? ?????
??????????? ?????,
?????? (????? ???? ????? ??????????),
25???? ?????