ECON 626: Applied Microeconomics. Lecture 4: Instrumental Variables
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1 ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables Professors: Pamela Jakela and Owen Ozer Department of Economcs Unversty of Maryland, College Park
2 Wald When two varables are measured wth error, how do we estmate ther true relatonshp? ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 3
3 Wald Underlyng relatonshp y x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 4
4 Wald Underlyng relatonshp, estmated y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 4
5 Wald Nose n Y y x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 5
6 Wald Nose n Y, estmated y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 5
7 Wald - attenuaton bas Nose n X y x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 6
8 Wald - attenuaton bas Nose n X, estmated: attenuaton bas y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 6
9 Wald - attenuaton bas Nose n both Y and X y x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 7
10 Wald - attenuaton bas Nose n X, estmated: attenuaton bas y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 7
11 Wald - attenuaton bas Suppose we have one more pece of nformaton: whether, for each observaton, the underlyng x value (wthout the measurement error) s above or below 0.5. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 8
12 Wald - attenuaton bas Suppose we have one more pece of nformaton: whether, for each observaton, the underlyng x value (wthout the measurement error) s above or below 0.5. Ths nformaton wll prove to be an nstrument. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 8
13 Wald - overcomng attenuaton bas Nose n X, estmated: attenuaton bas y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 9
14 Wald - overcomng attenuaton bas Nose n both Y and X y x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 9
15 Wald - overcomng attenuaton bas Grouped observatons y x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 9
16 Wald - overcomng attenuaton bas Grouped observatons wth group means y x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 9
17 Wald - overcomng attenuaton bas Grouped observatons wth Wald estmator y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 9
18 Wald - overcomng attenuaton bas Grouped observatons wth Wald estmator, 50 obs (I) y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 10
19 Wald - overcomng attenuaton bas Grouped observatons wth Wald estmator, 50 obs (II) y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 11
20 Wald - overcomng attenuaton bas Grouped observatons wth Wald estmator, 50 obs (III) y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 11
21 Wald - overcomng attenuaton bas Grouped observatons wth Wald estmator, 50 obs (IV) y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 11
22 Wald - overcomng attenuaton bas Grouped observatons wth Wald estmator, 1000 obs y estmated b: x ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 12
23 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 13
24 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 13
25 Wald - extendng to endogenety Data generatng process: Z U(0, 2) ν 1, ν 2, ν 3 N (0, 1)..d. ξ = 2ν ν 1 η = 3ν ν 2 ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 14
26 Wald - extendng to endogenety Data generatng process: Z U(0, 2) ν 1, ν 2, ν 3 N (0, 1)..d. ξ = 2ν ν 1 η = 3ν ν 2 ξ and η not ndependent; strongly negatvely correlated. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 14
27 Wald - extendng to endogenety Data generatng process: Z U(0, 2) ν 1, ν 2, ν 3 N (0, 1)..d. ξ = 2ν ν 1 η = 3ν ν 2 ξ and η not ndependent; strongly negatvely correlated. X = Z + ξ Y = X + η ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 14
28 Wald - extendng to endogenety Data generatng process: Z U(0, 2) ν 1, ν 2, ν 3 N (0, 1)..d. ξ = 2ν ν 1 η = 3ν ν 2 ξ and η not ndependent; strongly negatvely correlated. X = Z + ξ Y = X + η Begn Wald approach by consderng a splt based on whether Z > 1. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 14
29 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 15
30 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 15
31 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 15
32 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 15
33 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 15
34 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 16
35 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 16
36 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 17
37 Wald - extendng to endogenety ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 17
38 Instrumental varables scenaros ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 18
39 Instrumental varables scenaros Problem: measure the causal casual effect of X end on Y. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 18
40 Instrumental varables scenaros Problem: measure the causal effect of X end on Y. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 18
41 Instrumental varables scenaros Problem: measure the causal effect of X end on Y. Inconsstency of least-squares methods when: measurement error n regressors, smultanety, or when causal equaton (Y ) error term s correlated wth X end (omtted varables). Dscusson n Cameron and Trved, secton 6.4, and Angrst and Pshke chapter 4. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 18
42 Instrumental varables scenaros Problem: measure the causal effect of X end on Y. Inconsstency of least-squares methods when: measurement error n regressors, smultanety, or when causal equaton (Y ) error term s correlated wth X end (omtted varables). Dscusson n Cameron and Trved, secton 6.4, and Angrst and Pshke chapter 4. Example: X end s schoolng; Y s wage; ablty drves both Y and X end, so may bas cross-sectonal regresson of Y on X end. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 18
43 Instrumental varables scenaros Problem: measure the causal effect of X end on Y. Inconsstency of least-squares methods when: measurement error n regressors, smultanety, or when causal equaton (Y ) error term s correlated wth X end (omtted varables). Dscusson n Cameron and Trved, secton 6.4, and Angrst and Pshke chapter 4. Example: X end s schoolng; Y s wage; ablty drves both Y and X end, so may bas cross-sectonal regresson of Y on X end. Example: X end s number of chldren; Y s labor force partcpaton; nclnaton to reman outsde the formal labor force drves Y down and X end up, so may bas cross-sectonal regresson of Y on X end. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 18
44 Instrumental varables scenaros Problem: measure the causal effect of X end on Y. Inconsstency of least-squares methods when: measurement error n regressors, smultanety, or when causal equaton (Y ) error term s correlated wth X end (omtted varables). Dscusson n Cameron and Trved, secton 6.4, and Angrst and Pshke chapter 4. Example: X end s schoolng; Y s wage; ablty drves both Y and X end, so may bas cross-sectonal regresson of Y on X end. Example: X end s number of chldren; Y s labor force partcpaton; nclnaton to reman outsde the formal labor force drves Y down and X end up, so may bas cross-sectonal regresson of Y on X end. Example: X end s medcal treatment; Y s health; pror llness drves Y down and X end up, so may bas cross-sectonal regresson of Y on X end. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 18
45 Instrumental varables bascs ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 19
46 Instrumental varables bascs Termnology of Instrumental Varables ( IV ) approach: ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 19
47 Instrumental varables bascs Termnology of Instrumental Varables ( IV ) approach: Frst stage: Z affects X end ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 19
48 Instrumental varables bascs Termnology of Instrumental Varables ( IV ) approach: Frst stage: Z affects X end Excluson restrcton: Z ONLY affects Y va ts effect on X end ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 19
49 Instrumental varables bascs Termnology of Instrumental Varables ( IV ) approach: Frst stage: Z affects X end Excluson restrcton: Z ONLY affects Y va ts effect on X end Z: nstrument(s) or excluded nstrument(s) Y : dependent varable or endogenous dependent varable X end : endogenous varable or endogenous regressor ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 19
50 Instrumental varables bascs Termnology of Instrumental Varables ( IV ) approach: Frst stage: Z affects X end Excluson restrcton: Z ONLY affects Y va ts effect on X end Z: nstrument(s) or excluded nstrument(s) Y : dependent varable or endogenous dependent varable X end : endogenous varable or endogenous regressor What about other covarates? X ex : covarates or exogenous regressors (Frst stage and excluson restrcton now condtonal on X ex.) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 19
51 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
52 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end + X ex α + η (causal model) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
53 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end E[η X ex + X ex α + η (causal model) ] = 0; E[ξ 1 X ex ] = 0; E[η ξ 1 X ex ] 0; E[η Z, X ex ] = 0; ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
54 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end E[η X ex + X ex α + η (causal model) ] = 0; E[ξ 1 X ex ] = 0; E[η ξ 1 X ex ] 0; E[η Z, X ex ] = 0; Y = ρ(π 11 Z + X ex π 10 + ξ 1 ) + X ex α + η ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
55 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end E[η X ex + X ex α + η (causal model) ] = 0; E[ξ 1 X ex ] = 0; E[η ξ 1 X ex ] 0; E[η Z, X ex ] = 0; Y = ρ(π 11 Z + X ex π 10 + ξ 1 ) + X ex α + η Y = ρπ 11 Z + X ex (ρπ 10 + α) + (ρξ 1 + η ) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
56 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end E[η X ex + X ex α + η (causal model) ] = 0; E[ξ 1 X ex ] = 0; E[η ξ 1 X ex ] 0; E[η Z, X ex ] = 0; Y = ρ(π 11 Z + X ex π 10 + ξ 1 ) + X ex α + η Y = ρπ 11 Z + X ex (ρπ 10 + α) + (ρξ 1 + η ) Y = π }{{} 21 ρπ 11 Z + X ex π 20 }{{} (ρπ 10+α) + ξ 2 }{{} (ρξ 1 +η ) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
57 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end E[η X ex + X ex α + η (causal model) ] = 0; E[ξ 1 X ex ] = 0; E[η ξ 1 X ex ] 0; E[η Z, X ex ] = 0; Y = ρ(π 11 Z + X ex π 10 + ξ 1 ) + X ex α + η Y = ρπ 11 Z + X ex (ρπ 10 + α) + (ρξ 1 + η ) Y = π 21 Z + X ex π 20 + ξ 2 ( Reduced form ) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
58 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end E[η X ex + X ex α + η (causal model) ] = 0; E[ξ 1 X ex ] = 0; E[η ξ 1 X ex ] 0; E[η Z, X ex ] = 0; Y = ρ(π 11 Z + X ex π 10 + ξ 1 ) + X ex α + η Y = ρπ 11 Z + X ex (ρπ 10 + α) + (ρξ 1 + η ) Y = π 21 Z + X ex π 20 + ξ 2 ( Reduced form ) ˆX end = ˆπ 11 Z + X ex ˆπ 10 (Estmated frst stage) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
59 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end E[η X ex + X ex α + η (causal model) ] = 0; E[ξ 1 X ex ] = 0; E[η ξ 1 X ex ] 0; E[η Z, X ex ] = 0; Y = ρ(π 11 Z + X ex π 10 + ξ 1 ) + X ex α + η Y = ρπ 11 Z + X ex (ρπ 10 + α) + (ρξ 1 + η ) Y = π 21 Z + X ex π 20 + ξ 2 ( Reduced form ) ˆX end = Z ˆπ 11 + X ex ˆπ 10 (Estmated frst stage) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
60 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end E[η X ex + X ex α + η (causal model) ] = 0; E[ξ 1 X ex ] = 0; E[η ξ 1 X ex ] 0; E[η Z, X ex ] = 0; Y = ρ(π 11 Z + X ex π 10 + ξ 1 ) + X ex α + η Y = ρπ 11 Z + X ex (ρπ 10 + α) + (ρξ 1 + η ) Y = π 21 Z + X ex π 20 + ξ 2 ( Reduced form ) ˆX end Y = ρ ( = Z ˆπ 11 + X ex ˆπ 10 (Estmated frst stage) end ˆX ˆX end + (X end )) }{{} X end +X ex α + η (plug nto causal model) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
61 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end E[η X ex + X ex α + η (causal model) ] = 0; E[ξ 1 X ex ] = 0; E[η ξ 1 X ex ] 0; E[η Z, X ex ] = 0; Y = ρ(π 11 Z + X ex π 10 + ξ 1 ) + X ex α + η Y = ρπ 11 Z + X ex (ρπ 10 + α) + (ρξ 1 + η ) Y = π 21 Z + X ex π 20 + ξ 2 ( Reduced form ) ˆX end = Z ˆπ 11 + X ex ˆπ 10 (Estmated frst stage) end Y = ρ( ˆX + (X end Y = ρ ˆX end ˆX end + X ex α + (η + ρ(x end )) + X ex α + η ˆX end )) ( Second stage ) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
62 Instrumental varables bascs X end = π 11 Z + X ex π 10 + ξ 1 ( Frst stage ) Y = ρx end E[η X ex + X ex α + η (causal model) ] = 0; E[ξ 1 X ex ] = 0; E[η ξ 1 X ex ] 0; E[η Z, X ex ] = 0; Y = ρ(π 11 Z + X ex π 10 + ξ 1 ) + X ex α + η Y = ρπ 11 Z + X ex (ρπ 10 + α) + (ρξ 1 + η ) Y = π 21 Z + X ex π 20 + ξ 2 ( Reduced form ) ˆX end = Z ˆπ 11 + X ex ˆπ 10 (Estmated frst stage) end Y = ρ( ˆX + (X end ˆX end )) + X ex α + η Y = ρ ˆX end + X ex α + (η + ρ(x end ˆX end )) ( Second stage ) Hence: Two-stage least squares, 2SLS or TSLS ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 20
63 Instrumental varables scenaros Example: quarter of brth / compulsory schoolng nstrument ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 21
64 Instrumental varables scenaros Example: quarter of brth / compulsory schoolng nstrument X end s schoolng (endogenous regressor); Y s wage (dependent var.); how do we fnd varaton n educaton that s not drven by the common (unobserved) causes of educaton and wage ( ablty )? ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 21
65 Instrumental varables scenaros Example: quarter of brth / compulsory schoolng nstrument X end s schoolng (endogenous regressor); Y s wage (dependent var.); how do we fnd varaton n educaton that s not drven by the common (unobserved) causes of educaton and wage ( ablty )? Z s quarter of brth (nstrument). Excluson restrcton? Frst stage? ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 21
66 Instrumental varables scenaros Example: quarter of brth / compulsory schoolng nstrument X end s schoolng (endogenous regressor); Y s wage (dependent var.); how do we fnd varaton n educaton that s not drven by the common (unobserved) causes of educaton and wage ( ablty )? Z s quarter of brth (nstrument). Excluson restrcton? Frst stage? Born n Q4: start school just before you turn 6. At age 16, you have completed 10+ years of school. Born n Q1: start school September after you turn 6. At age 16, you have completed 9 years and a few months of school. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 21
67 Instrumental varables scenaros Example: quarter of brth / compulsory schoolng nstrument X end s schoolng (endogenous regressor); Y s wage (dependent var.); how do we fnd varaton n educaton that s not drven by the common (unobserved) causes of educaton and wage ( ablty )? Z s quarter of brth (nstrument). Excluson restrcton? Frst stage? Born n Q4: start school just before you turn 6. At age 16, you have completed 10+ years of school. Born n Q1: start school September after you turn 6. At age 16, you have completed 9 years and a few months of school. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 21
68 Instrumental varables scenaros Example: quarter of brth / compulsory schoolng nstrument X end s schoolng (endogenous regressor); Y s wage (dependent var.); how do we fnd varaton n educaton that s not drven by the common (unobserved) causes of educaton and wage ( ablty )? Z s quarter of brth (nstrument). Excluson restrcton? Frst stage? Born n Q4: start school just before you turn 6. At age 16, you have completed 10+ years of school. Born n Q1: start school September after you turn 6. At age 16, you have completed 9 years and a few months of school. Fndng: wage returns to educaton va 2SLS slghtly larger than OLS. (Angrst and Krueger 1991) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 21
69 Instrumental varables scenaros Example: same-sex and twns nstruments ( human clonng ) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 22
70 Instrumental varables scenaros Example: same-sex and twns nstruments X end s number of chldren (endogenous regressor); Y s labor force partcpaton (dependent varable); how do we fnd varaton n famly sze that s not drven by the common (unobserved) causes of famly sze and labor force partcpaton ( nclnaton to reman outsde the formal labor force )? ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 22
71 Instrumental varables scenaros Example: same-sex and twns nstruments X end s number of chldren (endogenous regressor); Y s labor force partcpaton (dependent varable); how do we fnd varaton n famly sze that s not drven by the common (unobserved) causes of famly sze and labor force partcpaton ( nclnaton to reman outsde the formal labor force )? Z = two ndcators: twns at second brth; frst two chldren same sex (nstruments). Excluson restrcton? Frst stage? ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 22
72 Instrumental varables scenaros Example: same-sex and twns nstruments X end s number of chldren (endogenous regressor); Y s labor force partcpaton (dependent varable); how do we fnd varaton n famly sze that s not drven by the common (unobserved) causes of famly sze and labor force partcpaton ( nclnaton to reman outsde the formal labor force )? Z = two ndcators: twns at second brth; frst two chldren same sex (nstruments). Excluson restrcton? Frst stage? Fndng: famly sze decreases women s labor force partcpaton, but not by as much as OLS would suggest. (Angrst and Evans 1998, Mostly Harmless Table 4.1.4) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 22
73 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 23
74 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? Vetnam draft lottery ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 23
75 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? Vetnam draft lottery Job Tranng Partnershp Act (JTPA) randomzed tral ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 23
76 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? Vetnam draft lottery Job Tranng Partnershp Act (JTPA) randomzed tral Ocean weather ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 23
77 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? Vetnam draft lottery Job Tranng Partnershp Act (JTPA) randomzed tral Ocean weather Ranfall! (Paxson 1992; Mguel et al 2004: Maccn and Yang 2009; Madestam et al 2013; etc.) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 23
78 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? Vetnam draft lottery Job Tranng Partnershp Act (JTPA) randomzed tral Ocean weather Ranfall! (Paxson 1992; Mguel et al 2004: Maccn and Yang 2009; Madestam et al 2013; etc.) Electrfcaton... ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 23
79 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? Vetnam draft lottery Job Tranng Partnershp Act (JTPA) randomzed tral Ocean weather Ranfall! (Paxson 1992; Mguel et al 2004: Maccn and Yang 2009; Madestam et al 2013; etc.) Electrfcaton... slope of land (Dnkelman 2011) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 23
80 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? Other knds of scenaros ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 24
81 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? Other knds of scenaros Y = Chld IQ; X end = growng cotton; Z = born n US south ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 24
82 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? Other knds of scenaros Y = Chld IQ; X end = growng cotton; Z = born n US south Y = Happness, 1-5; X end = Far workplace, 1-5; Z = varaton n when a pay rase s announced to ndvduals ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 24
83 Instrumental varables scenaros Lkely source of OLS bas? Excluson restrcton? Frst stage? Other knds of scenaros Y = Chld IQ; X end = growng cotton; Z = born n US south Y = Happness, 1-5; X end = Far workplace, 1-5; Z = varaton n when a pay rase s announced to ndvduals Y = Satsfed w/ govt servces; X end = cty pruned tree branches over sdewalk recently; Z = cty repaved street recently ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 24
84 Instrumental varables: LATE (MHE Chapter 4.4) Consder a randomzed tral wth mperfect complance (as n JTPA). Termnology: Always-takers D 0 = D 1 = 1, so D = 1 regardless of Z Never-takers D 0 = D 1 = 0, so D = 0 regardless of Z Complers D 0 = 0; D 1 = 1, so D = Z Under heterogeneous treatment effects, havng not only complers but also defers would cause a problem. Defers: D 0 = 1; D 1 = 0, so D = (1 Z ). We need monotoncty for an nterpretable Local Average Treatment Effect when there are heterogeneous treatment effects: ether D 1 D 0, or D 1 D 0. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 25
85 Instrumental varables: Overdentfcaton Termnology: Exactly as many lnearly ndependent nstruments as endogenous regressors? ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 26
86 Instrumental varables: Overdentfcaton Termnology: Exactly as many lnearly ndependent nstruments as endogenous regressors? Just dentfed. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 26
87 Instrumental varables: Overdentfcaton Termnology: Exactly as many lnearly ndependent nstruments as endogenous regressors? Just dentfed. More lnearly ndependent nstruments than endogenous regressors? ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 26
88 Instrumental varables: Overdentfcaton Termnology: Exactly as many lnearly ndependent nstruments as endogenous regressors? Just dentfed. More lnearly ndependent nstruments than endogenous regressors? Overdentfed. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 26
89 Instrumental varables: Overdentfcaton Termnology: Exactly as many lnearly ndependent nstruments as endogenous regressors? Just dentfed. More lnearly ndependent nstruments than endogenous regressors? Overdentfed. Overdentfcaton, exogenety, and heterogeneous effects: Suppose we have two nstruments, one endogenous regressor, and there are statstcally sgnfcant dfferences between the 2SLS estmates gven by one nstrument as compared to the other. What does t mean? ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 26
90 Instrumental varables: Overdentfcaton Termnology: Exactly as many lnearly ndependent nstruments as endogenous regressors? Just dentfed. More lnearly ndependent nstruments than endogenous regressors? Overdentfed. Overdentfcaton, exogenety, and heterogeneous effects: Suppose we have two nstruments, one endogenous regressor, and there are statstcally sgnfcant dfferences between the 2SLS estmates gven by one nstrument as compared to the other. What does t mean? (at least two possbltes) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 26
91 Instrumental varables: Overdentfcaton Termnology: Exactly as many lnearly ndependent nstruments as endogenous regressors? Just dentfed. More lnearly ndependent nstruments than endogenous regressors? Overdentfed. Overdentfcaton, exogenety, and heterogeneous effects: Suppose we have two nstruments, one endogenous regressor, and there are statstcally sgnfcant dfferences between the 2SLS estmates gven by one nstrument as compared to the other. What does t mean? (at least two possbltes) Suppose we have two nstruments, one endogenous regressor, and there are not statstcally sgnfcant dfferences between the 2SLS estmates gven by one nstrument as compared to the other. What does t mean? ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 26
92 Instrumental varables: Overdentfcaton Termnology: Exactly as many lnearly ndependent nstruments as endogenous regressors? Just dentfed. More lnearly ndependent nstruments than endogenous regressors? Overdentfed. Overdentfcaton, exogenety, and heterogeneous effects: Suppose we have two nstruments, one endogenous regressor, and there are statstcally sgnfcant dfferences between the 2SLS estmates gven by one nstrument as compared to the other. What does t mean? (at least two possbltes) Suppose we have two nstruments, one endogenous regressor, and there are not statstcally sgnfcant dfferences between the 2SLS estmates gven by one nstrument as compared to the other. What does t mean?(at least two possbltes) ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 26
93 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
94 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
95 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
96 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
97 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
98 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
99 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
100 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
101 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
102 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
103 Instrumental varables: Weak nstruments ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 27
104 Instrumental varables: Weak nstruments 2SLS bas towards OLS (MHE ): E[ ˆβ 2SLS β] σ ηξ σ 2 ξ 1 F + 1 F =F statstc for the jont sgnfcance of the excluded nstruments. Just-dentfed 2SLS medan-unbased even wth weak frst stage, but many weak nstruments can lead to bas. Note: other IV estmators exst (and are mplemented n Stata), ncludng LIML. LIML may be less based than 2SLS w/ weak nstruments, but mposes dstrbutonal assumptons; less to gan under heteroskedastcty. See dscusson: end of Chapter 4 of MHE; Cameron and Trved secton 6.4. Also note: 2SLS confdence ntervals may be ncorrect for weak nstruments, but heteroskedastcty-robust Anderson-Rubn confdence ntervals can be constructed va user-wrtten Stata routnes. ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 28
105 Instrumental varables: Weak nstruments F=441.2; 1 1+F ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 29
106 Instrumental varables: Weak nstruments F=324.3; 1 1+F ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 29
107 Instrumental varables: Weak nstruments F=49.07; 1 1+F ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 29
108 Instrumental varables: Weak nstruments F=9.882; 1 1+F ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 29
109 Instrumental varables: Weak nstruments F=1.918; 1 1+F ECON 626: Appled Mcroeconomcs Lecture 4: Instrumental Varables, Slde 29
110 Try IV out for yourself.
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