1. Consider another simple model: y=Bo+ Bix + u. Let be a binary instrument variable for x. Let ya, xibe yi, xi when zi= 1, and yio, xio be i, xi when = 0. Show that the IV estimator can be written as the Wald estimator: where y₁ = y= = 1 Vi₁ n₁ ¹,o= B₁ n Ei=1 Yi n ΣΤΟ i=1 Vio no ΣΝ Σ(2₁-7)(yi-Y)_V₁-Vo N (2₁-2)(x₁-x) x₁-xo' [Hint: -1 Ziyi = 1 Yi₁; 7 = ²=1²1 n ₂x₁ = = = XX n1 n₁, n = Σ'0 l=1*10 no , and n₁ + no-n. !_Y₁ + ₁ = ₁ + y₁. Similar for x¡.] – n n
1. Consider another simple model: y=Bo+ Bix + u. Let be a binary instrument variable for x. Let ya, xibe yi, xi when zi= 1, and yio, xio be i, xi when = 0. Show that the IV estimator can be written as the Wald estimator: where y₁ = y= = 1 Vi₁ n₁ ¹,o= B₁ n Ei=1 Yi n ΣΤΟ i=1 Vio no ΣΝ Σ(2₁-7)(yi-Y)_V₁-Vo N (2₁-2)(x₁-x) x₁-xo' [Hint: -1 Ziyi = 1 Yi₁; 7 = ²=1²1 n ₂x₁ = = = XX n1 n₁, n = Σ'0 l=1*10 no , and n₁ + no-n. !_Y₁ + ₁ = ₁ + y₁. Similar for x¡.] – n n
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 50E
Related questions
Question
![1. Consider another simple model:
y = Bo + Bix + u.
Letz be a binary instrument variable for x. Let ya, xibe yi, x; when zi= 1, and yio,
Xio be yi, xi when i = 0. Show that the IV estimator can be written as the Wald
estimator:
where y₁
=
{i=1₁₁,₁
121
=
3₁ = 1=1 (21-2) (v1-V) _ V₁-Yo
Ei=1(Zi-Z)(x₁-x) x₁-xo'
=
N
i=1
Vio
no
, X1
=
Σ1
[Hint: -1 Ziyi = ₁ Yi₁; Z = 2i=1²i
n
Σ1,
²i=1*11
121
=
n1,
n
X0
=
Xio
no
and n₁ + non.
1
- ²-₁ ²-₁ Vi₁ + - Yio – 11 ₁+1 ₁. Similar for x;.]
Σi=1 Vi
=
=
y
n
n
n
n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a2af565-536b-41b6-a437-1b0d1b7c6de2%2Fc3b4a251-0ea9-4b57-ba4d-554fa2fbb065%2Fdak4kn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider another simple model:
y = Bo + Bix + u.
Letz be a binary instrument variable for x. Let ya, xibe yi, x; when zi= 1, and yio,
Xio be yi, xi when i = 0. Show that the IV estimator can be written as the Wald
estimator:
where y₁
=
{i=1₁₁,₁
121
=
3₁ = 1=1 (21-2) (v1-V) _ V₁-Yo
Ei=1(Zi-Z)(x₁-x) x₁-xo'
=
N
i=1
Vio
no
, X1
=
Σ1
[Hint: -1 Ziyi = ₁ Yi₁; Z = 2i=1²i
n
Σ1,
²i=1*11
121
=
n1,
n
X0
=
Xio
no
and n₁ + non.
1
- ²-₁ ²-₁ Vi₁ + - Yio – 11 ₁+1 ₁. Similar for x;.]
Σi=1 Vi
=
=
y
n
n
n
n
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