Question 1: Show the validity of the third equality in the IV representation of the FE estimator: NT βrc = (Xx) xy ΣΣ (xit - Xi) (xit - Xi)" - ") it i=1 t=1 -1 N Τ Ν Τ ΣΣ (x - Xi) x(t) ΣΣ (xit - Xi) yit i=1 t=1 i=1 t=1 || - NT NT ΣΣzx) ΣΣziyit \i=1 t=1 i=1 t=1 -1 N T ΣΣ (xit - Xi) (yit - Ji) i=1 t=1

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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Question 1:
Show the validity of the third equality in the IV representation of the FE estimator:
Bre=(x X) * Xy
(X
FE
- Σ
||
=
=
NT
ΣΣ (xit - Xi) (xit – Χ;)'
i=1 t=1
NT
ΣΣ (xit - Xi) Xit
\i=1 t=1
NT
ΣΣΕ Χ
\i=1 t=1
-1 N T
-1
1 NT
ΣΣ (xit - Xi) (yit - Ji)
i=1 t=1
-1 N T
ΣΕ ziyit
i=1 t=1
ΣΣ (xit - Ki) yit
i=1 t=1
Transcribed Image Text:Question 1: Show the validity of the third equality in the IV representation of the FE estimator: Bre=(x X) * Xy (X FE - Σ || = = NT ΣΣ (xit - Xi) (xit – Χ;)' i=1 t=1 NT ΣΣ (xit - Xi) Xit \i=1 t=1 NT ΣΣΕ Χ \i=1 t=1 -1 N T -1 1 NT ΣΣ (xit - Xi) (yit - Ji) i=1 t=1 -1 N T ΣΕ ziyit i=1 t=1 ΣΣ (xit - Ki) yit i=1 t=1
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