Appunti presi a lezione di Econometria

S

i

z Ortogonal To

- ↳ the

use

CAN

We metic

projection

M ↓ E

Mxy =

I ↓ Sub

is projecting into ortogona

m space

ef X

E spaymoret

all the of

elements S So we can

&

Q Mixz z

provides

x2 x

=

> =

- space

&

That are

into

remains the elements

anly X2

I

that is

Ortoford - Bi

BMixz atter

e

Y repression

+ + = me

= have

we created

7 that

the Of

residual epression

Is

di ONTO COSTANT

The

X2

Laud we set residuaus

ONTOSONOU have

regresson We to ertogonal repressors

use

-

If like.

regression

we have

=> a

y i

p + Bzz + u

= , I

that

assumed it 20:

we and ortogonal

o

za Y

⑪ -

significa

Questo

i ⑭

auder

onto and Z perpendic

rog . -

z -

Henave Y

au -

-

-

I u

↓ ad

V e

-

u I

IN

LESIDuals CASE

THIS I ie

AnE Fi

DISTANTE SEGNATE

Le

: in VENDE &

& z e

anto

ne

regreted y -i

M - + e

n

uz =

⑭

⑤ i

onto

y

ne rec . Ez = E

+

⑭tur

ny Bri

Be

D Mixz u

= +

+

merc

use

we = =

d

Il i

of

residual y onto

a neg of

and

↳ get resduals

the

d E Miy

regressions > =

-

project The

M Onto I

WACE

Motional of

B2M disturbances

Miy +

Xz

i

=

ANE INTERESTEA

We In respuars

B2

EXTIMATING and

y XXBz

Bi

X +

+

= e

,

nun and

Onto

THE X1

we Y

regression X2

:

>

- & -

and

get

and B u

u

,

mett

s

Max Bet

↓ Mono

Me

we regr e

ge T

to &

* EWL

THEONEME

Om and e

tan

Vand y

a d

red mode4)

-

() E

- AND

Al NELETANT

OUTHERS thESE

LEVERAGE ARE

POINTS

ANE POINTS

- >

- ?

EXTIME

OR

INFWENCE

↓ ↓ this

rilevance

The autier :

of on

depends

1

B(t) -

x)

B (x XI

+

=

= hT

1 -