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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

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Hill, C. R., W. E. Griffiths, and G. G. Judge, (2001), Undergraduate Econometrics. New York: John Wiley & Sons

2012423

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

Yt = 1+ 2Xt+et et ~N(0,1)

  • (yt) (xt )

  • x0y0

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

(SST) (SSR) (SSE)

SST = SSR + SSE

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

R2=

0 <R2 < 11

R2 = 1:

R2 = 0:y x

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • : R2 R2

  • : R2=0.32 Y 32% X 32% Y 68%

  • R2?

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

(1)r2 = R2, r = Cov(X,Y) /

=

r2=R2

(2) R2=(Yt, )=

r2 =

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

= 40.7676 + 0.1283 Xt R2 = 0.317

(22.1387) (0.0305) (s.e)

= 40.7676 + 0.1283 Xt R2 = 0.317

(1.84) (4.20) (t)

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • SR1 SR5

  • Transformation

    (1) : 2= slope

    (2)Reciprocal:

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

1.E(et)=0

2. Var (et)=2

3. Cov(ei,ej)=0

4. et~N(0, 2)

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • 1.plot

  • 2. Yt=1+2 Xt+et

  • 3.

  • 4.

  • 5. ?

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • Yt=1+2Xt3+et Zt3=Xt3/1000000

  • =0.874+9.68 Zt3 R2=0.751

    R2

  • Notice : heteroskedasticity autocorrelation

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

1.0

2.Jarque-Bera test for normality

Ho: H1:

P

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

JB

JB =

T:

S: skewness

k: kurtosis

Ex:

T=40S=0.396920K=2.874151

  • JB=1.077

    JB 5.99 = 22, 0.05

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

HoNormal distribution

JB

JB

P0.05 Ho

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • y=1+ 2X+3Z

  • 1 , 2 , 3

    Model:

    y=E(y)+et= 1+ 2X+3Z +et

  • :

    (1) E(et)=0 (2) Var(et)=2

    (3) Cov(et,es)=0 (4) et~N(0, 2)

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • (1) 2 Var(b2)

  • (2)T Var(b2)

  • (3)Var(X2 ) Var(b2)

  • (4)Cov(X2 , X3 ) Var(b2)

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

*

K:

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

SSE

SST

  • R2 =1-(SSE/SST)

  • R2

    R2

  • T-1 R2 =1

  • R2=1-

  • T

    K

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • R2R2 :

    * :

    R2

    * :

    (1)R2

    (2)R2

    (3)R2

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • t

  • F

  • F

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • :

    y=0 +1 X1 +2 X2+ 3 X3 + e

    H0: 2 = 3 = 0

    y= 0 +1 X1 + e

    F=

    F F(J,T-K, )

    P=PF(2,96) F0.05

J=2

T=(100)

K=4

SSER-SSEu/J

SSEu/(T-K)

2, 96, 0.05

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • H0: 2=0, 3=0 K=0

    H1: 20 3 0 K

    J=1 F= T2

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

:

y= 0 + 1 X1 + 2X22+ e

=22X2 X2y

=1 X1 y

dy

dX2

dy

dX1

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • y= 0 + 1 X1 + 2X2+ e

    H0: 1=2

    H1: 12

    y= 0 + 1 (X1 + X2)+ e

    F test F(1,T-3, )

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • :

    (1)

    (2)

    (3)MR1-MR6

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

1.

  • :y= 0 + 1 X1 + 2X2+ e

  • X2 ,

  • y= 0 +1*X1 + e

  • Cov(X1 ,X2) 0 1* 1

  • 2=0

  • Cov(X1 ,X2)=0

  • E(b1*)=1+2

Cov(X1, X2)

Var(X1)

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • TF

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • (1) y ()

    (2) H0

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • 1.P( H0)

    Accept H0 =>

  • 2.P( H0)

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • ?

    Y=0+1X1+2X2+e <= true model --------- (1)

  • Y=0+1X1+2X2+3X3+e --------- (2)

  • Var (b1),Var (b2),Var (b3) (2) (1)

  • X3X2X1X3Y

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

2. : RESET

  • :

    (1)

    (2)

    (3)

    (4)

  • RESETRegression Specification Error Test

  • RESET

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Hill c r w e griffiths and g g judge 2001 undergraduate econometrics new york john wiley

  • :

  • Y=0+1X1+2X2+e

  • =b0+b1X1+b2X2

  • Y=0+1X1+2X2+r1 2+e -------- (1)

  • Y=0+1X1+2X2+r1 2+ r2 3+e -------- (2)

  • (1) H0: r1=0 H1: r10

  • (2) H0: r1= r2=0 H1: r10 r20

  • H0

  • H0

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