Econometrics – lecture 5 – assumptions

HIGH COLINEARITY- EXAMPLEvariables is high?... HIGH COLINEARITY- CONSEQUENCE small tob => less chance to reject H0 only a problem if consequences are serious... HIGH COLINEARITY- SYMPTO

WHAT IF ASSUMPTIONS ARE

INVALID?

Dr Tu Thuy Anh

Faculty of International Economics

Chapter 5, 6 (selected) - S&W

BASIC ASSUMPTIONS

1 E(ui) = 0

2 Var(ui) = σ2

3 cov(ui, uj) = 0 for i #j

4 ui~ N(0, σ2)

vars

Assumptions

HIGH COLINEARITY- EXAMPLE

variables is high?

HIGH COLINEARITY- CONSEQUENCE

 small tob => less chance to reject H0

only a problem if consequences are serious

HIGH COLINEARITY- SYMPTOMS



Variable Coefficient Std Error t-Statistic Prob

C 1207.06 1575.06 0.77 0.45

P -146.90 479.15 -0.31 0.76

Wrong sign

R 2 =0.91

R2 large, but few significant

HIGH COLINEARITY- DETECTION

 If R2 is large?

 if VIF>10? VIF = 1/(1-R2))

Variable Coefficient Std Error t-Statistic Prob

Dependent variable: P

HIGH COLINEARITY- CAUSE/ CURE

growth

NORMALITY- CONSEQUENCES

 ui~ N(0, σ2)

estimates are still unbiased, but we will not be able to assess which parameters are

significant

distribution

F distribution

10

NORMALITY- DETECTION

The Jarque-Bera test:

where S and K are the sample Skewness and

Kurtosis statistics

The JB test has an asymptotic chi-square

distribution with two degrees of freedom

NORMALITY- CAUSE/CURE

even that u (hence Y) does not come from a

normal distribution, the parameters estimates will be asymptotically normal and consequently

we will be able to perform the usual inference

achieve normality in the parameter estimates?

can be not enough in some situations

only on N, but also on N-K, the degrees of

freedom

12

HETEROSCEDASTICITY- CONSEQUENCES

i

 => Confidence Intervals are invalid

 => Invalid t, F test

ˆ var(a j)

Need to be cured

HETEROSCEDASTICITY- DETECTION

 H0 : Var(ui) = σ2 for all i

 If

u X

X X

X X

X

e2  1  2 2  3 3  4 22  5 32  6 2 3 

) 1 (

) 1

2



Reject H0

=> R 2 (1)

2 2

( (1)) / ( 1)

( 1, ) (1 (1)) / ( )



k: n0 of coeffs in model 1

HETEROSCEDASTICITY- CAUSE/CURE

 etc

software

of heteroscedasticity

i = aK2

i

AUTOCORRELATION

 If the assumption does not hold: cov(ui; uj) # 0

for i # j

 Form of autocorrelation:

 ut = ρut-1 + vt =>AR(1);

 v(t): random error, satisfies assumptions 1-4

 If ρ >0: positive autocorrelation

 If ρ <0: negative autocorrelation

 If ρ =0: no autocorrelation

 ut = ρ1ut-1 + + ρput-p+ vt => AR(p)

AUTOCORRELATION -CONSEQUENCES

 Biased estimation of => invalid

Confidence Interval

ˆ var(a j)

2

ˆ



NEED TO BE CURED

AUTOCORRELATION - DETECTION

 Durbin Watson test, can be used in situations:

 AR (1)

 No lag value of the dependent variable in the model

 No missing observation

NO CONCLUSION

AUTOCORRELATION - DETECTION

 B-G test:

et = a1 + a2 Xt + ρ1et-1+ + ρp et-p +vt => R2(1)

et = a1 + a2 Xt + vt => R2(2) If:

) ( )

1

2

p

2

( (1) (2))/



or

Autocorrelation of order p

AUTOCORRELATION - CURE

 AR(1): ut = ρut-1 +vt

 Set: