Schema degli appunti presi in aula di Econometria

Y B Y B Y ut

−2

t 0 1 t−1 2 t

- Forecasting error

- Write the expression of RSMFE

√ 2

[ ]

^

( )

−

RMSFE= E Y Y

+1

T T+ 1∨T

- Write the expression of the RMSFE pseudo so called

Chose a date P for the start of the poos sample

o Re-estimate the model every period s = P-1, … , T-1

o Compute the poos forecast for S+1= P,…,T

o ~ ^

Compute the poos forecast errors =Y -

u

o Y

s+1 s+1 s+1|s

Compute the average of the squared forecast errors and then take its squared root

o

- Construct the forecast interval

- autocovariance and autocorrelation of order j

- Derive the variance

- X is exogenous

if E(u |X , X , X ,...) = 0.

t t t–1 t–2

- Strict Exogeneity

( past, present, and future) X is strictly exogenous if E(u |..., X , X , X ,...) = 0

t t+1 t t–1

- Make an estimation of this model

β β

e rappresentano l’elasticità della produzione rispettivamente al capitale

1 2

ed al lavoro. Ciò significa che ad una variazione percentuale in K o L rispettivamente

β β

comporta una variazione in Y pari a % o %.

1 2

- Sample autocorrelations

The jth sample autocorrelation is an estimate of the jth population autocorrelation:

- write an AUTO REGRESSIVE MODEL of second order

=β + + +u

Y β y β y i

−2

t 0 1 t−1 2 t

- write an ADL(2,2)

=β + + + + +u

Y β y β y β x β x i

−2 −1 −2

t 0 1 t−1 2 t 3 t 4 t

β β ?

- what represents and (D is a binary variable)

0 1

=β +

Y β Di+ui

t 0 1

β represents the expected value for a student when D=0

0

β rapresentes the difference between the expected value E(Yi|Di=1) – E(Yi|Di=0)

1

- Granger causality

In the 06 self evaluation (ex 4 point c) the test is commonly know as granger causality test. This

name can be misleading because it is not a causality test. It is a forecasting ability test.

- Write the dynamic and cumulative multipliers and draw the graph

Lag number Dynamic multipliers CI ±

0 1.2 1.2 1.96*0.3

±

1 0.3 0.3 1.96*0.2

±

2 0.1 0.1 1.96*0.2

±

3 -0.1 -0.1 1.96*0.2

Lag numbers Cumulative DM CI ^

0 1.2 ±

1.2 1.96*SE( δ )

1

^

1 1.5 ±

1.5 1.96*SE( )

δ 2

^

2 1.6 ±

1.6 1.96*SE( δ )

3

^

3 1.5 ±

1.5 1.96*SE( )

δ 4

Th cumulative dynamic multipliers can be estimated directly using a modification of the original

regression.

The SE needed to computed the required SE are therefore:

^

SE( )… where

δ 1

- Omitted variable  

>0 > 0

2 2

Over Under



Cov( , )>0

2 1 Under Over



Cov( , )<0

2 1

- Exercise chapter 9

This assumption implies that measurement error dues not comove with the true unobserved

variable. This might not be the case if the difference between the true and the reported value

depends on the true value.

- Chapter 15