6. A Model includes not only the current but also the
lagged (past) values of the explanatory variables
Past lag valuesCurrent lag value
Yt= α + β0 Xt + β1Xt-1 + β2Xt-2+ ut
7. The model which includes one or more lagged values of
the dependent variable among its
explanatory variables
Lagged value ofDependent variable
Yt = α + βXt + λ Yt-1 + u
17. Economists have used two rather different styles of research
in their attempts
• To assess the contribution of research and development
(R&D) expenditures.
• For economic growth
18. Paul R. Krugman
(Princeton University)
By
Maurice Obstfeld
(University of California, Berkeley)
B Marc J. Melitz
(Harvard University)
19. The J curve shows the effect of a devaluation of a currency on the net
export (exports minus imports). When the devaluation takes place
at t the net export falls from A to B, since the level of import is
unchanged, but the currency is worth less. As time goes on the net
export will gradually change since consumers buy less imported
goods, and other countries buy more goods from the country due
to the lower real price. At C the net export break even. With time
the net export will find equilibrium
27. Estimation of distributed lag
models
Yt= α + β0 Xt + β1Xt-1+ β2Xt-2+ ut
Lag weights
They define the pattern of how x affects y over time.
Stationary
Error term
28.
29. Infinite lag model:
Yt= α + β0 Xt + β1Xt-1+ β2Xt-2+ . . . + ut
Finite lag model:
Yt = α + β0 Xt + β1Xt-1+ β2Xt-2+ . . .+ βkXt-k+ ut
“k is specified”
30.
31. *
*
Since we are using the 1 past lag value so number of observation reduced from 30 to 29
No +ve autocorrelation
32.
33. Interpretation summary
Short run 1.142786 or a unit change in PPDI on average the PPCE will
increase up to 1.142 units
Long run 1.142786+(-0.144730)0.99805
Durbin Watson no positive autocorrelation
Observation 1 past lag value include so observation reduce from 30 to 29.
R square define up to 99.08% effect of PPDI on PPCE.
% of a total impact of a unit change in PPDI on PPCE :
1st year:1.1427/0.99805 11.4%
2nd year:0.14473/0.998011.44%
34.
35.
36.
37.
38.
39. • Maximum length of the lags.
• Fewer degree of freedom left
• Data mining (big data)
• Multicolinearity
40. Koyck approach
Adjustment of speed
slow 01
β0= βk λk
(k=0,1…)(0<λ<1)
(The higher the value of λ the
lower the speed of adjustment,
and the lower the value of λ the
greater the speed of adjustment)
fast
0.0
47. Yt = α(1 − λ) + β0 Xt + λYt−1 + vt
PPCEt = -1242.169 + 0.6033PPDIt + 0.4106PCEt−1 + vt
Rate of adjustment 1 - λ 1- 0.4106
RATE of adjustment 0.589
Short run : current year consumption of increment
Short run 0.6033
Long run:
Long run = coeff αt-1 /1- λ 1.0237
48. Yt = α (1 − λ) + β0 Xt + λ Yt−1 + vt
PPCEt = -1242.169 + 0.6033PPDIt + 0.4106PCEt−1 + vt
Median lag: median lag(time required) for 1st half
Median lag = log(2)/log λ log(2)/log (0.4106) 0.776
(on average with a unit change in income the median lag(time required) for 1st half is 0.776)
Mean lag: effect of change in in dependent to be felt on dependent variable
Mean lag = λ /1- λ 0.4106/0.5894 0.6966
(on average ,for the effect of change in ppdi to be felt on ppce)
49. Durbin h test (1-d/2)[n/1-n{var(αt-1 )} ]1/2
Durbin h test (0.4972) [(30/1-30(0.239) ]1/2
Durbin h test 5.1191
( Durbin h ~ Norm distribution , As h value exceed ±3 , so the probability is highly significant
Decision:
There is a positive autocorrelation ,
Yt = α (1 − λ) + β0 Xt + λ Yt−1 + vt
PPCEt = -1242.169 + 0.6033PPDIt + 0.4106PCEt−1 + vt