What is a distributed lag model?
Lagged values of the regressors as regressors
What is a model which includes the lagged regressant as a regressor?
Autoregressive, because it includes the error
What methods can resolve an infinite lag model?
-Ad hoc estimation
-How do we apply? In practise we don't ever actually have to deal with an infinite lag
How can one figure out the best lag model ad hoc?
Just keep on adding lags until the new coefficients become unsignificant
What is the Koyck approach?
Resolves infinite lag models.
Assumes all the Bi are of the same sign
The size of the slope coefficient declines geometrically
so: Bk = B0λk where λ is the rate of decline of the distributed lag
1-λ is the speed of adjustment
if λ is small, Y adjusts quickly to changes in Xi
Show how models are transformed in the Koyck procedure
Yt = ⍺ + B0Xt + B0λXt-1 + B0λ2Xt-2 + ... + ut
Yt-1 = ⍺ + B0Xt-1 + B0λXt-2 + B0λ2Xt-2+ ... + ut-1
So: Yt - λYt-1 = ⍺(1 - λ) + B0Xt + ut - λut-1
So: Yt = ⍺(1 - λ) + B0Xt + λYt-1 + vt
Is OLS appropriate for the Koyck aproach?
No, as we have a stochastic regressor (the regressant included as a lagged regressor).
IV, ML ect are reccomended instead.
Otherwise one can attempt to find a proxy for Yt-1 that is uncorrelated with vt, known as an instrument variable
How do we test for autocorrelation in autoregressive models?
Durbin h test
Explain the durbin h test
Yt = ⍺ + ⍺1Xt + ⍺2Yt-1
vt = ρvt-1 + εt
ρ^ = 1 - d/2
Does not matter how many X variables or lagged Y's, only variance of Yt-1 coefficient
for large n, where nVar(⍺2) < 1