Topic 14: Dynamic Econometric Models

Question 1

What is a distributed lag model?

Answer 1

Lagged values of the regressors as regressors

Question 2

What is a model which includes the lagged regressant as a regressor?

Answer 2

Autoregressive, because it includes the error

Question 3

What methods can resolve an infinite lag model?

Answer 3

• Ad hoc estimation
• Koych approach
• How do we apply? In practise we don’t ever actually have to deal with an infinite lag

Question 4

How can one figure out the best lag model ad hoc?

Answer 4

Just keep on adding lags until the new coefficients become unsignificant

Question 5

What is the Koyck approach?

Answer 5

Resolves infinite lag models.

Assumes all the B_iare of the same sign

The size of the slope coefficient declines geometrically

so: B_k = B₀λ^k 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 X_i

Question 6

Show how models are transformed in the Koyck procedure

Answer 6

Y_t = ⍺ + B₀X_t + B₀λX_t-1 + B₀λ²X_t-2+ … + u_t

Y_t-1 = ⍺ + B₀X_t-1 + B₀λX_t-2 + B₀λ²X_t-2+ … + u_t-1

So: Y_t - λY_t-1 = ⍺(1 - λ) + B₀X_t + u_t - λu_t-1

So: Y_t = ⍺(1 - λ) + B₀X_t + λY_t-1 + v_t

Question 7

Is OLS appropriate for the Koyck aproach?

Answer 7

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 Y_t-1 that is uncorrelated with v_t, known as an instrument variable

Question 8

How do we test for autocorrelation in autoregressive models?

Answer 8

Durbin h test

Question 9

Explain the durbin h test

Answer 9

Y_t = ⍺ + ⍺₁X_t + ⍺₂Y_t-1

vt = ρv_t-1 + ε_t

ρ^ = 1 - d/2

Does not matter how many X variables or lagged Y’s, only variance of Y_t-1 coefficient

for large n, where nVar(⍺₂) < 1