Economics 210
Handout # 9 Distributed Lag and Autoregressive Models
Model 1. Distributed Lags
Typical problems with this model are i) too many regressors and ii) multicolinearity
Estimation: Polynomial Distributed Lags
Geometric Distributed Lags
Model 2. Geometric Distributed Lags
Suppose that in the distributed lag model the effect of variable diminishes geometrically as the lag
gets larger. Specifically let’s assume that
Substituting into the distributed lag model we get
Note that for the last step we redefined the coefficients.
This transformation is known as a Koyck transformation.
Model 3. Adaptive Expectations
Suppose that depends upon the expected level of a variable x.
Expectations can be interpreted in different ways. might be interpreted as the expected level of x at
some time in the future, the expectations being formed toda y. Alternatively might be interpreted as
agent’s beliefs about the current level of x. In that case the equations for might be rewritten
.
Substituting for the expected level of x in the above we get
