A model that relates yt, the value of a dependent variable evaluated at time t, to the values taken by an explanatory variable x at times t, t−1,…. The general model is , for suitable values of the constants α, β0, β1,…. Here, xt−s is the value of x at lag s, and εt, εt−1,…, are the (possibly correlated) random errors.
One simple model of this type is the three-parameter Koyck model for which βs=γβs, where β and γ are positive constants. Another is the (k+1)-parameter Almon model in which , where n is known and , for constant γ0, γ1,…, γk.
The term ‘distributed lag’ was introduced by Irving Fisher in a 1925 paper entitled ‘Our Unstable Dollar and the so-called Business Cycle’.
Subjects: Probability and Statistics.