Distributed lag models are the models that contain only independent (explanatory) variables as lag variables.
Econometrics widely uses these models, as in most cases some economic factors influence the others not immediately, but with some time lag. The distributed lag method provides opportunities for studying this effect.
Let us study the factor Y. Its value at the current moment of time is yt; values of Y at the subsequent moments in time - yt+1, yt+2, …, yt+q; values of Y at the previous moments in time - yt-1, yt-2, …, yt-q.
When no autoregressive members are present, a distributed lag model is a model of the following type:
where:
xt. Lagged values of exogenous variables.
βq. Short-term multiplier. Describes the change in the average value Y at the time moment t under influence of a unit change in the value X at the time moment t-q.
The sum of all coefficients of the exogenous variables 
is a long-term multiplier. It describes the change in Y under the influence of a unit change in X at each of the observed time periods.
A sum of coefficients 
(p < q) is named an interim multiplier.
To calculate the speed, with which Y reacts to changes in X, the user needs to consider value of an average lag:
where:
- the contribution of a lag, or lag distribution.
Small values of average lag correspond to fast Y response rate to changes in X, large values of average lag correspond to slow response.
See also:
Library of Methods and Models | Polynomial Distributed Lag Model | Geometrical Distributed Lag Model | Modeling Container: The Linear Regression (OLS Estimation) Model | ISmLinearRegress