Distributed Lags Analysis - General Model
Suppose we have a dependent variable y and an independent or explanatory variable x that are both measured repeatedly over time. In some textbooks, the dependent variable is also referred to as the endogenous variable, and the independent or explanatory variable the exogenous variable. The simplest way to describe the relationship between the two would be in a simple linear relationship:
Yt = Σ βi*xt-i
In this equation, the value of the dependent variable at time t is expressed as a linear function of x measured at times t, t-1, t-2, etc. Thus, the dependent variable is a linear function of x, and x is lagged by 1, 2, etc. time periods. The Beta weights (βi) can be considered slope parameters in this equation. You may recognize this equation as a special case of the general linear regression equation (see the Multiple Regression Overviews). If the weights for the lagged time periods are statistically significant, we can conclude that the y variable is predicted (or explained) with the respective lag.