Distributed lag

Article summary

In statistics and econometrics, a distributed lag model is a model for time series data in which a regression equation is used to predict current values of a dependent variable based on both the current values of an explanatory variable and the lagged (past period) values of this explanatory variable. The starting point for a distributed lag model is an assumed structure of the form : y_t = a + w_0x_t + w_1x_{t-1} + w_2x_{t-2} + ... + \text{error term} or the form : y_t = a + w_0x_t + w_1x_{t-1} + w_2x_{t-2} + ... + w_nx_{t-n} + \text{error term}, where y t is the value at time period t of the dependent variable y, a is the intercept term to be estimated, and w i is called the lag weight (also to be estimated) placed on the value i periods previously of the explanatory variable x. In the first equation, the dependent variable is assumed to be affected by values of the independent variable arbitrarily far in the past, so the number of lag weights is infinite and the model is called an infinite distributed lag model. In the alternative, second, equation, there are only a finite number of lag weights, indicating an assumption that there is a maximum lag beyond which values of the independent variable do not affect the dependent variable; a model based on this assumption is called a finite distributed lag model.…

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