Transcription of CHAPTER 3 Distributed-Lag Models - Reed College
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CHAPTER 3 Distributed-Lag Models A Distributed-Lag model is a dynamic model in which the effect of a regressor x on y occurs over time rather than all at once. In the simple case of one explanatory variable and a linear relationship, we can write the model as ()0,ttts tstsyLx uxu == + + = + + ( ) where ut is a stationary error This form is very similar to the infinite-moving-average representation of an ARMA process, except that the lag polynomial on the right-hand side is applied to the explanatory variable x rather than to a white-noise process.
q, equation (3.1) can be written as . 0 q t s ts t s y xu − = =α+ β +∑. (3.5) In this case, the long-run cumulative effect is . 0 q s s= ∑β . If the moving-average representation converges to zero slowly as s goes to infinity rather than truncating at finite q, then the long-run cumulative effect is 0 lim q s q s →∞ = ∑β or 0 s ...
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