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Distributed Lag model

# Distributed Lag model - Time Series Econometrics...

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Time Series Econometrics - Distributed Lag Modeling Main Reading: Gujarati, Chapter 17, Griffith, Judge and Hall (2001)

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Time and Econometrics Time Series elements of cross-sectional (Retrospective designs) Univariate Time Series Models Multivariate Static Models Multivariate Dynamic Models Stationary Variables Non-Stationary Variables Panel Econometrics Note: Most of the methods we examine are single- equation methods so bear in mind potential extensions in to multi-equation methods
Some Time Series/Stochastic Processes Fertility in America Vote Share of the Democrats in the 20 th Century Ice-cream Consumption Barium Chloride Imports in to the US Capital Expenditures and Appropriations

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Introduction Economists are often interested in variables that change across time rather than across individuals. Simple Static models relate a time series variable to other time series variables. The effect is assumed to operate within the period.
Dynamic Models Dynamic effects. Policy takes time to have an effect. The size and nature of the effect can vary over time. Permanent vs. Temporary effects.

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Macroeconomics e.g. the effect of M on Y in short run vs. the long run this is know as impulse response function money supply increases by 1 in year 1 returns to normal afterwards what happens to y over time time Y
Distributed Lag Effect is distributed through time consumption function: effect of income through time effect of income taxes on GDP happens with a lag effect of monetary policy on output through time y t = α + β 0 x t + β 1 x t-1 + β 2 x t-2 + e t i t t i x y E - = δ δ β ) (

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The Distributed Lag Effect Economic action at time t Effect at time t Effect at time t+1 Effect at time t+2
The Distributed Lag Effect Effect at time t Economic action at time t Economic action at time t-1 Economic action at time t-2

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Two Questions 1. How far back? - What is the length of the lag? - finite or infinite 2. Should the coefficients be restricted? - e.g. smooth adjustment - let the data decide
Unrestricted Finite DL Finite: change in variable has an effect on another only for a fixed period e.g. Monetary policy affects GDP for 18 months the interval is assumed known with certainty Unrestricted (unstructured) the effect in period t+1 is not related to the effect in period t

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y t = α + β 0 x t + β 1 x t-1 + β 2 x t-2 + . . . + β n x t-n + e t n unstructured lags no systematic structure imposed on the β ’s the β ’s are unrestricted OLS will work i.e. will produce consistent and unbiased estimates
Problems 1. n observations are lost with n-lag setup. data from 1960, 5 lags in model implies earliest point in regression is 1965 use up degrees of freedom (n-k) 2. high degree of multicollinearity among x t-j ’s • x t is very similar to x t-1 --- little independent information imprecise estimates large stn errors, low t-tests hypothesis tests uncertain.

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3. Several LHS variables many degrees of freedom used for large n.
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Distributed Lag model - Time Series Econometrics...

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