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Unformatted text preview: sizes of the coefficients of the current and lagged values of the explanatory variables are important. Lag structure. However, too many lagged explanatory variables incur multicollinearity. Parsimonious lag structure would be ideal. 9 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Dynamic Models Some variables of interest are subject to substantial inertia That is, instead of explaining the dependent variable with the current explanatory variables, we include the lagged explanatory variables. The sizes of the coefficients of the current and lagged values of the explanatory variables are important. Lag structure. However, too many lagged explanatory variables incur multicollinearity. Parsimonious lag structure would be ideal. 10 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Dynamic Models Some variables of interest are subject to substantial inertia That is, instead of explaining the dependent variable with the current explanatory variables, we include the lagged explanatory variables. The sizes of the coefficients of the current and lagged values of the explanatory variables are important. Lag structure. However, too many lagged explanatory variables incur multicollinearity. Parsimonious lag structure would be ideal. 11 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Expectations Model Partial Adjustment Model Adaptive Adaptive Expectations Model Expectations play a key role in economic theories. However, expectations are not observed. Adaptive Expectation The size of the update of expectation Xte 1 − Xte is assumed to + be proportional to the discrepancy between the actual and expected value. Xte 1 − Xte = λ(Xt − Xte ) + Yt = β1 + β2 Xte 1 + ut + Xte 1 = λXt + (1 − λ)Xte + The expected value of X in the next time period is a weighted average of the actual value of X in the current time period and the value that had expected. Xte is unobserved for all t. How can we estimate this model? 12 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Expectations Model Partial Adjustment Model Adaptive Adaptive Expectations Model Substituting, we get: Yt = β1 + β2 λXt + β2 (1 − λ)Xte + ut But we still have the unobserved Xte . Substituting repeatedly we get: Yt = β1 + β2 λXt + β2 (1 − λ)Xt −1 + · · · + β2 (1 − λ)s−1 Xt −s+1 + β2 (1 − λ)s Xte s+1 + ut − Taking s large enough, we can ignore the further terms in Xte s+1 . Why? − 13 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Expectations Model Partial Adjustment Model Adaptive Adaptive Expectations Model Substituting, we get: Yt = β1 + β2 λXt + β2 (1 − λ)Xte + ut But we still have the unobserved Xte . Substituting repeatedly we get: Yt = β1 + β2 λXt + β2 (1 − λ)Xt −1 + · · · + β2 (1 − λ)s−1 Xt −s+1 + β2 (1 − λ)s Xte s+1 + ut − Taking s large enough, we can ignore the further terms in Xte s+1 . Why? − 14 / 62 Introduction Time Series and OLS Two Dynamic Models A...
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This document was uploaded on 03/12/2014 for the course ECON 202 at University of London University of London International Programmes (Distance Learning).

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