Eg measurement error simultaneous equations the

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Unformatted text preview: β2 Xte + ut −1 β2 Xte = Yt −1 − β1 − ut −1 Yt = β1 λ − (1 − λ)Yt −1 + β2 λXt + ut − (1 − λ)ut −1 In equilibrium, ¯ ¯ ¯ Y = β1 λ + (1 − λ)Y + β2 λX 21 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Expectations Model Partial Adjustment Model Adaptive Partial Adjustment Model Quite often, we are interested in a target value or desired value of a dependent variable. (eg. inventory...) Partial Adjustment Model The actual increase in the dependent variable Yt − Yt −1 is assumed to be proportional to the discrepancy between the desired value and the previous value. Yt − Yt −1 = λ(Yt∗ − Yt −1 ) This is another type of dynamic model: Yt∗ = β1 + β2 Xt + ut Yt − Yt −1 = λ(Yt∗ (Target ) − Yt −1 ) 22 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Expectations Model Partial Adjustment Model Adaptive Combining the two equations we obtain: Yt = β1 + β2 λXt + β2 (1 − λ)Yt −1 + λut Long run effect of X? Short run? 23 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Expectations Model Partial Adjustment Model Adaptive Combining the two equations we obtain: Yt = β1 + β2 λXt + β2 (1 − λ)Yt −1 + λut Long run effect of X? Short run? 24 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Assumption C7 Assumption C7 requires 2 conditions: ut is uncorrelated with Xjt ut is uncorrelated with Xjs for s = t The violation of the first part renders OLS biased and inconsistent. (eg. measurement error, simultaneous equations,...) The violation of the second part affects unbiasedness but does not affect consistency. 25 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Assumption C7 Assumption C7 requires 2 conditions: ut is uncorrelated with Xjt ut is uncorrelated with Xjs for s = t The violation of the first part renders OLS biased and inconsistent. (eg. measurement error, simultaneous equations,...) The violation of the second part affects unbiasedness but does not affect consistency. 26 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Assumption C7 Assumption C7 requires 2 conditions: ut is uncorrelated with Xjt ut is uncorrelated with Xjs for s = t The violation of the first part renders OLS biased and inconsistent. (eg. measurement error, simultaneous equations,...) The violation of the second part affects unbiasedness but does not affect consistency. 27 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Autocorrelation There are two main types of autocorrelation: AR(p): ut = ρ1 ut −1 + · · · + ρp ut −p + εt MA(q): ut = εt + λ1 εt −1 + · · · + λq εt −q but we will mainly focus on the special cases AR(1): u...
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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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