Econ_360-11-14-Chap.pdf

# Ordinary least squares ols dependent variable

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Ordinary Least Squares (OLS) Dependent Variable: Residual Explanatory Variable(s): Estimate SE t -Statistic Prob ResidualLag 0.839023 0.064239 13.06089 0.0000 Number of Observations 71 Estimated Equation: Residual = .0890 ResidualLag Critical Result: The ResidualLag coefficient estimate equals .8390; that is, the estimated value of ρ equals .8390. Table 17.4: Regression Results – Estimating ρ Estimate of ρ = Est ρ = .8390 Getting Started in EViews___________________________________________ Run the original regression; EViews automatically calculates the residuals and places them in the variable resid . EViews automatically modifies Resid every time a regression is run. Consequently, we shall now generate two new variables before running the next regression to prevent a “clash:” o residual = resid o residuallag = residual( 1) Now, specify residual as the dependent variable and residuallag as the explanatory variable; do not forget to “delete” the constant. __________________________________________________________________

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27 Step 3: Apply the Generalized Least Squares (GLS) Estimation Procedure Strategy: Our strategy for dealing with autocorrelation will be similar to our strategy for dealing with heteroskedasticity. Algebraically manipulate the original model so that the problem of autocorrelation is eliminated in the new model. That is, tweak the original model so that the error terms in the tweaked model are independent. We can accomplish this with a little algebra. We begin with the original model and then apply the autocorrelation model: Original model: y t = β Const + β x x t + e t Autocorrelation model: e t = ρ e t 1 + v t v t ‘s are independent Original model for period t: y t = β Const + β x x t + e t Original model for period t–1: y t 1 = β Const + β x x t 1 + e t 1 Multiplying by ρ ρ y t 1 = ρβ Const + ρβ x x t 1 + ρ e t 1 Rewrite the equations for y t and by ρ y t 1 : y t = β Const + β x x t + e t ρ y t 1 = ρβ Const + ρβ x x t 1 + ρ e t 1 Subtracting y t ρ y t 1 = β Const ρβ Const + β x x t ρβ x x t 1 + e t ρ e t 1 Factoring out β x y t ρ y t 1 = β Const ρβ Const + β x ( x t ρ x t 1 ) + e t ρ e t 1 Substituting for e t y t ρ y t 1 = β Const ρβ Const + β x ( x t ρ x t 1 ) + ρ e t 1 + v t ρ e t 1 Simplifying ( y t ρ y t 1 ) = ( β Const ρβ Const ) + β x ( x t ρ x t 1 ) + v t
28 In the tweaked model: New dependent variable: y t ρ y t 1 New explanatory variable: x t ρ x t 1 Critical Point: In the tweaked model, v t ‘s are independent; hence, we need not be concerned about autocorrelation in the tweaked model. Now, let us run the tweaked regression for our example; using the estimate of ρ we generate two new variables: New dependent variable: AdjConsDur t = y t Est ρ y t 1 AdjConsDur t = ConsDur t .8390 ConsDur t 1 New explanatory variable: AdjInc t = x t Est ρ x t 1 AdjInc t = Inc t .8390 Inc t 1 Ordinary Least Squares (OLS) Dependent Variable: AdjConsDur Explanatory Variable(s): Estimate SE t -Statistic Prob AdjInc 0.040713 0.028279 1.439692 0.1545 Const 118.9134 44.43928 2.675861 0.0093 Number of Observations 71 Estimated Equation: EstAdjConsDur = 118.9 + .041 Inc Interpretation of Estimates: b AdjInc = .041: A \$1 increase in real disposable income increases the real consumption of durable goods by \$.041.

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