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Spurious Regression

# Spurious Regression - Economics 245B Spurious Regressions...

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Economics 245B Spurious Regressions Consider the linear regression model Y t = + X 0 t ± + U t : In our previous analysis of the model, we have not mentioned serial correlation of the regressors and the dependent variable. If both the regressors and the dependent variable are highly correlated, then our standard regression inference can be very misleading. To understand why, recall that the OLS estimator of the coe¢ cients is A B ± = ² n P X 0 t P X t P X t X 0 t ³ 1 ² P Y t P X t Y t ³ : As long as Y t and X t are generated by stationary processes, our standard limit the- ory holds. If, however, Y t and X t are generated by nonstationary processes, then we must make adjustments. To equate serial correlation with nonstationarity, it is easiest to consider an autoregression Y t = ²Y t 1 + V t : If j ² j < 1 , then the serial correlation is attenuated enough so that the series is stationary. If j ² j = 1 , then the serial correlation is so severe that the series is not stationary. If j ² j = 1 , then Y t is a unit-root process. If, in addition, V t is white noise, then Y t is a random walk. Consider estimating the intercept model Y t = + U t : The estimator of the intercept is A = n 1 P Y t . If Y t contains a unit root, then

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Spurious Regression - Economics 245B Spurious Regressions...

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