Solncy variables in x and a previous value of y; see Example 4.4. a. For estimating B, why do we obtain the same estimator if the growth in y, log(y)- log(y 1), is used instead as the dependent variable? b. Suppose that there are no covariates x in the equation. Show that, if the dis- tributions of y and y-1 are identical, then a < 1. This is the regression-to-the-mean phenomenon in a dynamic setting. (Hint: Show that x1 = Corr[log(y), log(y-1)]-)

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
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Chapter5: Business And Economic Forecasting
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4.9. Consider a linear model where the dependent variable is in logarithmic form,
and the lag of log(y) is also an explanatory variable:
log(y) = Bo + xß + a1 log(y-1) + u,
E(u|x, y-1) = 0,
where the inclusion of log(y-) might be to control for correlation between policy
variables in x and a previous value of y; see Example 4.4.
a. For estimating B, why do we obtain the same estimator if the growth in y, log(y)-
log(y 1), is used instead as the dependent variable?
b. Suppose that there are no covariates x in the equation. Show that, if the dis-
tributions of y and y- are identical, then a < 1. This is the regression-to-the-mean
phenomenon in a dynamic setting. (Hint: Show that a, = Corr[log(y), log(y-)].)
Transcribed Image Text:4.9. Consider a linear model where the dependent variable is in logarithmic form, and the lag of log(y) is also an explanatory variable: log(y) = Bo + xß + a1 log(y-1) + u, E(u|x, y-1) = 0, where the inclusion of log(y-) might be to control for correlation between policy variables in x and a previous value of y; see Example 4.4. a. For estimating B, why do we obtain the same estimator if the growth in y, log(y)- log(y 1), is used instead as the dependent variable? b. Suppose that there are no covariates x in the equation. Show that, if the dis- tributions of y and y- are identical, then a < 1. This is the regression-to-the-mean phenomenon in a dynamic setting. (Hint: Show that a, = Corr[log(y), log(y-)].)
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