Introductory Econometrics: A Modern Approach, 3rd Edition by Jeffrey M. Woolridge

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By Jeffrey M. Woolridge

The fashionable method of this article acknowledges that econometrics has moved from a really good mathematical description of economics to an utilized interpretation in accordance with empirical study suggestions. It bridges the space among the mechanics of econometrics and sleek functions of econometrics by means of using a scientific technique stimulated via the foremost difficulties dealing with utilized researchers at the present time. during the textual content, the emphasis on examples supplies a concrete fact to monetary relationships and permits remedy of fascinating coverage questions in a practical and available framework.

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We have covered models containing natural logarithms here because they appear so frequently in applied work. The interpretation of such models will not be much different in the multiple regression case. It is also useful to note what happens to the intercept and slope estimates if we change the units of measurement of the dependent variable when it appears in logarithmic form. Because the change to logarithmic form approximates a proportionate change, it makes sense that nothing happens to the slope.

Because the change to logarithmic form approximates a proportionate change, it makes sense that nothing happens to the slope. We can see this by writing the rescaled variable as c1yi for each observation i. The original equation is log(yi) ϭ ␤0 ϩ ␤1xi ϩ ui. If we add log(c1) to both sides, we get log(c1) ϩ log(yi) ϭ [log(c1) ϩ ␤0] ϩ ␤1xi ϩ ui, or log(c1yi) ϭ [log(c1) ϩ ␤0] ϩ ␤1xi ϩ ui . 3 Summary of Functional Forms Involving Logarithms Dependent Variable Independent Variable Interpretation of ␤1 level-level y x ⌬y ϭ ␤1⌬x level-log y log(x) ⌬y ϭ (␤1/100)%⌬x log-level log(y) x %⌬y ϭ (100␤1)⌬x log-log log(y) log(x) %⌬y ϭ ␤1%⌬x Model now log(c1) ϩ ␤0.

The interpretation of such models will not be much different in the multiple regression case. It is also useful to note what happens to the intercept and slope estimates if we change the units of measurement of the dependent variable when it appears in logarithmic form. Because the change to logarithmic form approximates a proportionate change, it makes sense that nothing happens to the slope. We can see this by writing the rescaled variable as c1yi for each observation i. The original equation is log(yi) ϭ ␤0 ϩ ␤1xi ϩ ui.

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