Kyd

182 PART ONE: SINGLE-EQUATION REGRESSION MODELS

Symbolically, we have

where, as usual, A denotes a small change. Equation (6.6.12) can be written, equivalently, as

This equation states that the absolute change in Y ( = AY) is equal to slope times the relative change inX. If the latter is multiplied by 100, then (6.6.13) gives the absolute change in Y for a percentage change in X. Thus, if (AX/X) changes by 0.01 unit (or 1 percent), the absolute change in Y is 0.01(p2); if in an application one finds that p2 = 500, the absolute change in Y is (0.01)(500) = 5.0. Therefore, when regression (6.6.11) is estimated by OLS, do not forget to multiply the value of the estimated slope coefficient by 0.01, or, what amounts to the same thing, divide it by 100. If you do not keep this in mind, your interpretation in an application will be highly misleading.

The practical question is: When is a lin-log model like (6.6.11) useful? An interesting application has been found in the so-called Engel expenditure models, named after the German statistician Ernst Engel, 1821-1896. (See exercise 6.10.) Engel postulated that "the total expenditure that is devoted to food tends to increase in arithmetic progression as total expenditure increases in geometric progression."16

Was this article helpful?

0 0
Rules Of The Rich And Wealthy

Rules Of The Rich And Wealthy

Learning About The Rules Of The Rich And Wealthy Can Have Amazing Benefits For Your Life And Success. Discover the hidden rules and beat the rich at their own game. The general population has a love / hate kinship with riches. They resent those who have it, but spend their total lives attempting to get it for themselves. The reason an immense majority of individuals never accumulate a substantial savings is because they don't comprehend the nature of money or how it works.

Get My Free Ebook


Post a comment