Consider the linear model:
ln(wage)= a + b D + u
where D is a binary variable (say, female); in the texbook, it says that when D changes from 0 to 1, then b (equal to 0.067) has to be interpreted as follows:
bx100 = 6.7 percentage points of change in wage
However, I would say in this case:
6.7 percent change in wage (or a change in wage of 6.7%)
Am I right, or is the textbook right? Many thanks.
You are right. The nonlinear formulation is W=ae^(bd). Which means the the base wage a is multiplied by 1+b when the dummy variable has value 1.
Yep. It depends, however, on the baseline (omitted category). Suppose that D is a dummy for females. Then D = 1, if the individual is a woman; and D = 0 otherwise (man).
Then, given the log-lin formulation, the coefficient of D (b here) is interpreted as you have already stated, but a small detail is missing.
The wage of the given category (woman) is lower by 6.7% than the wage of the baseline category (man).
The textbook description is wrong and yours is (essentially) correct. The phase “percentage point change” refers to, well, a change in a percentage. Thus, if one observes that the share of women in the overall number of factory workers rises from 45% to 50%, one would say the share has risen by 5 percentage points (and not by 5% as most journalists seem prone to write). Meanwhile, when a dependent variable (the wage rate in the textbook example) has been expressed in natural logs (base e), then the coefficient on a right-hand variable in a linear regression expresses the growth rate as a percent (divided by 100) in the dependent variable to a one unit change in the right-hand variable under that condition that the growth rate is continuously compounded. In the textbook’s regression, if a man and a woman are otherwise identical as far as wage earning is concerned, and if the man receives $10 per hour and the coefficient is 0.067, then the woman is estimated to receive 10e^(1*0.067) = 10.693 per hour. This is not 6.7% but 6.93% greater using 10 as the base, while the man might be said to earn 6.48% less using 10.693 as the base. If the man and woman are not otherwise identical, then the coefficient expresses the difference in compound growth rate terms attributable to being a woman.
If b is 0 for women and 1 for men, then exp(a) is the (geometric) mean wage of women, and men earn on average exp(b)-1 percent more than women. b percent is an underestimation (because exp(b)=1+b+b²/2+b³/6+....), which is negligable for low b's, because the significance intervals of such an estimate may likely be considerably higher. In this example, I would say (write), that men earn about 7% more.
By the way, it is better to accept percent simply as a format of presenting a number, i.e. 0,067 can be shown as 67/1000, 67000 ppm, 6,7/100, 6,7% etc. If you write 0,067 into a cell of EXCEL and choose the format %, it will be shown as 6,7%. One should not use percent=value*100, as we have learned in school, because this could make things more complicated than necessary.
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