percent vs percentage points

[Marry Lee]

Dear all,

I have a question about how to deal with results in percent and percentage points.

On the one hand, I have an estimate of the effect of a public policy on education outcome using probit, then I used margins to get an estimate in terms of differences in probability
So I had: This policy increases the predicetd probability to qualify for high school by 12 percentage points

Then I wanted to see the effect of qualify for high school on the income using another sample from the same survey, since the income of the first sample is not available and the second sample is not affected by the policy.
I had: qualify for high school increases the income by 19 % compared to those who do not go to high school.

I want to give an estimate of the effect of the policy on the income, so can I do the following:

• 0.19 X 0.12 = 0.023 = 2.3%
• and say that the policy may have increased the income by 2.3 % ?

My question is : is it right to multiply a percent by a percentage point ?

Thank you!

[Clyde Schechter]

In terms of the correct use of percent and percentage points, that 2.3 figure would be percentage points, not percent.

But there is a much bigger issue here. It is not, in general, valid to take a 0.19 from one sample and a 0.12 from another sample and combine them in the way you have. The effect of high school on income might well be different from 0.19 in the population from which the first sample was drawn. And, unfortunately, you cannot find that out in your first sample because it has no income variable. Even if you knew somehow that the 0.19 is correct in the first sample as well, it would still not be correct to multiply as you have done because these effects may not be independent of each other, so that the expectation of the product is not necessarily the product of the expectations. Only if there is other information that justifies the assumption that the effects are independent of each other and that the 0.19 is also a correct estimate for the first population can you do this.

[Marry Lee]

Thank you so much Clyde Schechter

[Marry Lee]

Sorry for coming back with another 'stupid' question Clyde Schechter.
Aside from the probelms that arise from not respecting the 2 assumptions you mentioned, if we were really to consider the 2.3 figure, can we really say: "there may be an increase by 2.3 percentage points in income"? since income cannot be expressed in terms of percent, is it ok to talk about changes in percentage points? if we were talking about the probability of employment, for example, that may be ok since probability is expressed in percent, but probably not for the income?

[Clyde Schechter]

The difference in income would be based not on the 2.3 figure but only on the 0.19 figure. You did not say how you arrived at this being an increase of 19%--perhaps as a result from an analysis of log income? Anyway, if we take that at face value, you would refer to the change in income as 19%.

[Carlo Lazzaro]

Marry:
as an aside to Clyde's helpful advice, if I get your right, your second regression might be affecyted by latent variable endogeneity, as it does not include individual ability among the regerssors. Other things being equal, on average, smarter people have higher chance to qualify for high standing schools (your predictor) and negotiater better wage condition (your regressand).