calculating marginal effect of logged independent variable

[Vatana Chea]

Dear Statalists,

I have a question which I tried to look it up here to see if anyone has asked before but I could not seem to find it, so I decide to post here.

I am working on a topic to understand the effect of remittances on household educational expenditure. I also want compare between the impact of remittances and other income excluding remittances. The equation is given by

ln(educational expense) = b0 + b1*ln(remittances) + b2*ln(income) + X'B + u

the problem is that the coefficient is interpreted as "an increase in percentage" and one percent increase in remittances may not be similar to one percent increase in other income. and I want to compare between an increase in remittances and income of the same amount, say, 100 USD. Basically, the impact of remittances and income of the same amount on household educational expenditure. The question is how am I going to do it? I read some economic paper which did exactly like this by somehow retransforming the coefficient into "marginal effect" but they did not mention how to compute it. But I assume it is not as simple as exponentiating the coefficient.

I know some people may suggest not to turn the independent variable into logged form, and I did try to do so but as you may be aware of, income and expenditure often face heteroskedasticity. (And yes I know the way to turn 0 income into logged form).

[Clyde Schechter]

What you are proposing to do is ill-defined.

Here's the problem. If you are starting from an income of $100 and you add $100, you are doubling income, so ln income increase by ln 2 = 0.69 (approx.). But if you are starting from an income of $1,000 and you add $100, you are multiplying income only by 1.1, so ln income increase by only 0.095. Either of those increases in ln income would then get multiplied by the coefficient of ln income to give the associated difference in expected value of ln educational expense. So, in your logarithmic model, there is no such thing as "the effect of increasing income by $100." The effect of a $100 increase in come will depend on the starting income. That's inherent in models with log-transformed predictors.

So, you can either refine your question to stipulate a particular starting value for income that you are interested in, are perhaps you might prefer to get the average effect, averaged over all observed starting values of income in your sample, or something like that.

And yes I know the way to turn 0 income into logged form

Um, no you don't. Nobody does. There are various kludges that sometimes get used, but none of them are mathematically legitimate and they usually result in analyses that are very sensitive to the particular kludge chosen. If you have 0 values, you simply should not be log-transforming that variable, tout court. There are other logarithm-like transformations that can be used. And if the dependent variable is in question, you can use the untransformed variable in a generalized linear model with a log link function.

[Carlo Lazzaro]

As an aside to Clyde's (as always) excellent advice, Vatana may want to take a look at https://www.stata.com/bookstore/heal...s-using-stata/ (Chapters 5 and 6) for a comparison between regression with logged dependent variable and GLM. The latter performs better, especially when -margins- is invoked afterwards.

[Vatana Chea]

Clyde and Carlo, thank you very much for your important advices.

Clyde Schechter

I read a paper entitled "New Evidence on the Role of Remittances on Healthcare Expenditures by Mexican Households" (Dorantes & Pozo, 2011, p. 88) and I quote a sentence

The figures in Table 4 indicate that a 100 peso increase in income raises expected health care expenditures by approximately 2 pesos. This is much less than the 6 peso increment resulting from a 100 peso increase in remittances.

Does this mean there should be kind of a basedline for both income and remittances?

[Clyde Schechter]

If both income and remittances were log transformed (as you are proposing in #1) then, yes, you need a baseline for both.

[Vatana Chea]

Thank you very much again Clyde