Interpreting stata output with log dependent variable and % independent variables

[Dominique Descat]

Hello stata users,
Hope you are doing well.

I have a question regarding interpreting stata output in the following situation.

Regression is on monthly panel data.
The dependent variable is log transformed and the independent are percentages.
How to interpret an output as following:

y = 0.50 + 20*b1 + -110*b2 + e

Mean y: 0.4 SD: 1.5
Mean b1: 0.02 SD: 0.003
Mean b2: -0.001 SD: 0.04

y is the log of a first difference at monthly level.
b1 represents a yearly change (% change).
b2 is an interest rate.

Then the following question is:
In economics literature I often come across the following interpretation:
A 1-standard-deviation higher b1 leads to a .... pp increase of y.
How do the economists calculate this?

Looking forward to your handful insights!

Thank you in advance, best wishes Dominique

[Bruce Weaver]

Does this UCLA FAQ page address your question?

[George Ford]

Here is my thought.

1. I assume you don't mean ln(y - l.y) since that will fail for negative values. ln(y)-ln(l.y) is a percentage change (a log difference).
2. If you do the latter, you are regressing a percentage on a percentage for b1. So, it's a change in the percentage for a change in a percentage (an elasticity). A little squirrely given the month/year difference. You may need to adjust for that.
3. The interest rate variable is a bit different. It is a percent change in Y given a percentage point change in interest rate.

I find it is often worthwhile to use margins, at() to see what you are getting.

margins, at(b2 = (-0.001 -0.041)

gives you the y values at the mean and one-standard deviation above the mean for the interest rate.