0

Would anyone know how I could interpret the log-log regression with age below?

ln (Income) = const + 0.30 ln(Age) + ut

I don't understand how it is possible to say that if age increases by 1%, income increases by 30%. Age is a unit (count), you can't age by 1% that's why I have trouble interpreting it.

Thanks in advance

Pita Fouta
  • 101
  • Age is definitely not a count! When your child is three months hold, she will be 1% older in about a day. – whuber Jan 17 '22 at 16:27
  • The model is closer to being that if age increases by 1%, income increases by 0.3%. So if you go from age 25 to 26, that would be a 4% increase in age and the model suggests an increase in income of about 1.2% (subject to the $u_t$ term) – Henry Jan 17 '22 at 17:02

2 Answers2

1

The interpretation of the regression coefficient for age is

A one unit change in log(age) is associated with a change of 0.3 in the expected value of log outcome.

Age is not a count variable, you certainly can have fractional age. You've just not measured it as such.

Demetri Pananos
  • 36,121
0

The interpretation of the coefficient $\beta$ for Age is:

An increase of Age by a factor of $k$ is associated with an change in Income of $100(k^{\beta}-1)\,\%$.

For example: If Age increases by 10% (i.e. $k=1.1$), then Income is expected to change by $100(1.1^{0.3}-1)=2.9\,\%$.

See also here or here.

COOLSerdash
  • 30,198
  • Hello everyone, thank you very much for your answers.

    I wanted to know if the number of children is a variable count and if I can interpret it as you advised ln(Number of children). I also wanted to know if the size of a soccer field in a hectare is a count variable (ln(size)).
    I would have said that it is a continuous variable.

    I appreciate any help you can provide.

     – Pita Fouta Jan 18 '22 at 09:40