How do I find the change in a logged dependent variable for a one unit increase in an independent variable?

The independent variable is not logged.

Here's the example

ln(fees) = 0.52625(assets) + .....

where 0.52625 is beta, the coefficient



I want to derive the effect on fees. I'm pretty sure that the effect on fees is fees*e^(0.52625)for a one unit change in assets, but how can I go from the equation above to this result?How do I find the change in a logged dependent variable for a one unit increase in an independent variable?
You have ln(y(x)) = a + bx. The notation "y(x)" means "y evaluated at x" not y times x.



So for a unit change in x, that is, from x to x+1 we get



ln(y(x+1)) = a + b(x+1)

ln(y(x)) = a + bx



ln(y(x+1)) - ln(y(x)) = b



y(x+1)/y(x) = exp(b)



To conver to a % change per unit increase in x do the following:



100*(y(x+1)/y(x) - 1) = 100*(exp(b) - 1)





Math Rules!How do I find the change in a logged dependent variable for a one unit increase in an independent variable?
If ln(fees) = k*assets

then:

fees = e^(k*assets).

That is the definition of a base e logarithm, denoted by 'ln'.



If you have two lots f1 and f2 of fees withcorresponding assets a1 and a2, then:

f1 = e^(k*a1)

f2 = e^(k*a2)

f2 / f1 = e^(k * (a2 - a1)).