The book repeatedly says “a log-linear model captures growth at a constant rate”. My understanding is that log-linear trends are appropriate for exponential growth and that constant growth would be just linear. What am I missing? Why does the book continually say that growth at a constant rate is log-linear?
A linear graph has a constant growth _ amount _: as x increases by 1, y increases by adding a constant amount.
An exponential graph has a constant growth _ rate _: as x increases by 1, y increases by multiplying by a constant factor.
Okay. Thats correct. I would say a variable y with dy/dx = k, where k is a constant, has a constant growth rate , i.e. its partial differential with respect to the independent variable is a constant, but that is linear and we’re going to call that a constant growth amount and “constant growth” would be dy/dx = e^x (which I would call exponential growth but I guess the manual calls this constant?)
Think of constant growth rate as dy/dx = ky; then y = ae^kx.