Question

Im doing an econometric assignment and need to use the program STATA do estimate some linear regressions.

The dataset provided is the "natural log" of each variable.

What does the natural log mean? How is it calculated and how do I interoperate the data?

For example, a summary of the natural log of the unemployment rate shows:

Mean: -2.79

STD Deviation: 0.284

Min: -3.5833

Max: -1.9428

Answer 1

The natural log is the inverse of "e"(Exponential function).Natural log "ln(x)" is the time to reach amount 'x',assuming we grow continuously from 1.0. A linear relationship between a log tranformed outcome variable and a group of predictor variables is   log(yi)=β0+β1x1i+⋯+βkxki+ei, where y is the outcome variable and x1,⋯,xk are the predictor variables. In other words, we assume that log(y)–β is normally distributed, (or y is log-normal conditional on all the covariates). Since this is just an ordinary least squares regression, we can easily interpret a regression coefficient, say β1, as the expected change in log of y with respect to a one-unit increase in x1 holding all other variables at any fixed value, assuming that x1 enters the model only as a main effect. But what if we want to know what happens to the outcome variable y itself for a one-unit increase in x1? The natural way to do this is to interpret the exponentiated regression coefficients, exp⁡(β), since exponentiation is the inverse of logarithm function.