The logistic distribution is a continuous distribution similar to the normal distribution but with slightly heavier tails. It is widely used in discrete-choice and binary-outcome econometrics.
Core Mechanics
With location parameter (\mu) and scale (s>0), the cumulative distribution function is:
[ F(x) = \frac{1}{1 + e^{-(x-\mu)/s}} ]
The corresponding density is:
[ f(x) = \frac{e^{-(x-\mu)/s}}{s\left(1+e^{-(x-\mu)/s}\right)^2} ]
Why Economists Use It
In logit models, the logistic form gives convenient closed-form choice probabilities and interpretable odds ratios. That makes it practical for modeling labor participation, default events, policy take-up, and consumer choice.
Practical Interpretation
Compared with a normal-link setup, logistic tails imply a somewhat higher probability of extreme latent shocks. In many applications the empirical fit is similar, so choice between logit and probit is often guided by interpretability and convention.