In microeconomic theory, the concept of the marginal is unavoidable. In fact, it is the cornerstone of “modern” microeconomic theory (well, it depends on how you cast your individuals and players…).
In the simplest term, for me anyway, the “marginal” is the one that tilts the status quo. It is a dividing line, it makes you pursue a specific task, it tells you if something is a “go” or not, it tells you to STOP!
Are you the “marginal” player? The “marginal” consultant….. the one that makes the difference. The relevant one. The cat in Mrs. Lovett's pie?
In running regressions, we are oftentimes interested in the marginal effects of specific explanatory variables. The explanatory variable can be anything, from a continuous variable (say income) to a switch variable.
What is the effect of a 100 unit of increase in income in Y?
What is the effect of introducing a “pill” or a policy in utilization?
In the standard linear regression model, the computed betas are usually the “marginal” effects (ill show in another blog entry examples which show otherwise). Suppose you are running a logit or probit model, you are oftentimes not only interested in the direction, but in the degree and magnitude as well (effect of introducing a policy in the probability of pursuing a certain action).
In stata 10, some of the commands are
mfx, compute -- >for logit models
mfx, predict (pu0) --> for fixed or random effects logit models (xtlogit)
(there are variations of mfx depending on the model you are running, say an ologit or mlogit).
These two commands would give you the effect on the probability by the explanatory variables. HOWEVER, note that stata would compute the probabilities at the MEAN values of your explanatory variables. Say x1 is a dummy variable for “male” and 20% of your regression sample are males, the mfx will be computed at x1=0.2 (you have to make basic manual computations to get the predicted probability).
If you are lazy and do not want to bother with computations to get the predicted probability, you can use…
mfx, predict (p) at(male=0) à say you want to find out the change in the probability if the respondent is male.
A complication exists if one of the dependent variables is an interaction of two other variables. Or you are dealing with squared explanatory variables. Obviously, the “mfx, compute” command WILL NOT give you the marginal effects (say of age if there is age^2)….for the simple reason that stata WILL NOT BE ABLE to recognize a variable called age_square as a transformation of another variable. Unless explicitly specified, stata will simply treat age_square as an additional variable. (MORE ON THIS,,,,,LATER)
PS: for those using STATA 11, there is now a faster command, margins. Click here to learn more.