Marginal effects tells us how a dependent variable (outcome) changes when a specific independent variable (explanatory variable) changes. Other covariates are assumed to be held constant. Marginal effects are often calculated when analyzing regression analysis results.

The marginal effects for binary variables measure discrete change. For continuous variables, they measure the instantaneous rate of change. Both are typically calculated using software packages such as STATA.

For an independent variable x, we can define the marginal effect to be the partial derivative, with respect to x, of the prediction function *f*. The derivative (from calculus) gives us the rate of change over an interval which is very, very small—approaching 0.

## Types

**Average Marginal Effect (AME)**

As the name suggests, you can think of the AME as an “average derivative”. To find the AME, calculate the marginal effect of each variable x for each observation (taking into consideration any covariates). Then calculate the average.

**Marginal Effect at the Mean (MEM)**

This is very similar to the AME, except that instead of being kept at their observed values, the covariates are kept at their mean values instead.

**Marginal effects at representative values (MER)**

The difference here is that you would choose representative values (i.e. values of interest in your experiment or study) for your covariates.

## Calculating Marginal Effects in STATA

To calculate marginal effects in STATA, use the command “margins.” This command works only after you’ve run a regression, and so it acts on what it still holds in its memory: the results of the last regression command. For a continuous variable, you’ll want to specify exactly what point you want to know the marginal effects for using the at option.

After using the margins command, you can use the command “marginsplot” to print out the results of your margins command into a tidy graph.

## References

Bogard, Matt. Marginal Effects vs Odds Ratio. Econometric Sense, March 2016. Retrieved from

http://econometricsense.blogspot.com/2016/03/marginal-effects-vs-odds-ratios_11.html on May 9, 2018.

Boggess, May. StataCorp. Methods for Obtaining Marg. Effects. Retrieved from https://www.stata.com/support/faqs/statistics/marginal-effects-methods/ on May 9, 2018

Barron, Manuel. Econometric Tools 2: Marg. Effects in Stata. University of California, Santa Cruz, ECON 294A Lecture Notes. Retrieved from https://www.ocf.berkeley.edu/~manuelb/week7/LectureNotes07.pdf on May 9, 2018.

SSC Knowledge Base. Exploring Regression Results using Margins. Retrieved from https://www.ssc.wisc.edu/sscc/pubs/stata_margins.htm on May 12, 2018