A comparison of two common approaches for estimating marginal effects in binary choice models

Abstract

Two approaches for estimating marginal effects are examined: conditioning on sample means and averaging across observations. The difference between the two quantities are signed and it is found that the magnitude increases with both the slope parameters and the covariates' variability.

Acknowledgements

I am greatly indebted to Justin Tobias for his helpful advice on the development of this paper.

Notes

¹ For example, Greene (2000, p. 816, p. 668) states: ‘For computing marginal effects [in binary choice models], one can evaluate the expressions at the sample means of the data or evaluate the marginal effects at every observation and use the sample average of the individual marginal effects … in large samples these will give the same answer.’

² This result also follows directly from Jensen's inequality, noting that βφ(α + βx) is locally concave for β > 0, |α + βx| ≤ 1.

³ For interpretation purposes, results are presented as a percentage of the parameter in Equation 2. Formally, the entries in the table give

⁴ For a review of the aggregation problem in the context of discrete choice analysis, see either Train (1993) or Ben-Akiva and Lerman (1985).

⁵ This ability measure is the first principal component of the ten component tests, purged of age effects which is then standardized to have mean zero and unit variance. See Cawley et al. (1997, 2000) for more on the construction of this variable.

⁶ The point estimate of the intercept from a probit model was −0.22 and the slope was 0.873.