Congratulate your student on his/her inquisitive mind. The answer can be formulated rather simply:

The indirect effect of

XonZis the increase we would see inZwhile holdingXconstant and increasingYto whatever valueYwould attain under a unit increase ofX.Policy questions that depend on indirect effects are discussed in my paper R-273 (Direct and Indirect Effects).

See also my answer to Jacques Hagenaars.

This question represents one of several areas where standard SEM education should be reformed. Invariably, SEM textbook give but a cursory mention (if any) of the interpretation of structural parameters as effect coefficients and, once mentioned, this interpretation is not taken very seriously by authors and teachers. The bulk of SEM education focuses on techniques of statistical estimation and model fitting, and one can hardly find a serious discussion of what the model means, once it is fitted and estimated.

The weakness of this educational tradition surfaces when inquisitive students ask questions that deviate slightly from standard LISREL routines, the answers to which depend critically on the interpretation of structural coefficients and structural equations.

For example:

- Why should we define the total effect the way we do? (i.e., as sum of products of certain direct effects.) Is this an arbitrary definition, or is it compelled by the experimental setups relative to which total and direct effects are defined?
- Why should we define the indirect effect as the
*difference*between the total and direct effect? - How can we define direct effect in nonlinear systems or in systems involving dichotomous variables?
- How should we, in a meaningful way, define effects in systems involving feedback loops (i.e. reciprocal causation) so as to avoid the pitfalls of erroneous definitions quoted in SEM textbooks? (see
*Causality*, p. 164). - Would our assessment of direct and total effects remain the same if we were to take some measurements prior to implementing the action whose effect we attempt to estimate?

Readers of *Causality* will be pleased to note that many of these questions can now be given formal answers.

Best wishes,

========Judea Pearl