  Synthetic datasets generated by structural causal models (SCMs) are commonly
used for benchmarking causal structure learning algorithms. However, the
variances and pairwise correlations in SCM data tend to increase along the
causal ordering. Several popular algorithms exploit these artifacts, possibly
leading to conclusions that do not generalize to real-world settings. Existing
metrics like $\operatorname{Var}$-sortability and
$\operatorname{R^2}$-sortability quantify these patterns, but they do not
provide tools to remedy them. To address this, we propose
internally-standardized structural causal models (iSCMs), a modification of
SCMs that introduces a standardization operation at each variable during the
generative process. By construction, iSCMs are not
$\operatorname{Var}$-sortable, and as we show experimentally, not
$\operatorname{R^2}$-sortable either for commonly-used graph families.
Moreover, contrary to the post-hoc standardization of data generated by
standard SCMs, we prove that linear iSCMs are less identifiable from prior
knowledge on the weights and do not collapse to deterministic relationships in
large systems, which may make iSCMs a useful model in causal inference beyond
the benchmarking problem studied here.
