  We consider the numerical stability of the parameter recovery problem in
Linear Structural Equation Model ($\LSEM$) of causal inference. A long line of
work starting from Wright (1920) has focused on understanding which sub-classes
of $\LSEM$ allow for efficient parameter recovery. Despite decades of study,
this question is not yet fully resolved. The goal of this paper is
complementary to this line of work; we want to understand the stability of the
recovery problem in the cases when efficient recovery is possible. Numerical
stability of Pearl's notion of causality was first studied in Schulman and
Srivastava (2016) using the concept of condition number where they provide
ill-conditioned examples. In this work, we provide a condition number analysis
for the $\LSEM$. First we prove that under a sufficient condition, for a
certain sub-class of $\LSEM$ that are \emph{bow-free} (Brito and Pearl (2002)),
the parameter recovery is stable. We further prove that \emph{randomly} chosen
input parameters for this family satisfy the condition with a substantial
probability. Hence for this family, on a large subset of parameter space,
recovery is numerically stable. Next we construct an example of $\LSEM$ on four
vertices with \emph{unbounded} condition number. We then corroborate our
theoretical findings via simulations as well as real-world experiments for a
sociology application. Finally, we provide a general heuristic for estimating
the condition number of any $\LSEM$ instance.
