The Euler characteristic of ${\mathcal{A}}_g$ via Hodge integrals

We prove the Harder-Siegel formula for the Euler characteristic of ${\mathcal{A}}_g$ via the intersection theory of ${\bar{\mathcal{M}}}_g$ and a vanishing result for lambda classes on the boundary of the toroidal compactifications of ${\mathcal{A}}_g$, recently proven by Canning, Molcho, Oprea and Pandharipande.