  Parquet diagrams sum self-consistently Feynman graphs for the vertex function
with all two-particle multiple scatterings. We show how the complete parquet
equations for the Hubbard-like models can be integrated to a generating
functional from which all thermodynamic quantities are derived via (functional)
derivatives. An explicit Luttinger-Ward functional $\Phi[G;\Lambda,{\cal K};U]$
is constructed containing only the renormalized one-particle, $G$, irreducible,
$\Lambda$, and reducible, ${\cal K}$, two-particle propagators as independent
variational functions. The parquet approximation is proven to be a
thermodynamically consistent, $\Phi$-derivable theory obeying the necessary
conservation laws.
