  By solving a simple kinetic equation, in the relaxation time approximation,
and for a particular set of moments of the distribution function, we establish
a set of equations which, on the one hand, capture exactly the dynamics of the
kinetic equation, and, on the other hand, coincide with the hierarchy of
equations of viscous hydrodynamics, to arbitrary order in the viscous
corrections. This correspondence sheds light on the underlying mechanism
responsible for the apparent success of hydrodynamics in regimes that are far
from local equilibrium.
