  The Fay-Herriot model is a standard model for direct survey estimators in
which the true quantity of interest, the superpopulation mean, is latent and
its estimation is improved through the use of auxiliary covariates. In the
context of small area estimation, these estimates can be further improved by
borrowing strength across spatial region or by considering multiple outcomes
simultaneously. We provide here two formulations to perform small area
estimation with Fay-Herriot models that include both multivariate outcomes and
latent spatial dependence. We consider two model formulations, one in which the
outcome-by-space dependence structure is separable and one that accounts for
the cross dependence through the use of a generalized multivariate conditional
autoregressive (GMCAR) structure. The GMCAR model is shown in a state-level
example to produce smaller mean square prediction errors, relative to
equivalent census variables, than the separable model and the state-of-the-art
multivariate model with unstructured dependence between outcomes and no spatial
dependence. In addition, both the GMCAR and the separable models give smaller
mean squared prediction error than the state-of-the-art model when conducting
small area estimation on county level data from the American Community Survey.
