Before you start to look for Stata routines or other software you
should be more specific about the model that you are trying to estimate.
It cannot possibly make sense to estimate a model with spatial
correlations between 44,000 separate units and there is no software
that would enable you to do this - think of the size of the spatial
weighting or correlation matrix. What is more likely is that your
data is clustered in some sense - i.e. the spatial correlations are
between groups of individuals on whom you have observations. This is
a routine feature of large surveys and you can investigate the
options in Stata for estimating models with cluster-adjusted standard
errors - there are a number of -xt..- panel estimators with this
feature or you can look at the estimators for survey data.
A further consideration is whether your interest lies in the spatial
aspects of your data or merely in adjusting standard errors to allow
for spatial correlation. If it is the latter, then the -xtscc-
module provides Driscoll-Kraay robust standard errors. On the other
hand, if it is the former then you may need to write your own
routines in Mata. There is a rapidly growing literature on the
econometrics of spatial panel data - see papers by Baltagi, Pesaran,
Elhorst and many others - but relatively few packaged routines that
implement the methods which are described in the literature.
Routines to estimate models with spatial autocorrelation or spatial
lags are primarily designed for cross-section data and tend to assume
that you have or can calculate a spatial weighting matrix across all
units, which is not realistic in your case. This is why the
distinction between clusters and spatial units is so important.