is to shrink our parameter estimates somewhere between the pooled and
individual LS estimates. For simplicity we set to 
a
diagonal matrix. To allow for proper scaling of the different
coefficients we set the diagonal elements equal to the product of the
variance least squares estimates from the individual store models,
, and a scaling parameter, 
:
where p is the dimension of 
(or 192, i.e., 12
equations with 16 parameters each). We also set 
. The
relationship between 
and 
can be
seen by examining the mean and covariance matrix of this prior
distribution: 
and 
.