  Introducing common shocks is a popular dependence modelling approach, with
some recent applications in loss reserving. The main advantage of this approach
is the ability to capture structural dependence coming from known
relationships. In addition, it helps with the parsimonious construction of
correlation matrices of large dimensions. However, complications arise in the
presence of "unbalanced data", that is, when (expected) magnitude of
observations over a single triangle, or between triangles, can vary
substantially. Specifically, if a single common shock is applied to all of
these cells, it can contribute insignificantly to the larger values and/or
swamp the smaller ones, unless careful adjustments are made. This problem is
further complicated in applications involving negative claim amounts. In this
paper, we address this problem in the loss reserving context using a common
shock Tweedie approach for unbalanced data. We show that the solution not only
provides a much better balance of the common shock proportions relative to the
unbalanced data, but it is also parsimonious. Finally, the common shock Tweedie
model also provides distributional tractability.
