The dependency variable has been removed from the analysis.
The dependency ratio has not been included mechanically in most papers, as it is this one. It is supposed to pick up changes in demand for government expenditure, such as schooling and pensions. The general idea is that these have increased government expenditure, both because per-capita schooling and pensions have expanded and because the dependency ratio has increased. In most of the countries studied, as is well-known, the dependency ratio declined during the period studied, while expenditure per person probably increased. Japan is most likely an exception; it should have entered the demographic transition much earlier than the other countries. There is thus no a priory no reason to expect the dependency ratio to play an important role in the Wagner hypothesis in general. It can thus be removed from the analysis, or moved to a footnote. If the author(s) wish to pursue the approach of testing other potentially relevant variables, see Shelton 2007.