Several formats in which Wagner’s hypothesis has been formulated and tested have been listed on page 5 of the revision. That paragraph includes six different approaches.
The paper only lists one way of testing for Wagner’s hypothesis (i.e., analyzing the relation between the share on GDP of government spending and real GDP per capita) when in fact there are many ways of looking at the hypothesis. The authors should include at least a couple of recent ways of testing this law, in addition to the traditional way of testing for it.