# real or nominal GDP to compare to wage price index?

The recent Australian budget projects trends over the next four years. I'm looking at a summary here. If I want to calculate the share of GDP going to wages, should I compare the percentage changes in the Wage Price Index to the changes in Real GDP or Nominal GDP?

$$s_L = \frac{WL}{PY}$$
Where $$s_L$$ is the share, $$WL$$ are total wages (wages $$W$$ times labor input $$L$$) and $$PY$$ is nominal GDP (real GDP $$Y$$ times aggregate prices $$P$$). However, note it's not necessary to find statistics for $$P$$, $$Y$$, $$W$$ and $$L$$ separately most countries will track statistics for both $$PY$$ and $$WL$$ directly.
Note you cannot calculate it from wage price index alone. That is simply impossible. Wage price index only tells you how much wages risen over some period of time relative to some base point in time. That is insufficient information to figure out what was total compensation. In fact from wage price index you cannot even figure out what $$W$$ is, you can just use it to track how $$W$$ change over some period of time. And wage price index gives absolutely no information about $$L$$, so it is impossible to calculate the wage/labor share of income/output using only output and wage share index.