For negative values alone you can define relative change as:
This is quite common way to deal with rates of change when you have negative numbers. However, when the denominator is zero then the growth rate is not defined. This can solve any issue when zero is not a base.
When zero is the base unfortunately there is no way ...
I'm pretty sure he means "1 minus the labour share percentage", i.e. he's estimating the capital share of GDP as the proportion of GDP not going to labour. It's not typeset well, but he has used an em-dash (longer) after "GDP" and a minus sign (shorter) after "1".
I would say people usually use log-returns for continuous data (although no data is really continuous, not even tick data). And discrete returns when your data is discrete. In the case of GDP, you only get the data every 3 months, so that is as discrete as it gets.
Interesting question. In effect, while factor shares were thought to have remained fairly stable over a long time (the first of the Kaldor's facts), more recently they have varied, particularly in the direction of a fall in the labour share.
This short paper from (2012) shows that under such scenario, a growth accounting exercise which assumes constant ...