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Let $y=Y/L$ and $k=K/L$ be the per-worker levels of output and capital. Observe that $y=Ak^\alpha$. Steady state is given by: $$k^*=sy^*+(1-\delta)k^*,$$ or $$k^*=sA(k^*)^\alpha+(1-\delta)k^*.$$ Doing the algebra: $$k^*=\left(\frac{sA}{\delta}\right)^{\frac{1}{1-\alpha}}.$$ And: y^*=A\left(\frac{sA}{\delta}\right)^{\frac{\alpha}{1-\alpha}}=A^{\frac{1}{1-...

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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".

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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.

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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 ...

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