Growth Accounting with variable factor shares

Under the assumption of competitive markets, the usual growth accounting equation using Cobb-Douglass function is as follows:

$\Delta Y/Y = \Delta A/A+w_l\Delta L/L+w_k\Delta K/K$

• $Y$ is output

• $K$ & $L$ are factors of production

• $w_i$s are constant factor shares

Almost all empirical papers I've read so far assume constant factor share values $w_i$s regardless of the sample span. Usually the papers assume $w_l=0.7$ and $w_k=0.3$. I believe the results would be different if we let the factor share values vary over time in the growth accounting exercises.

Does anyone know of paper(s) that use growth accounting method by utilising actual data on factor shares?

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 factor shares leads to inconsistent results. The abstract reads:

Recent evidence shows that factor shares are not constant. Consequently, growth accounting exercises rely on a false assumption and a measurement problem arises. We propose an empirical methodology to solve the measurement issue and estimate TFP growth.

A more complete and recent analysis from the same author (plus another co-author) is here (and a theoretical model with these insights is here).

As you can see, this is a very topical issue, and there seems to be very little empirical analysis so far. I only found this one. As the authors in the second article linked conclude,

any efforts to align empirical growth research with the reality of the factor share data cannot be carried out using standard techniques. New techniques need to be developed.

There might still be some time until a satisfactory empirical method is developed.