Absolute Value of Total Factor Productivity in an Aggregate Cobb-Douglas Production Function A standard formulation of the Cobb-Douglas production function (e.g. here) is:
$$Y=AK^{\alpha}L^{\beta}$$
Have there been estimates, at aggregate level for any large economy, of the absolute value of total factor productivity $A$ (at a defined date, and for defined units of measurement of output $Y$, capital $K$ and labour $L$?).  Even a rough order of magnitude would be of interest.

From searching the web, there have been many studies that estimate changes in total factor productivity over time, but I could not find any that focused on its absolute magnitude.
Applying a regression model

$$\ln Y = \ln A + a\ln K + b\ln L$$

on a standard macroeconomic time-series data set from a country would immediately provide an estimate for $A$, essentially an average over the sample.  

The problem is that experience has shown us that we don't have $A$ but $A_t$, i.e. it is time-varying. As such, estimates of $A$ as though it was a constant seem rather meaningless or even misleading.   

More-over, in a time-varying coefficient framework, what is important is the change, rather than the absolute value, since it is essentially a mark-up index on the production function, and not something that can be meaningfully measured in absolute units. In this case, we take $A_0=1$ (the first period in the sample) and we track the percentage change over the sample.