Intuition behind value added as TFP measure

In some papers the authors use value-added over capital and labor as TFP measure, what is the intuition behind this? For example, in one paper I just read the authors use

$$\frac{VA}{(p_{K}K + p_{L}L)}$$, where VA = value added.

I'm a bit confused, since we normally use a standard Cobb-Douglas production function. Transforming the equation by this following simple step leads to a similar but still different measure of the TFP "A", i.e. here I have gross output in the nominator and in the denominator there is a multiplication and not an addition?

$$Q=AK^{α}L^{1-α}$$

$$\frac{Q}{(K^{α}L^{1-α})}=A$$

• Do you have any reference for your first "TFP measure"? I never saw this. If the profit is zero, then your TFP measure is 1 (and conversely). So your measure looks more like a kind of profit rate than a measure for TFP. Jan 6 at 15:20

Value added is nothing else just the prices times quantity of gross output $$=p_QQ$$. That is why the first expression has $$p_K K$$ and $$p_L L$$ in the numerator.