In micro-econometric work, prices may or may not be part of TFP.
The literature recognizes two versions:
- TFPQ (Quantity-based)
- TFPR (Revenue-based)
Clearly, TFPR must include prices (Revenue = quantity*prices).
Many scholars argue that TFPQ is the purer and most correct measure of TFP. In the sense that higher productivity means producing more output (quantity) for given input levels, that sounds appealing. Prices can also capture market power. So looking at revenues may conflate higher productivity (which is desirable) with high market power (which is undesirable). However, there are several problems with TFPQ.
First, how to define quantity? Especially for services, output can be hard to define in terms of quantity. E.g. what's the produced quantity of a food delivery service? Is it the number of deliveries? Is it the delivery distance? Does it depend on weather?
Second, how to compare quantities? Typically we want to say productivity is higher or lower in one firm/place than another. How do we compare the quantity of food delivery (however defined), to the "quantity" of other services, like watching a sports event? Revenues in dollar amounts, on the other hand, are perfectly comparable.
Third, there are data limitations. We just don't have quantity data normally, because lots of data comes from firm balance sheets, which are in values. Also, many firms are multi-product so "output data" is difficult to back out. Some papers by Syverson (see e.g. here and here) manage to use TFPQ for ready-mix concrete, but that's a special case.
Fourth, what about quality? For given inputs, a firm that produces one high-quality rug is arguably more productive than a firm producing one low-quality rug. These quality differences could be easily captured by prices and hence by TFPR. But TFPQ would have a hard time distinguishing these firms.
The debate and methodological issues continue and I'm sure I may have forgotten some. The bottom line is that prices may or may not be part of productivity.