# Pricing Power and Lower Potential GDP

One of the results of the Great Recession has been a severe downward revision in potential GDP across many countries. Laurence Ball just had a Vox post on this (h/t to Mark Thoma), finding that potential GDP is lower by 8.4% on average across the OECD, and up to 30% lower in places like Greece. This is similar to Fernald's recent finding that potential GDP is lower in the U.S., the only difference being that Fernald finds the slowdown in potential GDP started before 2007. Potential GDP is growing more slowly than previously because of slower capital accumulation, slowing (or falling) labor force participation, and/or lower growth in total factor productivity (TFP).

One interpretation of slowing TFP growth is that we are actively getting worse at innovating and/or bringing innovations to market. For Fernald, the burst of innovations coming from the IT revolution are running out. In a recent Brookings report, new firms are not starting up as quickly, possibly reducing the rate at which new innovations are brought on board. Ball doesn't really take a stand on what is happening, but the implication is that the Great Recession did something that is pulling down productivity levels.

The point I want to make here is that declining measures of TFP do not necessarily imply that our ability to innovate or bring innovations to market is declining. Measured aggregate TFP can decline, or grow more slowly, even though firms are just as technically productive as before, and are innovating at the same rate as before. Instead, measured TFP growth may be slowing down because of changes in the market power of firms during the recession.

When economists look at firms, they distinguish between revenue productivity and technical productivity. Technical productivity is how many widgets (cars, shoes, haircuts, TPS lines of code) that a firm can produce given a bundle of inputs. This is usually what people have in mind when they think of TFP; it's something similar to what an engineer would describe as productivity. It is this measure of productivity that determines our real living standard.

Revenue productivity, on the other hand, is how many dollars of revenue a firm can produce with a given bundle of inputs. So revenue productivity could go up (or down) because of changes in the price a firm can charge for it's good, or the prices of intermediate goods necessary in production, even if the number of widgets they produce is unchanged.

When we do aggregate analysis of TFP, which version of productivity are we capturing? While we'd like to think it's technical productivity, in reality it's probably revenue productivity. Seeing this gets a little equation-ish, but it's not too bad. First, when we want to back out a measure of aggregate TFP, we start with an aggregate production function like this:

$$Y = TFP \times X$$

where ${Y}$ is real GDP, ${TFP}$ is, well, TFP, and ${X}$ is our measure of the "bundle of inputs". We can ignore exactly how to calculate ${X}$ right now. To find TFP just rearrange the above into

$$TFP = \frac{Y}{X}.$$

So to calculate TFP we need a measure of real GDP and a measure of the aggregate input bundle ${X}$. Again, let's take the measure of ${X}$ as a given. Real GDP, ${Y}$, though, we should think a little harder about.

There is no such thing as measurable real GDP. We infer it as the following

$$Y = \frac{NGDP}{P}$$

where ${NGDP}$ is nominal GDP (something we can measure), and ${P}$ is some price index. So real GDP depends on how big ${NGDP}$ is relative to ${P}$. If ${NGDP}$ is growing slowly, but ${P}$ is growing relatively quickly, then we'd get falling real GDP, and vice versa. Putting this together with TFP, we've got that

$$TFP = \frac{NGDP}{PX}.$$

TFP movements depend on how ${NGDP}$ moves relative to both the price index ${P}$ and the measure of inputs, ${X}$.

What is NGDP? If output is produced by firms, then NGDP is just the total nominal output of firms. In other words, their revenue. (Actually, it's their value added. Which is revenues minus the cost of intermediate goods like fuel and such. If you want to think of this as dollars of value-added, no problem.) So we could write

$$TFP = \frac{\sum_i Rev_i}{PX}$$

where ${Rev_i}$ is the revenue of firm ${i}$, and we sum up the revenues of all the firms. Now, I'm going to wave my hand alge-magically, and give you this:

$$TFP = \frac{1}{P}\sum_i\frac{Rev_i}{X_i}\frac{X_i}{X}.$$

First we have the adjustment for the aggregate price level. That is the same as before. Inside the summation are now two fractions. The first is ${Rev_i/X_i}$, which is firm revenue divided by ${X_i}$, the firms specific input bundle. This is exactly the measure of revenue productivity that I described before. The second fraction is ${X_i/X}$, or firm ${i}$'s share of the total input bundle. So each firm's revenue productivity is weighted by how many of the inputs they use.

After all that, what do we know? The measure of productivity, TFP, is essentially based on measures of revenue productivity, not measures of technical productivity. So TFP going down, or TFP growing more slowly than before, could well be because firms are less able to generate revenue from their operations, even though they are just as capable (or even more capable) of generating output from their operations.

Now, why would firms be having trouble raising revenue? It could be that their pricing power is weaker during and after the Great Recession. People are shopping around more for good deals, and are generally willing to spend less money so competition is higher with other firms. Other firms are also shopping around, so if a firm produces an input into someone elses production process, they may not be able to charge as much. So revenues (${Rev_i}$) are not growing quickly compared to inputs, even if technically their real output is growing relative to inputs.

Even if individual firms are not experiencing a change in their pricing power, a shift in the composition of demand could alter aggregate TFP. Again, with people and other firms shopping around, they may shift towards products or firms that do not have pricing power (generic goods versus brand names, for example). So the weights (${X_i/X}$) are shifing towards firms with low revenue productivity. Regardless, shifting towards lower revenue productivity firms would show up as lower aggregate TFP.

If firms are having trouble raising prices and keeping revenue productivity high, shouldn't this also show up as a lower price index ${P}$? A lower price index ${P}$ would imply a higher level of TFP. Why doesn't this just offset the decline in revenue productivity by firms, and keep TFP from either falling or growing slowly? The price index is a different entity, and so it won't necessarily capture the same information.${P}$ is going to be based on final goods consumption, and so it doesn't necessarily have to move to exactly offset any changes in revenue productivity by firms.

I'm not claiming that declining revenue productivity by firms is the sole reason for slowing growth in TFP, or the lower implied path of potential GDP. But the slowdown in TFP growth and potential GDP could be in part due to changes in firms market power during or after the Great Recession. Declining market power (or a shift in demand towards firms with less market power) would likely show up in the statistics as slower growth in TFP (and hence real GDP), even though nothing fundamental changed about innovation or adoption of technologies.