Judge me by my TFP, do you?


I told you in the last post that I’m agnostic about the relationship of TFP and innovation. That was part of an on-going debate, mainly with Eli Dourado. I want to pause at the outset to say that this debate is great. It’s been respectful, interesting, and forced me to think hard about some things. So welcome to the 0.0001% of the internet that does not make you want to gouge your eyes out.

In the spirit of that, I’m going to start by telling you about how Eli is right.

And then I’m going to blow another 1200 words saying “Well, actually….”. It is a debate, after all.

Seeing the light

I’m paraphrasing what has been happening on Twitter and the blog, but I think I have all the important aspects of the discussion. The general question is whether TFP (or growth in TFP) is (a) something that is a useful metric for how innovative we have been and (b) is a useful thing to target as part of future innovation. The recent debate and this post are mainly about (b). Should we innovate with the goal of making TFP growth higher?

Let’s say that we have just two industries: Good and Services. Goods are, say, 33% of GDP, and Services are the other 67%. The question was then, would you rather have 10% productivity growth in Goods (and 1/3 x 10% = 3.3% TFP growth), or 10% productivity growth in Services (and 2/3 x 10% = 6.67% TFP growth)?

Eli’s answer was that because of the larger GDP share of Services, you’d want to focus there, as it would ensure maximum TFP growth. My initial response was that this wasn’t necessarily true, and it depended on things like elasticities of demand and such.

In thinking about it more, Eli is right under most reasonable assumptions about the world. I might be technically correct that it depends, but only in weird edge cases that don’t seem applicable.

Why is he right? Because the weights in GDP are …. the weights in GDP. If Services account for 2/3 of our output, then increasing productivity by 10% for 2/3 of what we produce is better than increasing productivity by 10% for 1/3 of what we produce. That is going to be true whether Goods and Services are complements or substitutes.

One thing I brought up in the last post is that the weights might change in response. That’s fine here, as per Eli’s algorithm you just keep pushing for productivity increases in the larger industry each period. So if you chose 10% productivity growth in Services today when they are 2/3 of GDP, that might cause (because things are complements) their share of GDP to fall to 1/3 (and Goods to rise to 2/3). Then tomorrow you would want to push for 10% productivity growth in Goods, as it would be the larger industry. With complements you are bouncing around trying to push up productivity in all industries over time because you care about consuming all things.

Research effetiveness

This is not my Damascene conversion, however. While acknowledging Eli’s point, I think there are other reasons it is not the appropriate way to think about using TFP to guide or measure innovation.

The first is that it isn’t possible to choose between “10% productivity growth in Goods or 10% productivity growth in Services”. Our actual choice is about how to allocate scarce resources: R&D dollars, time, and brainpower. How those resources translate into productivity growth is not obvious, and there is no reason to believe that this translation is similar in both Goods and Services. 10 “units” of R&D may deliver 9% growth in Goods productivity, but perhaps only 3% in Services.

There is plenty of prima facie evidence that productivity growth in Services is much harder to achieve than in Goods. Baumol’s original work on the cost disease was centered around why this was the case. I did a long post on this, and why the nature of time/labor use in different activities makes productivity growth easier or harder to achieve. More broadly, there is nothing to suggest that an equal amount of research effort on any specific project would yield precisely the same productivity improvement as another project.

What we really need to know is the relationship of productivity growth to R&D resources (or brainpower or time) for each industry individually. Here’s a quick example. If we put all our R&D resources into Goods, we could achieve 9% productivity growth, but if we put them towards Services we get only 3% productivity growth. Now, given the same GDP shares above, which is better?

The math is pretty straightforward. 1/3 times 9% is 3% growth in overall TFP if we choose Goods. 2/3 times 3% is 2% growth in overall TFP if we choose Services. In this case it would be better to choose Goods. More generally, if the effectiveness of R&D resources in Services in less than half of what it is in Goods, then you should choose Goods.

That decision point changes as the GDP shares change, as you’d expect. But the general point remains, and this isn’t some weird edge case I’m talking about. This is the observation that if you want to use TFP to allocate your R&D, you have to know the relationship of that R&D to productivity growth in all the different possible avenues for that R&D. The size of the industry is necessary to decide where you target R&D (big is good), but it is not sufficient.

How would you know the effectiveness of R&D resources? It depends on expected values of possible research projects, their probabilities of succeeding, and the cost of each one. In other words, there is no way you could assess all the possibilities. This is the kind of thing where I think you want prices to work their magic, in all their Hayekian information-discovery glory, and let the market figure out what the most efficient allocation of R&D resources would be.

Which doesn’t mean you can’t push in certain directions, but hold onto that idea for a moment.

The magic of miscellaneous profession services?

If we leave aside this issue of R&D effectiveness, there is still the question of using the GDP shares to target things. Which GDP shares? There are multiple ways to break down GDP across industries, sub-industries, and so on. The input/output account at the BEA tracks 71 industries, but also has a more refined breakdown across about 400 sub-industries. Which one do we use to target R&D?

If we stick with the 71, are we sure these are comparable? The NAICS codes that define these 71 industries were an outgrowth of SIC codes, and both sets of codes are skewed towards tracking manufacturing. Meaning that they are much more fine-grained within manufacturing than they are within services. So all the manufacturing industries will tend to look small because they are separated.

In 2018 the largest share is for “Misc. professional, technical, and scientific services”, at 13.6%. Wholesale trade is 10.9%. “Other Real Estate” is 9.8%, while “Housing” is 9.7%. “Admin and support services” is 8.9%.

Just for comparison, “Electrical equipment” is 1%. “Data processing, internet publication, etc.” is 2.5%. “Publishing (incl. software)” is 1.6%. “Hospitals” are 2.4%. “Ambulatory health care” is 3.8%. “Chemical products (incl. pharma)” is 4.6%. If I add up all the industries associated with energy production, I get to about 7%.

Do we use these shares to make our decisions? Does focusing on “Misc. professional, technical, and scientific services” sound right compared to energy? Do we want innovation in “Other real estate” relative to hospitals, pharmaceuticals, or health care in general?

If I add up all the manufacturing industries, I can get to a number like 25-30%. So does that mean we should focus on manufacturing over Wholesale Trade? Or do I add Wholesale and Retail together? Do we focus on manufacturing to exclusion of everything other industry, because when disaggregated they happen to be smaller?

Our attempt to try and focus R&D using possible TFP growth is going to be arbitrary, as there is no “right” way to classify economic activity. The classification is a choice, and we could justify all sorts of R&D spending allocations by making different choices, even if we had perfect information on the effectiveness of R&D.

Unpriced goods

Ok, the last section was a little snotty, I admit. I have a long-standing annoyance with industrial classification systems that are too focused on “industrial” due to inertia and a notion that the only thing that counts as “real” economic activity involves steel. Which is entirely besides the point.

More relevant for this post is how even if we did trust our industrial classifications, they probably don’t point us towards a welfare-maximizing allocation of R&D. That’s because a lot of what we (I think) hope to innovate on is unpriced and not included in GDP.

The clear example here is energy and climate change. Based solely on its contribution to GDP, the energy industry would not attract a ton of innovation. As I noted above, it is only about 7% of GDP. Energy is already cheap. That’s not the problem. The problem is that it’s dirty.

From an overall welfare standpoint we care about clean energy. But because the cleanliness of energy doesn’t show up in GDP, it doesn’t show up in TFP. Hence TFP could well be underweighting the importance of innovation in energy relative to other areas.

Go back to the original question above. Let’s say that the hypothetical 10% increase in productivity in Services does just that, but has no impact on the environment. But the hypothetical 10% increase in productivity of Goods also involved a reduction in emissions or pollution (e.g. solar panels make electricity cheaper and cleaner). Then the value of doing innovation on Goods could well be higher than doing innovation on Services, even though Services make up a larger part of GDP, and even though innovating on Goods would result in lower measured TFP growth.

“Could well be higher” is the problem. We don’t know the weight to put on the environmental benefits from Goods innovation. But not knowing the weight doesn’t mean the weight is zero. Unfortunately looking only at TFP assumes that weight is exactly zero.

The most concise way of stating it is that GDP (and GDP share) is measured at market prices, and those market prices don’t incorporate (all) externalities. To the extent you can, you want to institute subsidies and taxes to build in those externalities. Those externalities would make the GDP share of dirty or unhealthy industries higher, and the GDP share of clean or healthy industries lower. Eli’s decision mechanism would get closer to the right answer on innovation if the shares reflected the externalities.

But even if you did that you’d still have the problem with unknown research effectiveness. At this point, though, if we got the prices to reflect the externalities you could let the Hayek-info-discovery price mechanism do it’s magic, and it would shunt resources towards the highest value innovations. Which I don’t think Eli would disagree with. He’s right that you want to push R&D towards the most valuable use. I think we just disagree on how to establish that value.

I’m clinging to my TFP agnosticism for now.

Oh, remember that nice comment about the quality of the debate and the 0.0001% of the internet that doesn’t suck? Yeah, about that:

Ted Cruz is a seditious grifter who should resign.

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