To encourage production of new terrain, a tax subsidy for maps


This is a post about a paper I just put out to Elsevier’s SSRN, because I believe every academic paper should have a blog post explaining why it is useful.

The paper is about the intellectual property (IP) box. The proposal is to provide a lower tax rate to profits associated with a patent or other IP. IP boxes currently exist in a few countries, and a few bills have been introduced in the U.S. Congress to set up an IP box.

The bills proposing IP boxes—which they refer to as innovation boxes—could possibly be traced to a measurement problem. Innovation is hard to define, let alone measure, so many academics will use patent rates as a proxy, in a classic case of looking under the lamppost and replacing a complex concept with something that can be counted and looked up in a database. This seems to have become ingrained, and arguments about patent boxes seem to depend upon the assumption that patents==innovation. This column traces where that substitution leads us.

The math in the paper is a mixed-strategy Nash equilibrium of a two-player game, which produced actually policy-relevant results. I don’t see solutions of equilibria in continuous strategies all that often, so even if you think the IP box politics is uninteresting you may get something out of the paper by skipping straight to the game and its solution in the appendix.

Every IP box has a different definition of what is qualifying IP: some include movies, some include only patents, and so on. For simplicity I’m going to assume just patents here; see the paper for the details.

Claim: innovations are patented

Let us define research as inquiry that leads to knowledge in the public domain, and development as inquiry that leads to private property like a patent. Laws of nature are not patentable, so anything we have learned about mathematics, chemistry, biology, is research, not development. Even within the realm of inventing gadgetry, there are wide ranges of things, like software as such or “obvious to try” developments, that can not be patented.

Claim: Each patent is an innovation.

A lot of patents—I’d say most—provide an incremental step forward on something rather uninteresting. They are definite steps forward, but not necessarily what we picture as innovation.

There are some parties that benefit greatly from maintaining a general belief that there are distinct innovation industries that work differently from others. Maybe you’ve noticed that the software industry has lately taken to calling itself the “tech industry”. Especially given how broad some IP boxes are (including know-how or designs), chair makers and restaurants could claim IP box credits.

Claim: The spillover benefits to important inventions, like transistors or CT scans, are immense. If these had not existed, society would be much worse off.

This is true, but to make this statement useful for policy it is important to know the counterfactual of what would have happened if our favorite major inventions were not invented by their inventors. Pop history likes to characterize the people who invented fundamental technologies as Great Men without whom the invention would never have existed. But the academics who study these inventions, anecdotally or using data from various sources, find that simultaneous invention is the norm, and if the Great Men who got there first didn’t do so, humankind would be deprived of the invention by a few months or years, not forever.

This makes it hard to measure the spillover benefit from a single patent. If a grain provider has a higher-quality product than its competitors, it can charge a penny a pound more, and there’s our measure of the added benefit. If an inventor gets a patent first, then the second to invent (or second to file, let’s not get in to it now) is locked out entirely. With grain, the counterfactual of what life would be like if the better grain maker didn’t exist is easy—check the next one. With an invention, the counterfactual is an exercise in creative alt history. But only if we believe the Great Man theory—and I can’t find a non-pop writer who does—will the benefits provided beyond the counterfactual be the full benefits of a new invention.

Claim: Subsidizing development has immense gains because inventions have immense gains.

If we don’t know what would happen if an inventor were somehow halted, we also don’t know what would happen if an inventor were subsidized. Maybe we’d get something that would otherwise be impossible; maybe we’d get something two weeks earlier.

Note that we’re still talking only about subsidizing development. Research has a commons problem, meaning that if we don’t subsidize many threads of research, they are economically infeasible and may indeed never get done.

Claim: When patents leave the country, the country is less innovative.

A patent has an inventor and an assignee. If we believe that having smart people who come up with interesting ideas geographically close is beneficial to the economy (and I do), then we want to have nearby inventors of patents, of artwork, of all kinds. The assignee, meanwhile, signs the contracts and takes in the royalties.

Having the assignee geographically close has little or nothing to do with invention. It may be a holding corporation with zero employees. It may be registered in the island nation of Sargasso, but have all its cash in an account at Bank of America, where the funds are used to support loans to U.S. startups.

WTO trade treaties prohibit making restrictions on where a patent can be assigned. The inventor may be unable to leave or enter a country, but the ownership assignment must be able to.

Claim: Patents leaving the country is costing billions in lost tax revenue.

This is true, but shouldn’t be. Say that WidgetCo holds a widget-making patent, and sells it to HoldingCo for $10 million. WidgetCo wants to keep making widgets, so they pay HoldingCo royalties of $1 million every year for the next eleven years, at which point the patent in our example expires. So WidgetCo has effectively shifted its risk to HoldingCo, and turned a long stream of future income into a big chunk of present cash. HoldingCo absorbed the risk, so it should make some profit off the transaction, but if it made too much then WidgetCo should have done all this with somebody else who would offer a better rate. In short, a patent reassignment paired with a licensing deal should be largely revenue neutral, and therefore also largely tax neutral. This would especially be the case with a patent portfolio, where the risk of dozens of patents are pooled.

This is not what we’re seeing in real life among U.S. companies and their subsidiaries overseas. When these companies assign a patent to their own sub, they consistently take a payment that is absurdly low relative to the future royalty stream: sell the right to a holding company in Sargasso for a million, creating an obligation to ship 100 million a year in royalty payments overseas. The million coming in to the U.S. is taxed; the 100 million a year going out is not. Incorrect transfer pricing is what makes IP shifting a tax avoidance scheme.

Claim: If we just lower tax rates to below Ireland’s, we can get those patents back.

A lowered rate is one step in a sort of auction for the assignation of the patents. As a baseline, consider a situation where two countries are bidding for the right to tax some mobile capital. They each have their own fixed capital in the country, and declare some tax rate at which both mobile and fixed capital will be taxed. The mobile capital will then flee to the lower-tax country.

If this were played as an alternating, turn-based game, the bids would never settle down. Bids would get lower and lower until one bidder realizes that it is better to just tax the fixed capital to the max than go so low chasing after the mobile. But then the other bidder won’t bid so low, and raises to just underbid the max-taxing bidder, and so on.

This is where mixed strategy equilibria come in, giving us a stable distribution to describe the outcomes. The claim that countries would randomly draw tax rates is a clear fiction, but it’s at least not incoherent, acknowledges that the U.S. setting its rate is not the last step, and produces predictions that are in line with reality.

First, in the unique mixed strategy Nash equilibrium, the country with larger capital, let’s call it the USA, will let the mobile capital go to the smaller country (the fictional tax haven of Sargasso) with a likelihood increasing in the disparity between capital rates. In the sequential game, Sargasso loses less in taxes from fixed capital when it bids lower, so it can always underbid the USA, and this fact from the equilibrium reflects that part of the storyline.

However, Sargasso doesn’t have to bid so low if the USA isn’t willing to bid low because of a loss of taxes associated with fixed capital. So the expected tax rate that the mobile capital sees is an increasing function of the amount of fixed capital held by the USA.

As a corollary, the expected tax revenue the USA sees from just the mobile capital is an increasing function of the amount of fixed capital it is taxing at the same rate. It wins the right to tax the mobile capital less often as it is less willing to bid low, but the rise in expected rates is enough to offset that.

Claim: The USA could better compete in the race to the bottom if there were a separate tax rate for IP.

How would we modify the model to describe an IP box? As it is, there is some fixed capital that is taxed at the same rate as the mobile capital, but the point of the IP box is to eliminate that linkage. If our interest is the tax rate on the mobile capital, the fixed capital associated with that rate is near zero.

We can then read the results off the model, and they’re not good for the taxing entities. The expected tax rate on the fixed capital goes to zero, and the expected revenue to the USA goes to zero.

Claim: Ireland and Luxembourg already have IP boxes, and the sky didn’t fall.

This is true, but is uninformative when considering a U.S. IP box. The model results are all asymmetric, primarily keyed to the fixed capital of the larger country. Why should Sargasso lower rates to zero if the USA can’t lower its rates below some high threshold without losing domestic revenue?

This is especially salient because, due to recent history, a lot of the high-tech happenings just aren’t in the countries that have IP boxes (it’s debatable whether China has an IP box, by the way), so the competition is still focused between countries with a higher high-tech stock like the USA and smaller countries trying to gain a foothold.

Claim: A lowered tax rate on IP-related profits would lead to increased research and development

First, remember that the lower rate on patent-related work isn’t about research at all. We’re not using tax revenue to fund the NIH or NSF, we’re lowering tax revenue to encourage patenting.

As for development, we already have some incentives that are proportional to the level of research and experimentation. The IP box incentive is proportional to the level of profits associated with R&E. The extra steps of finding associated profits give wide latitude to game the system. If you associate profits with R&E (taxed at 10%) but associate expenses with ordinary profits (taxed at 35%), you can score a negative tax rate from adding a profitable business line. If you contract out your lab to a bigger firm with a larger scale of profits (something that can be done entirely on paper), the bigger firm gets more IP box benefit, and then you can split the savings. The third part of the paper brainstorms all the ways you can game an IP box without doing additional bona fide research or development. It was fun to write.

Claim: An IP box leads to an overall lower corporate tax rate.

This claim is true. But the right way to lower corporate tax rates is to lower corporate tax rates, rather than producing something that can be gamed like crazy, would only win patent assignments back from Ireland if Ireland somehow was unable to respond, and is likely to distort behavior in many ways unrelated to expanding human knowledge.


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