# The Brookings Patent Report is Bogus

Brookings has a new report out by Jonathan Rothwell, José Lobo, Deborah Strumsky, and Mark Muro that “examines the importance of patents as a measure of invention to economic growth and explores why some areas are more inventive than others.” (p. 4) Since I doubt that non-molecule patents have a substantial effect on growth, I was curious to examine the paper’s methodology. So I skimmed through the study, which referred me to a technical appendix, which referred me to the authors’ working paper on SSRN.

The authors are basically regressing log output per worker on 10-year-lagged measures of patenting in a fixed effects model using metropolitan areas in the United States.

$\ln y_{i,t} = c + \beta_{1} \ln ( patenting_{i,t-10}) + \beta_{2} \ln ( Population_{i,t-10}) + \beta_{3} \ln ( y_{i,t-10}) + \beta_{4} \ln ( \text{predicted productivity}_{i,t-10}) + \beta_{5} \ln ( \text{educational attainment}_{i,t-10}) + \text{place and dummy variables} + \varepsilon_{i,t}$

The model is structured in this relatively standard way to reduce endogeneity—there might be more patents filed where labor productivity is highest, rather than higher labor productivity where the most patents are filed. And if the only concern were reverse causality, then it would be a good way to study the question of patents and innovation.

The authors find positive coefficients on the patenting variables and conclude that patents drive economic growth both in local areas and in general.

This report documents how a strong national innovation system plays out across a dispersed array of U.S. metropolitan areas, contributing to economic growth in both local places and across a large and diverse country.

Clear in these pages is the continued vibrancy of the U.S. innovation as well as the general utility of the nation’s patenting system. (p. 28, emphasis added)

These conclusions are unwarranted given the model and findings expressed in the paper. To see that this is the case, assume temporarily that patents do nothing to incentivize real innovation, and that they merely transfer wealth from consumers at large to the patent holder through firm profits. If this were the case, then we would find that measured output per worker was higher in metropolitan areas with more patents—exactly what the authors found!—because they are gaining profits at the expense of consumers in metropolitan areas with fewer patents. In other words, the authors could be laboring under a fallacy of composition. Just because patents enrich the MSAs that generate them doesn’t mean that they are a source of prosperity for the nation as a whole or that they increase social welfare.

Alternatively, assume temporarily that patents do nothing to incentivize real innovation, but that firms that produce valuable innovations must defensively patent them to avoid being taken to court for using their own inventions. If this were the case, then patents would correlate with real innovation, and therefore with output per worker, but they would not cause an increase in productivity. In addition, at least some of the measured increase in output would come from an influx of highly-paid intellectual property attorneys, which by assumption does not represent real added productivity. Note that the top-patenting MSA in the study is Silicon Valley, the part of the country where people are most concerned about defensive patenting. But the word “defensive” does not appear even one time in the report, the appendix, or the working paper.

The authors have done nothing to identify the effect of patents on productivity, which is to say, nothing to rule out either of the possible assumptions above. They are simply relying on the assumption that more patents means more innovation.

This flaw in the paper makes all of their policy conclusions suspect. For example, if patents represent a mere transfer, then encouraging patent-generating institutions is socially destructive. It might nevertheless be rational for a single MSA to encourage such institutions, because residents of the MSA would enrich themselves at the expense of other MSAs. In this case, we should adopt federal policies to discourage patent-generating institutions. If patents merely correlate with innovation due to defensive patenting in some domains, then the U.S. patent system is not working as intended, which is again the opposite of what the authors conclude.

On point, the Winter 2013 Journal of Economic Perspectives is out this week, featuring a four-paper symposium on patents. The lead article is by Boldrin and Levine, entitled “The Case Against Patents.” Here is the first paragraph:

The case against patents can be summarized briefly: there is no empirical evidence that they serve to increase innovation and productivity, unless productivity is identified with the number of patents awarded—which, as evidence shows, has no correlation with measured productivity. This disconnect is at the root of what is called the “patent puzzle”: in spite of the enormous increase in the number of patents and in the strength of their legal protection, the US economy has seen neither a dramatic acceleration in the rate of technological progress nor a major increase in the levels of research and development expenditure.

Petra Moser’s article does a historical comparison of countries with strong and weak patent laws and concludes:

Overall, the weight of the existing historical evidence suggests that patent policies, which grant strong intellectual property rights to early generations of inventors, may discourage innovation. On the contrary, policies that encourage the diffusion of ideas and modify patent laws to facilitate entry and encourage competition may be an effective mechanism to encourage innovation. (emphasis in original)

I hope that policymakers don’t rely on Brookings’s strong reputation and infer that our patent system is the strong engine of economic growth that Rothwell et al. suggest it is.

# A Difficulty in the Concept of Social Welfare

Welcome to the third installment in our series of discussions of the Most Insightful Articles in economics. Today we are discussing Ken Arrows’s 1950 article A Difficulty in the Concept of Social Welfare.

If you’re interested in politics, you may have done the following thought experiment. Suppose there are three voters—1, 2, and 3—and three alternatives—A, B, and C. Voter 1 prefers A to B to C. Voter 2 prefers B to C to A. Voter 3 prefers C to A to B. By a vote of 2-1, “society” prefers A to B. It also prefers B to C. If a rational person prefers A to B and B to C, then that person prefers A to C. But in this example, “society” prefers C to A! Is society irrational? Is this just a problem with majority rule? To cut to the chase, in this paper Arrow shows that it is a general problem. Any method of aggregating individual preferences is either irrational or has some other properties that are arguably undesirable.

One can envision collective decision-making as selecting a social welfare function and then using it to compare states of the world. Arrow defines five conditions to which a social welfare function ought to hold:

1. The function is universally defined. There are not certain preferences that people can have that cause the function to be indeterminate (though the function is allowed to express indifference).
2. If someone decides that X is more desirable than he initially thought, and nothing else changes, the social welfare function cannot penalize X.
3. The function should provide the same ranking for a subset of options as it would for that subset within a complete set of options. Adding or removing an option should not affect the ranking of other options.
4. No preferences are taboo. Any social preference ordering is possible if people have the right individual preferences.
5. The function must be collective in the sense that it does not simply mimic one person’s preferences.

Seems reasonable, no? Arrow’s proof proceeds by contradiction. He assumes that there are two individuals, three alternatives, and a social welfare function that satisfies the above conditions. These assumptions lead to three consequences:

1. If both individuals prefer one outcome to another, then the social welfare function prefers it as well.
2. “[I]f in a given choice, the will of individual 1 prevails against the will of individual 2, then individual 1’s views will certainly prevail if 2 is indifferent or if he agrees with 1.”
3. If individual 1 prefers X to Y and individual 2 prefers Y to X, then the social welfare function must be indifferent between X and Y.

Now, suppose that individual 1 prefers X to Y to Z and individual 2 prefers Z to X to Y. By consequence 1, the social welfare function prefers X to Y. By consequence 3, the function is indifferent between Y and Z. Since the function prefers X to Y and is indifferent between Y and Z, the function must prefer X to Z. However, also by consequence 3, the function must be indifferent between X and Z. This is a contradiction, which means that one of our assumptions cannot hold. In Arrow’s words:

If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be defined for a wide range of sets of individual orderings are either imposed or dictatorial.

What does this mean? There is no “will of the people,” at least not if that phrase is to encompass what we normally think of as rationality. Rousseau is incoherent. Democracy can be manipulated by agenda control, as Levine and Plott show in a hilarious article in Virginia Law Review.

How can we get around this conclusion? One way is if preferences are unidimensional and single-peaked. If all voters think in terms of a single liberal-to-conservative spectrum and prefer candidates that are closer to some optimum point, then you can no longer demonstrate the contradiction. Another way is if you allow some way of expressing intensity of values (interpersonal comparisons of utility), such as by bidding with dollars, though this may undermine some of Arrow’s conditions.

For discussion: Voter preferences are shockingly unidimensional, are they not? People who favor high taxes tend also to be pro-choice on abortion. What do these have to do with each other? Does this correspondence save democracy from the charge of irrationality? Or is it further evidence of it? Does Arrow’s result explain why everyone is so dissatisfied with the government basically all of the time? In light of Arrow’s result, are some voting systems better than others? Does the fact that collective choice is incoherent mean that collective morality is also incoherent?

Next time, we will discuss Ronald Coase’s 1960 paper The Problem of Social Cost. If Arrow had read Coase, he would not have made the errors that he made on p. 334. See you in the comments!