What Does a Football Manager Do?

I am watching the Benfica–Juventus match, and I couldn’t help but notice some of the behavioral patterns of members of both teams. The players are clearly following rules that they learn during their training, and that are both generalized (for all matches) and specific (to deal with specific qualities of the opposing team). It reminded me of a comment Atlético de Madrid manager said a couple days ago. He said that managing is not so much about motivation, because all top division players are winners; rather, managing is about providing players with a specific set of instructions, to help them along with their own skills and intelligence. What characterizes a good football team?  A good set of instructions, or rules.

There is a similarity between what makes a good football team and what makes a well-off society. My discussion on rules and football serves as an analogy for rules, or institutions, and coordination between society’s members. Likewise, it may serve as a more direct analogy for what makes the firm what it is.

A football manager is similar to an entrepreneur, in that this person is responsible for finding the best way of allocating the inputs (the players) at his disposal. He is responsible for finding and producing along some demand curve. The way the manager does this is by imputing on to his team a set of tactics. Tactics specifies how the different players interact between each other, and therefore how they are allocated. But, it’s not enough to just organize your players on the field — i.e. decide on a formation —, and then let your players simply decide for themselves what to do on the field. Well, a manager could do this, but he wouldn’t be very successful (and they rarely are).

Good teams are well drilled. There are decision-making heuristics that players must known by second-nature. Defenders have to know when to challenge for the ball, and when only to harass the opponent; it might be that by challenging they can break their own defense, if they make a mistake. Players need to know when to press and when to track back. They need to be drilled on how to decide when to launch ambushes, to try to swarm an opposing player and rob the ball. In football, the team is greater than the sum of its parts. These rules are to in place to guide decision-making such that it is mostly congruent with the general tactics the manager has imposed. For the team to work the manager wants it to, the individual has to choose in certain ways that make the team work well.

Juventus provides one piece of evidence. Dominated by Benfica, they formed two lines of four, with Tévez and Vicinic looking for the counter-attack. Benfica’s midfield was passing it between themselves in front of the Italian team’s defensive lines. You could see Paul Pogba and, I think, Andrea Pirlo trotting back and forth as Benfica’s men passed it in front of them. In fact, the entire defense was synchronized. These players have internalized a set of rules that help them the display a high degree of unity and discipline as a team, oftentimes at the expense of the individual. In a Europa League semifinal, this type of intensity is to be expected, but an average team does not display this degree of tactical rigor in an average game — because they are not well drilled, that is they don’t always follow the rules.

Rules are important in attack, as well. Players are taught how to coordinate counter-attacks with each other, by passing into open spaces ahead of them and relying on their individual strengths to beat their rivals to the ball. They develop heuristics on who to seek, and what the best way of providing a teammate the ball is. A team, for example, might have a distributor, which other players might seek. This player is the lynchpin in the transition from defense to attack, because he distributes the ball to wingers or strikers. The decision to seek out a specific player to set up the counter-attack is based on a rule, because that rule leads to the best outcome on average.

If the ball is lost, a good, title-winning team needs to be drilled on how to press, and how to track-back the defense if they can’t recover the ball soon after losing it. A well drilled team will shave a good number of seconds in the amount of time it takes to recompose their defense if their counter-attack is cut short. Players need to be given instructions on how to judge when to press, when to ambush, when to track back, and how to maintain cohesion. In fact, a great example of the advantage of a well-drilled defense is Benfica’s defense during this semifinal with Juventus: their defense responded as quickly as Juventus’ counter-attack.

This Benfica–Juventus match provides yet another example of how rules are used in football. In the first half, Benfica managed to essentially nullify Juventus’ midfield. They did this by minimizing Pirlo’s interaction with the ball. How? The Benfica manager, Jorge Jesus, instructed his midfield to organize in what almost looks like a box, with four men surrounding Pirlo and moving to block passing spaces. Remember, the manager has to think about how to best associate his inputs with each other, to produce the highest value product possible. Jorge Jesus is denying Juventus the use of one of their most important inputs, their playmaker. Juventus’ manager, Antonio Conte, did not provide Pirlo, and other players, a set of rules to deal with these kind of situations. The Juventus midfield is doing better this second half, so maybe Conte has issued a new set of instructions.

Why are rules so important? A player can respond to a situation in many different ways. If he does not consider anything else but his own circumstances, there will be some optimal decision that he will come to. But, there may be circumstances which matter, but which he does not consider because he’s not aware of them. The player has an imperfect set of knowledge. Rules help him overcome this “ignorance.” Rules are informed by disparate circumstances. Good rules guide individual decision-making for the good of the team, because they help the player decide as if he held knowledge on circumstances other than his own.

The more complex a system is, the more difficult it is to plan and impose a set of rules. Rules have to be informed by many different circumstances, and the less of these any one person is aware of, the less any one person is capable of designing a set of good set of rules for the system. In complex societies, many rules may arise spontaneously. They may be developed by players, but they become popular because they work — it’s a sort of institutional evolution, of the kind Hayek had in mind. But, orders of lower complexity can be well understood, and once abstract rules come to be well-known, they can be imposed. A good manager is a good central planner, because he can devise a set of rules that allows his inputs to work best with each other and produce the most value product.

Unemployment’s Demand Side

About four months ago, I wrote on a for-fun empirical model, to test whether cyclical unemployment is predominately supply- or demand-driven. At the time, the results suggested that aggregate demand was the main determinant, although “labor freedom” (the only statistically-significant supply-side factor) could explain quite a bit in countries where unemployment is highest. I wanted to come back and see what the results look like if I try to incorporate the Phillips curve. Also, it would be interesting to know whether a demand shortage’s effect accumulates as “labor freedom” decreases.

The model is,

Unemployment Rate = β0 + β1Labor Freedom + β2Business Freedom + β3Fiscal Freedom + β4Property Rights + β5%ΔMoney + β6%ΔMoney2 + β7%ΔMoney×Labor Freedom + ε

Unemployment data is from the IMF, money growth data is from the World Bank, and the Heritage Foundation provides the rest. Definitions and rationales for the variables,

(a) Labor freedom: A proxy for labor market flexibility. Where labor regulations increase hiring costs, we expect greater unemployment.

(b) Business freedom & property rights: These were included to test the regime uncertainty thesis. According to the theory, lower business freedom and ambiguous property rights are disincentives to investment (and indirectly, employment).

(c) Fiscal freedom: This is a measure of tax burden. One belief is that higher taxes are a disincentive to invest. There is also a related argument that reducing taxes is stimulating, because it increases private spending. Either way, the supply-side argument expects positive correlation between tax burden and unemployment.

(d) Percent change in the money supply: This is the aggregate demand variable — and the data i for base money. I agree, maybe NGDP may have been a better choice. I’m not entirely convinced, because I think changes in money supply might test aggregate demand as a policy more directly. There is probably a choice that’s better than both of them, because changes in aggregate income can be caused by both supply- and demand-side factors.

Unemployment v. Money Growth (version 2)

The Phillips curve is introduced through the quadratic. The accumulation effect is represented by the interaction term %ΔMoney×Labor Freedom. Surprisingly, the interaction term is statistically insignificant. At least, it was surprising to me, because, for countries with very high unemployment rates (e.g. Spain and Greece), the coefficients for the linear approximation did not seem able to explain, on their own, the extent of their unemployment. So, when these two factors interact, maybe their effect is much worse than simply their sum. The data says no.

The two statistically significant variables are the quadratic term and labor freedom.

Unemployment Rate = 23.05 + –0.1021Labor Freedom + –.5726%ΔMoney + 0.0138%ΔMoney2

Introducing a Phillips curve actually very slightly decreases the effect of monetary policy. The prediction is that a one percentage point increase in rate of growth of the money supply will reduce the unemployment rate by –.5576 + .0276(%ΔMoney) percentage points. What this implies is that there are diminishing returns to monetary policy, and that as monetary policy growth rates become smaller, the negative effect becomes greater. The data is in line with the position that the worst monetary policy — whether public (central bank) or private (e.g. a clearinghouse issuing its own emergency notes) — is pro-cyclical, but that excess supplies of money at first have only a relatively minor negative effect on unemployment and then a gradually growing positive effect. Here, negative and positive have reverse meanings, because a positive coefficient implies a growing unemployment rate.

The marginal effect of labor freedom has also slightly increased, from –0.0961 to –0.1021. The original test, therefore, slightly underrepresented the role of inflexible labor markets. Still, labor inflexibility explains relatively little. For example, 2012 U.S. had a ranking of 95.5 out of 100; the most it could increase its labor flexibility is by 4.5 points, or a decrease in the unemployment rate by –.4595 percentage points. For cases like these, the coefficient is probably overstated, because it’s probably not the case that an increase in labor freedom from 95 to 96 is as significant as a change from 50 to 51. Likewise, if Greek labor markets were as flexible as U.S.’, the 2012 Greek unemployment rate would be 5.4521 percentage points lower. Even in cases where labor inflexibility is significant, it cannot explain even the majority of cyclical unemployment.

Because it’s interesting to some, that neither business freedom or property rights are statistically significant suggests that regime uncertainty is not a relevant explanation for cyclical unemployment — at least, not in this recession.

Stagnation and Technology

One line of reasoning tells us that growth is stagnating, because we have picked the majority of “low hanging fruit” and we haven’t been adequately reproducing it through technological invention. Tyler Cowen and Robert Gordon may, for example, claim that the internet is incomparable to the railroad, the automobile, et cetera. On the one hand, maybe their judgment on the value added by the internet is flawed; on the other, maybe their judgment of 19th century inventions is too,

On this basis the social saving made possible by the 59,000 million ton-miles of non-agricultural freight service provided by railroads in 1890 was $189 million. The last figure added to the ” pure ” agricultural saving yields a total of $329 million on all commodities. Thus, the availability of railroads for the transport of commodities appears to have increased the production potential of the economy by about 3% of gross national product.

— Robert W. Fogel, “Railroads as an Analogy to the Space Effort: Some Economic Aspects,” p. 40.

Institutional Discrimination Against North American Football

Why don’t Spanish teams recruit heavily from Spanish-speaking leagues in North America (all those north of, and including, Panama)? While these countries produce the occasional star, the average quality of their players is relatively lower than that of South America and Europe. Panamanian, Nicaraguan, even Mexican (the strongest league in North America), players do not attract the lucrative offers that many South American players do. Why is that? Because the way regional football associations are organized. The average quality of their continental tournament is much, much lower than South America’s. Thus, their players are exerted less as they develop, and their average quality is lower when compared internationally.

It makes sense to recruit from countries with lower transaction costs. There are, for example, many African players who leave for France early in their careers. 19 out of 20 Ligue 1 (top flight) teams have African players on their roster (for Paris Saint-Germain, few transaction costs are high enough to impede them from signing players). France’s national team’s last roster include two players born in Africa. 20 out of 20 Belgian Pro League teams include African players in their roster. English Premier League clubs also buy relatively heavily from African leagues, but often French clubs act as intermediaries. Spain recruits heavily from Argentina, and has started to increase recruitment in Chile and Colombia; countries which have built strong national teams without (originally) having access to strong players playing in strong European leagues.

Why are transaction costs lower? Countries with shared history — namely, colonialism — form “linkages,” such as a widely known common language, oftentimes looser immigration laws — especially for those with high MVP (marginal value product) —, strong immigrant communities in receiving states, et cetera. Apart from the attractive relative real cost (weighing for average skill) of African players, linkages also make assimilation within teams easier. A team with relatively perfect substitutes performs better than those with relatively imperfect substitutes on average, because the strength of the relationship between the players matters a lot in football (it’s a common characteristic in teams with high discipline, relative to other teams in their league).

Although Spain colonized much of North America, including most of the geography between the western United States and Panama, it does not draw on players born in these countries nearly as often as those originating in South America. I suspect the reason for that is that the average quality of the North American player simply cannot compete with those of the South American and African leagues (growing African migration to Spain also creates a network effect through migrant communities, lowering transaction costs). The reason this is the case is because of the way continental FIFA associations are organized: CONCACAF is one of the weakest associations. It is one of the weakest associations because of the countries which make it up.

Consider the size of national football markets in CONCACAF nations. Most of Latin American enjoys football as its major sport, but most Latin American countries have very small national economies — they are not comparable to those of larger South American and European nations —, and in the two largest economies, United States and Canada, football (i.e. soccer) is not big compared to rival sports (basketball, American football, hockey, and baseball). In other words, the football market in CONCACAF is very small, and therefore much less competitive (assuming the football industry enjoys increasing returns to scale). In less competitive environments, the motivation to innovate  is relatively low, and top leagues do not have to very internationally competitive to be regionally competitive. Think of Mexico’s domination of CONCACAF (on the league level especially), but the relative paucity of Mexican players in Europe.

Inter-regional competition matters. European leagues are strong because the UEFA Champions League is strong. The Copa Libertadores is a much more difficult competition than the CONCACAF Champions League — the latter almost exclusively dominated by Mexican clubs. Being inter-regionally competitive is attractive because it means higher revenue flows, largely as a result of prize money. Atlético Madrid, in Spain, has an average revenue between 120–140 million, and typically makes a loss (and has to sell players, on net, to make a profit). So far, UEFA will pay them ~40€ million for participating in the Champions League, a 33 percent increase in revenue. Most teams do not earn that much, but the prize money is lucrative and all participants draw from the cash pot. Regional competitions are strong when national football markets are large in association member countries. UEFA benefits from England, France, Portugal, Spain, Italy, Germany, Belgium, Netherlands, et cetera (the list is long); strong local economies, where football is the main sport.

Size of the market matters because of the assumption of increasing returns to scale. A few implications are,

  1. Larger markets will enjoy lower average costs, shifting the long-run average cost schedule down, and increasing the amount of firms in an imperfectly compMonopolistically Competitive Marketetitive market. In the football industry, this can mean stronger overall football associations, because of stronger competition between national leagues (stated another way, Spain’s second division is much better than Mexico’s). This creates a good environment for innovation and progress. Most groundbreaking tactical discoveries are made by UEFA teams — e.g. catenaccio, total football, and tiki-taka;
  2. Returns to scale internal to the firm will increase profits as average cost falls (and output increases). Relatively wealthy clubs have a broader recruitment base, as they can offer higher salaries (and often a wealthy life in the receiving state) than local competitors. They also typically have better youth programs, so they can better exploit the qualities of non-national players;
  3. If there are external economies of scale, lower average costs bring with them a cumulative advantage relative to competing regional industries. These industries attract more investment, at a higher rate than clubs in associations with relatively high average costs.

CONCACAF simply cannot compete with UEFA or CONMEBOL (yea, FIFA abbreviations are absolutely horrid) in average quality. I reckon that CAF (Africa) is marginally more competitive than CONCACAF. But, it’s not because their local markets are strong — well, that explains comparatively little. However, most of Africa enjoys strong, and exclusive, linkages with many European nations (France, England, Belgium, Netherlands, Italy). These same European countries do not recruit as heavily from Spanish-speaking countries (except for Brazil and Argentina, because of the strength of their leagues — CONMEBOL is the second-most competitive association in FIFA). Likewise, France, England, and Belgium recruit more Africans than Spanish team do on average. Spain often serves as an intermediary for South American players, who pass through Spanish clubs and then move on to other European squads. Thus, African players have a large market for their labor that is exclusive to them. National teams draw on their players who play for European clubs, and therefore perform more strongly than what the strength of their leagues suggests.

But, CAF also has decently sized economies where football is the primary sport. Africa might be the poorest continent in per capita income, but it has several large countries in population. Many of these countries also have large deposits of highly valued raw materials. Their national associations are most likely subsidized, and in absolute terms subsidies (and cash prizes) are likely to be higher in larger economies. CAF clubs have done better than CONCACAF clubs in the FIFA Club World Cup. The CAF Champions League is relatively competitive. Mexican teams have won six out of ten of their continental competitions. If the MLS is slowly improving it’s not because of CONCACAF, it’s because of the growing market for the sport in the United States.

Another piece of evidence is Australia’s national football association’s, the FFA, 2006 decision to leave the OFC (Oceania) confederation for AFC (Asia). While Australia dominated the OFC, not only enjoying the major share of regional cups, but almost virtually guaranteed entry into the World Cup finals, it judged that it could simply not grow in quality unless it benefited from stronger competition. And, the A-League and the Australian national team have benefited from this change. Regional competitions matter. They determine the total size of the market. Regional associations, or what are also known as confederations, which have large markets will be stronger than those which have small markets.

I originally asked why Spain recruits much more from South African than it does from North America, While there are many countries in CONCACAF that have strong linkages with Spain, the low average quality of their confederation makes CONCACAF players relatively less attractive. Where soccer as a sport is strong, the national economies are usually very small. Mexico is an exception to the rule, but neither is Mexico as wealthy as England, Germany, France, Italy, and Spain. Canadian soccer is probably the most uncompetitive in the region. And, the market in the U.S. is still comparatively small (although growing). Therefore, Spanish clubs prefer to recruit from South America and Africa. The geographic fate of North American Latin America has condemned it to facing an extreme inequality in football quality, from the perspective of the worst-off (excepting AFC and OFC). Only very exceptional North American players are recruited by European teams, and its the rules which determine membership within regional associations that are fault.

Quote of the Week

To be sure, older individuals are certainly richer on average than younger ones. But the concentration of wealth is actually nearly as great within each age cohort as it is for the population as a whole. In other words, and contrary to a widespread belief, intergenerational warfare has not replaced class warfare.

— Thomas Piketty, Capital in the Twenty-First Century (Cambridge: Belknap Press, 2014), pp. 245–246.

Crony Capitalism, Crony Communism, and Crony Anarchism

Over at Bleeding Heart Libertarians, Matt Zwolinski poses a challenge to libertarians who defend capitalism by suggesting that its current iteration is “impure.” He shows that there may be some hypocrisy if we also critique communism because it has historically led to oppressive dictatorships — that communism could be just as “impure” as current capitalism. This is not the first time I have read this challenge, and I feel that it has been largely ignored by libertarians — but, I think there is an intuition behind that choice.

In the comments, I wrote,

You can make a case that the “pure” communist society leads to an authoritarian, extractive dictatorship. You can also make the case that a capitalist system leads to a liberal society. I think the empirical evidence is broadly in favor of this interpretation.

But, I’m not entirely satisfied with my answer. I believe that a welfare state, of a size determined endogenously, is perfectly compatible with capitalism (which does not mean that all welfare states are compatible). But, those who disagree with me will still consider that a state of “impure” capitalism.

One way to look at social change is to interpret (part of) history as a gradual improvement of institutions. These institutions make our weaknesses less relevant, and they promote coordination between agents. Consider institutions such as property and contract rights, the rules that make bad people less relevant in government (there are positive outcomes, regardless of the intentions of a single agent), et cetera. Economists interpreted these institutions, but only within a narrow time frame: ~1700–present. They called the institutional framework they saw “capitalism,” referring to a narrow set of institutions that define “the market.”* Government was seen as exogenous to market institutions, but this probably isn’t right. Institutions of governance form part of the process of social change just as much as institutions of markets, and the often are interrelated.

A critique of communism could be: communism disrupts this process of change for the worst, causing institutions to deteriorate, rather than improve. Capitalism, on the other hand, embraces the process of change, causing institutions to improve. I think the first is right, and the second is wrong. What we define as capitalism today is the product of institutional change, and if we force the process towards a defined end — what some may call “pure” capitalism (anarcho-capitalism?) — we will end up with institutional deterioration. In that sense, “pure capitalism” and “pure communism” may not be that different. Both “pure capitalism” and “pure communism” are ideals we construct, but as such they are both equally weak to the accusation of a “fatal conceit.”

* Marx, however, did not interpret market institutions so narrowly. He thought that capitalism led to a deterioration of political institutions, or crony capitalism.

Frank Hollenbeck’s Parallel Universe

I have a hard time believing that “The Sad State of the Economics Profession” was written by a professional economist. It is entirely wrong, including in its assessment of the profession, and it’s narrow, idealized history of thought. Frank Hollenbeck, the author, makes a number of claims, which are extremely unorganized, making it difficult to write a general comment. I want to address certain specific arguments,

  1. Hollenbeck’s attempt to contrast between economists who specialize in disproving “popular misconceptions” and those who “have sold themselves to the enemy” (government — maybe Hollenbeck should quit the University of Geneva, since it’s a public research school).
  2. The claim that mathematical models are not useful in economics, because “the parameters are not constant, most of the variables are interrelated with constantly changing interrelationships and omitted variables, like expectations, some of which being immeasurable, are conveniently assumed away as unimportant.”
  3. That empiricism is useless, because “it is difficult to distinguish between association and causation or correctly determining the direction of causation.” (Economists must be idiots for missing such a simple fact!)

If there is any element of truth in those three statements, Hollenbeck has done them a great disservice, because his defense of those claims is very weak.

I

The irony in Hollenbeck’s piece is that he accuses his peers of corruption, and supports his theory by building a mythology. All theory — except, I assume, that put forth by economists friendly to Mises — since 1930 is retrogressive, because it was all developed to legitimize false truths. Yes, Hollenbeck makes this argument explicitly,

The profession is always moving forward, right? In economics, we wrongly take the same attitude. Macroeconomics as a profession has not advanced but has regressed. We had a better understanding of macroeconomics 80 years ago. Politicians put Keynes on a pedestal because he gave them the theoretical foundation to justify policies that had been justifiably ridiculed in the past by the classical economists.

Nevermind that the academic popularity of Keynes’ ideas was a result of how well they persuaded his peers, not because of their congruency with public policy of the time. Although, I suppose all of Keynes’ peers were also corrupt, except (conveniently) whichever one of them might have advanced a theory that Hollenbeck actually agrees with (but may just be unaware of, because his history of thought is so poor). But, my intention is not to defend Keynes, just to point out that Hollenbeck mistakes reasonable disagreement for corruption and malice.

Economics is tough, because society is complex. Because of reality’s complexity, economists must build theories, or ideal types, that help us explain what we observe. But, this implies a certain disconnect between theory and the real world, because ultimately the former is only an interpretation. This interpretation was made by someone who only knows only some fraction (0 < x < 1) of the facts. Because we are cognitively limited, which is the reason why complex systems are difficult to understand, the ideal types we build will be similarly limited. And, because we all have asymmetric sets of priors, our posteriors are unlikely to be exactly the same. In English: economics is exactly the kind of subject over which there will be a lot of disagreement.

Hollenbeck’s approach to this disagreement is to dismiss it as corruption. I suppose this option is attractive to someone who does not know much about, or sees no merit, in post-interwar economics. The lack of merit position is hard to square, however, with the undeniably insightful theoretical advancements since 1930: the transaction cost theory of the firm (I forgot, Coase is a socialist), New Trade Theory, asymmetric information, et cetera. Those are three examples of hundreds more. Our understanding of the economy is incomparable to that of the 19th century — it is superior. J.B. Say did not benefit from the same degree of understanding of institutions, for example, or international trade, or price theory. Although, J.B. Say was smart enough to know better than Hollenbeck on monetary theory — so, I guess that some economists’ understanding has indeed retrogressed.

What about disagreement before 1930, was it also caused by intellectual corruption within the profession? Was Adam Smith a pawn of the state for preferring a dynamic, private supply of money? I am assuming that David Hume was the economists’ equivalent of a Jedi, because he advocated for a fixed money supply. Dark forces must have been behind the disagreements between Carl Menger and W.S. Jevons. J.S. Mill’s utilitarianism must have been developed to justify public policy of the mid- and late 19th century. It’s easy to play Hollenbeck’s game, but it’s obvious that the game is bunk.

What makes Hollenbeck’s approach so unfortunate, and so disheartening (as an Austrian sympathizer), is it runs contrary to the other common claim that the mainstream simply ignores what heterodox economists have to offer (and, by heterodox, I mean “Austrian” specifically). The truth is that the ignoring works the other way: heterodox economists like to ignore the mainstream, or dismiss it is as all wrong — which is essentially the same thing. But, how could a serious economist ever take a critique like Hollenbeck’s seriously? I am sure he has good ideas, but he does them an injustice by instead accusing his peers of intellectual corruption. This being an accusation that only someone terribly ignorant of the state of economics could make.

II

Forget, for a second, about mathematics and formal economics. Take any theory, such as Ricardo’s theory of comparative advantage. This theory says that exchange will be organized in such a way to minimize opportunity cost, because people will specialize where they have a comparative advantage. You have a comparative advantage in specializations where your opportunity cost is lower relative to others’. This can be generalized, and we can say that countries will specialize where they have a comparative advantage. Ricardo missed, however, — or at least it was not explicit in his model — that factor endowments help determine comparative advantages, and so initial endowments can go some way in explaining international trade. As it turned out, Ricardo’s model of trade was missing out an entire independent cause! Economies of scale can also explain trade, and it might even do a better job at it! These were factors which Ricardo had omitted from his model.

It’s strange that Hollenbeck does not level the same criticism against all economic theory. If we have to build ideal types, abstractions, to understand the real world, and these ideal types will suffer from incompleteness (because of the incompleteness of our knowledge), then they all are burdened by the same probability of omitted factors. The truth is that all economists, including Hollenbeck, are aware of this and they embrace it. That is why there is an academic process of scientific advancement. We know that our theories are not good enough, so we continue to develop them. Hollenbeck’s critique of mathematical models on account of “omitted factors” is simply nonsense.

The claim that mathematical models are useless, because their parameters are non-constant, is weak, and is equally applicable to theory in general. Theory is about positing, and rationalizing, certain relationships between variables. It’s no different whether you present a theory in words, or whether you present it in math. If you read a good theoretical economics paper, what you find is a model that is largely qualitative, in the way that I think most people understand that word. The model does not say that an increase in price by five percent will lead to a decrease in demand by one. It abstracts from those kind of specifics, focusing instead on the relationships. This is true whether the model is presented in words or in math.

Why use math at all? The problem with the written word is that it’s easy to be vague. An economist might advance a theory, their critiques would respond, and that economist might claim that his critiques completely misunderstood him. Math helps make the model more explicit. This also helps the economist to present a stronger, more complete theory, since he has to figure out the explicit model before he can present it. In other words, math helps the economist think about what he is omitting. In other words, Hollenbeck’s critique is actually stronger against the form of communication he prefers, than it is against math.

While Hollenbeck does not bring this up, one other objection to math might be that the type of assumptions that have to be made are typically much more strict, and less plausible. I think there is merit to this criticism, but it’s also something that most economists are aware of when they are drawing conclusions from their model. Mathematical models have to worry about being tractable, so that they can be worked with. Good models are always very careful about their assumptions, however, and if the simplification is too strong the model is not very useful. Economists often put work into defending their assumptions. And, when it comes to drawing conclusions, economists consider their assumptions when generalizing the results of the model.

If you think there is an “obvious case” against the use of math in economics, you are wrong.

III

This needs to be made clear: all economists know that correlation is not causation.

This is something students are told in the first or second week of an introductory econometrics class. Your model must be informed by theory. There has to be a reason that you assume a relationship between two variables. I mean, duh. It doesn’t make sense to use econometric techniques to test a theory if you aren’t actually basing your model on any theory. But, if your theory says that any increase in the money supply will cause a general rise in prices, then we have good reason to expect correlation between those two variables. We use econometrics to get an idea of what the direction of joint variation is, if there is direction at all. The theorist imputes causation, and the empiricists tests whether there is association at all.

Why would we want to test theory? People can make mistakes in their reason. In fact, they can make mistakes they are unaware of. We all do it all the time. We all have had that experience where we’ve thought something to be true for the longest time, we suddenly see it from another angle, and what was once true is now false. The false belief, at the time, seemed very reasonable. We even looked down on those who disagreed with us, because we thought they were missing something obvious (obvious to us, at any rate). But, it was only we who were missing something! Empiricism cannot definitely disprove or prove theory, but it can help to update our priors. It helps us to see which correlations in the data there actually are, to weed out theories that are irrelevant. And, if we posit a causal relationship between A and B, but we observe that B doesn’t occur, despite A, it might lead us to revise our assumptions. It might cause us to see the world a different way, and to discover something that we previously hadn’t considered.

All in all, Hollenbeck’s article is very confused. His readers deserve better, because they are being misled. That his arguments are very weak, however, doesn’t mean that my beliefs are right. That’s alright. Disagreement is a part of business, and we have to communicate to resolve them. But, accusing me of intellectual dishonesty is not a way to go about that. Neither is leveling a barrage of “obvious” problems at the profession, “obvious” problems that on second look are not problems with the profession at all.