A Giant of Economics: In Memory of Kenneth Arrow

Ken Arrow receiving the National Medal of Science from President George W. Bush Source: CNBC

On Tuesday, February 21st, Kenneth Arrow passed away at the age of 95. As numerous obituaries noted, he had an immense effect on the field of modern economics. His work invented several new fields of economic analysis and strengthened society’s understanding of several more. He was an early winner of the Nobel Memorial Prize in Economics, alongside John Hicks for their contribution to general equilibrium theory. Yet if he had never written the papers that won him the award, he would almost certainly have won it for another contribution.

His theories were also not abstractions from the world as modern critics of economics would argue. His major contributions have immediate social and political consequences and many of his other works directly explore social issues using economic methodology and tools. Thus, exploring the breadth of his works illuminates both the applicability of economics ideas to social issues and those issues themselves.

General Equilibrium: Arrow’s Nobel-winning contribution was for general equilibrium theory and welfare economics. In his work, he contributes to two important proofs. First, he and Gerard Debreu proved the existence of a general equilibrium across all goods markets, which accounts for feedback effects between markets. Previously, formal economics focused on partial equilibrium models, ignoring the interactions between nominally-separate markets.

Although the proof of general equilibrium is based in abstract mathematics, the shift from partial to general equilibrium has immense consequences for political thinking. Often, politicians rely on simplistic economic thinking to justify their political priors, a tendency sometimes satirized as ‘101-ism’ for its inability to move beyond concepts from introductory economics courses.

For example, opponents of minimum wage laws declare that minimum wages always reduce employment and raise prices by increasing the cost of labour. Under a partial equilibrium model, this thinking would be correct: a price floor set above the equilibrium wage rate leads to lower equilibrium employment.

However, under general equilibrium, the higher wages also translate to greater demand for products and services by those employees, increasing demand for labour. Thus, the certainty of the simple partial equilibrium model masks the inherent feedback effects in an economy. It also shows the necessity of careful empirical study over self-assured proclamations (for minimum wages, studies reveal a small, but still negative impact on aggregate employment.)

Welfare Economics: Arrow’s proof of general equilibrium also characterized the welfare effects of general equilibrium in the two fundamental theorems of welfare economics. The First Theorem states that under perfect competition, the competitive equilibrium will be Pareto optimal, and the Second Theorem states that any possible Pareto optimal outcome can be achieved through direct income transfers and market competition.

The two theorems have somewhat contradictory political implications. Conservatives tend to leap on the First Theorem to promote unrestricted markets. They argue that if competitive markets produce a Pareto optimal outcome, and by implication uncompetitive markets may fail to do so, then society should embrace competition as the cure for all ills.

However, Arrow himself dismissed this thinking. He noted that the assumptions necessary for the First Theorem to hold are restrictive, so the government has a potentially-expansive role to play in ensuring fair competition in the market. These restrictions also led to an immense literature on market imperfections, exploring the myriad ways that markets can produce inefficient outcomes.

This thinking also disregards the Second Theorem, which fellow Nobel-winner Amartya Sen once described as “a revolutionary’s handbook.” When this theorem holds, the government could engage in radical income redistribution without upending the efficiency of the market. For example, they could create a truly meritocratic system by redistributing income to fully neutralize any effect of inheritance or upbringing on one’s prospects, then letting market competition proceed.

In this theorem, redistribution is not a sin against the market system, but an intrinsic feature of it. In Arrow’s words,

“The freedom to make choices in a market economy demands the ability to choose jobs and goods. I therefore have a built-in belief that reducing income inequality is not in contradiction to economic freedom but part of it.”

Social Choice Theory: Arrow’s other landmark contribution was his eponymous Impossibility Theorem. His theorem demonstrated that no possible ordinal voting mechanism can convert individual preferences into a collective ranking without either violating certain fairness criteria, such as ‘if every voter prefers X to Y, then the collective ranking must prefer X to Y,’ or making one voter into a dictator whose preferences alone determine the outcome.

Today, many politicians claim to speak for ‘the will of the people,’ implicitly assuming that the collective will of their constituents is clear and coherent. Yet the Arrow Impossibility Theorem demonstrates that no such collective will could exist. Electoral results don’t necessarily represent the will of the people; they represent the will of the system’s creators, embodied in the electoral rules.

In the United States, Trump won the election while losing the popular vote. The combination of the Electoral College and Senate privileges small states and narrowly-divided states over large, politically-homogenous ones. Clinton won California by around 4.3 million votes, a gap greater than the population of 24 states and approximately equal to the population of the 6 smallest states combined. Yet this victory was worth exactly the same as if she had won the state by one vote.

In Canada, the Liberal government reneged on a campaign promise to replace first-past-the-post voting with another system, creating an uproar among those who hoped for a change to electoral rules. Yet Arrow’s theorem shows that the proposed replacements, despite their potential advantages over FPTP, would also have inherent flaws.

Endogenous Growth: When studying the sources of economic growth, Arrow proposed a model of learning-by-doing to explain productivity growth. He theorized that productivity in the production of goods and services comes from practice. As a firm produces more goods over time, it generates knowledge about the production process. Some of this knowledge leads to internal gains, reducing costs and increasing output, while some leaks out from the firm, boosting economy-wide productivity.

With this theorem, Arrow slightly predates BCG’s creation of the experience curve in the mid-1960s and provides a foundation for the 10,000 hours of practice rule decades before Malcolm Gladwell popularized it. It also explains the existence of industry clusters, such as Silicon Valley, since these beneficial ‘leaks’ are more likely in close geographic proximity.

More contentiously, learning-by-doing also justifies the ‘infant industry’ argument for economic protectionism. The idea is that immediately exposing domestic manufacturing to foreign competition would deprive it of the opportunity to improve through practice. Thus, the government should shelter so-called infant industries until they reach a sufficient scale to compete on the global market.

This argument is bolstered by its empirical record. Many industrialized countries developed while restricting international trade. For example, South Korea limited trade while its chaebol grew and developed the skills necessary to compete in electronics and other high-value manufacturing. China directly encouraged these leaks by mandating knowledge sharing as a condition of market access and often chose to look away when domestic companies stole their international partners’ IP.

Information Economics: Several years before Akerlof and others formalized the analysis of asymmetric information, Arrow noted the implications of it for health care. He argued that healthcare services, such as primary care by a doctor, had vast informational challenges and that these challenges would make free competition in health markets impossible.

He also noted the tension inherent in health insurance, where eliminating the cost to consumers would lead them to over-consume health services, straining the system, but that charging for services would create price-based rationing, harming the poor and vulnerable.

His insights echo in today’s debate in America over health insurance and health care. Contrary to Republicans’ claims, health services cannot be easily compared as one might do with boxes of cereal. These services rely on the trust between a patient and their doctor, limiting competition in the health market. Thus, pure competition will neither drive prices down, nor lead to superior patient choice.

Additionally, the tension between moral hazard and insurance remains in the opposing positions of Republicans and Democrats. Republicans argue that price signals are necessary to force patients to be careful consumers of health services, while Democrats retort that forcing individuals to forego medical treatment due to their income is inhumane.

Racial Discrimination: Finally, Arrow turned his attention to racial discrimination, something he called, “an evil even if grounded in widespread popular support.” He examined possible reasons why income and wealth gaps might persist between races, even when the legally-sanctioned racism of Jim Crow had ended.

First, he considered the possibility that wage gaps represented differences in productivity, but largely dismissed it as inconsistent with the evidence. He also considered the possibility that the wage gap represented active, albeit covert, prejudice against minority workers. This explanation says that employers either deliberately give minorities lower pay, due to their prejudice, or pay white workers more to compensate them for working with minorities. Yet he also dismisses both explanations as inconsistent with empirical evidence.

The theory he proposes instead does not rely on prejudice by any living individual. He argues that past discrimination would have created a wealth and income gap, alongside strong homophily in personal networks. If affluent individuals are more likely to have opportunities they can offer to friends and only offer these opportunities within their personal network, then an income gap can become self-perpetuating.

This theory provides an outline of a system that, despite no individual harbouring personal prejudice, nevertheless leads to discriminatory outcomes. Despite lacking the formal terms for it, Arrow distinguished between personal racism and systemic racism decades before the terms became widespread.

In Memoriam: Even this list leaves off several of Arrow’s contributions to both economics and society. It does not cover his analysis of risk and state-contingent goods, which led to a flowering of financial research. It ignores his arguments in favour of environmental conservation based on uncertainty and irreversibility of environmental choices. Arrow was undoubtedly one of the greatest economists of all time, someone who thought carefully about economic questions and grounded it in a deep compassion for humanity.

He will be sorely missed.