Tag Archives: mathematical economics

Unorthodox Economics: 3. What Is Scientific about Economics?

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This is the third entry in what I hope will become a book-length series of posts. That result, if it comes to pass, will amount to an unorthodox economics textbook. Here are the chapters that have been posted to date:

1. What Is Economics?
2. Pitfalls
3. What Is Scientific about Economics?
4. A Parable of Political Economy
5. Economic Progress, Microeconomics, and Macroeconomics

Perhaps the biggest pitfall that awaits an economist, student of economics, or reader of economic literature is the belief that economics is a science because of its mathematical and statistical content. David S. D’Amato takes a clear-headed view in “Is Economics a Hard Science?” (The American Spectator, January 4, 2017):

[E]conomists and social scientists are gathering and analyzing statistical data constantly. [But] those data are limited by the density of the causal atmosphere of the environment from which they emerge, a rich and variable sea of causes and effects. Isolating one or even a few factors becomes impossible.

As Jim Manzi explains in his book Uncontrolled, “[W]e can never be sure that any experiment actually has controlled for every possible alternative cause of an outcome.” And while this is, of course, true in every field of inquiry, the problem is especially acute within the social sciences, so-called. That’s because, as Manzi observes, “human social organizations have a causal density that dwarfs anything astrophysics considers.”…

For any given observable phenomenon, the scientist must attempt to parse a convoluted web of actual and potential causes. Unable to control the experiment, its environmental inputs, groups, etc., the social scientist is unable to know whether the hypothesis being tested has been confirmed. This causal density means economic data must always be the subject of several competing explanations, informed by ideology and extra-economic social theory…

…The great classical liberal political economist Jean-Baptiste Say foresaw the complacency of today’s economists, their tendency to oversell the power of data and mathematics. Anticipating the praxeology of Ludwig von Mises, Say held the proper foundations for economics are “the rigorous deductions of undeniable general facts,” not “new particular fact[s]” (i.e., statistics), but basic laws of human action….

If empirical data are often too messy, too causally intricate, without the help of a philosophical or interpretative framework, then mathematical models are in a sense too neat to tell us very much about reality; they reduce enormously complex concepts and arguments about economic behavior to sterile formulae. Sometimes this is useful, as in the case of an economic model that explains the relationship between supply and demand. But as economists address their model-building processes to more difficult questions, the serviceability of the models diminishes. And if we are to believe the critics of “mathiness,” whom we can find all over the spectrum of ideas, the preoccupation with practically useless mathematical models has all but completely overtaken the economics profession.

Mathematical models, agglomerations of equations using multivariable calculus, are, it turns out, not a language suited to the task of describing something as dynamic as human behavior. Among the axioms of modern economics is the idea that economic value is something assigned to good and services subjectively by individual buyers and sellers. As Austrian School economists frequently point out, there is an irreducible subjectivity at the heart of all economic action. This explanation of value in terms of subjective preference and marginal utility replaced classical theories that made value a function of the quantities of labor expended during a good’s production. If value subjectivism holds, then, for example, one’s partiality for Chicago-style pizza as opposed to New York-style pizza is simply not the kind of preference that can be quantified. There is, as the saying goes, no accounting for taste.

It’s a simple example, but it points to a much more general and far-reaching truth: Formal logic and mathematics are not a stable foundation for the economist. This has been borne out by the inability of computer models to anticipate the movements of actual markets. For all their complex mathematics and pretensions to rigorousness, these models rely on crude oversimplifications. As New York University economist Mario J. Rizzo notes, “Ceteris paribus prediction is prediction of ‘stylized facts,’” whose connection to the real world is tenuous at best.

Yet, as Arnold Kling explains in “An Important Emerging Economic Paradigm” (TCS Daily, March 2, 2005), many (perhaps most) economists have lost sight of the axioms of economics in their misplaced zeal to emulate the methods of the physical sciences:

The most distinctive trend in economic research over the past hundred years has been the increased use of mathematics. In the wake of Paul Samuelson’s (Nobel 1970) Ph.D dissertation, published in 1948, calculus became a requirement for anyone wishing to obtain an economics degree. By 1980, every serious graduate student was expected to be able to understand the work of Kenneth Arrow (Nobel 1972) and Gerard Debreu (Nobel 1983), which required mathematics several semesters beyond first-year calculus.

Today, the “theory sequence” at most top-tier graduate schools in economics is controlled by math bigots. As a result, it is impossible to survive as an economics graduate student with a math background that is less than that of an undergraduate math major. In fact, I have heard that at this year’s American Economic Association meetings, at a seminar on graduate education one professor quite proudly said that he ignored prospective students’ grades in economics courses, because their math proficiency was the key predictor of their ability to pass the coursework required to obtain an advanced degree.

The raising of the mathematical bar in graduate schools over the past several decades has driven many intelligent men and women (perhaps women especially) to pursue other fields. The graduate training process filters out students who might contribute from a perspective of anthropology, biology, psychology, history, or even intense curiosity about economic issues. Instead, the top graduate schools behave as if their goal were to produce a sort of idiot-savant, capable of appreciating and adding to the mathematical contributions of other idiot-savants, but not necessarily possessed of any interest in or ability to comprehend the world to which an economist ought to pay attention.

. . . The basic question of What Causes Prosperity? is not a question of how trading opportunities play out among a given array of goods. Instead, it is a question of how innovation takes place or does not take place in the context of institutional factors that are still poorly understood.

Economic models usually are clothed in the language of mathematics and statistics. But those aren’t scientific disciplines in themselves; they are tools of science. Expressing a theory in mathematical terms may lend the theory a scientific aura, but a theory couched in mathematical terms is not a scientific one unless (a) it can be tested against facts yet to be ascertained and events yet to occur, and (b) it is found to accord with those facts and events consistently, by rigorous statistical tests. In sum, modeling is not science.

Economics is a science only to the extent that it yields empirically valid insights about  specific economic phenomena (e.g., the effects of laws and regulations on the prices and outputs of specific goods and services). The Keynesian multiplier, about which I’ll say more in a later chapter, is not a scientific theory. It is a hypothesis that rests on a simplistic, hydraulic view of the economic system. (Other examples of pseudo-scientific economic theories are the labor theory of value and historical determinism.)

A scientific theory is a hypothesis that has thus far been confirmed by observation, and which has not yet been refuted (falsified) by observation.* (The Keynesian multiplier has been falsified.) Every scientific theory rests eventually on axioms: self-evident principles that are accepted as true without proof. Economics, as D’Amato notes, is no exception. It rests on these self-evident axioms:

1. Each person strives to maximize his or her sense of satisfaction, which may also be called well-being, happiness, or utility (an ugly word favored by economists). Striving isn’t the same as achieving, of course, because of lack of information, emotional decision-making, buyer’s remorse, etc

2. Happiness can and often does include an empathic or expedient concern for the well-being of others; that is, one’s happiness may be served by what is usually labelled altruism or self-sacrifice.

3. Happiness can be and often is served by the attainment of non-material ends. Not all persons (perhaps not even most of them) are interested in the maximization of wealth, that is, claims on the output of goods and services. In sum, not everyone is a wealth maximizer. (But see axiom number 12.)

4. The feeling of satisfaction that an individual derives from a particular product or service is situational — unique to the individual and to the time and place in which the individual undertakes to acquire or enjoy the product or service. Generally, however, there is a (situationally unique) point at which the acquisition or enjoyment of additional units of a particular product or service during a given period of time tends to offer less satisfaction than would the acquisition or enjoyment of units of other products or services that could be obtained at the same cost.

5. The value that a person places on a product or service is subjective. Products and services don’t have intrinsic values that apply to all persons at a given time or period of time.

6. The ability of a person to acquire products and services, and to accumulate wealth, depends (in the absence of third-party interventions) on the valuation of the products and services that are produced in part or whole by the person’s labor (mental or physical), or by the assets that he owns (e.g., a factory building, a software patent). That valuation is partly subjective (e.g., consumers’ valuation of the products and services, an employer’s qualitative evaluation of the person’s contributions to output) and partly objective (e.g., an employer’s knowledge of the price commanded by a product or service, an employer’s measurement of an employees’ contribution to the quantity of output).

7. The persons and firms from which products and services flow are motivated by the acquisition of income, with which they can acquire other products and services, and accumulate wealth for personal purposes (e.g., to pass to heirs) or business purposes (e.g., to expand the business and earn more income). So-called profit maximization (seeking to maximize the difference between the cost of production and revenue from sales) is a key determinant of business decisions but far from the only one. Others include, but aren’t limited to, being a “good neighbor,” providing employment opportunities for local residents, and underwriting philanthropic efforts.

8. The cost of production necessarily influences the price at which a good or and service will be offered for sale, but doesn’t solely determine the price at which it will be sold. Selling price depends on the subjective valuation of the products or service, prospective buyers’ incomes, and the prices of other products and services, including those that are direct or close substitutes and those to which users may switch, depending on relative prices.

9. The feeling of satisfaction that a person derives from the acquisition and enjoyment of the “basket” of products and services that he is able to buy, given his income, etc., doesn’t necessarily diminish, as long as the person has access to a great variety of products and services. (This axiom and axiom 12 put paid to the myth of diminishing marginal utility of income.)

10. Work may be a source of satisfaction in itself or it may simply be a means of acquiring and enjoying products and services, or acquiring claims to them by accumulating wealth. Even when work is satisfying in itself, it is subject to the “law” of diminishing marginal satisfaction.

11. Work, for many (but not all) persons, is no longer be worth the effort if they become able to subsist comfortably enough by virtue of the wealth that they have accumulated, the availability of redistributive schemes (e.g., Social Security and Medicare), or both. In such cases the accumulation of wealth often ceases and reverses course, as it is “cashed in” to defray the cost of subsistence (which may be far more than minimal).

12. However, there are not a few persons whose “work” is such a great source of satisfaction that they continue doing it until they are no longer capable of doing so. And there are some persons whose “work” is the accumulation of wealth, without limit. Such persons may want to accumulate wealth in order to “do good” or to leave their heirs well off or simply for the satisfaction of running up the score. The justification matters not. There is no theoretical limit to the satisfaction that a particular person may derive from the accumulation of wealth. Moreover, many of the persons (discussed in axiom 11) who aren’t able to accumulate wealth endlessly would do so if they had the ability and the means to take the required risks.

13. Individual degrees of satisfaction (happiness, etc.) are ephemeral, nonquantifiable, and incommensurable. There is no such thing as a social welfare function that a third party (e.g., government) can maximize by taking from A to give to B. If there were such a thing, its value would increase if, for example, A were to punch B in the nose and derive a degree of pleasure that somehow more than offsets the degree of pain incurred by B. (The absurdity of a social-welfare function that allows As to punch Bs in their noses ought to be enough shame inveterate social engineers into quietude — but it won’t. They derive great satisfaction from meddling.) Moreover, one of the primary excuses for meddling is that income (and thus wealth) has a  diminishing marginal utility, so it makes sense to redistribute from those with higher incomes (or more wealth) to those who have less of either. Marginal utility is, however, unknowable (see axioms 4 and 5), and may not always be negative (see axioms 9 and 12).

14. Whenever a third party (government, do-gooders, etc.) intervene in the affairs of others, that third party is merely imposing its preferences on those others. The third party sometimes claims to know what’s best for “society as a whole,” etc., but no third party can know such a thing. (See axiom 13.)

15. It follows from axiom 13 that the welfare of “society as a whole” can’t be aggregated or measured. An estimate of the monetary value of the economic output of a nation’s economy (Gross Domestic Product) is by no means an estimate of the welfare of “society as a whole.”

That may seem like a lot of axioms, which might give you pause about my claim that some aspects of economics are scientific. But economics is inescapably grounded in axioms such as the ones that I propound, just as much of modern physics is inescapably grounded in the principle of uniformity.**

It is important to distinguish between axioms, which are self-evidently true, and biases that stem from normative views of what ought to be. Behavioral economists, for example, see the world through the lens of wealth-and-utility-maximization. Their great crusade is to force everyone to make rational decisions (by their lights), through “nudging.” It almost goes without saying that government should be the nudger-in-chief. (See “The Perpetual Nudger” and the many posts linked to therein.)

Other economists — though not as many as in the past — are obsessed by monopoly and oligopoly (the domination of a market by one or a few sellers). They’re heirs to the trust-busting of the late 1800s and early 1900s, a movement led by non-economists who sought to blame the woes of working-class Americans on the “plutocrats” (Rockefeller, Carnegie, Ford, etc.) who had merely made life better and more affordable for Americans, while also creating jobs for millions of them and reaping rewards for the great financial risks that they took. (See “Monopoly and the General Welfare” and “Monopoly: Private Is Better than Public.”) As it turns out, the biggest and most destructive monopoly of all is the federal government, so beloved and trusted by trust-busters — and too many others. (See “The Rahn Curve Revisited.”)

Nowadays, a lot of economists are preoccupied by income inequality, as if it were something evil and not mainly an artifact of differences in intelligence, ambition, and education, etc. And inequality — the prospect of earning rather grand sums of money — is what drives a lot of economic endeavor, to the benefit of workers and consumers. (See “Mass (Economic) Hysteria: Income Inequality and Related Themes” and the many posts linked to therein.) Remove inequality and what do you get? The Soviet Union and Communist China, in which everyone is equal except party operatives and their families, friends, and favorites. As George Orwell put it in Animal Farm, “all [people] are equal, but some [people] are more equal than others.”

When the inequality-preoccupied economists are confronted by the facts of life, they usually turn their attention from inequality as a general problem to the (inescapable) fact that an income distribution has a top one-percent and top one-tenth of one-percent — as if there were something especially loathsome about people in those categories. (Paul Krugman shifted his focus to the top one-tenth of one percent when he realized that he’s in the top one percent, so perhaps he knows that’s he’s loathsome and wishes to deny it — to himself, at least.)

Crony capitalism is trotted out as a major cause of very high incomes. But that’s hardly a universal cause, given that a lot of very high incomes are earned by athletes and film stars beside whom most investment bankers and CEOs earn slave wages. Moreover, as I’ve said on several occasions, crony capitalists are bright and driven enough to be in the stratosphere of any income distribution. Further, the breeding ground of crony capitalism is the regulatory power of government that makes it possible.

Many economists became such, it would seem, in order to promote big government and its supposed good works — income redistribution being one of them. Joseph Stiglitz and Paul Krugman are two leading exemplars of what I call the New Deal school of economic thought, which amounts to throwing government and taxpayers’ money at every perceived problem, that is, every economic outcome that is deemed unacceptable by accountants of the soul. (See “Accountants of the Soul.”)

Stiglitz and Krugman — both Nobel laureates in economics — are typical “public intellectuals” whose intelligence breeds in them a kind of arrogance. (See “Intellectuals and Society: A Review.”) It’s the kind of arrogance that reveals itself in a penchant for deciding what’s best for others, even beyond the arrogance of behavioral “nudgers.”

New Deal economists like Stiglitz and Krugman carry it a few steps further. They ascribe to government an impeccable character, an intelligence to match their own, and a monolithic will. They then assume that this infallible and wise automaton can and will do precisely what they would do: Create the best of all possible worlds. (See the preceding chapter, in which I discuss the nirvana fallacy.)

I hold economists of the New Deal stripe partly responsible for the swamp of stagnation into which the nation’s economy has descended. (See “Economic Growth Since World War II.”) Largely responsible, of course, are opportunistic if not economically illiterate politicians who pander to rent-seeking, economically illiterate constituencies. (Yes, I’m thinking of pensioners and the many “disadvantaged” groups with which “compassionate” politicians have struck up an alliance of convenience.)

Enough said, for now. Some economics is science. Too much of it is nothing more than special pleading cloaked in the jargon of economics, and pseudo-scientific theorizing overlaid with a veneer of mathematics or statistics.

Caveat lector.
__________
* This is from Karl Popper‘s classic statement of the scientific method. Richard Feynman, a physicist (and real scientist), had a different view. I see Feynman’s view as complementary to Popper’s, not at odds with it. What is “constructive skepticism” (Feynman’s term) but a gentler way of saying that a hypothesis or theory might be falsified and that the act of falsification may point to a better hypothesis or theory?

** The principle of uniformity is a fundamental axiom of modern physics, most notably of Einstein’s special and general theories of relativity. According to the principle of uniformity, for example, if observer B is moving away from observer A at a certain speed, observer A will perceive that he is moving away from observer B at that speed. This statement holds only if A and B can’t see another object. But suppose, for example, there’s an object C that’s visible to A, and which A perceives as stationary. If A sees that B is moving away from C as well as from A, then A will perceive that B is in motion while A is at rest (relative to C, at least). That aside, A still doesn’t have an absolute velocity or direction of travel. Velocity and direction are always relative to an arbitrary reference point.

Mathematical Economics

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This is the fourth entry in a series of loosely connected posts on economics. Previous entries are here, here, and here.

Economics is a study of human behavior, not an exercise in mathematical modeling or statistical analysis, though both endeavors may augment an understanding of human behavior. Economics is about four things:

  • wants, as they are perceived by the persons who have those wants
  • how people try to satisfy their wants through mutually beneficial, cooperative action, which includes but is far from limited to market-based exchanges
  • how exogenous forces, including government interventions, enable or thwart the satisfaction of wants
  • the relationships between private action, government interventions, and changes in the composition, rate, and direction of economic activity

In sum, economics is about the behavior of human beings, which is why it’s called a social science. Well, economics used to be called a social science, but it’s been a long time (perhaps fifty years) since I’ve heard or read an economist refer to it as a social science. The term is too reminiscent of “soft and fuzzy” disciplines such as history, social psychology, sociology, political science, and civics or social studies (names for the amalgam of sociology and government that was taught in high schools way back when). No “soft and fuzzy” stuff for physics-envying economists.

However, the behavior of human beings — their thoughts and emotions, how those things affect their actions, and how they interact — is fuzzy, to say the least. Which explains why mathematical economics is largely an exercise in mental masturbation.

In my disdain for mathematical economics, I am in league with Arnold Kling, who is the most insightful economist I have yet encountered in more than fifty years of studying and reading about economics. I especially recommend Kling’s Specialization and Trade: A Reintroduction to Economics. It’s a short book, but chock-full of wisdom and straight thinking about what makes the economy tick. Here’s the blurb from Amazon.com:

Since the end of the second World War, economics professors and classroom textbooks have been telling us that the economy is one big machine that can be effectively regulated by economic experts and tuned by government agencies like the Federal Reserve Board. It turns out they were wrong. Their equations do not hold up. Their policies have not produced the promised results. Their interpretations of economic events — as reported by the media — are often of-the-mark, and unconvincing.

A key alternative to the one big machine mindset is to recognize how the economy is instead an evolutionary system, with constantly-changing patterns of specialization and trade. This book introduces you to this powerful approach for understanding economic performance. By putting specialization at the center of economic analysis, Arnold Kling provides you with new ways to think about issues like sustainability, financial instability, job creation, and inflation. In short, he removes stiff, narrow perspectives and instead provides a full, multi-dimensional perspective on a continually evolving system.

And he does, without using a single graph. He uses only a few simple equations to illustrate the bankruptcy of macroeconomic theory.

Those economists who rely heavily on mathematics like to say (and perhaps even believe) that mathematical expression is more precise than mere words. But, as Kling points out in “An Important Emerging Economic Paradigm,” mathematical economics is a language of “faux precision,” which is useful only when applied to well defined, narrow problems. It can’t address the big issues — such as economic growth — which depend on variables such as the rule of law and social norms which defy mathematical expression and quantification.

I would go a step further and argue that mathematical economics borders on obscurantism. It’s a cult whose followers speak an arcane language not only to communicate among themselves but to obscure the essentially bankrupt nature of their craft from others. Mathematical expression actually hides the assumptions that underlie it. It’s far easier to identify and challenge the assumptions of “literary” economics than it is to identify and challenge the assumptions of mathematical economics.

I daresay that this is true even for persons who are conversant in mathematics. They may be able to manipulate easily the equations of mathematical economics, but they are able to do so without grasping the deeper meanings — the assumptions and complexities — hidden by those equations. In fact, the ease of manipulating the equations gives them a false sense of mastery of the underlying, real concepts.

Much of the economics profession is nevertheless dedicated to the protection and preservation of the essential incompetence of mathematical economists. This is from “An Important Emerging Economic Paradigm”:

One of the best incumbent-protection rackets going today is for mathematical theorists in economics departments. The top departments will not certify someone as being qualified to have an advanced degree without first subjecting the student to the most rigorous mathematical economic theory. The rationale for this is reminiscent of fraternity hazing. “We went through it, so should they.”

Mathematical hazing persists even though there are signs that the prestige of math is on the decline within the profession. The important Clark Medal, awarded to the most accomplished American economist under the age of 40, has not gone to a mathematical theorist since 1989.

These hazing rituals can have real consequences. In medicine, the controversial tradition of long work hours for medical residents has come under scrutiny over the last few years. In economics, mathematical hazing is not causing immediate harm to medical patients. But it probably is working to the long-term detriment of the profession.

The hazing ritual in economics has as least two real and damaging consequences. First, it discourages entry into the economics profession by persons who aren’t high-IQ freaks, and who, like Kling, can discuss economic behavior without resorting to the sterile language of mathematics. Second, it leads to economics that’s irrelevant to the real world — and dead wrong.

Reaching back into my archives, I found a good example of irrelevance and wrongness in Thomas Schelling‘s game-theoretic analysis of segregation. Eleven years ago, Tyler Cowen (Marginal Revolution), who was mentored by Schelling at Harvard, praised Schelling’s Nobel prize by noting, among other things, Schelling’s analysis of the economics of segregation:

Tom showed how communities can end up segregated even when no single individual cares to live in a segregated neighborhood. Under the right conditions, it only need be the case that the person does not want to live as a minority in the neighborhood, and will move to a neighborhood where the family can be in the majority. Try playing this game with white and black chess pieces, I bet you will get to segregation pretty quickly.

Like many game-theoretic tricks, Schelling’s segregation gambit omits much important detail. It’s artificial to treat segregation as a game in which all whites are willing to live with black neighbors as long as they (the whites) aren’t in the minority. Most whites (including most liberals) do not want to live anywhere near any “black rednecks” if they can help it. Living in relatively safe, quiet, and attractive surroundings comes far ahead of whatever value there might be in “diversity.”

“Diversity” for its own sake is nevertheless a “good thing” in the liberal lexicon. The Houston Chronicle noted Schelling’s Nobel by saying that Schelling’s work

helps explain why housing segregation continues to be a problem, even in areas where residents say they have no extreme prejudice to another group.

Segregation isn’t a “problem,” it’s the solution to a potential problem. Segregation today is mainly a social phenomenon, not a legal one. It reflects a rational aversion on the part of whites to having neighbors whose culture breeds crime and other types of undesirable behavior.

As for what people say about their racial attitudes: Believe what they do, not what they say. Most well-to-do liberals — including black one like the Obamas — choose to segregate themselves and their children from black rednecks. That kind of voluntary segregation, aside from demonstrating liberal hypocrisy about black redneck culture, also demonstrates the rationality of choosing to live in safer and more decorous surroundings.

Dave Patterson of the defunct Order from Chaos put it this way:

[G]ame theory has one major flaw inherent in it: The arbitrary assignment of expected outcomes and the assumption that the values of both parties are equally reflected in these external outcomes. By this I mean a matrix is filled out by [a conductor, and] it is up to that conductor’s discretion to assign outcome values to that grid. This means that there is an inherent bias towards the expected outcomes of conductor.

Or: Garbage in, garbage out.

Game theory points to the essential flaw in mathematical economics, which is reductionism: “An attempt or tendency to explain a complex set of facts, entities, phenomena, or structures by another, simpler set.”

Reductionism is invaluable in many settings. To take an example from everyday life, children are warned — in appropriate stern language — not to touch a hot stove or poke a metal object into an electrical outlet. The reasons given are simple ones: “You’ll burn yourself” and “You’ll get a shock and it will hurt you.” It would be futile (in almost all cases) to try to explain to a small child the physical and physiological bases for the warnings. The child wouldn’t understand the explanations, and the barrage of words might cause him to forget the warnings.

The details matter in economics. It’s easy enough to say, for example, that a market equilibrium exists where the relevant supply and demand curves cross (in a graphical representation) or where the supply and demand functions yield equal values of price and quantity (in a mathematical representation). But those are gross abstractions from reality, as any economist knows — or should know. Expressing economic relationships in mathematical terms lends them an unwarranted air of precision.

Further, all mathematical expressions, no matter how complex, can be expressed in plain language, though it may be hard to do so when the words become too many and their relationships too convoluted. But until one tries to do so, one is at the mercy of the mathematical economist whose equation has no counterpart in the real world of economic activity. In other words, an equation represents nothing more than the manipulation of mathematical relationships until it’s brought to earth by plain language and empirical testing. Short of that, it’s as meaningful as Urdu is to a Cockney.

Finally, mathematical economics lends aid and comfort to proponents of economic control. Whether or not they understand the mathematics or the economics, the expression of congenial ideas in mathematical form lends unearned — and dangerous — credibility to the controller’s agenda. The relatively simple multiplier is a case in point. As I explain in “The Keynesian Multiplier: Phony Math,”

the Keynesian investment/government-spending multiplier simply tells us that if ∆Y = $5 trillion, and if b = 0.8, then it is a matter of mathematical necessity that ∆C = $4 trillion and ∆I + ∆G = $1 trillion. In other words, a rise in I + G of $1 trillion doesn’t cause a rise in Y of $5 trillion; rather, Y must rise by $5 trillion for C to rise by $4 trillion and I + G to rise by $1 trillion. If there’s a causal relationship between ∆G and ∆Y, the multiplier doesn’t portray it.

I followed that post with “The True Multiplier“:

Math trickery aside, there is evidence that the Keynesian multiplier is less than 1. Robert J. Barro of Harvard University opens an article in The Wall Street Journal with the statement that “economists have not come up with explanations … for multipliers above one.”

Barro continues:

A much more plausible starting point is a multiplier of zero. In this case, the GDP is given, and a rise in government purchases requires an equal fall in the total of other parts of GDP — consumption, investment and net export. . . .

What do the data show about multipliers? Because it is not easy to separate movements in government purchases from overall business fluctuations, the best evidence comes from large changes in military purchases that are driven by shifts in war and peace. A particularly good experiment is the massive expansion of U.S. defense expenditures during World War II. The usual Keynesian view is that the World War II fiscal expansion provided the stimulus that finally got us out of the Great Depression. Thus, I think that most macroeconomists would regard this case as a fair one for seeing whether a large multiplier ever exists.

I have estimated that World War II raised U.S. defense expenditures by $540 billion (1996 dollars) per year at the peak in 1943-44, amounting to 44% of real GDP. I also estimated that the war raised real GDP by $430 billion per year in 1943-44. Thus, the multiplier was 0.8 (430/540). The other way to put this is that the war lowered components of GDP aside from military purchases. The main declines were in private investment, nonmilitary parts of government purchases, and net exports — personal consumer expenditure changed little. Wartime production siphoned off resources from other economic uses — there was a dampener, rather than a multiplier. . . .

There are reasons to believe that the war-based multiplier of 0.8 substantially overstates the multiplier that applies to peacetime government purchases. For one thing, people would expect the added wartime outlays to be partly temporary (so that consumer demand would not fall a lot). Second, the use of the military draft in wartime has a direct, coercive effect on total employment. Finally, the U.S. economy was already growing rapidly after 1933 (aside from the 1938 recession), and it is probably unfair to ascribe all of the rapid GDP growth from 1941 to 1945 to the added military outlays. [“Government Spending Is No Free Lunch,” The Wall Street Journal (online.WSJ.com), January 22, 2009]

This is from Valerie A. Ramsey of  the University of California-San Diego and the National Bureau of Economic Research:

. . . [I]t appears that a rise in government spending does not stimulate private spending; most estimates suggest that it significantly lowers private spending. These results imply that the government spending multiplier is below unity. Adjusting the implied multiplier for increases in tax rates has only a small effect. The results imply a multiplier on total GDP of around 0.5. [“Government Spending and Private Activity,” January 2012]

In fact,

for the period 1947-2012 I estimated the year-over-year percentage change in GDP (denoted as Y%) as a function of G/GDP (denoted as G/Y):

Y% = 0.09 – 0.17(G/Y)

Solving for Y% = 0 yields G/Y = 0.53; that is, Y% will drop to zero if G/Y rises to 0.53 (or thereabouts). At the present level of G/Y (about 0.4), Y% will hover just above 2 percent, as it has done in recent years. (See the graph immediately above.)

If G/Y had remained at 0.234, its value in 1947:

  • Real growth would have been about 5 percent a year, instead of 3.2 percent (the actual value for 1947-2012).
  • The total value of Y for 1947-2012 would have been higher by $500 trillion (98 percent).
  • The total value of G would have been lower by $61 trillion (34 percent).

The last two points, taken together, imply a cumulative government-spending multiplier (K) for 1947-2012 of about -8. That is, aggregate output in 1947-2012 declined by 8 dollars for every dollar of government spending above the amount represented by G/Y = 0.234.

But -8 is only an average value for 1947-2012. It gets worse. The reduction in Y is cumulative; that is, every extra dollar of G reduces the amount of Y that is available for growth-producing investment, which leads to a further reduction in Y, which leads to a further reduction in growth-producing investment, and on and on. (Think of the phenomenon as negative compounding; take a dollar from your savings account today, and the value of the savings account years from now will be lower than it would have been by a multiple of that dollar: [1 + interest rate] raised to nth power, where n = number of years.) Because of this cumulative effect, the effective value of K in 2012 was about -14.

The multiplier is a seductive and easy-to-grasp mathematical construct. But in the hands of politicians and their economist-enablers, it has been an instrument of economic destruction.

Perhaps “higher” mathematical economics is potentially less destructive because it’s inside game played by economists for the benefit of economists. I devoutly hope that’s true.