Resolving the Glasner-Sumner Dispute

David Glasner and Scott Sumner are arguing about whether saving = investment is an identity or an equilibrium condition. So I thought I would step in and resolve this dispute. Instead of using textbook accounting identities, let’s consider a framework everyone is familiar with — a two-period consumption model.

1. Consider a Robinson Crusoe economy. There is one guy on an island with production opportunities, but no market opportunities. For simplicity, think of a two-period model. In the first period, the individual receives an endowment, Y. The individual can invest that endowment to generate future production or consume the endowment. The individual transforms Y into P1, production now, and P2, production later. It follows that investment is defined as I = Y – P1. Savings is defined as S = Y – C1, where C1 is consumption in the first period. Since there is only one guy on the island, it must be true that P1 = C1. These decisions are both determined by the individual’s rate of time preference. Thus, S = I is an identity.

2. Consider the same guy on an island, but who now has market opportunities. Now we have the same definitions for saving and investment. Saving is

S = Y – C1
I = Y – P1

Note that with exchange opportunities, it is very unlikely that C1 = P1. Thus, at the individual level, savings probably doesn’t equal investment. Combining these conditions, we get

S = I + P1 – C1

for the individual. Now sum across all terms and we get

Now in equilibrium, market-clearing requires that total production equals total consumption. Thus, market clearing implies that total savings is equal to total investment:

Saving = Investment is therefore an equilibrium condition.

3. Finally, David’s issue is that he doesn’t think that gross domestic income and gross domestic expenditure are the same thing. Empirically, he’s correct. This is why we have GDP Plus.

On Fiat Money

Why do people accept fiat money? It is, after all, intrinsically useless. David Glasner has written a thoughtful post on fiat money. Glasner writes:

Why should a fiat money not be able to retain value? Well, consider the following thought experiment. For a pure medium of exchange, a fiat money, to have value, there must be an expectation that it will be accepted in exchange by someone else. Without that expectation, a fiat money could not, by definition, have value. But at some point, before the world comes to its end, it will be clear that there will be no one who will accept the money because there will be no one left with whom to exchange it. But if it is clear that at some time in the future, no one will accept fiat money and will then lose its value, a logical process of backward induction implies that it must lose its value now.

So why are people willing to accept it? Glasner suggests that the reason is because the government accepts money as payment for taxes. This is the chartalist view and has been around for some time. Glasner traces this back to Wicksteed. Ross Starr provides an analysis within the context of general equilibrium theory. However, I would like to suggest another proposition. To do so, we need to talk about two different questions: (a) why does fiat money exist?, and (b) why do people accept it?

There are a number of ways that have been suggested to explain the use of money. However, I would like to focus on one in particular. As emphasized by Brunner and Meltzer (1971) and Ostroy (1973), money is a substitute for information. To illustrate this point, consider an example. Suppose that there are three people, three goods, and three time periods. Person 1 produces Good 1 in Period 1, but wants to consume Good 2. Person 2 produces Good 2 in Period 2, but wants to consume Good 3. Person 3 produces Good 3 in Period 3, but wants to consume Good 1. Notice that there is a basic double coincidence of wants problem. This problem, however, does not necessarily require money. For example, the three individuals could get together and make a multilateral arrangement in which each individual promises to deliver the desired good to the appropriate trader in each period. No money is necessary.

The example above, however, requires that the individuals can perfectly commit to those actions. In reality, the individuals have an incentive to renege on their promises. For example, Person 3 could promise to give Good 3 to Person 2 in Period 3 so long as Person 1 supplies Good 1. However, if there is disutility associated with production, Person 3 has no incentive to produce anything given that they have already received their consumption good. But even this isn’t sufficient to require money. If trading histories are perfectly monitored and costly available to all parties, this would provide an incentive for individuals to behave honestly.

This latter assertion, however, bears little resemblance to the world in which we live. We do not have costless access to the trading histories of every possible counterparty. As such, when individuals cannot perfectly commit and there is imperfect monitoring, money is essential in the language of Hahn in that it expands the possible allocations available to economic agents. The role of money in this context is as a substitute for information. Money is memory.

The informational role of money makes money essential and is therefore preferable to other arrangements. However, this does not resolve the solution by backward induction that Glasner suggested above. Thus, we need to answer question (b) above.

In search models of money it is standard to denote the price of money as . The price of money refers to the goods price of money rather than the money price of goods as we are usually accustomed to thinking. It is important to think about the price of money because it is possible that this price could be zero (i.e. we have a non-monetary economy). A condition for a monetary equilibrium in these models is that

This implies that it must be true that the price of money today is greater than or equal to the present discounted value of the price of money tomorrow. In more familiar language to monetary theorists, it must be true that the inflation rate is greater than or equal to minus the rate of time preference.

According to Glasner, we know that at some date, T, the world ends and therefore nobody would accept money. Through backward induction, nobody would accept money today. However, the solution by backward induction is contingent upon knowing the date at which the world ends. For example, suppose that the probability of the world ending tomorrow is where is the information available at time t. Thus, the expected future value of the price of money at time t is:

Thus, we can re-write the necessary condition for equilibrium as:

So long as the probability of the world ending is not equal to one, a monetary equilibrium obtains and is therefore not subject to the backward induction critique. Fiat money can therefore be thought of as a rational bubble. We do not need to appeal to irrationality as Glasner suggests. Rather as a trader I know that money increases the set of feasible allocations in trade and therefore I have an incentive to use it and accept it so long as I anticipate that others will accept it in the future. In addition, I know that it is intrinsically worthless, but so long as the future is not certain (or time is considered infinite) it can have positive value because of its role as medium of exchange. As a result, fiat money trades above its fundamental value.

Pet Peeves: Monetary Policy Edition

A recent op-ed in the WSJ posits the following claim:

A few critics of quantitative easing (QE) and the zero interest rate (ZIRP) have correctly pointed out that these policies weaken the dollar and thereby reduce the purchasing power of American paychecks. They increase the risk of future inflation, obscure the true cost of the unsustainable fiscal policy the federal government is running, and transfer wealth from savers to debtors.

But QE and ZIRP also reduce long-term economic growth by punishing savers, reducing saving and investment over the long run. They encourage the misallocation of resources that at a minimum is preventing the natural rebalancing of our economy and could sow the seeds of another painful boom-bust.

There is a lot going on in these statements. Also, I don’t like thinking about monetary policy in terms of interest rates. Nonetheless, here are my main points of rebuttal:

(a) Does the Fed control real interest rates in the long run? In other words, the author seems to think that by having the Fed target a federal funds rate near zero that this effects savings and investment (i.e. lower interest rates lead to lower savings and since savings=investment this means lower investment and lower growth). But don’t people make savings and investment decisions based on real interest rates whereas the Fed is targeting a nominal interest rate? Consider an example to illustrate my point. Suppose that the Fed came out tomorrow and said that they wanted to promote savings and investment and therefore were raising their target of the federal funds to 5%. Holding inflation expectations constant, the Fisher equation implies that the real interest rate would rise substantially. However, we cannot hold inflation expectations constant in this example because that policy would necessarily have an effect on inflation expectations. In fact, it is very likely that this policy would induce expectations of deflation. The policy would do nothing to raise real interest rates.

(b) The use of “boom-bust” is clearly a reference to the Wicksell-Hayek business cycle model. However, in that model the boom (which leads to a subsequent bust) is caused by malinvestment due to the fact that the market rate of interest is set below the natural rate of interest. Assuming that this view is empirically valide, what is the current natural rate of interest? One empirically testable hypothesis from this view is that when the market rate of interest is held below the natural interest rate, this results in ever-accelerating inflation. Do we observe ever-accelerating inflation? Do we at least observe rapidly growing productivity in the face of stable inflation? I think that the answer to those questions is no.

(c) Does inflation reduce the purchasing power of American paychecks? First, this depends on how we measure things and the time horizon. If American paychecks have less purchasing power, then we would expect to see real compensation declining. We don’t. Perhaps the author is referring to the purchasing power relative to other currencies. Have we seen a marked depreciation in the USD relative to the Euro or the Pound sterling? No.

Do not mistake this analysis for downplaying the costs of inflation. The costs associated with inflation can be significant. However, just because something costs more in nominal or real terms does not necessarily mean that individuals are worse off. For example, we have seen a large increase in the price level since 1970. Nevertheless, given that an 18 cubic foot refrigerator cost about $400 in 1971 and the same size refrigerator costs about $450 today, the average worker in 1971 would have had to work about 107 hours to purchase that refrigerator (based on average wages) whereas the worker in 2011 would only have had to work about 23 hours.

Rising prices aren’t a cost of inflation, they are the definition of inflation.

(The costs of inflation are the things that would have been avoided in the absence of inflation. For example, the inflation tax on money holdings, “shoe leather” costs, costs associated with shorter contract durations and negotiation, etc. Read Axel Leijonhufvud, for example.)

(d) Inflation reallocates wealth from savers to borrowers only when it is unexpected. Has inflation been higher than expected?

Allocating Scarce Resources

A Best Buy in Howell, New Jersey was selling 24-packs of bottled water for $40.56. A question for principles students: Should Best Buy be celebrated or derided for charging such a price? What would be the implications for the allocation of bottled water if Best Buy were to significantly lower their price?

In Defense of Mitt Romney

I try to stay away from politics on the blog and focus on economics. However, presidential candidate Mitt Romney is being castigated in the media for making a simple, factual statement.

In response to a question from an audience member, Mitt Romney stated, “corporations are people, my friend.” According to NPR, this was “an early Christmas gift” to Democrats because it “made their goal of pushing the narrative that he is a tool of corporate America much easier by providing them with that handy piece of video.”

Color me confused. What did Romney say that (a) suggests he is a tool of corporate America, or (b) is factually inaccurate? Corporations are people. The revenue generated by a firm ultimately goes to individuals whether in the form of wages or profits that go to the owners of the firm (which, in the case of public companies, are the stockholders). Costs beyond wages for a particular firm are paid to other individuals and firms for supplies, services rendered, etc. This is a basic fact and the reason that one will, at times, hear an economist claim that “corporations don’t pay taxes, people do.”

This simple fact, however, has either been misunderstood or misconstrued by the commentariat. In fact, the NPR post explicitly misses this point as the reporter writes:

Anybody these days fortunate to have a 401(k) retirement plan, or even a job with a corporation, understands that when a company makes a profit, there’s a benefit to that firm’s “stakeholders,” as executive-types like to say.

This, however, is only part of the story. It goes beyond profit. Anybody who works for a corporation or who owns or works for a firm that sells goods and services to a corporation benefits from that corporation’s existence. This is what it means to say that corporations are people. Romney was correct.

Markets in Everything: Dance Partners

From the Washington Post:

The shortage of men at Edgewater Pointe Estates is a perennial fact of life at retirement communities and nursing homes around the country, where women often outnumber men 3-to-1. Forget finding a mate – finding a man to dance with is tough enough.

Edgewater’s solution? Hire them.

Bruce and another dancing aficionado, Nick Zaharias, are paid to make sure the surplus of women have a chance for a spin on the dance floor. The complex also brings in volunteers from a local college fraternity.

HT: David Henderson

Why I Love Markets

Whenever economists are asked why they love markets, they inevitably respond that “markets lead to prosperity” or that “markets efficiently allocate resources” or some other such answer than one could find by reading a textbook. What I love about markets is sometimes mundane (I love one-size-fits-all soft drink lids, for example) and other times technologically impressive. In other words, what I especially love about markets is the innovation that they inspire. I was reminded of this reading the WSJ this morning:

For more than 100 years, researchers have tried to come up with adjustable eyeglasses; a Baltimore inventor filed a patent on the idea in 1866. But a workable product that’s easy to adjust, thin, lightweight and accurate proved elusive.

Stephen Kurtin, a California inventor who previously devised one of the first word-processing programs, turned to the problem in the early 1990s. His solution, TruFocal eyeglasses, mimic the way that the lens of the human eye stretches and contracts to adjust focus.

[…]

Once the TruFocal lenses are adjusted, the entire field of vision is in focus, unlike bifocals and progressive lenses, which keep only a limited area in sharp focus. So a user can adjust the glasses to focus only on the book he’s reading, then look up and readjust them to focus solely on the TV across the room.

Prisoner’s Dilemma

The prisoner’s dilemma illustrated via YouTube:

HT: John Taylor

UPDATE: Scott Sumner writes, “I’ve never been more proud to be human.”

Quote of the Day

“Thomas Friedman talks a good game. He speaks as if he is sure he has identified the growth industries of the century, but has he put his money where his mouth is? If he is so certainly right, has he mortgaged his house(s) and invested accordingly? I’d bet he has not.”

— Roger Koppl

Happy (Division of) Labor Day!

In keeping with tradition, we celebrate the division of labor on Labor Day.