New Solutions to Old Problems

There was an interesting exchange over the last couple of days between two of my favorite bloggers; Frances Coppola, aka Femina Spectabilis, and Brad DeLong, aka Distinguitur Oeconomicarum. Frances delivered a talk at my alma mater,  Manchester University, on the need to use non-linear models and to recognize the importance of multiple equilibria. Brava! Brad Delong, over at Equitable Growth, takes umbrage at Frances’ charge and rushes to the defense of his former teacher, Olivier Blanchard, aka Nobilis Vir. 

Here is Frances at full tilt

… some of the most influential people in macroeconomics have spent their lives developing theories and models that have been shown to be at best inadequate and at worst dangerously wrong. Olivier Blanchard’s call for policymakers to set policy in such a way that linear models will still work should be seen for what it is – the desperate cry of an aging economist who discovers that the foundations upon which he has built his career are made of sand. He is far from alone.

Perhaps a little harsh. But Frances has a point here Olivier. It's one that was made sometime ago by my emeritus colleague Axel Leijonhufud who referred to what he called corridor effects. Using Axel’s metaphor, Olivier is simply calling for policy makers to keep the economy in the corridor. And who could disagree with that?

Not Brad DeLong for sure, who is supportive of this position. And Brad has a prescription for what it means...

...as long as you can keep the economy on the upward-sloping rather than the flat part of the LM curve, linear models should be good enough for practical purposes. And the government has mighty fiscal policy and credit policy tools at its disposal that it can use to keep high-quality bonds, even short-term bonds, from going to par. 

Quite! The key in this paragraph is the call for policy makers to use  ‘credit policy tools’ in normal times as an additional component of stabilization policy. What might that involve? In my view, central banks and treasuries must recognize their responsibility to counteract the wild swings in asset markets that are the root cause of financial crises.

Horror! Surely, we should leave the allocation of financial capital to those who know best. The decisions of billions of people, freely contracting in markets, can surely make better choices that a cadre of appointed mandarins who purport to understand the economy  better than the markets. Not so. As I argued in the Guardian last year,

The ratio of the stock market price to cyclically adjusted earnings, the PE ratio, is a highly persistent, volatile process. It has been as low as 5 in the 1920s and as high as 45 in the 1990s. When the PE ratio is above its long run average, an investor can profit from selling the market short. When it is below its long run average, a winning strategy is to borrow money and invest it in shares. But although that is sound investment advice in theory, in the real world there is no private investor with a long enough horizon and deep enough pockets to make those trades. As Keynes famously said: "Markets can remain irrational for longer than you can remain solvent."

What can possibly go wrong with private markets? Quoting again from my Guardian op Ed,

Economic theory teaches us that free trade in markets leads to efficient allocations. But a precondition of that doctrine is that everyone who is affected by trade is free to participate in the market. That condition does not hold in the context of the financial markets. We cannot buy insurance over the state of the world into which we are born.

The problem of excess financial volatility is one that cannot be solved by any individual; but it can be solved by government. The Treasury has the power to make commitments on behalf of future generations. The FPC, by exercising that power on behalf of the Treasury, can make trades in the financial markets that capitalise on the inefficient boom-bust financial cycles that are the source of so much human misery. In this way, the FPC will at the same time stabilise volatility in the market and promote financial stability.

There is a growing awareness that free trade in the financial markets does not lead to Pareto efficient outcomes. And, as we have learned only too painfully; pain on Wall Street leads to pain on Main Street. Monetary policy cannot ensure financial stability and stable prices with only one instrument. We must manage the risk composition of the central bank’s balance sheet as well as its size.

Yes David: Unemployment is Sometimes Involuntary

My pal David Andolfatto doesn't like it when I say that some unemployment is involuntary. Here is my response:

David

I am happy with the way you characterize my beliefs in the first paragraph of your blog. Unemployment is clearly not Pareto optimal.  Everything you say after that is at best misleading and at worst dismissive of everything we (at least some of us) learned from Keynes. 

The idea of involuntary unemployment was introduced by Keynes in the General Theory. But you already knew that. It is defined as a situation where (in modern language) the ratio of the marginal disutility of work to the marginal utility of consumption is not equal to the real wage. That seems a pretty accurate description of the equilibrium outcome of labor search models.

Bob Lucas cast a spell over the profession in a series of papers in the 1970s. You are accurately summarizing Bob's view. That view was tied to a three decade long campaign by economists predominately located in Chicago, Minnesota and Rochester (at the time) to discredit Keynesian economics. Tom Sargent reputedly advised his students not to read the General Theory. That was a tragic mistake and we are still suffering from the consequences.

You are right to assert that the important distinction is between equilibria that are Pareto optimal and those that are not. You are wrong to assert that the term 'involuntary unemployment' has no useful meaning. 

I accept your categorization of the allocation of time between three competing ends. Every family, and every member of that family, chooses every day whether they will choose to participate in the labor force. As long as they are in the labor force, they may be employed or unemployed. Those who are unemployed do not choose that state. They must wait for a job offer to appear. In some states, that job offer may take a couple of days to arrive. In others, it may take a couple of years. The activity of waiting for a job, even when it involves active search, can meaningfully be called involuntary unemployment.

The dismissal of 'involuntary unemployment' from the lexicon of the modern economist was introduced as part of a deliberate attack on Keynesian economics. It is time to roll back that attack. As I have shown here, 'involuntary' unemployment is a useful way of distinguishing unemployment that is part of a social optimum, from unemployment that is not.

Labor Force Participation is Secular: Unemployment is Cyclical!

Updated data at the request of Andrew Sentence on participation and unemployment in the U.S.  

Business cycles are about unemployment; not about changes in the participation rate.

(c) Roger E. A. Farmer March 2015

See my twitter posts today on this topic. 

If people choose to look for a job; that's their business. If people can't find a job; that's our collective business as a society.

Participation is a voluntary choice.  Unemployment is not. 

The idea that unemployment is voluntary is classical nonsense.

Anybody want to explain to me why they think labor force participation is a cyclical phenomenon?

Participation is not cyclical! Unemployment is!  

The secular trend in participation dwarfs the cyclical movement. That's an important fact! 

Follow me on twitter @farmerrf 

Sam and Janet go to College

My reading list on the overlapping generations model has already generated some questions. Rather than respond in the comment section to each question individually, I will answer these questions in a new post. Here goes.

In a comment on my previous blog Brian Romanchuck has a “good grounding in mathematics” and he “understands the [overlapping generations] models.” He is my ideal reader. Brian raises a number of points that may be shared by others with a similar background. If you also have a good grounding in mathematics and you think you understand the models: this post is for you.

Let's start with a little background about the overlapping generations (OLG) model. When Samuelson introduced the model in 1958 it revolutionized the way that economists think about the interest rate. Economists have long wondered why the interest rate is positive. The dominant view, before Samuelson’s article, was that most people prefer to consume early in life rather than later in life: a bird in the hand is worth two in the bush. The interest rate is compensation for waiting and it is governed by what we call, the ‘rate of time preference’.

Samuelson pointed out that, in equilibrium models with overlapping generations, there is another possibility. The interest rate may be equal to the rate of population growth, even when everyone has a positive rate of time preference. The ‘biological theory of the rate of interest’ was born.

Does the overlapping generations model explain money?
Most people earn very little when they are young, and very little when they are old. The bulk of earnings arise in middle age. The balance of earnings over a persons life is called his or her income profile. For income profiles that are tilted towards youth, there is an equilibrium in the OLG model in which the interest rate is less than the growth rate. If the size of the population is constant, this is a negative number.

Samuelson pointed out that, an equilibrium where the interest rate is negative, is inefficient. This is true in every dynamic equilibrium model and it is referred to as dynamic inefficiency. In the simplest case, everyone lives for two periods and has one apple when young and none when old. The equilibrium, in the absence of government, is that everyone eats their apple when young and starves when old.

Samuelson thought that this model can explain why money has value. He pointed out that the initial old generation could invent what he called the ‘social contrivance’ of money. This is a worthless piece of paper that the old pass to the young in exchange for one half of their apple. This contrivance supports a new equilibrium in which the interest rate is equal to the population growth rate and everyone is better off forever.

Some economists took this idea seriously as a model of money. See for example, the conference volume edited by Kareken and Wallace. However, other economists pointed out that the object that is passed from old to young does not have to be money. Anything that is valued and in fixed supply will have the same effect; for example, Rembrandt paintings.

The consensus now is that the OLG model is not a model of money. But it IS the best way of thinking about the determination of the interest rate in the world in which we live. That is a world where we have finite lives and not all of us care enough about our children to leave them bequests.

The issue of dynamic efficiency is important because it has implications for the impact of government debt on the welfare of different generations. Do we live in a world that is dynamically inefficient? Abel and co-authors say no.

Can the OLG model explain inflation?
I do not personally believe that Samuelson’s  contrivance of money is a good description of why we use money. But the OLG framework CAN be used to understand money and inflation.

There is a group of purists who insist that we model money by explaining the frictions that cause us to use money in exchange. The new monetarists, Randy Wright and Steve Willamson are in this camp. My own view is that it is acceptable to assume that the real value of money yields utility, as first suggested by Don Patinkin in his seminal book Money Interest and Prices. 

If you accept this point of view, explaining money in an overlapping generations model is no different from explaining money in any other inter-temporal general equilibrium model. Money is an asset that is held because it is useful in exchange and it is different from government debt because as Robert Clower famously stated:

Money buys goods and goods buy money but in a monetary economy goods do not buy goods. 

General equilibrium theorists have used a variety of devices to capture this idea varying from cash-in-advance, to money in the production function, money in the utility function or money that reduces transactions costs.  Here is a link to Olivier Blanchard's MIT lecture notes on this topic,

Does the OLG model offer useful policy insights?
Of course it does. It is one of two widely used frameworks to think about intertemporal macroeconomics: the other is the infinite horizon Ramsey/Cass/Koopmans model. The OLG model is indispensable for asking, and answering questions related to the design of pension schemes and for all issues relating to intergenerational allocation of resources.

For examples of practical questions that can only be addressed by overlapping generations models, see the book by Auerbach and Kotlikoff or the set of generation accounts prepared by Auerbach Gokhale and Kotlikoff.

Is the OLG model unrealistic?
Some might think that because the original model has only three periods of life that it is an unrealistic description of the world we live in. Although many of the insights of the model have been developed in a two or three period framework, the model is easily extended to multiple periods and the same insights remain. 

Economists often construct seventy period models that they solve and simulate on a computer to answer important questions about the incidence of taxes and transfers on welfare.

Olivier Blanchard, the research director of the IMF, developed an elegant version of the OLG model in which people have long lives, but they die each period with some probability. Olivier’s model is set up in continuous time, but adapting it to a discrete model with a period of a year or a quarter to match real world data is a simple task.

Do these models ignore intragenerational trade?
Absolutely not. The model accommodates lives of arbitrary length, many people of different types and many goods within each generation. The best source for the general overlapping generations model with many people and many goods is the Econometrica paper by Tim Kehoe and David Levine.

If you are interested in how all of these pieces fit together and like Brian, you have a good grounding in mathematics, try reading my book, The Macroeconomics of Self-Fulfilling Prophecies.

Economics is a fascinating subject that combines economic history and the history of thought with mathematics and mathematical statistics to shed light on important issues of public policy. All of the questions that commentators have left on my blog were answered in the literature more then forty years ago but understanding these answers, sometimes, takes a little effort.

The Great Blog Debate about Debt: A Reading List

I applaud everyone who has weighed in on the Great Blog debate about debt (Simon,  Bob,  me, and others too numerous to link. All of the issues that have been raised on Nick's blog were the topic of frontier research in economics journals in the 1950s -- 1970s.  Nick has links to earlier posts here.

The paper that started all of this (at least in the English speaking world) was by Paul Samuelson. "An exact consumption-loan model of interest with or without the social contrivance of money", Journal of Political Economy 1958, Vol 66 No. 6. The French lay claim to an earlier version by Maurice Allais, but that's another story. 

Samuelson's paper was a revelation to economists because it provided an example where markets don't work. In Samuelson's example, there is an equilibrium, (people optimize taking prices as given and all markets clear) that can be improved upon by a government institution. Samuelson's paper is a good starting point for those who would like to read more about this.

Samuelson provided a model of pure exchange, like the examples Nick has developed. In a pure exchange model there is no production. In 1965, Peter Diamond introduced capital to this model and he discussed the role of government debt in "crowding out" private capital. His paper was published in the American Economic Review, Vo. 55, no 5 under the title "National Debt in a Neoclassical Growth Model". Peter uses a mathematical tool called a 'difference equation'; and if you are sticking with my reading program, you will need to know a little bit about difference equations. There are many good undergraduate books on the topic; I like "Fundamental Methods of Mathematical Economics" by Chiang, but that probably dates me.

The next paper I would recommend in this literature is by a mathematician, David Gale, "Pure Exchange Equilibria of Dynamic Economic Models" Journal of Economic Theory 6 (1973). I include David's paper on the reading list of my first year Ph.D. class. In it, David distinguishes what he calls a "Samuelson economy' from a 'classical economy' and he shows that every overlapping generations model has at least two steady state equilibria; one in which the interest rate equals the population growth rate and one in which the aggregate saving by the young is zero. This divide is the key to understanding when government debt is a burden in the sense we have been discussing.

Throughout the 1960s and 1970s there was a very muddled discussion in the journals, trying to understand why markets can sometimes fail to be optimal. Some people thought that it was because not everybody can meet, due to the one way flow of time. That issue was cleared up by Karl Shell in 1971, "Notes on the Economics of Infinity", Journal of Political Economy, Vol. 79. Karl attributed the problem to what he called the 'double infinity' of people and goods. This is the paper to cite at parties if you want to appear knowledgeable about the topic. It probably won't enlighten you much unless you're enrolled in an economics Ph.D. program.

Any question that you have has, almost surely, been answered already in the literature. How do the conclusions of the model depend on the assumption of no bequests? What happens if some people live forever? What happens if there are multiple goods in each period? Many of these questions are answered in my book "The Macroeconomics of Self-Fulfiling Prophecies".

I'm sorry if the answers are not always obvious, or the papers I have cited seem impenetrable to you. But realize that mathematics is a language and often it is the best language for answering questions of logic. "Everything should be made as simple as possible, but no simpler".

If you think that we are debating esoteric issues that are unrelated to the real world; you are entitled to that opinion. An economic model is only useful if helps us to understand the world. I happen to think that the overlapping generations model contains a great deal of useful insight. If you read, and understand, all of the papers I have cited, you will never again utter the phrase: "debt is money that we owe to ourselves".