Scott Sumner and Musical Chairs

Since 2009, Scott Sumner has been a big proponent of nominal GDP targeting. He sees nominal wages as slow to adjust and he has sketched a simple model, the musical chairs model, to explain why his policy should be adopted.

I am a new convert to these arguments. That is my loss. I had assumed, incorrectly, that Scott was proposing that central banks should simply adjust the coefficients on their interest rate policies, so called Taylor Rules, to raise the nominal interest rate when nominal GDP growth is above target and to lower it when nominal GDP growth is below target. I will refer to that variant of NGDP targeting, as growth rate targeting. An alternative, NGDP level targeting, would make these interest rate adjustments in response to deviations of nominal GDP from a target growth path.

Viewed in this light; NGDP targeting, of either variety, is not a particularly new idea. Nor does it represent a departure from the body of New Keynesian economics that grew up in the decades since 1983, when Ed Prescott sought to banish money from macroeconomic models. Scott is saying much much more than that.

The novel aspect of Scott’s proposal, and one that I endorse wholeheartedly, is the means that he advocates to achieve his goal. Scott proposes that central banks and/or national treasuries should set up markets for nominal GDP futures. Robert Shiller has made a similar suggestion. He proposes that national treasuries finance their borrowing by issuing securities that pay off a dividend that is proportional to nominal GDP. He calls these ‘Trills’; where a Trill is a claim to one trillionth of GDP in perpetuity.

In my own work, I have drawn attention to the remarkable stable connection between the real value of the stock market, and the unemployment rate. I interpret that connection through the lens of a causal theory in which expectations drive asset values, and asset values drive aggregate demand. I have suggested that central banks trade an exchange traded fund to stabilize real economic activity. Hold that thought as the word ‘real’ represents a significant point where Scott and I differ.

Trading Trills, trading GDP futures and trading an ETF, are all methods of targeting nominal wealth. I do not want to quibble over the exact method: and I readily concede that Trills or GDP futures have advantages over ETFs.

The important insight here, is that wealth, or permanent income, drives aggregate demand and that expectations cause inefficient fluctuations in aggregate demand that can be stabilized through relatively straightforward interventions.

In the simplest macroeconomic models, GDP measured in wage units, is proportional to employment:

PY/W = bL

where P is ‘the’ price level, Y is real output, W is the money wage, L is employment and b is the inverse of labor’s share of income. Scott points out that money wages move slowly and that, as a consequence, stabilizing PY will stabilize employment, and eventually, wages and prices. Scott  bases his ideas on Samuelson’s neoclassical synthesis (see Pearce and Hoover). According to this idea, the economy is Keynesian in the short run, when prices and wages are sticky, and classical in the long-run. 

In Scott’s world, the economy homes in on the natural rate of unemployment just as surely as a heat-seeking missile converges to its target. Scott’s intellectual heritage is firmly monetarist. If Milton Friedman were alive today, one might imagine that Scott would find a supporter for his ideas.

My own heritage is different. I have sought to wed post-Keynesian insights with new-classical ideas by resuscitating the idea that the economy is not self-stabilizing. There are many equilibrium unemployment rates and any one of them may be an equilibrium. 

I wholeheartedly endorse Scott’s proposal for open market trades in GDP futures. And, like Robert Shiller, I would like to see the creation of a market for Trills. Unlike Scott, I do not endorse the proposal to stabilize either the level or the growth rate of nominal GDP. Trades in GDP futures should aim to stabilize the unemployment rate. And here is my biggest difference from Scott: trades in GDP futures should be seen as a complement to inflation targeting: not as a substitute.

As I explained in my 2013 book,  How the Economy Works, the economy is not a rocking horse, always returning to the same rest point, a metaphor that originates with Wicksell. It is a boat on the ocean with a broken rudder that requires active political interventions to steer it to a safe harbor.

Policy interventions have two dimensions: not one. Central banks should continue to set the overnight interest rate in an effort to target the inflation rate. They should adopt a second instrument, the purchase and sale of GDP futures, to target real economic activity. For more on this idea, stay tuned. I have forthcoming book in 2016  with 

Oxford Univesity Press with the working title: Prosperity for All. It will be available in mid 2016.

Demand Creates its Own Supply

I have been teaching basic Keynesian economics this week to my undergraduate class and I have just completed a new book manuscript with the working title of Prosperity for All, that will be coming soon to a book store near you. I am thus highly attuned to the debate over the connection between savings and investment. That debate resurfaced with a vengeance this morning on Twitter when Noah Smith and Jo Michell, among others, engaged in a sometimes testy exchange on the role of the State in promoting investment. Since that debate is at the core of Keynesian economics, and since my class is prepping for Monday’s midterm, this seems like a great opportunity to enlighten readers of all varieties on what Jo and Noah were on about.

Keynesian economics begins with a basic definition. To sharpen the discussion, I will abstract from the role of government and I will abstract from foreign trade. In an economy with no government, and no foreign trade, we may define all of the goods produced in the economy to be of two types; a consumption good or an investment good. Since all of the income earned by the factors of production is earned from producing either consumption goods or investment goods, it is IDENTICALLY TRUE that:

1) YN = CN + IN

Here, YN is the dollar value of all of the incomes earned by workers, capitalists and landowners in the process of producing consumption goods worth CN dollars and investment goods worth IN dollars. The letter N stands for “nominal”.

In recent discourse, economists have sometimes resorted to the fiction of the one good representative consumer model in which we assume that the economy produces a single good from capital and labor. That IS NOT what I am assuming here. YN IS NOT a single good. It is the dollar value of all final goods produced in a given year.

To move from nominal values, to real values, we need to deflate equation (1) by a nominal index. The Keynes of the General Theory made a very sensible suggestion that has been ignored for the past eighty years and that I resuscitated in my book, Expectations Employment and Prices. He suggested dividing both sides of identity (1) by a measure of the money wage. That is a great way to normalize measurements over time because the money wage grows for two reasons. It grows when there is inflation in the dollar. And it grows when there is real economic progress. Dividing equation (1) by the money wage leads to the following identity where Y, C and I represent GDP, consumption and investment measured in wage units.

2) Y = C + I

Equation (2) is, at this point, still an identity. Now comes the economics. Keynes introduced two simple pieces: A theory of aggregate supply. And a theory of aggregate demand.

The Keynesian theory of aggregate supply asserts that firms will increase or decrease the number of workers they employ in order to produce as many goods as are demanded. The French Economist John Baptiste Say, famously asserted that: Supply creates its own demand. Keynes turned this proposition on its head. In Keynesian economics: Demand creates its own supply.

Keynes argued that the economy is typically producing at less than full employment. And as long as there is any involuntary unemployment: everything that is demanded will be supplied. That central proposition can be represented by a graph in which expenditure appears on the vertical axis, and income appears on the horizontal axis. A line at 45 degrees to the origin, for which income equals expenditure, IS the Keynesian aggregate supply curve.

Keynes did not explain why firms would respond to deficient demand by reducing employment, as opposed to cutting wages. He thought that workers would resist reductions in their wages, but he did not believe that sticky wages were central to his argument. Although Keynes never provided a fully articulated theory that would reconcile his ideas with microeconomics: I have provided such a theory. In my published research, I explain why the forty five degree line is an aggregate supply curve. My work is grounded in the microeconomics theory of search. But I digress. More on aggregate supply in a future post.

Recall that my purpose here, is to explain the debate between Noah and Jo on the equality of savings and investment. In order to move forward with that purpose, let us accept, for now, the Keynesian theory of aggregate supply and move to the Keynesian theory of aggregate demand.

Keynes asked, what determines expenditure on consumption and investment goods? He claimed that aggregate expenditure on consumption goods, by a community of people, will increase when the income of the community increases. But it will increase less than proportionally. He called the constant of proportionality, the marginal propensity to consume. We may represent that idea by equation (3):

3) C = a + bY

Here, ‘a’ is a constant that I will call autonomous consumption expenditure and ‘b’ is the marginal propensity to consume.

Finally, we need a theory of investment. Investment, in the basic version of Keynesian theory, is a highly unstable variable that is driven by the animal spirits of investors. Each year, investors make plans and they enact those plans by placing orders for new machines and factories. I will represent the planned expenditures of investors with the symbol IP. Let me also use the symbol X to represent total expenditure and XP to represent planned expenditure. That leads to the following equations, 

4) X = C + I

5) XP = C + IP

and, using the theory of consumption from (3)

6) X = (a+I) + bY

7) XP = (a+IP) + bY

Equations (6) and (7) distinguish expenditure, X, from planned expenditure, XP. It is identically true that

8) X = Y

But it is only true, in equilibrium, that

9) XP = Y

The difference between I and IP is that goods that are produced, but not sold, are DEFINED to be investment goods. If Toyota builds 100,000 cars, but only 20,000 are sold, the 80,000 unsold cars are defined to be investment expenditure. But they are not defined to be part of planned investment expenditure. An economy in which unplanned inventories increase by the real value of 80,000 cars is not in equilibrium. To restore equilibrium, Keynes argued that Toyota will fire workers, those workers will spend less, and income will fall to the point where saving equals planned investment.

What about the equality of savings and investment? By definition, every dollar not spent, is saved.

10) S = Y – C

Here, S represents savings. A little further algebra establishes that, when Y = XP, it is simultaneously true that

11) S = IP

Here, finally, is the answer to the exchange between Jo and Noah. It is always true, in equilibrium, that savings is equal to investment. In Keynesian theory, it is income and employment that adjust to make this so. In Keynesian economics: Demand creates its own supply.

A Bridge Too Far?

There is much current angst on the difficult problem of how to escape a liquidity trap. Paul Krugman points out that in Japan, the ratio of debt to GDP is growing, leaving little room for a further tame fiscal expansion. He favors something more aggressive.

Tony Yates argues instead for a helicopter drop. Print money and give it to Japanese citizens. The benefit of that approach is that it does not leave the government with an increase in interest bearing debt. Simon Wren Lewis looks more closely at the technical aspects of this idea.

What are the differences between aggressive fiscal expansion financed by debt creation; and printing money and giving it to citizens? There are two.

First, an aggressive fiscal expansion, as envisaged by Keynesians, would be spent on infrastructure. A money financed transfer would be spent by citizens.

Second, an aggressive fiscal expansion, as envisaged by Keynesians, would be financed by issuing long term bonds. A money financed transfer would be financed by printing money.

While infrastructure expenditure is sorely needed, at least in the U.S., I see no reason to give up on sound cost benefit analysis to decide which projects are worth pursuing and which are not. That’s why I favor giving checks to citizens over building a bridge to nowhere.

Once we decide how the fiscal expansion is to be distributed, we face the second question: how should it be financed? Print money? Or issue long term debt. Standard Economic models tells us that it doesn’t matter. At the zero lower bound, money and three month T-bills are perfect substitutes. And financing expenditure by three month T-bills has the same effect as financing it by thirty-year bonds because the composition of the government’s liabilities is supposed to be irrelevant. That of course, is nonsense. The composition of government liabilities matters. And it matters a lot.

Why does the composition of debt matter? Because the asset markets are incomplete. Our children and our grandchildren cannot participate in asset markets that open before they are born. And none of us can sell our human capital or buy the human capital of others. Once you realize that the composition of the governments portfolio matters, it is a short step to recognize that it is all that matters.

Why be wary of building bridges that are financed with 30 year bonds? Because the yield on these bonds is low; but it is not yet zero. A big increase in public sector borrowing, at the long end of the yield curve, will drive up rates and crowd out some private investment. A big increase in public sector borrowing at the short end of the yield curve will not crowd out private sector investment because rates at the short end of the yield curve are currently zero.

That observation suggests a third alternative to building bridges or to a helicopter drop. Buy back long term government debt and refinance it by printing money. That strategy would, one hopes, lower yields at the long end of the yield curve and stimulate private companies to invest in new capital projects.

I prefer private sector investment over government sector investment. But there are also good arguments for more public infrastructure projects. Build a bridge if it is needed; but make sure that it goes somewhere first. More importantly; finance the project by printing money: not by issuing thirty year bonds.

Give me a One Armed Economist

I'm glad to see that Olivier Blanchard and Yanis Varoufakis have come out in favor of my plan for People's QE.

The following passage is from How the Economy Works, (HTEW) page 151.

Economists are famous for hedging their bets. A typical response to the question of how to run fiscal policy might be: “On the one hand we should raise taxes but on the other we should balance the budget”. President Harry Truman who instituted the Council of Economic Advisors famously quipped; “give me a one-armed economist.”

Here's what I said about fiscal stimulus in HTEW. 

A large fiscal stimulus may or may not be an important component of a recovery plan. My own view is that there is a better alternative to fiscal policy that I explain in [How the Economy Works, Chaper 11]. But if a fiscal policy is used it should take the form of a transfer payment to every domestic resident; not an increase in government expenditure.

Well ok, I didn't call it peoples QE. "Peoples QE", was coined by a speech writer for Jeremy Corbyn, the new leader of the Labour Party in the UK and its one of the less crazy parts of the Corbyn platform.  Why do I believe that? Because I also believe something that may seem contradictory. Its time to get interest rates into positive territory. SOON. Quoting again from an impeccable source (HTEW page 152).

Here are my views on monetary policy. Short term interest rates should be increased as soon as feasible, because a positive interest rate is needed if a national central bank is effectively to control inflation. In future, central banks should use the interest rate for this purpose and not to prevent recessions.

Why do I favor a fiscal transfer, rather than currently popular bandwagon of infrastructure expenditure? Two reasons.

• Because the work of Christina and David Romer suggests that tax multipliers (and by implication, transfer multipliers) are big. 

• Because I trust markets to decide how to allocate a fiscal stimulus more than I trust the government.

So: Raising interest rates is necessary to eventually raise inflation. I'm with the "neo-Fisherians" here. But an interest rate hike must be offset by some other expansionary policy to prevent the normalization of rates from creating a new recession. Here's what I said about that in HTEW.

But if a central bank raises the domestic interest rate without independently managing confidence, the result will be a drop in the value of the national stock market and a further deterioration in the real economy. To prevent this from happening, central banks need a second instrument.

So: Janet, Mark, Mario: yes: raise rates. Please. But give us QE too.

Beliefs are Fundamental: Whatever your Religion

A couple of weeks ago, I had the pleasure of attending a very interesting conference at the Federal Reserve Bank of Saint Louis. The topic

of the conference was the relationship between income inequality and monetary policy, but the papers, more broadly, were all trying to cope with the intellectual problem of rebuilding monetary economics to incorporate the lessons of the Great Recession.

I discussed a fascinating paper, presented by Jim Bullard, joint with Costas Azariadis, Aarti Singh and Jacek Suda (ABSS). ABSS Built a 241 period overlapping generations model in which the people who inhabit the model are permitted to trade one period nominal bonds: but nothing else. They focused on one particular equilibrium of their model and they showed that, conditional on this equilibrium, a central bank can help the economy to function efficiently. Here is a link to the paper and here is a link to my discussion.

In this blog post I am going to give a synopsis of some general points that I made in my discussion, with a slight change of notation to make it blog friendly. 

Gather round and I will tell you a story. It is a story of how classical economists from the dark side bamboozled the Keynesian children of the light into accepting their dark version of the truth.

I don’t see how to discuss this issue without a little notation. So bear with me, and you will be rewarded. I promise.

For the past thirty years, most monetary models were built around a three equation New Keynesian monetary model.

Eqn 1. R – (PF-P) – (YF-Y) = Rstar + Dshock

Eqn 2. R = beta1*(PF-P) + beta2*(Y-Ybar) 

Eqn 3. H(PF-P,Y-Ybar) = Sshock

Here, P is this year’s price index, PF is next year’s price index (the F is for future) Y is GDP this year, YF is GDP next year and R is the money interest rate. Rstar is Wicksell's natural rate of interest and Ybar is potential GDP. 

Dshock and Sshock are random variables that represent demand and supply shocks. All variables are written as natural logarithms so PF-P is the inflation rate and YF-Y is the growth rate of real GDP. The star means multiplication and beta1 and beta 2 are numbers that describe policy.

Equation 1 (sometimes called the Fisher equation) is derived, in New Keynesian models, from the choices made by a representative person with superhuman powers of perception who chooses to optimally allocate resources between the present and the future. It says, in words, that the price of future goods, relative to current goods, is proportional to the ratio of consumption this year to next.

Equation 2 reflects central bank policy and it is sometimes called a Taylor Rule after John Taylor who showed that an equation like this does a pretty good job of describing how the Fed actually behaved in the period preceding the Great Recession.

Equation 3 specifies how the real and the monetary economy interact, and, in the New-Keynesian model, it takes the form,

Eqn 3A. P-PL = PF-P + k(Y-Ybar) + Sshock

where k is a number and PL is last year’s price index. This is called the New Keynesian Phillips curve and it plays the same role in New Keynesian economics that the Nicene creed plays in Christianity.

Almost all of the papers at the conference last week accepted equation 2 and most of them accepted some version of equation 3. 

The focus of pretty much every paper at the St. Louis Fed conference was on how to replace Equation 1. That is an interesting development, which reflects the fact that monetary economists have woken up to the fact that there is a problem with the representative agent assumption.

That is a start. And it is a good start. But, as I argued, in my discussion of ABSS, the problem with monetary economics is deeper than replacing the representative agent assumption: although that is certainly a big part of the problem. The problem is with the rational expectations assumption.

The New Keynesian monetary model is a child of the rational expectations revolution. In the dark days, before Robert Lucas wrote his game changing paper, Expectations and the Neutrality of Money, economists had a more nuanced approach to super-human powers of perception. Here is the monetary model we worked with back then.

Eqn 1B. R – (EPF-P) – (YF-Y) = Rstar + Dshock

Eqn 2B. R = F(EPF-P,Y-Ybar)

Eqn 3B. H(P-PL,Y-Ybar) = Sshock

This looks superficially like the New Keynesian model. But the differences are deep. First, I have replaced PF, the realization of the future price, with EPF, our current belief about what PF will be.  (I could have done the same with YF, but changing PF to EPF is sufficient to make my point.) Second, back in the dark days, we worked with a version of the Phillips curve that was purely backward looking. More on that point in a future blog.

Let me deal first, with expectations. By replacing PF with EPF I have added a new variable. The belief about what the future price will be is NOT the same as what it actually is. And because beliefs are not always correct, we need another equation. That equation, pre Lucas, was called adaptive expectations and it took the form

Eqn 4B.  EPF-P = F1(X)

where X is stuff we observe this year.

In words, expected inflation between this year and next year is some function of things we can observe this year. For example, Friedman used the following form for the function F1( )

Eqn 5B.  EPF-P = lambda*(P-PL) + (1-lambda)*(EPFL-PL)

which says that our belief of inflation is a weighted average, with weight lambda, of last period’s belief of this year's inflation rate and the inflation rate that actually happened. People don’t have superhuman powers of perception. They do, pretty much, what econometricians do.

So how were we bamboozled into accepting rational expectations? Bob Lucas argued that, just as econometricians add random shocks to their models, so should theorists. And if the theorists’ model has shocks: the people who inhabit the model should recognize that fact. According to Bob, EPF is not the same as PF because PF is a random variable.

If people inhabit a stationary environment, they will learn that every time they see X, P is equal to P(X). The rule that they use to forecast PF is irrelevant. In equilibrium, people will learn to forecast in a way that is unbiased. In equilibrium, PF will not equal EPF every time. But these two variables will be equal on average.

This was a brilliant and beautiful argument. But Bob slipped in an unwarranted assumption. He assumed that for given fundamentals, there is a unique rational expectations equilibrium. That assumption is false in every monetary general equilibrium model that anyone has ever written down. And it was false in the model that Bob used to make his point as Mike Woodford and I pointed out at the time and as I have tried to hammer home in pretty much everything I’ve ever written since then.

So how does this relate to the papers at the St Louis Fed conference? And how should it shape the way we move forward?

Let me be clear. Rational expectations is a great assumption. In the words of Abraham Lincoln: you can’t fool all of the people all of the time. But, even in a stationary environment where the world is not changing in unpredictable ways, RATIONAL EXPECTATIONS IS NOT ENOUGH TO DETERMINE BELIEFS. The forecast rule, equation 4B, is a separate independent equation that represents beliefs. 

The moral of my story is this: Beliefs are fundamental: whatever your religion.