Sunday, December 28, 2014

Where's the Multiplier?

Robert Waldmann thinks there are "non-Keynesians" who are excessively dismissive of the Keynesian multiplier:
Various non Keynesians have argued that the pattern of public spending and GDP in the USA during the current recovery (that is since June 2009) undermines the Keynesian hypothesis that the Government spending multiplier is positive. In particular JOhn Cochrane and Tyler Cowen argue that, if Keynesians were right, sequestration should have caused at least a decline in GDP growth rates.
Waldmann shows us a chart, calculates a correlation coefficient (complete with standard error and t-statistic), showing that, for the last 19 quarters, quarterly growth in real government spending and growth in real GDP are positively correlated, and concludes:
...19 data points can’t prove anything, but the few data support the Keynesian hypothesis about as strongly as could be imagined. I am impressed by the unreliability of casual empiricism conducted by idealogues. Some people look at this period and see the opposite of what I see. Even now, I am shocked that economists didn’t bother to look up the data on FRED before making nonsensical claims of fact.
First, I think Christian Zimmerman will be very pleased to learn that FRED has become so user-friendly that failure to consult it has become proof that one is a dim-wit. In fact, my cat was using FRED the other day to sort out some empirical facts. Apparently she's been getting tips from FRED Blog. Second, I'll go Waldmann one better, and include two more observations, so that I can include the whole post-recession time series. Then, the scatter plot of output growth vs. growth in government spending looks like this:
From Waldmann's standpoint, this is even better - a correlation coefficient of 0.50 to his 0.34.

I can see why Waldmann is worried that 19 observations might be too skimpy, though. If you include all the data from 2008Q1 to 2014Q3, you get this:
That doesn't look so great. In that scatter plot, the correlation coefficient is -0.12 which, by Waldmann's criteria, would be a win for the non-Keynesians. But, my cat is is looking over my shoulder and telling me "not so fast." My cat, in addition to knowing FRED, also took an intro-to-macro course, and knows all about the Keynesian Cross. She's a big Paul Krugman fan too.

So, as I learned from Dick Lipsey in 1975, and my cat learned last fall, Keynesian Cross is

(1) C = A + cY,

(2) Y = C + I + G,

where C is consumption, Y is output, I is investment, and G is government expenditures, with 0 < c < 1 and A > 0. Y and C are endogenous, and A, I, and G are exogenous. We can solve for C and Y as follows (my cat checked my algebra):

(3) C = [A + c(I + G)]/(1-c)

(4) Y = (A + I + G)/(1-c)

Here, 1/(1-c) is the multiplier. Krugman, with whom Waldmann appears to be quite sympathetic, has told us that IS/LM is truth, truth is IS/LM - that is all we know on earth, and all we need to know. Better than that, since late 2008, when we entered the liquidity trap and the LM curve became flat, Keynesian Cross has become our even simpler truth. My cat agrees that (3) and (4) are rich with implications and policy conclusions. She has also pointed out that it's not quite fair to be drawing conclusions from the last chart above. Suppose, says my cat, that A and I are random variables, that the government sees the realizations of A and I before choosing G, and that the government has a target level of output, Y*. Then, Y = Y* and Y and G would be uncorrelated. Alternatively, suppose that the government is constrained, so that it can only close a fraction of the output gap, under any circumstances. Then, we could observe something like the last chart. There was a big demand shock in 2008, the government didn't do enough, and so we see government spending going up when output is going down during 2008.

So, my cat reasons, maybe Waldmann has the right idea. After the end of the recession in mid-2009, the demand shock is long gone, and the government has been behaving in a random fashion. Then, if we see a positive correlation between output growth and growth in government spending post-recession, that's consistent with Keynesian Cross. My cat has an inquiring mind though, and she's thinking about equation (3). She understands that the Keynesian multiplier works through consumption, and that (3) implies that we should see a positive correlation between consumption growth and government expenditure growth over the period Waldmann looks at, if Keynesian Cross actually describes the data. No such luck though:
I showed my cat how to use Matlab to compute the correlation coefficient for the data in the chart, and she gets -0.07. Now she's pissed, and is hiding under the sofa.

Obviously, my cat has a lot to learn. I'll have her read Hal Cole's post on the aggregate effects of government spending, for starters. It's also important that my cat understand that there are few economic policy problems that can be solved in a blog post. We're very lucky if looking at raw correlations helps us to discriminate among economic models, or to draw policy conclusions. Indeed, normal economics tells us that there are various mechanisms by which increases in government spending can cause aggregate output to increase. Government spending could be totally unproductive, but lead to an increase in output because of a wealth effect on labor supply. Government spending could be complementary to private consumption, and if the complementarities are large enough, there could be large multipliers. There could be multiple equilibria. But, when we start to think in terms of normal economics, it becomes clear that the effects of government spending depend on what the government spends on, how the spending is financed, etc. And we start asking more questions - interesting ones. Indeed, I think my cat would quickly go back to watching squirrels, if (1)-(4) were all the economics she had to think about.

Sunday, December 21, 2014

Inflation at the Zero Lower Bound

I'm going to try to clear up some issues in the blog discussion among Ambrose Evans-Pritchard, Paul Krugman, and Simon Wren-Lewis, among others, about zero-lower-bound monetary policy. Rather than parse the thoughts of others, I'll start from scratch, and hopefully you'll be less confused.

I'll focus narrowly on the issue of what determines inflation at the zero lower bound or, as Evans-Pritchard states:
The dispute is over whether central banks can generate inflation even when interest rates are zero.
As it turns out, David Andolfatto and I have a paper (shameless advertising) in which we construct a model that can address the question. And that model is actually a close cousin of the Lucas cash-in-advance framework that Krugman uses to think about the problem. There is a continuum of households, and each one maximizes
We'll simplify things by assuming that there are only two assets, money and one-period government bonds, and no unsecured credit. We can be more explicit about how assets are used in transactions, but to make a long story short, think like Lucas and Stokey. There are two kinds of consumption goods. The first can be purchased only with money, and the second can be purchased with money or government bonds. We can think of this as standing in for intermediated transactions. That is, people don't literally make transactions with government bonds, but with the liabilities of financial intermediaries that hold government bonds as assets. We can also extend this to more elaborate economies in which government debt serves as collateral, to support credit and intermediation, but allowing government bonds to be used directly in transactions gets at the general idea.

So, suppose a deterministic world in which the economy is stationary, and look for a stationary equilibrium in which real quantities are constant forever. Further, restrict attention to an equilibrium in which the nominal interest rate is zero. Let m and b denote, respectively, the quantities of money and government bonds, in real terms. We'll assume that the government has access to lump sum taxes and transfers. Starting the economy up at the first date, the first-period consolidated government budget constraint is
where T is the real transfer to the private sector at the first date, i.e. the government (the consolidated government - at this stage we won't differentiate the tasks of the central bank and the fiscal authority) issues liabilities and then rebates the proceeds, lump sum, to the private sector. Then, in each succeeding period, since the nominal interest rate is zero, the consolidated government budget constraint is
where T* is the real transfer at each succeeding date, and i is the inflation rate, which is constant for all time.

A zero nominal interest rate will imply that consumption of the two goods is the same, so per-household consumption is c = y, where y is output. First, suppose that government bonds are not scarce. What this means is that, at the margin, government bonds are used as a store of wealth, so the usual Euler equation applies:
Therefore, i = B - 1, i.e. there is deflation at the rate of time preference. Further, output y solves
This is basically a Friedman rule equilibrium, and we could use results in Ricardo Lagos's work, for example, to show that there exists a wide array of paths for the consolidated government debt that support the Friedman rule equilibrium. An extra condition we require here is that this economy be sufficiently monetized, i.e.
so that the central bank's balance sheet is sufficiently large, and there is enough money to finance consumption of the good that must be purchased with money.

The Friedman rule equilibrium is Ricardian. At the margin, government debt is irrelevant. As well, there is a liquidity trap - open market operations, i.e. swaps of money for government bonds by the central bank, are irrelevant. Thus, the central bank cannot create more inflation. But neither can the fiscal authority. What about helicopter drops? Surely the fiscal authority can issue nominal bonds at a higher rate, and the central bank could purchase them all? But, as long as government bonds are not scarce, equation (3) must hold at the zero lower bound, which determines the rate of inflation. Basically, this is the curse of Irving Fisher. Under these conditions, it is impossible to have higher inflation at the zero lower bound. Helicopter drops may indeed raise the rate of inflation, but this must necessarily imply a departure from the zero lower bound.

Note that, in the Friedman rule equilibrium in which government debt is not scarce, there is sustained deflation at the zero lower bound, which doesn't seem to fit any observed zero-lower-bound experience. Average inflation in the Japan in the last 20 years has been about zero, and inflation has varied mostly between 1% and 3% in the U.S. for the last 6 years. But if government debt is scarce in equilibrium, we need not have deflation at the zero lower bound in our model. What scarce government debt means is that the entire stock of government bonds is used in transactions, which implies, in general, that the nominal interest rate is determined by
where R(t) is the nominal interest rate. So now there is a liquidity premium on government debt, which is determined by an inefficiency wedge in the market for goods that trade for money and government bonds. Then, in a zero-lower-bound equilibrium, the inflation rate is determined by
Note as well, that in this equilibrium, y = m + b, so the total quantity of consolidated government debt constrains output. Clearly, this equilibrium is non-Ricardian - government debt matters in an obvious way. But, there's still a liquidity trap. If the central bank swaps money for bonds, this is irrelevant. The central bank can't change the rate of inflation through asset swaps.

But, when government debt is scarce, fiscal policy can determine the inflation rate, as the fiscal authority can vary the rate of growth of total consolidated government liabilities (which determines the inflation rate), and this in turn will affect the real quantity of consolidated government liabilities held in the private sector, and the liquidity premium on government debt. To explore this in more detail, suppose that the utility function is constant relative risk aversion, with CRRA = a > 0. Then, equation (7) gives us a relationship between output and the inflation rate:
Then, since y = m + b, we can substitute in the consolidated government's budget constraints to obtain
In (9) and (10), s = 1/(1+i), 1 - s is the effective tax rate on consolidated government debt, and T* is the revenue from the inflation tax, where the inflation tax applies to the entire outstanding nominal consolidated government debt.

So, if the fiscal authority chooses an inflation rate i > 1/B -1, then it expands the government debt at the rate i per period, the central bank buys enough of that debt each period that the nominal interest rate is zero forever, and the government collects enough revenue from inflation every year to fund a real transfer T* which, as a function of s, is shown in the next chart.
Note that this is essentially a Laffer curve. Infinite inflation (s = 0) implies zero revenue from the inflation tax, as does zero inflation (s = 1), and transfers are negative when the inflation rate is negative (s > 1). The higher the rate of inflation, the lower is the real quantity of consolidated government debt, output and consumption - more inflation reduces welfare. The central bank cannot control inflation, but the fiscal authority can.

Therefore, in this model, it is indeed correct to state that, at the zero lower bound, the central bank has no control over the inflation rate. The fiscal authority may be able to control inflation at the zero lower bound, but only by tightening liquidity constraints and increasing the liquidity premium on government debt. Of course, in this model the government debt all matures in one period. What about quantitative easing? QE may indeed matter, particularly when government debt is scarce. In a couple of papers (this one and this one) I explore how QE might matter in the context of binding collateral constraints. First, if long-maturity government debt is worse collateral than is short-maturity debt, then central bank purchases of long-maturity government debt matter. As well, if the central bank purchases private assets, this can circumvent suboptimal fiscal policy that is excessively restricting the supply of government debt. But in both cases this works in perhaps unexpected ways. In both cases, unconventional asset purchases by the central bank act to reduce inflation.

Wednesday, December 3, 2014

Economics: The View From Sociology

Some people (Noah Smith, Paul Krugman) have recently written about The Superiority of Economists by Fourcade et al. This is a paper written by two sociologists and an economist, who give us a sociological perspective on the economics profession. To get my bearings I found the most fitting definition:
Sociology: the scientific analysis of a social institution as a functioning whole and as it relates to the rest of society.
So, that seems very promising. Some scientists, who specialize in the analysis of institutions and the role those institutions play in society, are going to figure out the economics profession.

Here's what I'm thinking. I've never taken a sociology course, but being a social scientist maybe I can guess how a sociologist might think about the institution of economics. What is the social role of the economics profession? First, human beings have a need for pure scientific knowledge - we just want to know what is going on. How do economic systems work? Why are some countries and individuals so poor, and why are some so rich? Why do prices of goods, services, and assets move around over time? Second, human beings have a need for applied science. How do we take what we know about economics and use that knowledge to make human beings collectively better off? Third, we might be interested in where economics came from. Who were the first economists, and how did they put together the seeds of economic knowledge? How is the economics profession organized? How is economics taught? Fourth, what makes economics different from other disciplines? If there are large differences in economics, are the human beings who do economics somehow different, for example do they self-select as economists due to particular skills they possess? Is economics different by chance, or is there something about the nature of things that economists study that makes the field different? Finally, how does the organizational structure of the economics profession help it to perform its key social role? Are there ways we could improve on this organizational structure? This could be pretty interesting, and I'm pleased, in principle, that there are scientists who care about these things, and are willing to help out.

First, I'll tell you some of what I know about the economics profession. Economics is clearly successful - in economic terms. Economics is a high enrollment major in most universities, one can make a decent living selling economics textbooks to undergraduates (as I can attest), an economics undergrad major pays off handsomely, and PhD economists are very well-paid - as academics, in the financial sector, and in government. Economists are also influential. They are called on to run key interational institutions like the IMF and World Bank, they more often than not serve as the chief officers in central banks, and they hold important positions in government. Further - and this must be unique among scientific pursuits - you can become extremely rich as a specialist in bad-mouthing your fellow economists.

Economics is very different from other academic pursuits, as any economist who has had to educate a Dean (of Liberal Arts, Social Sciences, Business, whatever) can tell you. In most academic fields, jobs are scarce, and mobility is low. Not so in economics. It is typically hard work to convince a Dean that one needs to make 8 job offers to fresh PhDs in the hope of getting one or two acceptances, that senior job candidates may be even harder to get, and that departures from your economics department need not mean that good people are fleeing a bad department. Salaries are always an issue. Basically, you need to know some economics (though not much) to understand why the economists are paid much more than the philosophers. Economists have a well-organized fresh-PhD job market that operates under clear rules, and performs the function of matching young economists with employers. Economists are social and love to argue. If you are uninitiated and happen to walk into an economics seminar, you might think you should call the police. Don't worry, it's OK.

Fourcade et al. get some of the facts right, but I came away puzzled. Some data is marshalled, but I wouldn't call this paper science, and it's unclear what we are supposed to learn. The first argument the authors want to make is that economics is "insular." By this they mean that economists don't pay much attention to the other social sciences. The evidence for this is citations - apparently the flow of citations is smaller from economics to the rest of the social sciences than the other way around. Whether this is a good way to measure interaction is not clear. There is a very active area of research in economics - behavioral economics - that uses developments in psychology extensively. There is extensive interaction between economists and political scientists - especially those interested in game theory. But I don't think I have ever encountered a sociologist in an economics seminar, or at a conference. However, suppose that economists totally ignored the other social sciences. Could we then conclude that this is suboptimal? Of course not. Maybe what is going on in the rest of the social sciences is actually of no use to economists. Maybe it is of some use to us. Certainly Fourcade et al. don't give us any specific examples of things we're ignoring that might help us out.

And economists are far from insular, especially if we look beyond the social sciences. Economics is a big tent. To gain admission to an economics PhD program requires some background in mathematics and statistics typically, but we don't necessarily require an undergraduate economics degree. People come into economics from history, engineering, math, psychology, and many other fields. As well, an undergraduate degree in economics is an excellent stepping stone to other things - professional degrees in business and law, or graduate degrees in other social sciences. Economic science did not come out of nowhere. Indeed, it often went by "Political Economy" in the early days, and sometimes still does. Most of our technical tools came from mathematicians and statisticians, though econometricians have developed sophisticated statistical tools designed specifically to deal with inference problems specific to economics, and macroeconomists took the dynamic optimization methods invented by mathematicians and engineers and adapted them to general equilibrium economic problems.

The authors of "The Superiority of Economists" see us as hierarchical, with a power elite that controls the profession. PhD programs are indistinguishable, and publication and recruiting are regimented. Seems more like the army than an institution that is supposed to foster economic science. Well, baloney. People of course recognize a quality ranking in academic institutions, journals, and individual economists, but I don't think that's much different from what you see in other fields. Powerful people can dominate particular subfields, but good ideas win out ultimately, I think. In the 1970s, there was a revolution in macroeconomics. That did not happen because the research of the people involved was supported by the Ivy League - far from it. But modern macro research found supporters in lesser-known places like Carnegie-Mellon University, the University of Minnesota, and the University of Rochester. People like Bob Lucas and Ed Prescott got their papers published in good places - eventually - and then got their share of Nobel Prizes in Economics. The economics profession, though it could do better in attracting women, is very heterogeneous. I have no hard evidence for this, but my impression is that the fraction of foreigners teaching economics in American universities is among the highest across academic disciplines. I don't think you would see that in a rigid profession.

Ultimately, Fourcade et al. think that our biggest problem is our self-regard. Of course, people with high self-regard are very visible, by definition, so outsiders are bound to get a distorted picture. We're not all Larry Summers clones. But if we do, on average, have a high level of self-regard, maybe that's just defensive. Economists typically get little sympathy from any direction. In universities, people in the humanities hate us, the other social scientists (like Fourcade et al.) think we're assholes, and if we have to live in business schools we're thought to be impractical. Natural scientists seem to think we're pretending to be physicists. In the St. Louis Fed, where I currently reside, I think the non-economists just think we're weird. Oh well. It's a dirty job. Someone has to do it.

Monday, November 24, 2014


So you've all forgotten who Thomas Piketty is, right? Recall that he is the author of the 685-page tome, Capital in the Twentieth Century, a bestseller of the summer of 2014, but perhaps also the least-read bestseller of the summer of 2014. I was determined, however, not to be like the mass of lazy readers who bought Capital. I have slogged on, through boredom, puzzlement, and occasional outrage, and am proud to say I have reached the end. Free at last! Hopefully you have indeed forgotten Piketty, and are not so sick of him you could scream. Perhaps you're even ready for a Piketty revival.

Capital is about the distribution of income and wealth. For the most part, this is a distillation of Piketty's published academic work, which includes the collection and analysis of a large quantity of historical data on income and wealth distribution in a number of countries of the world. Of course, data cannot speak for itself - we need theory to organize how we think about the data, and Piketty indeed has a theory, and uses that theory and the data to arrive at predictions about the future. He also comes to some policy conclusions.

Here's the theory. Piketty starts with the First Fundamental Law of Capitalism, otherwise known as the definition of capital's share in national income, or

(1) a = r(K/Y),

where a is the capital share, r is the real rate of return on capital, K is the capital stock, and Y is national income. Note that, when we calculate national income we deduct depreciation of capital from GDP. That will prove to be important. The Second Fundamental Law of Capitalism states what has to be true in a steady state in which K/Y is constant:

(2) K/Y = s/g,

where s is the savings rate, and g is the growth rate of Y. So where did that come from? If k is the time derivative of K, and y is the time derivative of Y, then in a steady state in which K/Y is constant,

(3) k/K = y/Y.

Then, equation (3) gives

(4) K/Y = k/y = (k/Y)/(y/Y) = s/g,

or equation (2). It's important to note that, since Y is national income (i.e. output net of depreciation), the savings rate is also defined as net of depreciation.

So, thus far, we don't have a theory, only two equations, (1) and (2). The first is a definition, and the second has to hold if the capital/output ratio is constant over time. Typically, in the types of growth models we write down, there are good reasons to look at the characteristics of steady states. That is, we feel a need to justify focusing on the steady state by arguing that the steady state is something the model will converge to in the long run. Of course, Piketty is shooting for a broad audience here, so he doesn't want to supply the details, for fear of scaring people away.

Proceeding, (1) and (2) imply

(5) a = r(s/g)

in the steady state. If we assume that the net savings rate s is constant, then if r/g rises, a must rise as well. This then constitutes a theory. Something is assumed constant, which implies that, if this happens, then that must happen. But what does this have to do with the distribution of income and wealth? Piketty argues as follows:

(i) Historically, r > g typically holds in the data.
(ii) There are good reasons to think that, in the 21st century, g will fall, and r/g will rise.
(iii) Capital income is more more concentrated among high-income earners than is labor income.

Conclusion: Given (5) and (i)-(iii), we should expect a to rise in the 21st century, which will lead to an increasing concentration of income at the high end. But why should we care? Piketty argues that this will ultimately lead to social unrest and instability, as the poor become increasingly offended by the filthy rich, to the point where they just won't take it any more. Thus, like Marx, Piketty thinks that capitalism is inherently unstable. But, while Marx thought that capitalism would destroy itself, as a necessary step on the path to communist nirvana, Piketty thinks we should do something to save capitalism before it is too late. Rather than allow the capitalist Beast to destroy itself, we should just tax it into submission. Piketty favors marginal tax rates at the high end in excess of 80%, and a global tax on wealth.

Capital is certainly provocative, and the r > g logic has intuitive appeal, but how do we square Piketty's ideas with the rest of our economic knowledge? One puzzling aspect of Piketty's analysis is his use of net savings rates, and national income instead of GDP. In the typical growth models economists are accustomed to working with, we work with gross quantities and rates - before depreciation. Per Krusell and Tony Smith do a nice job of straightening this out. A key issue is what happens in equation (2) as g goes to zero in the limit. Basically, given what we know about consumption/savings behavior, Piketty's argument that this leads to a large increase in a is questionable.

Further, there is nothing unusual about r > g, in standard economic growth models that have no implications at all for the distribution of income and wealth. For example, take a standard representative-agent neoclassical growth model with inelastic labor supply and a constant relative risk aversion utility function. Then, in a steady state,

(6) r = q + bg,

where q is the subjective discount rate and b is the coefficient of relative risk aversion. So, (6) implies that r > g unless g > q and b is small. And, if g is small, then we must have r > g. But, of course, the type of model we are dealing with is a representative-agent construct. This could be a model with many identical agents, but markets are complete, and income and wealth would be uniformly distributed across the population in equilibrium. So, if we want to write down a model that can give us predictions about the income and wealth distribution, we are going to need heterogeneity. Further, we know that some types of heterogeneity won't work. For example, with idiosyncratic risk, under some conditions the model will essentially be identical to the representative agent model, given complete insurance markets. Thus, it's generally understood that, for standard dynamic growth models to have any hope of replicating the distribution of income and wealth that we observe, these models need to include sufficient heterogeneity and sufficient financial market frictions.

Convenient summaries of incomplete markets models with heterogeneous agents are in this book chapter by Krusell and Smith, and this paper by Heathcote et al. In some configurations, these models can have difficulty in accounting for the very rich and very poor. This may have something to do with financial market participation. In practice, the very poor do not hold stocks, bonds, and mutual fund shares, or even have transcations accounts with banks in some circumstances. As well, access to high-variance, high-expected return projects, for example entrepreneurial projects, is limited to very high-income individuals. So, to understand the dynamics of the wealth and income distributions, we need to understand the complexities of financial markets, and market participation. That's not what Piketty is up to in Capital.

How might this matter? Well suppose, as Piketty suggests, that g declines during the coming century. Given our understanding of how economic growth works, this would have to come about due to a decline in the rate of technological innovation. But it appears that technological innovation is what produces extremely large incomes and extremely large pots of wealth. To see this, look at who the richest people in America are. For example, the top 20 includes the people who got rich on Microsoft, Facebook, Amazon, and Google. As Piketty points out, the top 1% is also well-represented by high-priced CEOs. If Piketty is right, these people are compensated in a way that is absurdly out of line with their marginal productivities. But, in a competitive world, companies that throw resources away on executive compensation would surely go out of business. Conclusion: The world is not perfectly competitive. Indeed, we have theories where technological innovation produces temporary monopoly profits, and we might imagine that CEOs are in good positions to skim off some of the rents. For these and other reasons, we might imagine that a lower rate of growth, and a lower level of innovation, might lead to less concentration in wealth at the upper end, not more.

Capital is certainly not a completely dispassionate work of science. Piketty seems quite willing to embrace ideas about what is "just" and what is not, and he can be dismissive of his fellow economists. He says:
...the discipline of economics has yet to get over its childish passion for mathematics and for purely theoretical and often highly ideological speculation, at the expense of historical research and collaboration with the other social sciences.
Not only are economists ignoring the important problems of the world, the American ones are in league with the top 1%:
Among the members of these upper income groups are US academic economists, many of whom believe that the economy of the United States is working fairly well and, in particular, that it rewards talent and merit accurately and precisely. This is a very comprehensible human reaction.
Sales of Capital have now put Piketty himself in the "upper income group." Economists are certainly easy targets, and it didn't hurt Piketty's sales to distance himself from these egghead ivory-tower types. This is a very comprehensible human reaction.

To think about the distribution of income and wealth, to address problems of misallocation and poverty, we need good economic models - ones that capture how people make choices about occupations, interhousehold allocation and bequests, labor supply, and innovation. Economists have certainly constructed good models that incorporate these things, but our knowledge is far from perfect - we need to know more. We need to carefully analyze the important incentive effects of taxation that Piketty either dismisses or sweeps under the rug. Indeed, Piketty would not be the first person who thought of the top 1% as possessing a pot of resources that could be freely redistributed with little or no long-term consequences. It would perhaps be preferable if economists concerned with income distribution were to focus more on poverty than the outrageous incomes and wealth of the top 1%. It is unlikely that pure transfers from rich to poor through the tax system will solve - or efficiently solve - problems of poverty, in the United States or elsewhere. My best guess is that our time would be well spent on thinking about human capital accumulation and education, and how public policy could be reoriented to promoting both in ways that have the highest payoff.

Thursday, November 13, 2014

Neo-Fisherians: Unite and Throw off MV=PY and Your Phillips Curves!

I've noticed a flurry of blog activity on "Neo-Fisherianism," and thought I would contribute my two cents' worth. Noah Smith drew my attention to the fact that Paul Krugman had something to say on the matter, so I looked at his post to see what that's about. The usual misrepresentations and unsubstantiated claims, apparently. Here is the last bit:
And at the highest level we have the neo-Fisherite claim that everything we thought we knew about monetary policy is backwards, that low interest rates actually lead to lower inflation, not higher. At least this stuff is being presented in an even-tempered way.

But it’s still very strange. Nick Rowe has been working very hard to untangle the logic of these arguments, basically trying to figure out how the rabbit got stuffed into the hat; the meta-point here is that all of the papers making such claims involve some odd assumptions that are snuck by readers in a non-transparent way.

And the question is, why? What motivation would you have for inventing complicated models to reject conventional wisdom about monetary policy? The right answer would be, if there is a major empirical puzzle. But you know, there isn’t. The neo-Fisherites are flailing about, trying to find some reason why the inflation they predicted hasn’t come to pass — but the only reason they find this predictive failure so puzzling is because they refuse to accept the simple answer that the Keynesians had it right all along.
Well, at least Krugman gives Neo-Fisherites credit for being even-tempered.

Let's start with the theory. Krugman's claim is that "all of the papers making such claims involve odd assumptions that are snuck by readers in a non-transparent way." Those sneaky guys, throwing up a smoke screen with their odd assumptions and such. Actually, I think Cochrane's blog post on this was pretty clear and helpful, for the uninitiated. I've written about this as well, for example in this piece from last year, and other posts you can find in my archive. More importantly, I have a sequence of published and unpublished papers on this issue, in particular this published paper, this working paper, and this other working paper. That's not all directed at the specific issue at hand - "everything we thought we knew about monetary policy is backwards" - but covers a broader range of issues relating to the financial crisis, conventional monetary policy, and unconventional monetary policy. If this is "flailing about," I'm not sure what we are supposed to be doing. I've taken the trouble to formalize some ideas with mathematics, and have laid out models with explicit assumptions that people can work through at their leisure. These papers have been presented on repeated occasions in seminars and conferences, and are being subjected to the refereeing and editorial process at academic journals, just as is the case for any type of research that we hope will be taken seriously. The work is certainly not out of the blue - it's part of an established research program in monetary and financial economics, which many people have contributed to over the last 40 years or so. Nothing particular odd or sneaky going on, as far as I know. Indeed, some people who work in that program would be happy to be called Keynesians, who are the only Good Guys, in Krugman's book.

So, let me tell you about a new paper, with David Andolfatto, which I'm supposed to present at a Carnegie-Rocheser-NYU conference later this week (for the short version, see the slides) . This paper had two goals. First, we wanted to make some ideas more accessible to people, in a language they might better understand. Some of my work is exposited in terms Lagos-Wright type models. From my point of view, these are very convenient vehicles. The goal is to be explicit about monetary and financial arrangements, so we can make precise statements about how the economy works, and what monetary policy might be able to do to enhance economic performance. It turns out that Lagos-Wright is a nice laboratory for doing that - it retains some desirable features of the older money/search models, while permitting banking and credit arrangements in convenient ways, and allowing us to say a lot more about policy.

Lagos-Wright models are simple, and once you're accustomed to them, as straightforward to understand as any basic macro model. Remember what it was like when you first saw a neoclassical growth model, or Woodford's cashless model. Pretty strange, right? But people certainly became quickly accustomed to those structures. Same here. You may think it's weird, but for a core group of monetary theorists, it's like brushing your teeth. But important ideas are not model-bound. We should be able to do our thinking in alternative structures. So, one goal of this paper is to explore the ideas in a cash-in-advancey world. This buys us some things, and we lose some other things, but the basic ideas are robust.

The model is structured so that it can produce a safe asset shortage, which I think is important for explaining some features of our recent zero-lower-bound experience in the United States. To do that, we have to take a broad view of how assets are used in the financial system. Part of what makes new monetarism different from old monetarism is its attention to the whole spectrum of assets, rather than some subset of "monetary" assets vs. non-monetary assets. We're interested in the role of assets in financial exchange, and as collateral in credit arrangements, for example. For safe assets to be in short supply, we have to specify some role for those safe assets in the financial system, other than as pure stores of wealth. In the model, that's done in a very simple way. There are some transactions that require currency, and some other transactions that can be executed with government bonds and credit. We abstract from banking arrangements, but the basic idea is to think of the bonds/credit transactions as being intermediated by banks.

We think of this model economy as operating in two possible regimes - constrained or unconstrained. The constrained regime features a shortage of safe assets, as the entire stock of government bonds is used in exchange, and households are borrowing up to their credit limits. To be in such a regime requires that the fiscal authority behave suboptimally - basically it's not issuing enough debt. If that is the case, then the regime will be constrained for sufficiently low nominal interest rates. This is because sufficient open market sales of government debt by the central bank will relax financial constraints. In a constrained regime, there is a liquidity premium on government debt, so the real interest rate is low. In an unconstrained regime the model behaves like a Lucas-Stokey cash-in-advance economy.

What's interesting is how the model behaves in a constrained regime. Lowering the nominal interest rate will result in lower consumption, lower output, and lower welfare, at least close to the zero lower bound. Why? Because an open market purchase of government bonds involves a tradeoff. There are two kinds of liquidity in this economy - currency and interest-bearing government debt. An open market purchase increases currency, but lowers the quantity of government debt in circulation. Close to the zero lower bound, this will lower welfare, on net. This implies that a financial shock which tightens financial constraints and lowers the real interest rate does not imply that the central bank should go to the zero lower bound. That's very different from what happens in New Keynesian (NK) models, where a similar shock implies that a zero lower bound policy is optimal.

As we learned from developments in macroeconomics in the 1970s, to evaluate policy properly, we need to understand the operating characteristics of the economy under particular fiscal and monetary policy rules. We shouldn't think in terms of actions - e.g. what happens if the nominal interest rate were to go up today - as today's economic behavior depends on the whole path of future policy under all contingencies. Our analysis is focused on monetary policy, but that doesn't mean that fiscal policy is not important for the analysis. Indeed, what we assume about the fiscal policy rule will be critical to the results. People who understand this issue well, I think, are those who worked on the fiscal theory of the price level, including Chris Sims, Eric Leeper, John Cochrane, and Mike Woodford. What we assume - in part because this fits conveniently into our analysis, and the issues we want to address - is that the fiscal authority acts to target the real value of the consolidated government debt (i.e. the value of the liabilities of the central bank and fiscal authority). Otherwise, it reacts passively to actions by the monetary authority. Thus, the fiscal authority determines the real value of the consolidated government debt, and the central bank determines the composition of that debt.

Like Woodford, we want to think about monetary policy with the nominal interest rate as the instrument. We can think about exogenous nominal interest rates, random nominal interest rates, or nominal interest rates defined by feedback rules from the state of the economy. In the model, though, how a particular path for the nominal interest rate is achieved depends on the tools available to the central bank, and on how the fiscal authority responds to monetary policy. In our model, the tool is open market operations - swaps of money for short-term government debt. To see how this works in conjunction with fiscal policy, consider what happens in a constrained equilibrium at the zero lower bound. In such an equilibrium, c = V+K, where c is consumption, V is the real value of the consolidated government debt, and K is a credit limit. The equilibrium allocation is inefficient, and there would be a welfare gain if the fiscal authority increased V, but we assume it doesn't. Further, the inflation rate is i = B[u'(V+K)/A] - 1, where B is the discount factor, u'(V+K) is the marginal utility of consumption, and A is the constant marginal disutility of supplying labor. Then, u'(V+K)/A is an inefficiency wedge, which is equal to 1 when the equilibrium is unconstrained at the zero lower bound. The real interest rate is A/[Bu'(V+K)] - 1. Thus, note that there need not be deflation at the zero lower bound - the lower is the quantity of safe assets (effectively, the quantity V+K), the higher is the inflation rate, and the lower is the real interest rate. This feature of the model can explain why, in the Japanese experience and in recent U.S. history, an economy can be at the zero lower bound for a long time without necessarily experiencing outright deflation.

Further, in this zero lower bound liquidity trap, inflation is supported by fiscal policy actions. The zero nominal interest rate, targeted by the central bank, is achieved in equilibrium by the fiscal authority increasing the total stock of government debt at the rate i, with the central bank performing the appropriate open market operations to get to the zero lower bound. There is nothing odd about this, in terms of reality, or relative to any monetary model we are accustomed to thinking about. No central bank can actually "create money out of thin air" to create inflation. Governments issue debt denominated in nominal terms, and central banks purchase that debt with newly-issued money. In order to generate a sustained inflation, the central bank must have a cooperative government that issues nominal debt at a sufficiently high rate, so that the central bank can issue money at a high rate. In some standard monetary models we like to think about, money growth and inflation are produced through transfers to the private sector. That's plainly fiscal policy, driven by monetary policy.

In this model, we work out what optimal monetary policy is, but we were curious to see how this model economy performs under conventional Taylor rules. We know something about the "Perils of Taylor Rules," from a paper by Benhabib et al., and we wanted to have something to say about this in our context. Think of a central banker that follows a rule

R = ai + (1-a)i* + x,

where R is the nominal interest rate, i is the inflation rate, a > 0 is a parameter, i* is the central banker's inflation target, and x is an adjustment that appears in the rule to account for the real interest rate. In many models, the real interest rate is a constant in the long run, so if we set x equal to that constant, then the long-run Fisher relation, R = i + x, implies there is a long-run equilibrium in which i=i*. The Taylor rule peril that Benhabib et al. point out, is that, if a > 1 (the Taylor principle), then the zero lower bound is another long run equilibrium, and there are many dynamic equilibria that converge to it. Basically, the zero lower bound is a trap. It's not a "deflationary trap," in an Old Keynesian sense, but a policy trap. At the zero lower bound, the central banker wants to aggressively fight inflation by lowering the nominal interest rate, but of course can't do it. He or she is stuck. In our model, there's potentially another peril, which is that the long-run real interest rate is endogenous if there is a safe asset shortage. If x fails to account for this, the central banker will err.

In the unconstrained - i.e conventional - regime in the model, we get the flavor of the results of Benhabib et al. If a < 1 (a non-aggressive Taylor rule), then there can be multiple dynamic equilibria, but they all converge in the limit to the unique steady state with i = i*: the central banker achieves the inflation target in the long run. However, if a > 1, there are two steady states - the intended one, and the zero lower bound. Further, there can be multiple dynamic equilibria that converge to the zero lower bound (in which i < i* and there is deflation) in finite time. In a constrained regime, if the central banker fails to account for endogeneity in the real interest rate, the Taylor rule is particularly ill-behaved - the central banker will essentially never achieve his or her inflation target. But, if the central banker properly accounts for endogeneity in the real interest rate, the properties of the equilibria are similar to the unconstrained case, except that inflation is higher in the zero-lower-bound steady state. How can the central banker avoid getting stuck at the zero lower bound? He or she has to change his or her policy rule. For example, if the nominal interest rate is currently zero, there are no alternatives. If what is desired is a higher inflation rate, the central banker has to raise the nominal interest rate. But how does that raise inflation? Simple. This induces the fiscal authority to raise the rate of growth in total nominal consolidated government liabilities. But what if the fiscal authority refused to do that? Then higher inflation can't happen, and the higher nominal interest rate is not feasible. In the paper, we get a set of results for a model which does not have a short-term liquidity effect. Presumably that's the motivation behind a typical Taylor rule. A liquidity effect associates downward shocks to the nominal interest rate with increases in the inflation rate, so if the Taylor rule is about making short run corrections to achieve an inflation rate target, then maybe increasing the nominal interest rate when the inflation rate is above target will work. So, we modify the model to include a segmented-markets liquidity effect. Typical segmented markets models - for example this one by Alvarez and Atkeson are based on the redistributive effects of cash injections. In our model, we allow a fraction of the population - traders - to participate in financial markets, in that they can use credit and carry out exchange using government bonds (again, think of this exchange being intermediated by financial intermediaries). The rest of the population are non-traders, who live in a cash-only world.

In this model, if a central banker carries out random policy experiments - moving the nominal interest rate around in a random fashion - he or she will discover the liquidity effect. That is, when the nominal interest rate goes up, inflation goes down. But if this central banker wants to increase the inflation rate permanently, the way to accomplish that is by increasing the nominal interest rate permanently. Perhaps surprisingly, the response of inflation to a one time jump (perfectly anticipated) in the nominal interest rate, looks like the figure in John Cochrane's post that he labels "pure neo-Fisherian view." It's surprising because the model is not pure neo-Fisherian - it's got a liquidity effect. Indeed, the liquidity effect is what gives the slow adjustment of the inflation rate.

The segmented markets model we analyze has the same Taylor rule perils as our baseline model, for example the Taylor principle produces a zero-lower-bound steady state which is is the terminal point for a continuum of dynamic equilibria. An interesting feature of this model is that the downward adjustment of inflation along one of these dynamic paths continues after the nominal interest rate reaches zero (because of the liquidity effect). This gives us another force which can potentially give us positive inflation in a liquidity trap.

We think it is important that central bankers understand these forces. The important takeaways are: (i) The zero lower bound is a policy trap for a Taylor rule central banker. If the central banker thinks that fighting low inflation aggressively means staying at the zero lower bound that's incorrect. Staying at the zero lower bound dooms the central banker to permanently undershooting his or her inflation target. (ii) If the nominal interest rate is zero, and inflation is low, the only way to increase inflation permanently is to increase the nominal interest rate permanently.

Finally, let's go back to the quote from Krugman's post that I started with. I'll repeat the last paragraph from the quote so you don't have to scroll back:
And the question is, why? What motivation would you have for inventing complicated models to reject conventional wisdom about monetary policy? The right answer would be, if there is a major empirical puzzle. But you know, there isn’t. The neo-Fisherites are flailing about, trying to find some reason why the inflation they predicted hasn’t come to pass — but the only reason they find this predictive failure so puzzling is because they refuse to accept the simple answer that the Keynesians had it right all along.
Why? Well, why not? What's the puzzle? Well, central banks in the world with their "conventional wisdom" seem to have a hard to making inflation go up. Seems they might be doing something wrong. So, it might be useful to give them some advice about what that is instead of sitting in a corner telling them the conventional wisdom is right.

Tuesday, November 11, 2014

Monetary Policy Normalization

Here's a common view of how the Fed implemented monetary policy prior to the financial crisis.
The chart shows a typical framework, pre-financial crisis, that was used in hitting a particular fed funds rate target, depicted by R* in the figure. The downward-sloping curve is a demand curve for reserves, which essentially captures a short-run liquidity effect. The larger the quantity of reserves in the system overnight, the lower the fed funds rate. But, a key problem for policy implementation was that this demand curve was highly unstable, shifting due to unanticipated shocks to the financial system, and with anticipated shocks related to the day of the week, month of the year, etc. Operationally, the way the Fed approached the problem of hitting the target R* was, effectively, to estimate the demand curve each day, and then intervene so as to assure that Q* reserves were in the market, implying that the market would clear at R*, if the demand curve estimate were correct. Note in the figure that the fed funds rate was bounded above by the discount rate (no depository institution, or DI, would borrow from another institution at more than the Fed was offering) and by the interest rate on reserves, IOER (no DI would lend to another DI at less than what the Fed was offering). Prior to the financial crisis, the IOER was zero.

There were certainly other approaches the Fed could have taken to implementing policy during the pre-crisis period. For example, since the Fed was typically intervening by varying its quantity of lending in the overnight repo market, an alternative approach might have been to follow a fixed-rate, full-allotment procedure, i.e. fix the repo rate, and lend whatever quantity the market wanted to take at that rate. That would work very nicely if the overnight repo rate and the fed funds rate were identical, but they are not. Typically, overnight interest rates move together, but there can be a substantial amount of variability in the margin between the repo rate and the fed funds rate, for various reasons. For example, fed funds lending is unsecured while repos are secured; lending one day and settlement the next day happen at different times in the two markets, etc. So, given that the directive from the FOMC was in terms of a fed funds target, pegging the repo rate need not be the best way to carry out the directive. One could make an argument that targeting a secured overnight rate makes more sense than targeting the fed funds rate, but that would have required revamping the whole structure of FOMC decision making.

An important point to emphasize is that, contrary to central banking myth, the mechanics of the fed funds market pre-crisis had little to do with reserve requirements. The myth is that fed funds market activity was driven by the need of DIs to meet their reserve requirements - if reserves were too low, a DI would borrow on the fed funds market, and if reserves were too high it would lend. But the same would hold true if there were no reserve requirements, as reserve balances must be nonnegative overnight. Indeed in Canada, for example, where reserve requirements were eliminated long ago, the Bank of Canada operates within a channel system. The overnight target interest rate is bounded by the Bank of Canada's lending rate (on the high side), and the counterpart of the IOER in Canada (on the low side). Overnight reserves in Canada are typically zero, effectively, but we could characterize Bank of Canada intervention in roughly the same manner as in the figure above.

Before the Fed was permitted to pay interest on reserves, people speculated (see for example, see this paper by Marvin Goodfriend) that the IOER would establish a floor for the fed funds rate. Indeed, as Goodfriend pointed out, with sufficient reserves in the system, the IOER should determine the fed funds rate. Essentially this is what happened in Canada from spring 2009 until mid-2010, when the Bank of Canada operated with a floor system and an overnight rate (equal to the interest rate on reserves) of 0.25%. But, since the Fed began paying interest on reserves in late 2008, the effective fed funds rate has traded below the IOER, which as been at 0.25%.
The margin between the IOER on the fed funds rate has been substantial - sometimes as much as 20 basis points.

In a previous post I discussed some details of Fed proposals to modify its approach to financial market intervention. Since then, the FOMC has made its plans for "normalization" explicit in this press release from September 17. Normalization refers to the period after liftoff - the point in time at which the FOMC decides to increase its policy rate. Basically, the FOMC will continue to articulate policy in terms of the fed funds rate, and proposes to control the fed funds rate through two means: the IOER, and an overnight repurchase agreement (ON RRP) facility. As explained in my previous post, ON RRPs are overnight loans to the Fed from an expanded list of counterparties. ON RRPs do not "drain" reserves, as they are effectively reserves by another name. Reserve accounts are held by only some financial institutions in the United States, and not all financial institutions with reserve accounts (the GSEs - government-sponsored enterprises) can earn interest on reserves. Thus, ON RRPs expand the market for Fed liabilities, and allow more institutions to receive interest on overnight balances held with the Fed.

The Fed's plans for modifying policy implementation will actually matter little for the how monetary policy works. Whatever the means, the basic idea is to use monetary policy to influence short-term nominal interest rates by targeting an overnight interest rate, just as was the case before the financial crisis. The key issue in the implementation appears to be how the ON RRP facility should be managed. What should the ON RRP rate be? Should there be quantity caps on ON RRPs? If there are caps, how large should they be? A smaller difference between the IOER and the ON RRP rate potentially tightens the bounds on the fed funds rate. However, the majority of fed funds market activity currently consists of activity to (imperfectly) arbitrage the difference between the interest rate that GSEs can earn on reserve balances (zero) and the IOER. That arbitrage activity should disappear if the IOER/ON RRP rate margin decreases sufficiently, in which case the effective fed funds rate could actually increase above the IOER. As well, the smaller the IOER/ON RRP rate spread, the larger the quantity of ON RRPs relative to reserves on the liabilities side of the Fed's balance sheet. This distributes Fed liabilities differently in the financial system, in ways that we perhaps do not understand well, and with unclear implications.

How long after liftoff will the Fed's altered financial market intervention persist? This depends on how long it takes for the Fed's balance sheet to "normalize." In this case, normality means a balance sheet for which currency accounts for most of the Fed's liabilities, as was the case prior to the financial crisis. Currently, total Fed liabilities are about $4.5 trillion, of which $1.3 trillion is currency and $3.2 trillion consists of other liabilities, including reserves and ON RRPs. Currency as a fraction of total Fed liabilities can increase through two means: (i) assets disappear from the Fed's balance sheet; (ii) the demand for currency goes up. Assets can disappear from the Fed's balance sheet because they mature or are sold. The FOMC Policy Normalization Principles and Plans state no plans for selling assets - either Treasury securities or mortgage-backed securities. The plans specify that reinvestment in assets will continue until after liftoff, i.e. currently the size of the Fed's asset portfolio is being held constant in nominal terms. Therefore, there are currently no plans to reduce the quantity of assets on the Fed's balance sheet until after liftoff. Thus, for now, reductions in the quantity of non-currency liabilities will happen only as the stock of currency grows.

So, how long will it take until the Fed is in a position to conduct policy exactly as before the financial crisis? If the Fed continued its reinvestment program, and if currency grew at 5% per year, it would take more than 25 years for Fed liabilities to consist of currency alone. An end to reinvestment could mean that normalization could happen in 10 years or less, barring circumstances in which the Fed chooses to embark on new quantitative easing programs. Thus, in any case, and under current announced plans by the FOMC, the current regime - a type of floor-on-the-floor monetary regime - should be with us for some time.

Wednesday, October 22, 2014

What's More Scary, Ebola or Deflation?

David Wessel gives us five reasons to worry about deflation. Should we worried? Well, probably not for the reasons Wessel mentions, which are:

Deflation is a generalized decline in prices and, sometimes, wages. Sure, if you’re lucky enough to get a raise, your paycheck goes further–but those whose wages decline or who are laid off or work fewer hours are not going to enjoy a falling price index.
Here's what I think Wessel might be trying to say. Imagine a Woodford cashless world in which money serves only as a unit of account. As well, there are no sticky prices or sticky wages, but suppose there are labor market frictions, so that there is always some churn in the labor market and some unemployment. In this world, the inflation rate does not matter. Wages, prices, unemployment insurance benefits, etc., are all indexed to the aggregate price level. That's a useful starting point. You can see that Wessel is a little confused though, as in such a world, there's really nothing to "enjoy" about deflation. We really wouldn't care.

It can be hard (though, as we’ve seen, not impossible) for employers to cut nominal wages when conditions warrant; it’s easier to give raises that are less than the inflation rate, which is what economists call a real wage cut. And if wages are, as economists say, marked by “downward nominal rigidity,” then employers will hire fewer people.
So, suppose that there is a sustained deflation of, say, -2% per year. Also, suppose that there is a law stating that no firm can reduce an existing employee's nominal wage rate. Question: Will that constraint bind in enough circumstances to matter in an economically significant way? Answer: Probably not. Why? First, on average, real wages increase over time with productivity growth. Of course, if we are experiencing productivity growth of 1% per year, and an inflation rate of -2% per year, average nominal wages should be falling at about 1% per year. But, supposing all workers are identical, it can still be the case that each individual living in this world can have an increasing nominal wage profile over his or her lifetime, since individual productivity can be growing at a much higher rate than aggregate productivity, as the individual gains experience (and thus accumulates human capital) over his or her lifetime. But individuals are not identical. People experience random shocks to their health that affect their productivity, and particular skills become more or less valuable in the market as technology changes and demand shifts among goods and services. So, if everyone were paid their marginal products, this would in general require downward nominal wage adjustments for some workers in the face of generalized deflation. But there are ways to get around a constraint on reducing the nominal wage rate for a given worker in a given job. It may be possible to adjust the worker's assigned tasks - i.e. change the job instead of the wage. Also, benefits can be adjusted. There is always job turnover, so it is possible for a given firm to adjust wages for its workforce through attrition. Further, of course firms are not literally constrained to refrain from downward nominal wage adjustment. In the face of a persistent deflation, it's straightforward for managers to point that out to workers - presumably most workers know what the CPI is. As well, firms that find ways to reduce nominal compensation where appropriate in the midst of a deflation will do better than those who don't, and most workers faced with losing their jobs or taking a nominal wage cut would choose the latter. So, I can't see that this is a serious problem. If a nonnegativity constraint on nominal wage changes were serious business, I think labor economists would be paying more attention to it. The fact that they don't is important, I think.

As economic textbooks teach, the prospect that things will cost less tomorrow than they do today encourages people to put off buying. If enough people do that, then businesses are less likely to hire and invest, and that makes everything worse.
If people actually put this idea in textbooks, that is a bad thing. It's certainly not in mine. See my comment on #1. If deflation is just a sustained decrease in the unit of account, and nothing else, then it can't have any consequences for consumption/savings decisions. To say something about that we have to go more deeply into what is causing the deflation, its effects on rates of return on assets, etc. #3 makes no more sense than to say that there will be higher consumption and lower savings if the inflation rate is 5% rather than 3%. It's not clear why.

Deflation is terrible for debtors. Prices and wages fall, but the value of your debt does not. So you’re forced to cut spending. This applies to consumers and to governments, and it is one of the biggest issues in Europe right now. As Yale University economist Irving Fisher wrote decades ago, debtors are likely to cut spending more than creditors increase it, and this can turn into a really bad downward spiral. (The experience of Japan, though, proves that an economy can have a prolonged period of moderate deflation without falling into that downward spiral.)
Unfortunately, Wessel does not make clear the difference between anticipated deflation and unanticipated deflation. #1 through #3 seem to be about anticipated deflation, while #4 is about unanticipated deflation. Most debt contracts are written in nominal terms, so if the inflation rate is lower than anticipated, this will redistribute wealth from debtors to creditors. The debtors are not actually "forced to cut spending." That might be one margin on which to make adjustments, but debtors might also work harder, or default on their debt. Does this redistribution of wealth just net out in the aggregate, as the creditors are better off, and will consume more, work less, and not be repaid if debtors default? Wessel invokes Irving Fisher to argue no, but I think the more important factor here - which Fisher never thought about, as far as I know - is the asymmetry due to bankruptcy costs. In contrast to inflation that is higher-than-anticipated, lower-than-anticipated inflation induces more bankruptcies, and the ensuing bankruptcy costs are a net loss to society. That could be important. But note that this is not particularly associated with inflation going into negative territory, but simply a feature of disinflation in general. But, note that the disinflation that occurred between 1980 and 1985 was in the neighborhood of 10 percentage points, depending on the inflation measure we look at. That experience was of course associated with a severe recession, but the U.S. economy bounced back quickly - no signs of a "bad downward spiral." So if central banks fall short of 2% inflation targets by one, two, or three percentage points, that doesn't seem like such a big deal. I'll discuss Japan below, but I don't think that's quite the unanticipated disinflation experience Wessel is looking for.

Cutting interest rates below zero is very hard. Yes, one way that central bank magic works is that the Federal Reserve and the European Central Bank cut inflation-adjusted interest rates below zero when times are bad, hoping to spur borrowing, spending and investment. But it’s almost impossible for them to cut rates below zero. (Sure, there are some examples of negative interest rates, but they’re not very negative.)

If there’s 4% inflation, a zero interest rate works out to a -4% real (or inflation-adjusted) rate. At no inflation, a zero interest rate is, well, zero. And with deflation, a zero interest rate is a positive real rate. Deflation just makes all this harder to do.
I think what Wessel is getting at is that, with short term nominal interest rates at zero, a central bank is limited in its power to raise inflation, if we think that the way to lower inflation is to lower the nominal interest rate. Actually, as I'll explain below, short-term nominal interest rates at zero have a lot to do with why inflation is low in the world, as Irving Fisher (who Wessel seems to approve of) told us.

What causes deflation? Is deflation a good thing or a bad thing? It is now well understood that central banks can and should control inflation. So, if we observe low inflation, or outright deflation, this should have something to do with monetary policy. In standard monetary models, deflation can happen when the nominal interest rate stays at zero indefinitely. Indeed, a ubiquitous result is that a Friedman rule is optimal. Under a Friedman rule for monetary policy, the nominal interest rate is zero forever. Milton Friedman's argument was that a positive nominal interest rate represents a distortion. This distortion can be removed if the central bank acts to give money the same rate of return as other safe assets, which will typically imply deflation, at least on trend. So, theory tells us that deflation can be a good thing.

If that is correct, then why do so many central banks think that 2% inflation is a good idea? Perhaps there are good reasons to have a positive inflation tax. Currency systems are costly to operate. It requires real resources to replace worn-out currency and prevent counterfeiting. As well, currency is used for various nefarious things - tax avoidance and illegal drug purchases, for example. So, maybe it is optimal to have positive inflation as an implicit tax on currency holdings. As well, it may not make much difference for long-run economic welfare whether the inflation rate is 2%, 4%, 0%, or -2%. But having a stable inflation rate is welfare-improving, as this minimizes the unanticipated redistributions between creditors and debtors that occur with unexpected changes in the inflation rate, as discussed above. To achieve a stable inflation rate, the central bank has to announce an inflation target, and then set policy in a way that achieves this inflation target, thus establishing credibility. If the central bank's inflation target is 2%, and there is persistent deflation, then deflation is bad because it undermines the central bank's credibility.

Do we have any experience with economies that look more or less like Friedman rule economies? Japan, of course, is the standard - and only - example. From mid-1995 to the present, the overnight interest rate in Japan has been below 1%, and for much of that period close to zero.
Over this period there has certainly not been sustained deflation. If we confine attention to the pre-2014 period in the chart, the CPI inflation rate (year-over-year) has fluctuated between, roughly, -2.5% and 2.5%. The next chart shows the CPI level over the same period.
This last chart shows that, at the end of 2013, the price level was about the same as in mid-1995, so the average inflation rate over the period 1995-2013 was about zero. Thus, as far as experience in Japan tells us, if the central bank maintains the short-term nominal interest rate at close to zero for a long period of time, this produces volatile inflation, but not deflation (on average). Thus, the worry reflected in Wessel's piece concerning deflationary sprirals, or deflationary traps, seems not to be rooted in experience - or theory for that matter.

Wessel's concern of course was not specifically with Japan, but with recent low inflation as reflected in European consumer prices and world commodity prices. We could also add that recent inflation data has been on the low side in Sweden, Switzerland, the U.K., and in the U.S. What do all of these economies have in common with Japan during the period we examined above? Short-term nominal interest rates in all of these instances have been close to zero for extended periods. So what causes low inflation over long periods of time, and raises the possibility of deflation? Low short-term nominal interest rates over long periods of time.

Why can economies get stuck at the zero lower bound (essentially) on nominal interest rates for long periods of time - or forever? Theory tells us something about this. Work by Benhabib et al. summarized by Jim Bullard shows how a central banker who conforms to the Taylor rule can cause the economy to converge to a zero-lower-bound steady state. The Taylor-rule central banker sees low inflation, and persists in trying to raise inflation by keeping the nominal interest rate at zero. But this only serves to maintain inflation at a low rate - in fact, there is deflation, in the framework considered. Effectively, in the long run the real interest rate is determined by factors outside the control of monetary policy, under any circumstances. But then, if the nominal interest rate is zero for a long time, the inflation rate will then be determined by those non-monetary factors.

But what would be the harm in having a zero-lower-bound economy indefinitely? To answer this question, it's useful to look at the performance of the Japanese economy from 1995 until now. In the labor market, the unemployment rate was not indordinately high, ranging from about 3% to 5.5%.
As well, the employment rate for people 15-64 is currently 3 percentage points higher than in mid-1995.
What about real GDP and consumption?
There has certainly been trend growth in real GDP and consumption in Japan since 1995, but the growth rate has been low relative to the United States. In Japan, average growth in consumption over the entire period was 0.8%, and average growth in real GDP was 0.9%. It's important to note, though, that demographic trends are much different in Japan than in the U.S. Since 1995, total population in Japan has been essentially flat, and the fraction of retired people in the population has increased. So in terms of per capita real GDP growth, this tends to push U.S. and Japanese experience closer together.

To summarize some of the demographic effects in one measure, the next chart looks at average labor productivity (real GDP divided by employment) in the U.S. and Japan from 1995-present.
In the chart, I've normalized to make productivity equal in the two countries in mid-1995. You can see that the U.S. performed better over the whole period, but the better performance of the U.S. was over the period 1995-2000, and post-Great Recession (somewhat). Over the period from 2000-2008, productivity growth in the two countries was about the same.

So, overall, real economic performance in Japan during the zero-lower-bound period was not a disaster, nor was it particularly good. It's hard to say, though, from this cursory evidence, that low or negative inflation had much to do with any substandard performance of the economy. What is clear from the zero-lower-bound Japanese experience is that inflation was quite variable, as shown in the first chart. Clearly, if the Bank of Japan was trying to stabilize the inflation rate over this period, it was not doing a a good job. But perhaps there are unconventional monetary policies that the Bank could have pursued that would have permitted it to do better.

Indeed, in April 2013, the Bank of Japan embarked on a massive quantitative easing (QE) program. We can see the effects of that on the liabilities side of the Bank of Japan's balance sheet in the next chart, where we show the Japanese monetary base.
From the Bank of Japan's web site, here are the details of the Bank of Japan's QE program:
The Bank introduced "Quantitative and Qualitative Monetary Easing" (QQE) in April 2013 to achieve the price stability target of 2 percent in terms of the year-on-year rate of change in the CPI at the earliest possible time, with a time horizon of about two years. Under the QQE, the Bank continues to pursue a new phase of monetary easing both in terms of quantity and quality. It will double the monetary base and the amounts outstanding of Japanese government bonds (JGBs) as well as exchange-traded funds (ETFs) in two years, and more than double the average remaining maturity of JGB purchases.
So, given the two-year time frame, the Bank of Japan has about 6 months more to achieve its 2% inflation goal. How has it done? Here's the CPI path from April 2013:
So, this makes it appear that the Bank of Japan should come close to meeting its target. However, a large fraction of the increase in the CPI over this period is due to an increase from 5% to 8% in the consumption tax in Japan, which is effectively reflected one-for-one in the CPI. The tax increase occurred in April 2014, which you can readily see in the data. So, if we take out the effects of the tax increase, the CPI has been almost flat for the last year. So, there is no evidence that QE has had the effects on inflation that the Bank of Japan would like.

The Japanese experience therefore seems consistent with the following conclusions about the operating characteristics of an economy at the zero lower bound for a long time:

1. The central bank will fail to meet a 2% inflation target, on average.
2. The inflation rate will be highly variable.
3. If the central bank is counting on QE to help it hit a 2% inflation target while the short-term nominal interest rate is at the zero lower bound, good luck.