Thursday, April 14, 2016

Neo-Fisherian Denial

Accepting neo-Fisherism is a 12-stage program. The first stage is admitting you have a problem. The twelfth stage is helping others to admit that they have a problem too. Going from stage one to stage twelve may be a tough battle - many could temporarily fall off the wagon. But take it one day at a time. Most people, for example Larry Summers, are still at stage one. In this video, about two minutes in, after the jokes, Summers says that neo-Fisherism is most likely to be remembered as a confusion. So, if the problem is only confusion, I would like to help him out.

Neo-Fisherism says, basically: "Excuse me, but I think you have the sign wrong." Conventional central banking wisdom says that increasing interest rates reduces inflation. Neo-Fisherites say that increasing interest rates increases inflation. Further, it's not like this is some radical, novel theory. Indeed, a cornerstone of Neo-Fisherism is:

Neo-Fisherian Folk Theorem: Every mainstream macroeconomic monetary model has neo-Fisherian properties.

Let me illustrate that. A nice, simple, version of the standard New Keynesian (NK) model is the one in Narayana Kocherlakota's slides from this conference put on by the Becker Friedman Institute. I'll use my own notation. NK's version of the NK model is a reduced form, with two equations. The first comes from a pricing equation for a nominal bond - what's often called the "NK IS curve," or
Here, y is the output gap, the difference between actual output and what is efficient, pi is the inflation rate, R is the nominal interest rate, r is the subjective rate of time preference, and a is the coefficient of relative risk aversion. The second equation is
That's just a Phillips curve, with b >0 determined by the degree of price stickiness. In the underlying model, some fraction of firms is constrained to set prices to the average price from last period. Thus, there's no expectations term in the Phillips curve, as there's no forward-looking pricing. That makes the model easy to solve.

So, substitute for y in equation (1) using the Phillips curve equation, to get
So, you can see why people think this type of model is a foundation for conventional central banking ideas. If inflation expectations are "anchored," which I guess means exogenous, on the right-hand side of the equation, then an increase in the current nominal interest rate would have to imply that the current inflation rate goes down. Indeed, if the central banker experiments, by choosing the nominal interest rate each period at random, then he or she will observe a negative correlation between inflation and nominal interest rates, which would tend to confirm conventional beliefs.

But consider the following. Suppose we look at the deterministic version of the model, and use (3) to solve for a first-order difference equation in the inflation rate:
Then, an equilibrium is a sequence of inflation rates solving (4), and we can solve for output from (2). As is typical of monetary models, there's no initial condition to tie things down, so there are potentially many equilibria. We can say, however, that in a steady state, from (1),
And then (2) gives
So, what "anchors" inflation and inflation expectations in the long run is the long run nominal interest rate. And then the Phillips curve determines output. That's the first Neo-Fisherian property of this standard model.

Next, from the difference equation, (4), if the nominal interest rate is a constant R forever, then there is a continuum of equilibria, indexed by the initial inflation rate, and they all converge to a unique steady state, which is given by (6) and (7). To see this, start with any initial pi, and solve (4) forward. So, we know that the long run is Fisherian. But what about the short run?

We'll consider the transition to a higher nominal interest rate. In the figure, the nominal interest rate is constant until period T, and then it increases permanently, forever. In the figure, D1 is the difference equation (4) with a lower nominal interest rate; D2 is (4) with a higher nominal interest rate. We'll suppose that everyone perfectly anticipates the interest rate increase from the beginning of time. Again, there are many equilibria, and they all ultimately converge to point B, but every equilibrium has the property that, given the initial condition, inflation will be higher at every date than it otherwise would have been without the increase in the nominal interest rate. A straightforward case is the one where the equilibrium is at A until period T, in which case the inflation rate increases monotonically, as shown, to a higher steady state inflation rate. Inflation never goes down in response to a permanent increase in the nominal interest rate. That's consistent with what John Cochrane finds in a related model.

So, that's the second Neo-Fisherian property, embedded in this NK model. The NK model actually doesn't conform to conventional central banking beliefs about how monetary policy works. What's going on? From equation (1), an increase in the current nominal interest rate will increase the real interest rate, everything else held constant. This implies that future consumption (output) must be higher than current consumption, for consumers to be happy with their consumption profile given the higher nominal interest rate. But, it turns out that this is achieved not through a reduction in current output and consumption, but through an increase in future output and consumption. This serves, through the Phillips curve mechanism, to increase future inflation relative to current inflation. Then, along the path to the new steady state, output and inflation increase. But, if you read Narayana's Bloomberg post from five days ago, you would have noted that he thinks that lowering the nominal interest rate raises inflation and output:
Monetary policy makers should be seeking to ease, not tighten. Instead of satisfying a phantom need to “normalize” rates, the Fed should do what’s needed to get employment and inflation back to normal.
Apparently he's thinking about some other model, as the one he constructed tells us the opposite.

For more depth on this, you should read this paper by Peter Rupert and Roman Sustek. Here's their abstract:
The monetary transmission mechanism in New-Keynesian models is put to scrutiny, focusing on the role of capital. We demonstrate that, contrary to a widely held view, the transmission mechanism does not operate through a real interest rate channel. Instead, as a first pass, inflation is determined by Fisherian principles, through current and expected future
monetary policy shocks, while output is then pinned down by the New-Keynesian Phillips curve. The real rate largely only reflects consumption smoothing. In fact, declines in output and inflation are consistent with a decline, increase, or no change in the ex-ante real rate.

Conventional central banking wisdom is embedded in Taylor rules. For simplicity, suppose the central banker just cares about inflation, and follows the rule
Here pi* is the central bank's inflation target. Under the Taylor principle, d > 1, i.e. the central bank controls inflation by moving interest rates up when inflation goes up - and the nominal interest rate adjustment is more than one-for-one. It's well known from the work of Benhabib et el. that Taylor rules have "perils," and this model can illustrate that nicely. The difference equation determining the path for the inflation rate becomes
In the next figure, A is the intended steady state in which the central bank achieves its inflation target, and that is one equilibrium. But there are many equilibria for which the initial inflation rate is greater than -r and smaller than the inflation target, and all of these equilibria (like the one depicted) converge to the zero lower bound (ZLB), where the central banker gets stuck, with an inflation rate permanently lower than the target. Potentially, there could be equilibria with an initial inflation rate higher than the inflation target, which have the property that inflation increases forever. But in this model, that also implies that output increases without bound, which presumably is not feasible.

Rules with -1 < d < 1 all have the property that there are multiple equilibria, but these equilibria all converge to the inflation target - there's a unique steady state in those cases. Note that the Taylor rule central banker is Neo-Fisherian if d < 0, and that this can be OK in some sense. But aggressive neo-Fisherism, i.e. d < -1 -2(a/b), is bad, as this implies that the inflation rate cycles forever without hitting the inflation target.

But if the central banker actually wants to consistently hit the inflation target, there are better things to do than (8). For example, consider this rule:
Plug that into (4), and you'll get
And so, (10) implies that
So, under that forward-looking Taylor rule, the central bank always hits its target, and in equilibrium the central bank is purely Fisherian. If it wants to increase its inflation target - and actual inflation - it just increases the nominal interest rate one-for-one with the increase in the inflation target. So, I've lost count now, but I think that's Neo-Fisherian property 3 [see the addendum below. There's a glitch that needs to be fixed in the rule (10) to account for the ZLB.]

The rule (10) specifies out-of-equilibrium behavior that kills all of the equilibria except the desired steady state. Why does this work? If the central banker sees incipient inflation in the future, he or she knows that this will tend to increase current output, increase current inflation, and increase future output, which will also increase current inflation. To nullify these effects, the central banker commits to offset this completely, if it happens, with an increase in the nominal interest rate. In equilibrium the central banker never has to carry out the threat. Maybe you think that's not plausible, but that's the nature of the model. NK adherents typically emphasize forward guidance, and that's not going to work without commitment to future actions.

Some people (e.g. Garcia-Schmidt and Woodford) have argued that Neo-Fisherian results go out the window in NK models under learning rules. As was shown above, these models are always fundamentally Fisherian in that any monetary policy rule has to somehow adhere to Fisherian logic on average - basically the long-run nominal interest rate is the inflation anchor. But there can also be learning rules that give very Fisherian results. For example, suppose that the economic agents in this world anticipated that next period's inflation is what they are seeing this period, that is
Plug that into equation (1), and we get
So, for this learning rule, inflation is determined period-by-period by the nominal interest rate - this is about as Fisherian as you can get.

Thus, if conventional central bankers are basing their ideas on some model, it can't be a mainstream NK model, since increasing the nominal interest rate makes inflation go up in mainstream NK models. But don't get the idea that it's some other mainstream model they're thinking about. As the Neo-Fisherian Folk Theorem says, all the mainstream models have these properties, though some of the other implications of those models differ. For example, it's easy to show that one can get exactly the same dynamics from Alvarez, Lucas and Weber's segmented markets model. That's a model with limited participation in asset markets and a non-neutrality of money that comes from a distribution effect. Everyone in the model has fixed endowments forever, and they buy goods subject to cash-in-advance. The central bank intervenes through open market operations, but the people on the receiving end of the initial open market operation are only the financial market participants. The model was set up to deliver a liquidity effect, i.e. if money growth goes up, this increases the consumption of market participants (and decreases everyone elses's consumption), and this will reduce the real interest rate. Thus, you might think (like the NK model) that this produces the result that, if the central bank increases the nominal interest rate, then inflation will go down.

But, the inflation dynamics in the Alvarez et al. segmented markets model are identical to what we worked out above. In fact, the model yields a difference equation that is identical to equation (4), though the coefficients have a different interpretation. Basically, what matters is the degree of market participation, not the degree of price stickiness - it's just a different friction. And all the other results are exactly the same. But the mechanism at work is different. The quantity theory of money holds in the segmented markets model, so what happens when the nominal interest goes up is that the central bank has to choose a path for open market operations to support that. This has to be a path for which the inflation rate is increasing over time, but at a decreasing rate. This will imply that consumption grows over time at a decreasing rate, so that the liquidity effect (a negative real interest rate effect) declines over time, and the Fisher effect increases.

So, once you get it, you can form your own Neo-Fisherian support group. Moving from denial to advocacy is important.

Addendum1: Thanks to Narayana. This took some work, but this is a Taylor rule that assures that the central banker hits the inflation target period-by-period, implying that the nominal interest rate is constant in equilibrium, and will move one-for-one with the inflation target. If future inflation is anticipated to be sufficiently high, then the central banker follows the forward looking rule (10):
This rule offsets incipient high inflation, and assures that the central bank hits the inflation target. But, low inflation is a problem for (16), as the ZLB gets in the way. So, if there is incipient low inflation, the central banker follows the rule:
And the critical value for future inflation is
How does (17) work? Any equilibrium has to satisfy (4), but (4) and (17) imply
So future inflation must be greater than the inflation target. But (17) says that the central banker chooses this rule only when future inflation is less than pi**, which is less than the inflation target. So this can't be an equilibrium. I like (17), as the central banker is Neo-Fisherian - he or she kills off low inflation with a high nominal interest rate.

Addendum 2: This is interesting too. Suppose the policy rule is
Then there is a critical value for the initial inflation rate,
such that, if the initial inflation rate is below this critical value, then the inflation rate goes to the inflation target in the next period and stays there. If the initial inflation rate is above the critical value, then the initial nominal interest rate is zero, and the inflation rate falls to the inflation target, and stays at the target forever. So, that's a Fisherian rule that has nice properties.

Addendum 3: Here's another one. Central bank follows rule (20) if current inflation is below the inflation target. Central bank follows rule (10) if current inflation is at or above the inflation target. With inflation below the target, this implies raising the nominal interest rate to get inflation to target. With inflation at or above the target, the central bank promises to raise the nominal interest rate in response to incipient inflation. At worst, this implies one period of inflation below target in equilibrium.

Thursday, April 7, 2016

Fiscal Theory of the Price Level, Helicopters, and Central Bank Balance Sheets

Last week, I attended a conference on the fiscal theory of the price level (FTPL) in Chicago. Eric Leeper claims that I'm actually a closet FTPL person, and seems to have thought I belonged there, which is certainly fine with me. The assignment was to talk about research ideas. Some people had papers, and some (like me) didn't. My slides are posted here.

Here's the idea. The FTPL came out of research done by Eric Leeper, Mike Woodford, Chris Sims, and John Cochrane, among others, beginning in the early 1990s, so this stuff has been around for quite a while. Indeed, there are precedents in the work of Sargent and Wallace, and Aiyagari and Gertler in the 1980s, for example. Sometimes FTPL practitioners seem to be shooting for an alternative quantity theory. Under the quantity theory of money - Old Monetarism basically - we were supposed to think that the demand for money was a stable function of some small set of observable economic variables, so that the supply of money by the central bank would determine the price level and inflation. Under the FTPL it's the quantity of government debt (or in some versions the quantity of consolidated government debt - including the central bank's liabilities) that's important, and it's also important that the counterpart of "demand" for this debt need not be stable. The FTPL starts with the consolidated government's intertemporal budget constraint and, typically, writes it (after some manipulation) with the real quantity of government debt outstanding on the left-hand side (nominal debt divided by the price level), and the expected discounted value of government surpluses on the right-hand side. Therefore, if the stuff on the right-hand side of this equation is given, the nominal quantity of government debt determines the price level. Alternatively, the expected discounted value of future government surpluses is the analog of the demand for money in the quantity theory of money, so reductions in the future government promises backing the government's debt will reduce the demand for government debt and its current value - increase the price level - given the supply of government debt in nominal terms.

John Cochrane provides some intuition in terms conventional asset pricing. That is, think of the expected discounted future government surpluses as analogous to the payoffs on any asset, and the real value of government debt as the value of the asset, and it all makes sense. That's not even an analogy - the intertermporal consolidated government budget constraint can literally be rewritten as an asset pricing equation.

OK, so where does this theory go then? Sometimes the FTPL people got sidetracked with issues such as whether the consolidated government budget constraint is a constraint or an equilibrium relationship, whether the government is similar to, or different from, a private household, in terms of its budget constraint, etc. Some of that discussion was unproductive for this research program, I think. Also, one might get the idea from this literature that central banks cannot fundamentally be independent, and that the fiscal authority is always in the inflation driver's seat, which I don't think is the right way to think about the fiscal-monetary interaction. But, the fiscal-monetary interaction is the message of the theory, and that's very interesting. For example, central banks have recently been engaged in quantitative easing policies, which sometimes look like conventional fiscal debt-management. That might be viewed as central banking jumping into the fiscal driver's seat.

So, what's in my slides? There are three parts to this: (i) a model with minimal government; (ii) a model with open market operations; (iii) a non-Ricardian model with a government debt shortage. The models are very simple, with no uncertainty. The minimal government (MG) model and open market operations (OMO) models are simple cash-in-advance setups with fixed endowments - output and consumption are fixed, and we're only going to be concerned with determining inflation and the price level. The non-Ricardian (NR) model has production.

Start with the MG model, and consider this a thought experiment. The basic idea is to show that we can set up a central bank with no connection to fiscal policy, and this central bank will have no problem determining the price level and inflation. There are households in this economy, and they have fixed endowments each period, but can't consume their own goods and can only trade subject to cash-in-advance - they need currency to buy goods. There is a role for the government, but it's minimal, i.e. the government grants a monopoly to a central bank to issue currency, and I'm supposing the government can costlessly enforce the monopoly. The government also issues shares in the central bank to the households, and constrains the central bank to turn over its profits, period-by-period, to its shareholders. The central bank can issue currency and reserves as liabilities, and uses the liabilities to finance lending to the households. Reserves cannot be used in retail transactions - purchases of goods - and they bear interest, otherwise people would not hold them. Reserves are convertible into currency, one-for-one, and vice-versa. I've assumed away banks, so reserves are just debt instruments of the central bank that anyone can hold.

The MG central banking structure has something in common with what was envisioned by the framers of the 1913 Federal Reserve Act, or with how the European Central Bank works. That is, money is injected through central bank lending rather than open market operations. We could add details like private banks and collateralized lending, but those things don't matter for the general ideas here.

What does the central bank do in the MG model? The model is dynamic, but think in terms of one-time policy decisions that give a stationary equilibrium - a constant inflation rate, and a constant quantity of reserves, in real terms. The central bank fixes the nominal interest rate it charges on its loans at a constant R forever. This does two things. First, it determines the spread the central bank earns on lending financed with currency issue, though the central bank makes zero profits intermediating loans by issuing reserves, as the interest rate on reserves is R in equilibrium. Second, through standard asset pricing, R determines the inflation rate - that's just Irving Fisher. This is an economy in which the real rate is a constant (we'll relax this later). Finally, the the central bank sets the nominal path for its profits, and the nominal path for its total liabilities. And that does it. This determines the initial price level, the inflation rate, and how the stock of central bank liabilities is split between reserves and currency.

Then, in the MG equilibrium, increasing R increases the inflation rate one-for-one, and the central bank can produce as much inflation as it wants. Holding all the other elements of central bank policy constant, a level increase in the stock of nominal outside money is irrelevant for prices and inflation. This just increases the quantity of reserves. That's a liquidity trap result, but you get the liquidity trap no matter what R is. Further, the growth rate in total outside money is disconnected from inflation. While the nominal stock of currency grows at the inflation rate in equilibrium, the total stock of central bank liabilities need not.

The key thing here is that the central bank determines prices and inflation without any fiscal support. If the idea you got from the FTPL is that fiscal policy is necessary to determine the price level and inflation, that's not correct.

Next, go to the OMO model in which the central bank buys and sells government debt, and there is a fiscal authority that can tax households lump sum. Otherwise the model is the same as MG, except now the central bank's profits are turned over to the fiscal authority. Here, we'll suppose that the fiscal authority determines on its own the real transfers over time that are required to support the government debt. At the first date, the fiscal authority issues debt, some of which the central bank purchases by issuing outside money (reserves and currency), and the fiscal authority then rebates the proceeds of the debt issue to households. Then, the fiscal authority levies future taxes to pay the interest on the government debt, which will be constant in equilibrium, so we can think about what is going on. This economy is Ricardian, so the present value of the fiscal authority's transfers is zero. But as in the MG economy, transfers with a positive present value are generated from the central bank's activities. Those transfers are determined by R, and we'll assume that fiscal policy is constant (government debt held constant in real terms) and does not depend on R.

In the OMO economy, monetary policy works much as in the MG economy. Inflation is determined in a Fisherian fashion, and the central bank can have a large balance sheet, but if there are positive reserve holdings forever, having more outside money in this economy has no effect. Given R, the extra money is held as reserves. Further, "helicopter drops" cannot produce more inflation. Given all the other features of policy, if the fiscal authority increases transfers - in real terms, say - then in this Ricardian economy that has no effect. Further, there will be no effect on prices if the central bank purchases the extra debt issued with outside money. The money will just be held as reserves - it's irrelevant whether the increase in transfers is financed with reserves or government debt. Indeed, the central bank could issue currency to finance the transfers, and this will just be converted into reserves and held that way - nothing happens.

In terms of the FTPL, the point here is that FTPL results are derived simply from assumptions that imply that the fiscal authority is in the inflation driver's seat. Here, I've just made natural assumptions about central bank independence and, again, the central bank determines the price level and can have as much inflation as it wants.

Now that we've got those basic ideas nailed down, we can get more sophisticated and think about an economy - the NR economy - with exchange involving secured credit and currency. This works a bit like a cash goods/credit goods model. Here government debt serves as collateral in credit transactions. If the collateral constraint binds, this implies that government debt carries a liquidity premium, and the real interest rate will be low. Then the economy is non-Ricardian. More government debt will relax the collateral constraint and improve efficiency, but we'll assume that the fiscal authority behaves suboptimally, and the central bank responds to that.

So, what happens?

1. If the collateral constraint binds, this implies the central bank should set R > 0 at the optimum. The friction that makes the real interest rate low implies that the central bank should not be at the zero lower bound.
2. Given R, expansion in the central bank's balance sheet is again neutral - swapping reserves for government bonds does not matter, provided these two assets serve equally well as collateral.
3. A policy of increasing transfers financed with government debt, with a permanent expansion in government debt, is beneficial policy, as this relaxes the collateral constraint. But it doesn't matter if this is financed by an increase in outside money (a helicopter drop). If so, the extra money is held as reserves. Further, this action doesn't increase inflation - it reduces inflation. If the central bank wants to increase inflation, it has to raise R. Neo-Fisher again.
4. If reserves are worse collateral than government debt (true in practice, basically, if we think of collateral as, in part, supporting bank liabilities) then a balance sheet expansion by the central bank is bad - it just tightens collateral constraints. This increases inflation alright, but there's a welfare loss.

So, the conclusions are:

1. FTPL forces us to think seriously about fiscal/monetary interaction, and that's very important. But fiscal support is not necessary for monetary policy to work, nor is it useful to think of fiscal policy determining inflation on its own - the central bank can indeed be independent.
2. Fiscal/monetary interaction becomes really important when we start thinking about the liquidity properties of government debt.
3. Helicopter drops? Forget it. This is not some cure-all for a low-inflation problem.
4. QE can be harmful, as it soaks up useful collateral and replaces it with inferior assets.
5. Neo-Fisherian denial is not good for you. Central banks that want to increase inflation need to increase nominal interest rates.

Friday, March 25, 2016

Central Bank Forecasts: What's in a Dot?

There has been some discussion of central bank forecasts and policy projections, including some blog posts by Tony Yates, Tony Yates part II, Narayana, David Andolfatto, and an editorial on Bloomberg.

The FOMC's dot plots are part of the economic projection materials published four times per year after the March, June, September, and December FOMC meetings. Many central banks in the world publish forecasts. For example, several times a year, the Bank of England publishes detailed forecasts in its Inflation Report. As far as I can tell, the Bank does not offer a projection of its policy rate, though it reports a market-based forecast of the policy rate. The Swedish Riksbank publishes forecasts, and also prominently displays a projection of its policy rate at the top of its home page, as a fan chart. The Bank of Canada offers inflation projections, but does not project its policy rate.

What's the value of a central bank's forecasts? For the most part, the central bank does not have any important information you don't have, that would be relevant for a macroeconomic forecast. Nor does the central bank possess any special knowledge about how to conduct macroeconomic forecasts. Basically, any professional forecasting firm should be able to do it as well or better. So, we're not interested in a central bank's forecasts because these are good forecasts. But perhaps we care about the central bank's forecasts because this tells us something about what the central bank will do. For example, the central bank could be pessimistic, and wrong, but I pay attention because monetary policy matters for my decisions. I'm better off if I know about the pessimistic central bank forecast than if I did not know.

There are aspects of central bank forecasting that are very different from private forecasting, however. For example, the Bank of England, the Swedish Riksbank, and the Bank of Canada all target inflation at 2%, and they provide forecasts of inflation, which is the thing they are trying to control. Thus, implicit in the central bank's forecast is a policy exercise. The ultimate forecast is conditioned on a particular path for policy instruments, and the process by which that policy path was chosen involved alternative policy simulations - which would produce different forecasts. If monetary policy really matters to me, I would want to know a lot about that process. Indeed, I would like to know the path for policy instruments that underlies the forecast, the whole structure of the model that was used to generate the forecasts, and the add factors that were applied to the model to produce the forecast (trust me, the add factors are really important). But most central banks are too secretive to give me all that stuff (that's "me" as if I were you).

So what about the dot plots? In principle, this provides some of the information that people affected in important ways by monetary policy are looking for. Narayana gives a good description here of how the dot plots are constructed. Each dot represents what an individual FOMC member thinks the optimal policy rate would be at the end of each future calendar year, given his or her forecast of other macroeconomic variables. That's important. This is not an individual's forecast of what the FOMC will actually do, it's what the individual thinks he or she would do in the future if the world evolves in the way he or she thinks it will, and if he or she has ultimate decision-making power. Of course there's a lot the dot plots don't tell you. Which dot is who? Maybe that dot doesn't get to vote this year? What's the forecast of other variables associated with each dot? What's the model (if any) that was used to evaluate policy? It would be nice to know which dots are associated with who, so that I could at least know who to ask which questions.

Let's look at some dot plot examples (all from the Board's web site). Here's one from January 2012:
So, in January 2012, of 17 FOMC members, 3 think liftoff should happen by the end of 2012, 6 by the end of 2013, and 11 by the end of 2014. And in the long run, they're collectively thinking that the policy rate will be above 4%. So, what actually happened (liftoff in December 2015) appears delayed relative to that projection. But so what? Maybe the economy evolved in ways that these FOMC participants did not anticipate? Let's look at another one. This is for March 2014:
So you can see, comparing this chart to the last, that the committee's views have changed in two years' time. In 2012, they thought they would be lifting off by the end of 2014, but in March 2014 all but one are convinced that liftoff by December 2014 is off the table. For 2014 and 2015, the March 2014 projection is consistent with what actually happened - no liftoff in 2014, and liftoff by December 2015 (just barely). But, in March 2014, FOMC participants were predicting a policy rate that, on average, was above 2% by the end of 2016. That appears to be unlikely now.

Finally, this is the dot plot for September 2015:
This shows how liberally the projection exercise can be interpreted by the participants. Note the outlier - one participant thought it would be optimal to have a negative policy rate, at least until the end of 2016. As Janet Yellen pointed out in Congressional testimony in February, she is not entirely clear that negative interest rates on reserves are even feasible in the United States, given both the legalities and our institutional structure. So, if one were to say, in September 2015, that negative interest rates would be optimal in December of 2015, and in December of 2016, it's not clear what that means, as the feasibility of such a policy still appears unsettled.

Some people are worried that the dot plots might be interpreted as commitments. If they were interpreted this way, that would be bad. The September 2015 dot plot above, interpreted as a commitment, says the FOMC was committing in September 2015 to roughly five quarter-point rate hikes by the end of 2016. If so, we would say they were failing. But that's not the right interpretation. What we should be doing is asking what has happened since September 2016 to change FOMC participants' views, how those views have changed, and whether that makes any sense. And the dot plots help you make that assessment, though maybe they don't tell you everything you want to know.

The Bloomberg editorial suggests the dot plots should go: would help more to stop releasing information that begs to be misunderstood as a commitment to a specific path for interest rates, when the Fed is making no such commitment.
By this logic, I think, saying anything at all means you are "begging to be misunderstood." By now, I think the dot plots have helped people understand what the FOMC's policy statements mean. For example, the information in fed funds futures has typically predicted a lower policy rate trajectory for some time than what is in the dot plots - and typically the market has been right.

Narayana has some other suggestions about forecasts. From the Bloomberg editorial:
...Narayana Kocherlakota offered two other suggestions. First, delay publication of the dot plot to coincide with release of the Fed minutes: That way, it would be seen in the context of the Fed's internal debate on policy, rather than as part of its collective judgment on interest rates. Second, release a collective medium-term forecast of output and employment, modeled on the Bank of England's so-called fan charts.
The first suggestion would seem to make us worse off. This delays useful information, which is costly, and there is not much benefit to be had. The information in the minutes is only an outline of the FOMC discussion, and there is little to connect with information in the dot plots - hard to connect the dots, basically, even given the minutes. Second, a "collective medium-term forecast..." by all FOMC participants is not feasible, given the decentralized structure of the Federal Reserve System. So much for that.

Saturday, March 5, 2016


David Andolfatto draws some useful comparisons between Canada, 1990-1999, and the U.S., post-2008. As he points out, Canada experienced a decade-long slump in the 90s which featured a depressed participation rate and employment/population ratio. It's useful, I think, to show how this experience was different from what we're seeing now in the U.S.

First, suppose we look at the paths of the unemployment rate in Canada, 1990-1999, and the U.S. from the beginning of 2008 to the present:
So, for the Canadian slump, the unemployment rate took about 40 months to reach its peak, vs. 20 months in the U.S., but from the peak in unemployment, it's about 80 months until the slump is over (i.e. unemployment is back to its pre-slump level) in both cases.

Next, let's look at the unemployment rate and the participation rate in Canada, 1990-1999 (deviations from the mean in the sample, to highlight what is going on):
Note that the participation rate bottoms out and begins increasing about 3 years after the unemployment rate reaches its peak.

Now the U.S., post-2008,
In this case, the unemployment rate peaks in October 2009, but three years later the participation rate was still falling. Indeed, we can't say for sure whether it has stopped falling, even though the slump is over. There's a recent upturn in the participation rate, but the time series is noisy, so it's not clear whether this will be sustained.

So, if you think the 1990-1999 period in Canada tells us that the labor force participation rate in the U.S. is on the way up, you should be more skeptical. But labor force behavior in other countries, including Canada, is illuminating concerning what is going on in the U.S. right now. Canada has had similiar real GDP growth to the U.S. since the last recession, and has similar demographics, but its participation rate did not fall like the U.S. participation rate did recently, as David shows. So what's causing the U.S. participation rate to fall? I don't think it's anything to do with wages. Here's the times series, since 2007, of average labor productivity and real wages.
You can measure both in some different ways. What I've done here is to take hours of payroll employment divided by real GDP as my average labor productivity measure, and the average hourly earnings of private non-farm payroll employees, divided by the pce deflator, as my real wage measure. You can see that average growth in productivity and the real wage have been about the same since early 2007. So nothing funny going on there, apparently.

Another interesting feature of the data is what is going on with the long-term unemployed. Here's the number unemployed 27 weeks and more as a percentage of the labor force:
That's still high relative to recent history, and represents a little less than one third of total unemployment. So, we currently have an unusually low number of short-term unemployed and an unusually large number of long-term unemployed in the U.S. And the long-term unemployment rate appears to have leveled off and is not budging. So, if if the long-term unemployed are not finding work, it's hard to see how discouraged workers who left the labor force are going to have an easier time of it. My best guess is that what is going on is related to mismatch (between the demand for skills and the skills people want to supply), and it will take higher productivity growth (and thus higher real wage growth) to induce a sustained increase in labor force participation.

Thursday, March 3, 2016

What's Going on with Inflation?

Last week's numbers on the January pce deflator seemed to have sparked optimism in some people, though my non-macro friends are wondering why anyone is excited about more inflation. Here are what the 12-month inflation rates look like for the raw pce deflator and pce deflator excluding food and energy:
The FOMC most recently stated its inflation goals in this document. In particular,
...inflation at the rate of 2 percent, as measured by the annual change in the price index for personal consumption expenditures, is most consistent over the longer run with the Federal Reserve’s statutory mandate. The Committee would be concerned if inflation were running persistently above or below this objective.
That concern is reflected in the last FOMC statement:
In light of the current shortfall of inflation from 2 percent, the Committee will carefully monitor actual and expected progress toward its inflation goal.
So, apparently, inflation (according to the FOMC's chosen measure, the raw pce deflator) is moving toward the 2% goal, and for those who care about core inflation measures, the same thing is happening.

But what if we measure inflation in different ways, just to check. The next chart shows average inflation, for both the raw pce and core pce, calculated over the last month, the last two months, etc. That is, "months" on the horizontal axis is the number of previous months over which we're calculating the average inflation rate:
This chart tells us that the increases in core inflation have been concentrated in the last six months. For raw pce inflation, the story is mixed. Inflation is actually at its highest, at about 1.3%, when we look at the standard measure, which is a 12-month average. But over the last six months, average inflation is 0.3%, and over the last two years, it is 0.7%. So maybe we want to take the first chart with a grain of salt.

Next, let's look at the components - here we'll look at the CPI components, as that's more convenient. The large price increases in the recent data are coming mainly from non-energy services:
That chart shows total non-energy services, and the two largest components, shelter and medical care. Basically, the trend increase in non-energy services is dominated by shelter, which has a weight of about 32% in the total CPI, and about 15% in the raw pce deflator. Inflation in the price of shelter has been increasing and currently runs in excess of 3%.

Shelter prices are a bit unusual in the way they are measured and incorporated in the CPI, and in the pce deflator. In particular, in the CPI about 2/3 of the weight in the shelter price is accounted for by imputed rent of ownership housing. The idea is that, implicitly, you rent your house from yourself, and the price of the services you are receiving is measured as the rent that you would pay to a landlord for a similar dwelling in the rental market. In terms of the distortions that might be caused by inflation, this seems odd as, for the most part, there are no transactions associated with most of the existing housing stock - only a small fraction of the stock turns over in a given year. Further, what is being counted in these price indexes is some shadow price of a non-market service. If we're going to count imputed rent on ownership housing in our inflation measure, why don't we count imputed rent on my refrigerator, the shadow price of the dishwashing services I'm supplying, etc? Go figure.

Just for good measure, let's look at the prices we're dropping when we measure core inflation. Here's food:
And here's energy:
So, food inflation and energy price inflation are at their lowest in the last 5 years. Thus, the core inflation measure is stripping out the prices that are at rates below (for food) and much below (for energy) the average. "Core" measures have been with us since the 1970s, and strip out food and energy prices, as these prices have been historically volatile. You can certainly see that in the last chart, though in the previous one you can see that the variability in food prices has been much smaller recently than for energy. Core inflation measures adjust in a crude fashion for the fact that a large increase or decrease in food or energy prices typically reflects a temporary increase or decrease in relative prices. Possibly monetary policy should not respond to such shocks. But there are at least four reasons why a policy focus on core measures of inflation may not be a good idea:

1. Surely policymakers are smart enough to make judgments about which movements in inflation are due to temporary non-monetary factors, and which are not.
2. Large movements in the relative prices of food and energy can be highly persistent.
3. People might be tempted to think that, if food and energy prices had behaved in different ways, that core prices would have behaved in the same way they actually did. That can't be true.
4. Stripping out food and energy means putting even more weight on the price of shelter, which we know doesn't reflect actual transactions prices, for the most part.

To expand on the third point, if energy prices had not fallen dramatically, then holding constant nominal incomes (possibly not a great assumption, but what the heck), consumers would have had less to spend on other goods and services, and those other prices would be lower than they actually are.

So, what's going to happen to prices in the future? So far we're not yet seeing any turnaround in the raw pce inflation measure - as we showed above the increase in 12-month inflation is just a quirk in the data. But since the price of crude oil has started to increase again, if the prices of services continue to increase at 3% or more, we will indeed see raw pce inflation start approaching 2%. But that's just it. There's no good reason to think that, if energy price inflation increases, other components of inflation won't decrease.

Monday, February 29, 2016

Technical Change and Commitment

I sometimes entertain myself by reading the liner notes on old vinyl records. This isn't liner notes, but I found this stuff on the cover of "Another Side of Bob Dylan," (1964).

Stereo "360 Sound." Playable on mono equipment. For best results use stereo needle.
This Columbia GUARANTEED HIGH FIDELITY recording is scientifically designed to play with the highest quality of reproduction on the phonograph of your choice, new or old. If you are the owner of a new stereophonic system, this record will play with even more brilliant true-to-life fidelity. In short, you can purchase this record with no fear of its becoming obsolete in the future.

Sunday, February 14, 2016

The End of Central Banking

Strange thing happened the other day. I was looking for news stories on the keen insight and deft policy decisions of central bankers, and couldn't find any. Here are some of the other, less-flattering stories:

New York Times: "Swedish Bank Move Creates a Global Shudder"

David Beckworth: "China's Coming Devaluation: Another Consequence of the Fed's Mistake of 2015"

Market Watch: "Is this the week central banks lost their market credibility?"

Zerohedge: "This is What Central Bank Failure Looks Like"

Scott Sumner: "Another Sign of Fed Incompetence"

I think you get the idea. What's going on? Well, I hate to pick on the Swedes, but the Swedish Riksbank is one of my favorite examples. As I discussed in a previous post, the Riksbank has a 2% target for inflation, but actual inflation has been in the neighborhood of 0% for about 3 years, though the Riksbank appears to be committed to returning inflation to target. On February 11, the Riksbank reduced its policy rate target by 15 basis points to -0.5%, and issued a statement, which reads in part:
The economy continues to strengthen but inflation is expected to be lower during 2016 than previously forecast. The period of low inflation will therefore be longer. This increases the risk of weakening confidence in the inflation target and of inflation not rising towards the target as expected. To provide support for inflation so that it rises and stabilises around 2 per cent in 2017, the Executive Board of the Riksbank has therefore decided to cut the repo rate by 0.15 percentage points to −0.50 per cent. Purchases of government bonds will continue for the first six months of this year, in accordance with the plan adopted in October. The Executive Board has also decided to reinvest maturities and coupons from the government bond portfolio until further notice. There is still a high level of preparedness to make monetary policy even more expansionary if this is needed to safeguard the inflation target.
This is a very familiar story in many countries, including the U.S. Inflation is not increasing as the central bank had been anticipating, and in the Riksbank's case a decision has been made to take corrective action. That corrective action is more of the same - pushing the policy rate further into negative territory, and conducting further quantitative easing. As well, there is forward guidance: the Riksbank will do even more of the same if they don't get results.

The Riksbank seems to have an orthodox view of how the inflation process works:
Growth in the Swedish economy is high and unemployment is falling, which suggests that inflation will rise in the period ahead.
Basically, the Riksbank believes in its Phillips curve. For it, lower unemployment means higher inflation and, presumably, it thinks a lower nominal interest rate will further reduce unemployment and increase inflation. So, that's a fairly typical view. Central banks experiencing low inflation are typically the ones who have done the most to put unconventional policies into practice - negative nominal interest rates and quantitative easing in particular.

Most of the people currently calling the Fed stupid are orthodox types. They have a Phillips curve view of the world, and they think of low nominal interest rates as "accommodative." And orthodox central banking views breed a "whatever it takes" set of actions - negative nominal interest rates, quantitative easing - in an attempt, as they see it, to get inflation back to target.

Noah Smith, who has been watching these things for a long time, seems puzzled and gloomy. Here's the puzzlement:
The more important point, though, is that no one really knows what is going on with monetary policy right now. No one knows what the Fed is really trying to accomplish, or what it can accomplish, or how to go about accomplishing it. Is it still set on raising interest rates in order to avoid the semblance of abnormality from keeping them close to zero? Is it worried about demand-side shocks from China’s slowdown? Does it want the public to think that it will never let inflation go above 2 percent, or does it want us to think that 2 percent is in the middle of the acceptable range? Is it trying to raise inflation and failing? And if it did want to raise inflation to 2 percent, would it do so by keeping interest rates low, or by raising them?
Here's the gloom:
It’s becoming clearer that the Fed's experiments during the Great Recession, dramatic as they were, taught us little about how monetary policy works.
Now I'm puzzled. Noah is a guy who loves experiments and empirical work, and thinks every econ 101 student should spend a lot of time staring at data. In the last 9 years, we have had a major financial economic event, coupled with major central bank crisis intervention, followed by an unusual recovery, sovereign debt crises, and many central banks experimenting with unconventional policy. But "us" did not learn anything. Go figure.

Here's something I've learned since the financial crisis. There's a paper by Benhabib, Schmitt-Grohe, and Uribe (BSU), "The Perils of Taylor Rules," that shows how an aggressive Taylor-rule central banker inevitably converges to the zero lower bound, and gets stuck there. A central banker following a Taylor rule sets a target for a short-term nominal interest rate, and increases that target interest rate if the inflation rate increases relative to its target level. Typically, Taylor rules include a term for the "output gap," but the argument doesn't depend on that. Basically, a typical Taylor rule embeds orthodox central banking - increasing the nominal interest rate should make the inflation rate go down. Further, an aggressive central banker is one who follows the "Taylor principle" - if the inflation rate increases relative to its target, then the nominal interest rate should go up more than one-for-one. Why? Again, that's part of orthodox central bank thinking. If the nominal interest rate increases more than one-for-one with an increase in the inflation rate, the real interest rate should go up in the short run, real economic activity should go down, and by orthodox Phillips curve logic, the inflation rate should fall.

But, if you work through BSU, you'll see that this results in many dynamic paths that end up at the zero lower bound (ZLB) for the nominal interest rate, which is a steady state. Once there, the orthodox central banker is stuck. Inflation stays below target, as there's nothing to make it go up, but the orthodox central banker is convinced that a lower nominal interest rate is what's needed to increase the inflation rate, and gets increasingly frustrated. Some people can see these things right away, but I usually have to work it out myself to understand it. I wrote this paper with David Andolfatto, which adds some stuff to BSU, including a scarcity of safe assets and low real interest rates.

If you understand BSU, it's only a short step to understanding the current behavior of central bankers. Frustrated by what they see as a ZLB problem, orthodox central bankers find other ways to be "accommodative." If you think about it a bit, or talk to Miles Kimball, you'll understand that zero isn't really a lower bond for the nominal interest rate - the orthodox central banker can go negative, as the Bank of Japan, the Danish central bank, the ECB, the Swiss National Bank, and the Swedish Riksbank have done. He or she can engage in quantitative easing (QE) - central bank purchases of various long-maturity assets, as the Fed, the Bank of England, the Swedish Riksbank, the Swiss National Bank, and the Bank of Japan have done. The orthodox central banker can also make promises about the future, in the hope that those promises are believed, and will have some effect today. And, the central banker who does not do those things, does them and stops, or doesn't do "all it takes," will find plenty of people willing to call him or her stupid (see the links at the beginning of this post, or see Narayana's web page). So, if you read BSU and thought that it would be easy for a central banker to get out of the low-inflation, low-nominal-interest-rate trap, better think again.

So, what should happen as central bankers fall into the ZLB, or ELB (effective lower bound) trap? Ultimately, people should start to understand that low inflation will persist for a very long time, and this will show up as low yields on nominal government bonds, and low anticipated inflation, by whatever measure. Here are 10-year yields on U.S. Treasuries, Japanese government bonds, and Swedish government bonds:
It's useful to include Japan here, as it's been in the trap since about 1995, with low interest rates, and inflation averaging about zero. As is well-known, the real interest rate, according to various measures, has fallen over this period, but you can see a "convergence to Japan" here - everyone's falling into the trap, and you can see the same thing if you look at government bond yields for other countries.

For the U.S., if we look at the 10-year bond yield and 10-year TIPS yield, we see:
So, the long-term real rate, as measured by the TIPS yield, hasn't changed much since 2013, but the nominal yield is about 100 basis points lower. Just for emphasis, we can look at the breakeven rate, the difference between the two yields in the previous chart, which is one measure of anticipated inflation:
The current 10-year breakeven rate is low, at 1.18%, relative to any period in the time series, excepting the financial crisis, a period during which bond yields were reflecting various market liquidity factors rather than inflation premia.

So that's ominous, and the reaction of a committed orthodox central banker is to just dig a deeper hole, as reflected in the Riksbank's statement earlier in this post. Lower measured anticipated inflation is just like lower actual inflation - it means greater frustration on the part of the orthodox central banker, and he or she wants to go more negative, and buy more assets, cheered on by various Kimballs, Kocherlakotas, etc.

What are the lessons for people outside central banks?

1. If you live in Sweden, for example, don't pay any attention to the Riksbank's forecasts. Pay attention to what the Riksbank says. Inflation is actually going to stay low - zero for a long time would be a good forecast I think - and the Riksbank is trapped in the hole that it dug for itself.
2. If the central bank starts using words like "Fisher effect," pay attention. This central bank means business.
3. Once stuck at the ZLB or ELB, there's nothing for the central bank to do. That's what I mean by "the end of central banking." Central banks can purchase all the assets they want - that's not important. What matters is the central bank's nominal interest rate policy target, and the rule for setting it.
4. Beware of other "tools" that people might think up. A recent one is "helicopter drops." More about that later.
5. Beware of changes in central bank objectives masquerading as changes in tools - e.g. nominal GDP targeting, price level targeting, or a higher inflation targets (4% for example). It's typically an orthodox economist or central banker projecting those ideas, which will similarly imply a path to ELB, or sticking there, if that state has already been attained.
6. Don't panic. Zero or negative inflation actually is OK. If someone tries to tell you about the black hole of deflation, plug your ears and start humming.
7. What is not OK is for people to continue to anticipate 2% inflation that a central bank promising but incapable of delivering. Again, for long-range planning purposes, think zero inflation indefinitely.
8. If you're an economist, pay attention to what your models are actually predicting, unless your model is straightforward IS/LM - Phillips curve. In that case, you need to learn some more economics. Standard off-the-shelf monetary models essentially all exhibit a neo-Fisherian effect. That's nothing special. The Fisher effect is important. Typically increases in nominal interest rates lead to increases in inflation. Orthodox people - particularly the ones with some technical facility - can think up examples where they think this doesn't happen. Don't buy it though. If they persist, you can always plug your ears and start humming.
9. For a non-interventionist, the low-inflation policy trap is a wonderful thing (John Cochrane, for example, seems to be fine with it). The interventionist orthodox central banker, in the process of trying to "do all it takes," sows the seeds of his or her own destruction, and becomes powerless. No high inflation, no hyperinflation, only low inflation - and inflation might be fairly stable. In the course of committing policy hara kiri, the orthodox central banker imposes some transition costs, but the steady state ain't so bad.

So, if you're confused, worried, or feeling like you haven't learned anything about how monetary policy works, there's no good reason for that. Cheer up.

Addendum: More othrodox central banking. Here's what Draghi said today:
We are very conscious, and wish interest rates could go up again, but this is not the case now. I don’t think anybody is thinking about changing policies, but if we were to change, it will lengthen the timing of inflation reaching 2%.