Friday, December 29, 2017

The Corporate Tax Rate, Part 2

John Cochrane posted a reply to my previous post on how changes in the corporate tax rate might affect investment. The key issues seem to relate to the specifics of what the tax code will allow as an expense. In my analysis, I treated investment spending by the firm as fully-expensed, which is not correct. However, the tax code does permit businesses to deduct interest on their debt, and depreciation, which I didn't include. What I'll do here follows - I think - a comment by Francois Gourio (Chicago Fed) on Twitter.

So, let's write down the firm's problem again, assuming a constant real interest rate r, which the firm's shareholders face (an important assumption - I'm neglecting taxes affecting the sharelholders). We'll assume that dividends are paid period-by-period to the firm's shareholders, with the firm maximizing the present value of dividends:
Here, K is the capital stock, N is the labor input, w is the wage rate, b is the firm's debt, and d is the depreciation rate. The firm's debt comes due in one period. Net proceeds for the firm in the current period consist of output minus the wage bill plus new debt issued, minus interest and principal on the debt issued in the previous period, minus investment, minus corporate taxes. The corporate tax rate t applies to output minus the wage bill, minus the interest payments on the debt, minus depreciation.

If the firm were to fund investment out of retained earnings (provided this does not violate a nonnegativity constraint) then a reduction in the corporate tax rate will indeed raise the after-tax marginal net payoff to investing. Alternatively, suppose that the firm always funds new investment by issuing debt, then pays the interest on the debt, retires debt as capital depreciates, and otherwise rolls the debt over. This implies that the firm's outstanding debt is always backed one-for-one by the firm's capital, or
Then, we can rewrite the first equation as
So, the firm's choice of labor input in each period, and its choice of capital in periods 1,2,3,... (equivalent to choosing investment) is independent of the tax rate t. Essentially, debt financing of investment permits full expensing of the investment expenditure - indirectly, through expensing of interest on the debt and depreciation.


1. We need to worry about how the household is taxed, which in this formulation determines what the objective function is for the firm.
2. To do a proper job here, we need to determine the optimal financial structure for the firm.

This is potentially quite complicated (not blog material), though I'm sure someone has addressed related problems in the taxation literature. To do the problem justice, we need a complete general equilibrium model. That said,

1. There's no presumption that the corporate tax rate reduction is going to matter much for intensive-margin decisions of the firm - decisions about labor input and investment.
2. Where the change in the corporate tax rate should matter is for entry decisions - here we need to start worrying about nonconvexities - e.g. fixed costs of entry. But some entry, relating to the treatment of pass-throughs, would just be a renaming of the productive unit - call yourself a business and you can be taxed at a lower rate. As well, firms may choose to relocate from other countries to the U.S., though as I mentioned in my previous post, those other countries won't give up without at fight.
3. There's a clear redistributive effect, as I mentioned in my previous post. Owners of stocks will benefit, and they tend to be richer people. Long-term, government transfers and expenditures on goods and services have to fall, and the burden of those reductions will be borne by the relatively poor.
4. If the Republican Congress actually wanted to increase investment spending, there are straightforward ways to do this through the tax code - an investment tax credit, for example.

Wednesday, December 27, 2017

Where's the Fallacy?

Here's John Cochrane, writing about the "buyback fallacy:"
Many commenters on the tax bill repeat the worry that companies will just use tax savings to pay dividends or buy back shares rather than make new investments.
But, John concludes:
Investment will increase if the marginal, after-tax, return to investment increases. Lowering the corporate tax rate operates on that marginal incentive to new investments. It does not operate by "giving companies cash" which they may use, individually, to buy new forklifts, or to send to investors. Thinking about the cash, and not the marginal incentive, is a central mistake.
But, suppose that we use a simple model of firm behavior, along the lines of what we teach to undergraduates (see for example, Chapter 11, of this fine intermediate macro book). In each period i = 0,1,2,..., the firm hires labor and invests in new capital. Output is produced using labor and capital each period, using a constant-returns-to-scale technology. Each period the firm hires labor on a competitive market, produces output, and invests in new capital. The firm's profits (the return to capital, not economic profits) are P(i) in periods i = 0,1,2,..., and the firm maximizes the present value of profits. Suppose no uncertainty, and that the real interest rate is a constant r forever. Capital depreciates at a constant rate. The firm maximizes the after-tax present value of profits
Profits are ultimately distributed as dividends to the firm's shareholders, but the firm can borrow and lend freely at the interest rate r, so the timing of the dividend payments is irrelevant.

What happens if the corporate tax rate goes up permanently, with the tax rate constant forever, or t(i)=t? This has no effect on investment or on the firm's hiring decisions in any period. That is, if VB is before tax profits, then (1-t)VB = V, so maximizing VB is the same as maximizing V, and the tax rate is irrelevant, not only for investment decisions, but for the firm's hiring decision. In the aggregate, there is no effect on labor demand, and therefore no effect on wages.

Basically, investment is an intertemporal decision for the firm. But the corporate tax rate affects per-period after-tax profits in exactly the same way in every period, so there is no effect on the after tax rate of return on investment the firm is facing. Therefore, the firm won't invest more with a lower corporate tax rate - if it's permanent. How can a change in the corporate tax rate make investment go up in 2018? If the corporate tax rate were temporarily higher in 2018, returning to its former level permanently in 2019, that would do the trick.

I could be missing some subtlety in the tax code, for example in how the firm's financing decisions are affected by taxation, but I don't think so. Please fill me in if you think there's something important I've left out.

So, I don't think there's any fallacious thinking in the popular view of the effect of changes in corporate taxation included in the tax bill. The primary effect is redistributive. Ownership of stocks is concentrated among the relatively wealthy, and a permanently lower corporate tax rate will show up immediately in higher stock prices, as we've seen. Owners of stocks can hold them and receive their higher future dividends, or they can sell their stocks at any time and realize their capital gain. As more GDP doesn't magically come out of nothing, higher spending by these richer folks has to be offset by less spending by poorer folks.

If there are effects of changes in the corporate tax rate, these could come from two places. First, the change in the US rate relative to corporate tax rates elsewhere in the world matters. In some instances, this will have no implications for the location of production for the firm (e.g. management consulting done in various locations in the world), but will matter for the firm's choice of corporate tax home. The tax rate goes down, which reduces tax revenue, but more firms choose the US as a corporate tax home, which increases tax revenue. The net effect on tax revenue depends on how elastic corporate tax home is with respect to the US corporate tax rate. Also, some firms producing tangible goods may choose to relocate production to the US. This necessarily implies some increase in domestic investment expenditure, but the effect is temporary, and probably small, particularly as we can't take for granted that other countries will not provide inducements to prevent firms from moving production to the US.

Second, there is another effect on the extensive margin. Some economic activity that would formerly show up as labor income will now be classed as business income, so as to qualify for the lower tax rate. As I showed, there are no implications for investment expenditure. The effects are lower tax revenue and redistribution to the rich from the poor, who either can't do this, or can't afford to pay an accountant.

If the intent of the tax bill had been to increase investment spending, there are obvious ways to to that - an investment tax credit for example. But, the tax bill is not about investment. The primary effect is redistribution. In the short run, the tax bill makes the rich richer and the poor poorer, and it lowers tax revenue. Permanently lower tax revenue has to show up, in the long run, as permanently lower government transfers and lower spending on government-provided goods and services. This will hit the poor disproportionately. So, this isn't tax legislation that appears to work on marginal anything - it's just wealth redistribution.

Sunday, November 5, 2017


Will Jay Powell do a good job of running the Board of Governors and the FOMC? He's certainly not an obvious choice. If Powell had not been appointed to the Board in 2011, nobody would be thinking of him as a candidate for the Chair's job now. Powell is a lawyer, with no formal training in economics (beyond the odd undergrad course), which puts him at a disadvantage in the Fed system. On the up side, he has a willingness to learn:
“When he showed up at the Fed, he basically did not know much about macroeconomics or monetary policy,” says Seth Carpenter, chief U.S. economist at UBS who spent 15 years at the Fed, including time overlapping with Powell. “He made a conscious decision to spend a lot of time with staff and colleagues to learn as deeply and completely as possible.”
So, Powell appears to be conscientious in seeking advice about things he doesn't know much about. But, the Board may actually not be a great place to learn macroeconomics - the Board staff aren't known for their independent thinking, for example. Further, a Board Governor is not in the best position to learn, as he or she does not have a staff, and is dependent on more-or-less randomly assigned economists to get their work done. Indeed, a Governor's job is thankless in more ways than one. He or she currently earns $179,700 per year, which is less than what a good Associate Professor in Economics is paid at a top research school. And the Presidents of the regional Feds are much better remunerated. Dudley (New York Fed) earns $469,500, Williams (San Francisco Fed) earns $468,600, and Bullard (St. Louis Fed) earns $359,100, for example.

But any of those salaries pale in comparison to what Powell had to be earning in the private sector, judging from his accumulated wealth, which appears to be between $20 million and $55 million. So, to his credit, we can infer that Powell is genuinely interested in public service, otherwise he would still be in the private sector, further feathering his own nest. At six years in, he has been at the job longer than is typical for Board Governors, who are appointed for 14 years, but rarely serve the full term, or anything close.

What are Powell's views on monetary policy? He certainly has not been outspoken about it. Brainard and Tarullo have had differences with the consensus view on the FOMC, and weren't shy about talking about it. Stan Fischer, given his long experience as an academic economist and central banker, certainly had a lot to say, and clearly had his own views on policy. Powell, not so much. A quick look through some of Powell's speeches indicates that he typically did not speak specifically on monetary policy. When he did, for example in a 2016 speech, it's boilerplate - basically the consensus FOMC view. I've seen Powell in action only once. I know he said something, but I can't remember what it was. You might say my memory isn't so great, but from the same occasion, I can remember key details of what Kocherlakota, Evans, Brainard, Lacker, Fischer, and Yellen were talking about. Powell, in the general view, is collegial, reasonable, and intelligent. But in instances where we need depth of experience in central banking and knowledge of economics, he'll have to be looking to other people. That's worrisome.

So why was Powell chosen? Some have suggested that, relative to Yellen, Powell leans more toward less financial regulation. That's too deep for Trump, though, I think. Most official high-level Trump appointments are of three types: (i) person bent on destroying the institution he or she is assigned to run; (ii) General - either active or retired; (iii) rich white male. Powell is type (iii). Just be thankful he isn't type (i) or (ii).

But why didn't Trump just stick with Janet Yellen? After all, he claimed he liked her, right? Well, Yellen is neither male nor rich, so she has two strikes against her, in Trump's mind. Further, Trump seems convinced that people he appoints owe him favors. In Trumpland, an Obama appointee just can't have the right predilections.

But is Yellen a great loss? The New York Times editorial board thinks so. Adam Davidson, in the New Yorker, says that Janet Yellen is a "master of thinking in public." Jena McGregor, in the Washington Post, collects a lot of favorable quotes relating to Yellen's record as Fed Chair, and remarks on the loss of a woman in a position of power, where there currently are few.

From my point of view, Yellen was successful in forging consensus on the FOMC. Apparently, she didn't force her views on others (unlike Greenspan, for example), and the FOMC seems to have operated in a collegial fashion for the last four years. There were some dissents, but given the context there really wasn't that much friction. After all, the Fed was dealing with a unique situation - the large balance sheet that had been built up under Bernanke, and an unprecedentedly long period of essentially-zero overnight nominal interest rates. Deciding when and how to unwind that was no easy task. That said, Yellen's training (PhD 1971) put her out of touch with modern macroeconomics, and she appeared to have a religious devotion to the Phillips curve. With respect to the latter, she has plenty of company in the rest of the central banking community, but that's no excuse. As well, Yellen is well-known for her reluctance to appear in public - Adam Davidson's characterization of her as a "master of thinking in public" is nonsense, I think. As far as I can tell, thinking in public and walking on hot coals are more or less equivalent for Janet Yellen. This is, I think, why Yellen persisted in holding press conferences only after every other FOMC meeting - a decision that implied that nothing would ever happen at FOMC meetings held in January, May, July, or October. Yellen always insisted that all meetings were live, but the off meetings were live in the sense that a person who is unconscious and on a respirator is live - he or she isn't about to get up and run around.

That said, it's hard to see how the Fed will be better-run under Powell than Yellen. The failure to reappoint Yellen is just another instance in this administration of a break with precedent that weakens American institutions - this time the damage is to Fed independence. Further, our progress toward being a gender-blind society has been set back, and that's a big deal.

Thursday, October 5, 2017

U.S. Monetary Policy: What's Up?

To frame the issues, let's look at some objective measures of the Fed's performance. Just to be fair, we'll evaluate performance in terms of the objectives laid out in the FOMC's January 2017 goals statement.

1. "...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." Note that the price index the Fed has chosen as most appropriate is the raw, headline pce deflator, not the pce deflator stripping out food and energy, the cpi, the core cpi, or any other measure. So we should hold them to that choice. Here's year-over-year inflation rates, since the last recession:
Obviously the Fed hasn't been hitting 2% inflation spot on, but what's actually feasible, or even desirable? The Bank of Canada, to take an example that's close at hand for me, actually sets a target band of 1-3% for inflation, so by that criterion the Fed has done pretty well - within the 1-3% band for most of the last seven years, except during 2015 after the fall in energy prices, which perhaps is understandable. The current inflation rate is 1.4%, which is tolerably close to the Fed's ideal. But the the Fed also has a "symmetric inflation goal." Missing the target sometimes is OK, but the FOMC would like to miss on the high side about as much as it misses on the low side - roughly, average inflation should be close to 2%. Over the last year, inflation was above 2% for two months, and below for 10 months, with an average of 1.6%. Not quite symmetric, but not so bad.

2. "... it would not be appropriate to specify a fixed goal for employment...Information about Committee participants’ estimates of the longer-run normal rates of output growth and unemployment is published...For example, in the most recent projections, the median of FOMC participants’ estimates of the longer-run normal rate of unemployment was 4.8 percent." For good reasons, the FOMC doesn't want to be specific about numerical goals related to the second part of its mandate - sometimes called "maximum employment," whatever that is. There's a hint though, about what the FOMC members might care about, which is the "long run normal" or natural rate of unemployment. This is rather ill-defined and hard to measure. To my mind, the economics profession would be better off if we refrained from mention of "natural" anything. One danger associated with the natural rate, as for any other ill-defined and hard-to-measure variable, is that a policymaker can start making stuff up, so as to manipulate the policy discussion. In the FOMC's most recent projections, the range of estimates for a long-run unemployment rate fall in a range of 4.4%-5.0%, with a median of 4.6%, so notions of what is normal have fallen since January 2017, when the FOMC put together its long-run plans revision. Here's what the actual unemployment rate looks like:
The current unemployment rate, at 4.4%, is as low as any FOMC participant thinks is normal over the long run, conditional on things going really well, apparently. So, by that measure the Fed is doing great.

Just to check, we can look at another measure, which is a measure of labor market tightness (or it's inverse, as conventionally measured in the labor literature). This is the ratio of the number of unemployed to total job openings:
Shortly after the last recession ended, this measure peaked at about 6.6 unemployed people per job opening, and it's now down to close to 1 unemployed person per job opening. Indeed, that's close to the lowest reading since the BLS started collecting this particular job vacancy data. So, by conventional measures the job market is very tight, which should be viewed as extremely good performance on the Fed's part.

What about growth in real GDP?
If we think that part of the Fed's job is to smooth growth in real GDP, then that chart looks pretty good. I've put in a 2% growth path, and the deviations from that growth path are small. Of course, people might complain that 2% growth is lower than the 3% (roughly) post-WWII average, but that shouldn't be the Fed's concern. Received wisdom in the economics profession is that monetary policy can't do much for long-run growth, other than keeping inflation low and predictable.

So, what's to fix here? Inflation is tolerably close to 2%, the unemployment rate is very low, the labor market is extremely tight, and real GDP is growing smoothly. The only improvement to be made is some fine tuning so that inflation fluctuates symmetrically around the 2% target. How should that be done? I'll assume, consistent with my last post, that QE doesn't matter. So the only issue is what should be done to the fed funds target range (or, more accurately, the interest rate on reserves and the interest rate on overnight reverse repurchase agreements), so that the average inflation rate is 2%? Well, you don't have to be a neo-Fisherite to understand that, if inflation is persistently lower than what you want, on average, then the nominal interest rate needs to be, on average, higher in the future. What's needed here is some tweaking of the Fed's policy interest rate target. How much? As mentioned above, the average inflation rate over the last year is 1.6%, so one or two more interest rate hikes will do the trick. Twenty five to fifty basis points' increase in overnight interest rates is small potatoes for real economic activity - note that the labor market continued to improve in the face of the last four interest rate increases.

So, that's what I'd do. What does the FOMC have on its mind? In the last FOMC projections, the median long-run prediction of Committee members for the fed funds rate is 2.8%, with a range of 2.3%-3.5%. That's come down considerably, with recognition by the committee that the low real rates of return on government debt we are observing are likely to persist. A persistently low real rate of return on short-term safe assets implies of course that the nominal short term interest rate consistent with 2% inflation is low. I'm saying that what Janet Yellen would call the "neutral interest rate" (the interest rate target at which the Fed achieves its goals in the long run) is more like 1.5%, and not 2.3%-3.5%.

To get more information on what the FOMC is likely to do over the near future, we'll look at Janet Yellen's last speech on "Inflation, Uncertainty, and Monetary Policy." First, Yellen tells us how inflation has been low, and then says why she thinks low inflation is bad:
Sustained low inflation such as this is undesirable because, among other things, it generally leads to low settings of the federal funds rate in normal times, thereby providing less scope to ease monetary policy to fight recessions. In addition, a persistent undershoot of our stated 2 percent goal could undermine the FOMC's credibility, causing inflation expectations to drift and actual inflation and economic activity to become more volatile.
The second sentence is important. The Fed committed to a 2% inflation target because the assurance of predictable inflation minimizes uncertainty, and makes credit markets, and (by some accounts) the markets for goods and services work more efficiently. If the Fed consistently undershoots its inflation target, people will either think the Fed is incompetent, or that it is willfully abandoning its promises, neither of which is good - for the institution or the economy. But in this instance, the Fed isn't missing by much, so what's the big worry? As I mentioned above, this requires some fine-tuning, but don't get bent out of shape about it.

The first sentence in the quote was really interesting. She's got the causality backward. Pretty much all of us now accept that it's the central bank that controls inflation. That is, central bank actions or, more accurately, the central bank's policy rule, causes inflation to be what it is, combined of course with other factors outside the Fed's control - including the factors determining the long-run real rate of interest on government debt. So, low inflation does not lead to "low settings of the federal funds rate." It's the low settings for the fed funds rate that lead to the low inflation. In a world in which the central bank targets the nominal interest rate to control inflation, that's how it works, and central bankers would be wise to absorb that idea. Stop the neo-Fisherian denial, and get with the program!

The speech uses a two-equation model (written down in the appendix) to frame the issues. It's a Phillips curve model. Arrgghh. Even Larry Summers recognizes that Phillips curves are unreliable. As he says:
The Phillips curve is at most barely present in data for the past 25 years.
For example, in the recent post-recession period, here's what we get when we plot inflation against the measure of labor market tightness I used above (ratio of unemployed to job seekers):
The line connects the observations in temporal sequence from right to left. Over this period of time, I think the Fed would claim that inflation expectations are more or less "anchored." So, what we should see in the chart, if the Phillips curve is to be at all useful, is a set of observations tracing out a downward-sloping relationship. But, more often than not, inflation and my "slackness" measure are moving in the same direction. There's nothing new about macroeconomists raising issues with the Phillips curve as a cornerstone for policy. It's been in disrepute for much of the last 45 years or so, both on theoretical and empirical grounds. Unfortunately, the Phillips curve was dragged out of the gutter, dressed up, and rehabilitated by New Keynesians, which is another story altogether.

But, like a lot of people, Janet Yellen is a true believer, and her staff will aid her in that belief by going on a fishing expedition and finding a Phillips curve, and a sample period, for which all the signs in the regressions (if not the magnitudes) come out "right." Here, "right" is whatever conforms to the beliefs of the boss. Sure enough, in the appendix to Yellen's speech, there is a two-equation Phillips curve model. Core inflation is determined by past core inflation, inflation expectations, resource slack, and the relative price of imported goods, and core inflation, energy price inflation, and food inflation determine headline inflation. Yellen's worries about future inflation outcomes are essentially those of the true believer. Do we have the right slackness measure, or the right inflation expectations measure, and how much should we worry if expected inflation falls?

Though Yellen lays out an explicit model of inflation, she doesn't exactly tell us how policy is supposed to work within that framework. Even true believers will sometimes tell you that "the Phillips curve is now very flat," meaning that they think a tighter labor market will put little or no upward pressure on inflation. If we want to stick with the Phillips curve framework, what's left then? The Fed has to focus on anticipated inflation. But how do they move that around? Modern macroeconomics tells us that our views about future outcomes are shaped by what we know about policy rules, in a manner consistent with what we know about how the world works. I got no sense from Yellen's talk of how the Fed thinks its policy rule affects inflation expectations.

But here's the essence of the FOMC's current policy view:
...without further modest increases in the federal funds rate over time, there is a risk that the labor market could eventually become overheated, potentially creating an inflationary problem down the road that might be difficult to overcome without triggering a recession.
So, in spite of the fact that the Phillips curve doesn't fit the data, the most recent manifestation being the failure of the very tight labor market to make inflation go up, policy going forward will be driven by the fear that the Phillips curve will somehow wake up and re-assert itself. Summers thinks that's wrong, and rightly so.

But, I think Yellen and her colleagues are actually following the right policy. Modest increases in the Fed's interest rate target in this context is the correct prescription. But doing the right thing for the wrong reason won't help you in the long run. We're fortunate, though, that not much is likely to go wrong here. If inflation stays low, and the FOMC loses its appetite for interest rate increases, so what? Low inflation is fine, and it's close enough to 2% as not to be embarrassing. No big deal.

Monetary policy is the least of our now-staggering problems. Unfortunately, the wingnut in the White House is busy creating more difficulty for us, and making the problems we have worse. Fortunately, he has as yet not screwed up the Fed, and the slate of would-be Fed Chairs doesn't include anyone outlandish. More on that later.

Wednesday, October 4, 2017

Whatever Happened to Normalization?

What's become of the Fed's normalization plans? To get this straight, recall what's been abnormal about Fed policy for the last nine years or so. Here's a chart of the effective fed funds rate, and securities held outright by the Fed:
Abnormal policy began at the height of the financial crisis in late 2008, when the FOMC agreed on a plan to target the fed funds rate in a range of 0-0.25% - a policy that continued until "liftoff" in December 2015. As well, beginning in early 2009, the Fed embarked on a sequence of quantitative easing (QE) exercises, which increased the quantity of securities held outright by a factor of more than five. Further, the Fed got rid of essentially all of its Treasury bill holdings, and increased the average maturity of Treasury bonds and notes held. The Fed also purchased a large quantity of mortgage backed securities (MBS) - close to $1.8 trillion. So, the Fed increased the size of its balance sheet substantially, lengthened the average maturity of securities held, and departed in a big way from a policy of "Treasuries only."

As outlined in this FOMC document, the FOMC began thinking seriously about how Fed policy might return to normal, and what "normal" might be, as early as June 2011. A formal normalization plan was posted by the FOMC in September 2014, and this is essentially what has been implemented since, more or less. The plan was:

(i) Begin increases in the fed funds rate target.
(ii) Reduce the size of the balance sheet by stopping the reinvestment policy, after increases in the target policy rate are well underway.

Increases in the fed funds rate target began in December 2015, and we have since had three more, with the target range increasing from 0-0.25% to 1-1.25% currently. Balance sheet reduction did not commence until October of this year, when the FOMC issued an addendum to the 2014 plan. The addendum contains explicit details about how the balance sheet reduction will occur. Reinvestment - a policy by which assets in the Fed's portfolio are replaced as they mature, holding the nominal size of the balance sheet constant - did not stop abruptly, but its cessation will be phased in. It appears that the New York Fed did not purchase assets with a view to smoothing quantities that mature over time, and the FOMC seems concerned that the balance sheet not decline in a lumpy fashion, as it would without the caps on portfolio reduction outlined in the addendum.

Some questions that might come to mind (or should) on normalization, along with my answers:

1. Why did normalization start with interest rate increases first, then reductions in balance sheet size? It might seem logical, since QE followed the reduction in the nominal interest rate target to zero (effectively), that the Fed would normalize by first reducing the balance sheet to a normal size, and then increase interest rates. Indeed, there are some good reasons why this is what should have happened. As short-term nominal interest rates increase, the profit that the Fed makes on the spread between the return on its assets and what it is paying out on its liabilities declines. As a result the Fed makes a smaller transfer to the Treasury each year. QE took place in the context of relatively low yields on Treasury bonds and MBS, and with a larger balance sheet, the asset portfolio is being financed by a larger fraction of interest-bearing reserves and a lower fraction of zero-interest currency. If short-term rates go high enough, transfers to the Treasury will stop. Economically, this is unimportant, as this amounts to the difference between interest paid on reserves by the Fed vs. interest paid on government debt by the Treasury, but politically this could be very dangerous territory. The Fed should not give ammunition to its enemies in Congress. Added to this is the argument that QE was an experiment, with poorly understood consequences. Thus, the sooner the Fed ended the program, the better. So why not reduce balance sheet size before engaging in liftoff? Likely, because the FOMC was spooked by its experience in 2013. At that time, after the FOMC meeting that ended on June 19, Ben Bernanke announced that a winding-down, or "tapering" of the Fed's QE program was likely to being later that year, and that the program would probably end in mid-2014. The financial market response to that announcement, and earlier public statements by Bernanke, is sometimes called the "taper tantrum:"
In the chart, you can see an increase of more than 100 basis points in the 10-year Treasury bond yield, observable in both the nominal yield and the inflation-indexed yield. Somehow, this wasn't the response the Fed expected, but if the market viewed Bernanke's statement as news about forthcoming interest-rate target increases, the reaction doesn't seem outlandish in retrospect. In any case, this experience appears to have colored FOMC views on the importance of QE, and made them skittish about unwinding the program. Thus the idea that interest rate increases should be well under way before the Committee would even think about balance sheet reduction.

2. What's different about raising interest rates when the Fed has a large balance sheet? In theory, when there are reserves in excess of reserve requirements in the financial system overnight, the interest rate on excess reserves (IOER) should determine the overnight rate. This is called a floor system, under which interest rate control is easy, as the overnight interest rate can be essentially administered by the central bank. But in the United States, things aren't so simple. For the details see this article, and this one. Basically, there are regulatory features of the US financial system that restrict arbitrage in the overnight market, so that the "effective" federal funds rate is typically lower than IOER. And, as was also the case before the Fed began paying interest on reserves in late 2008, all fed funds trades don't happen at one interest rate on a given day - indeed, much of the fed funds market is conducted over-the-counter. The Fed was concerned, before liftoff happened, about its ability to achieve a given target range for the fed funds rate - would the fed funds rate even go up with increases in IOER? To assure that this would happen, the Fed expanded the market for its liabilities by making use of an overnight reverse repurchase agreement (ON-RRP) facility. ON-RRPs are loans to the Fed, usually overnight, secured by securities in the Fed's portfolio. These Fed liabilities are just reserves by another name - they can be held, for example, by money market mutual funds, which are prohibited from holding reserve accounts with the Fed. Currently, IOER is set at 1.25%, the ON-RRP rate is set at 1.00%, and on most recent days the effective fed funds rate is 1.16%. Here's a chart showing what has happened with Fed interest rate control since liftoff:
The chart shows takeup on the ON-RRP facility (quantity of ON-RRPs outstanding) and the effective fed funds rate. Initially, the Fed was willing to commit up to $2 trillion in collateral to ON-RRPs, but takeup is typically in the range of $50 billion to $250 billion, running up to $400 billion to $500 billion only at quarter-end (this for regulatory reasons). As well, the effective fed funds rate has recently been coming in consistently at about 9 basis points below IOER (except at month-end, again for regulatory reasons), and more detailed data shows that most trades happen around the average. In one sense interest rate control since liftoff appears to be a success. But it's not clear that the ON-RRP facility is necessary for its stated purpose. The fed funds rate might be about where it is now even without an active ON-RRP facility. We could go further though, and question this whole operating strategy. There is no good reason for the Fed to focus on a fed funds rate target. Fed funds are unsecured, and currently most of the trade in this market is just a means for some GSEs to earn overnight interest on reserve balances. Even in pre-crisis times, it would have made much more economic sense if the Fed had announced its overnight interest rate target as a target for an overnight repo rate. In the current context, why isn't the ON-RRP rate set equal to IOER? Maybe that would kill the fed funds market, but so what?

3. What happens to reserves when Fed assets mature and there is no reinvestment? The balance sheet of the Fed balances, just as any balance sheet does, so for any transaction that occurs affecting either assets or liabilities, implying a debit or credit, there must be an offsetting debit or credit. Suppose first that the maturing asset is a MBS. The issuer of the MBS - which would be a GSE if the MBS is held by the Fed - pays the face value of the debt to the Fed, and the payment will be made by reducing the balance in the GSE's reserve account by that amount. But the MBS that the GSE issued is composed of bits and pieces of underlying mortgage debt. Suppose that the reason the MBS matured was that the underlying mortgage debt was paid off. Then, mortage payments are made to the GSE, and ultimately those payments will involve an increase in the GSE's reserve balances, and a reduction in reserve balances held by private financial institutions. So reserves held by private sector institutions (a Fed liability) and MBS holdings (a Fed asset) decrease by the same amount. Suppose, alternatively, that a Treasury security held by the Fed matures. The Treasury holds a reserve account with the Fed, and a maturing Treasury security implies that the Treasury's reserve account balance (the account is called the "General Account") falls by the face value of the debt. But that has no implications for the private sector - it's just an accounting transaction between the Fed and the Treasury, like internal budgeting transactions between the English department and the Economics department at the University (if such a thing ever happens). There would be implications for the private sector if the Treasury, now finding itself short of reserve balances to pay for stuff, issues more debt to replenish those reserve balances. Then, the new Treasury debt is purchased by the private sector (the Fed won't be buying it, as it's not reinvesting) with reserve balances, so reserves held in the private sector fall. If you think about this a bit, you'll see that, if we think the level of of reserve balances held by the private sector is part of monetary policy, then the Treasury can engage in monetary policy, by varying the quantity of reserves in its reserve account. Look at this:
Note that both the level and variability of balances in the Treasury's general account have increased by a huge amount since the financial crisis. Maybe the Treasury thinks this doesn't matter now, as it won't mess with monetary policy, but that view is at odds with what the Fed says - which is that QE matters in a big way. If QE matters so much, then the big increase in average balances in the General Account in 2016 should have been a significant "tightening" (because it implies a reduction in privately-held reserves) that the Fed would be concerned with. What's going on?

4. When will balance sheet reduction stop? What the FOMC's normalization addendum says is that they don't know, so let me fill you in on what the issues are. The Fed needs to decide on a long-run operating strategy for monetary policy. They could adopt a channel system for monetary policy, like what Canada has, for example. This would involve operating with a small balance sheet. For example, in Canada, where there are no reserve requirements, overnight reserves are essentially zero. The target overnight rate in such a system is bounded by the interest rate at which the central bank lends (the discount rate, for the Fed) on the high side, and IOER, on the low side. Alternatively, the Fed could stick with the floor system under which it operates now, according to which there are excess reserves in the system overnight. The question then is how much reserves you need to make the floor system work. Basically, financial institutions have to be more or less indifferent between lending to the Fed overnight, and lending to to private entities overnight, so that the interest rates on Fed liabilities determine all overnight rates. Evidence from the Canadian experience from Spring 2009 to Spring 2010 suggests that number is smaller than some people seem to think. Probably less than $100 billion. In addition there are issues concerning what overnight rate the Fed should be targeting. In many countries the central bank targets a repo rate, which makes sense, as the central bank should be interested in a secured overnight rate, that is not contaminated by risk. Why persist in speaking to a fed funds rate target, particularly in a financial crisis?

5. Did QE actually work? Don't expect to get good information from the Fed about this. Central bankers want to at least keep up appearances. Who wants a central banker who's not knowledgeable and trustworthy? As I mentioned above, the Fed has many enemies - in Congress and elsewhere - and it's typically optimal for the institution if Fed officials don't admit to not knowing stuff. Truth is that I've never seen any solid evidence that the people who implemented QE in the Fed system actually have a grip on how it might work - either in theory or in practice. Bernanke once said that"QE works in practice but not in theory." I've heard that repeated many times, usually by a person with a smug look on his or her face. Basically, the statement's B.S. The evidence that QE works is weak or nonexistent. I've written about this in more detail in this St. Louis Fed article. Most of the pro-QE evidence comes from questionable event studies, and the evidence we have seems consistent with QE having no effects for the Fed's ultimate objectives. For example, the Bank of Japan has for more than four years engaged in a massive QE experiment that has had no discernible effect on inflation. And QE does in fact work in theory - at least in the 1950s and 1960s vintage theories that Berananke trotted out to justify the policy in the first place. More careful thought might make one think that QE could actually be harmful, by withdrawing useful collateral from financial markets and replacing it with inferior reserves (talk to people who understand "financial plumbing," for example Peter Stella or Manmohan Singh) It's possible that QE could do some good, if the Fed had the proper liabilities at its disposal. QE is basically an attempt by the central bank to engage in debt management, which is the job assignment of the Treasury in the United States. Maybe the Fed can do a better job of debt management than the Treasury, but if so there should be a public discussion, and an explicit assignment of tasks. And if the Fed is doing debt management it needs to be able to issue tradeable debt instruments of all maturities.

So, where are we? With the unemployment rate at 4.4% and the inflation rate at 1.3%, the Fed is achieving its goals, within reasonable tolerance. We're no longer in emergency territory, yet the Fed has an emergency-sized balance sheet. The plan they have issued to reduce the balance sheet is overdue, and it's quite timid. For example, note that during the QE3 program (the final stage of the Fed's asset purchase program), the Fed bought $85 billion per month in long-maturity Treasuries and MBS and that, even after a phase-in period, under the disinvestment program the reduction will be $50 billion per month, at most. Chances are that, when a recession comes along, the balance sheet will still be large, the interest rate target will quickly go to zero, and asset purchases will resume. If the Fed's balance sheet achieves any semblance of "normal" in my lifetime, I'll be amazed.

Sunday, September 10, 2017

Lael Brainard: Phillips Curve Confusion

As background for this piece, you can read this forthcoming St. Louis Fed Review article,
"Inflation Control: Do Central Bankers Have It Right?"
and/or the accompanying slides from a presentation for the Australasian Macroeconomics Society in Canberra, August 2017. The paper gathers together informal stuff I have written on so-called Neo-Fisherism and monetary policy.

Conventional central banking inflation control is typically driven by Phillips curve (PC) theory. Roughly, PC theory says that current inflation increases as the difference between some measure of actual aggregate economic activity and some measure of potential economic activity decreases, and increases as some measure of anticipated inflation increases. I've never seen a central bank policy statement that didn't contain some explicit or implicit reference to the PC. For example, from the Bank of Canada's press release on September 6:
While inflation remains below the 2 per cent target, it has evolved largely as expected in July. There has been a slight increase in both total CPI and the Bank’s core measures of inflation, consistent with the dissipating negative impact of temporary price shocks and the absorption of economic slack. Nonetheless, there remains some excess capacity in Canada’s labour market, and wage and price pressures are still more subdued than historical relationships would suggest, as observed in some other advanced economies.
So, the Bank tells us that inflation is currently below its 2% target, but is expected to come back to target as "excess capacity" goes away - basically a PC mechanism.

In the old days, Lucas developed a theory of the Phillips curve, the upshot being that, as emphasized in the Lucas critique paper, policymakers should not be using observed PC relationships to guide policy, as such relationships are not structural. Indeed, the theory tells us that PC correlations could be positive or negative, and the slope of the PC curve depends on the policy regime in place. In more recent times, PC theory re-emerged in the New Keynesian (NK literature), but if we take NK models seriously, they give us more reasons to doubt the invariance of PC parameters to changes in policy rules (e.g. wage and price setting should change with policy).

In addition to theoretical concerns, the incoming data has not been kind to PC adherents. Lael Brainard, in her September 5 speech to the Economic Club of New York, recognizes this:
...what is troubling is five straight years in which inflation fell short of our target despite a sharp improvement in resource utilization.
If anything, this understates the case. Here's a plot of year-over-year headline PCE inflation vs. the difference between the unemployment rate and the CBO's measure of the natural rate of unemployment:
In the chart, the line connects post-recession quarterly observations, from right to left. That's certainly not tracing out a nice PC. More often than not, inflation and unemployment were actually moving in the same direction. And, in case you're thinking the most recent observations look more promising for the PC, consider the PCE deflator data, in levels:
In this chart, you can see a noticable recent reduction in inflation. Year-over-year, the inflation rate is 1.4%, and the average inflation rate since the beginning of 2017 is about zero. Consistent with what Brainard says, it appears the labor market is unusually tight. The unemployment rate is 4.4%, and the CBO claims that the natural rate of unemployment is 4.7%. If you really believe in PCs, that might make you think. Brainard says this is "troubling," which I guess means that the PC is in trouble, policymakers are in trouble, we are all in trouble, or some convex combination of the three.

As Brainard explains, if one has a PC view of the world, it's going to be hard to understand why inflation is so low. But she's going to give it a try:
In many of the models economists use to analyze inflation, a key feature is "underlying," or trend, inflation, which is believed to anchor the rate of inflation over a fairly long horizon. Underlying inflation can be thought of as the slow-moving trend that exerts a strong pull on wage and price setting and is often viewed as related to some notion of longer-run inflation expectations.
This makes is sound like this "underlying inflation" thing resides in most of the models that macroeconomists work with. While some (most?) undergraduates are taught some version of IS/LM/PC with exogenous inflation expectations, no monetary economist I know tries to analyze inflation in a model with exogenous "underlying or trend" inflation. And that's certainly not a feature of typical NK models, except versions with sticky expectations. But trend inflation is indeed a variable in the Board's FRB/US model, if you have the patience to wade through the documentation. Indeed, essentially everything important in FRB/US (real GDP for example) ultimately reverts to some exogenous trend. Board governors and Board economists have certainly been known to treat FRB/US very seriously, so it's not surprising that Brainard is like-minded.

Do we think inflation expectations have fallen? Perhaps the best we can do is to rely on market-based measures, for example the 10-year breakeven rate (nominal 10-year Treasury yield minus 10-year TIPS yield) looks like this:
The most recent observation is about 1.8%, which is certainly lower than the 2.2%-2.7% we typically observed before the financial crisis, but 1.8% is not all that low. Accounting for the fact that TIPS are indexed to the CPI (rather than the PCE), and adjusting for risk and other factors, this might perhaps translate to an anticipated PCE inflation rate of 1.5% or thereabouts for the next 10 years. If people are actually anticipating 1.5% inflation, that would seem to call for a modest adjustment of some sort in monetary policy, as the clear intent of the Fed is that people should anticipate 2% inflation forever, and be pretty sure about it.

But what sort of policy adjustment are we talking about? Is inflation too low because the Fed has been doing a bad job? Brainard says no. According to her, the problem is that the Fed has been constrained.
[An] explanation may be the greater proximity of the federal funds rate to its effective lower bound due to a lower neutral rate of interest. By constraining the amount of policy space available to offset adverse developments using our more effective conventional tools, the low neutral rate could increase the likely frequency of periods of below-trend inflation. In short, frequent or extended periods of low inflation run the risk of pulling down private-sector inflation expectations.
What's Brainard saying? First, the real rate of return on safe assets is low. For example, here's the fed funds rate minus the 12-month inflation rate - a proxy for what we're interested in:
By this crude measure, the real rate of return on overnight fed funds averaged -1.20% post-recession, and the most recent observation is -0.25%. But Brainard doesn't make reference to the actual real interest rate. She has another animal in mind - the "neutral rate of interest." What's that? Central-bank-speak, basically. Start with a standard Taylor rule, for example,

(1) R = r* + i* + a(i - i*) + b(y - y*).

In equation (1), R is the central bank's nominal interest rate target, r* is the long-run real rate of interest (supposing this is a well-defined object), i* is the central bank's inflation target, y is some measure of aggregate economic activity, and y* is "potential" economic activity (assuming, again, that this is well-defined). According to the Taylor principle, a is a parameter larger than 1, and typically b is a positive parameter. Then, r* + i* is the neutral rate of interest - the central bank's nominal interest rate target when it is achieving all of its goals.

So, given the Fed's inflation target of 2%, if r* is lower, as is consistent with what we can see in the last chart, this means that the neutral rate of interest is also lower. If r* is low, we should observe a low nominal interest rate target, on average, with the Fed responding to random shocks and missing its ultimate inflation and output targets on the low and high sides. But, what's a good estimate of r*? For this we need a model. In standard neoclassical growth models with some sort of appended role for monetary exchange, r* is a constant, and in some models it's endogenous, and dependent on monetary policy, among other things. Certainly, if we want to explain what is going on in the last chart, we can't rely on a theory that implies constant r*.

But whatever is driving r*, (a shortage of safe assets for example), we can certainly agree that r* is low. If it's as low as what we see in the last chart, post-recession, then r* = -1.2%, and the fed funds rate is currently well above where it should be. If r* = 0, say, then the current fed funds rate, at about 1.2%, is only 80 basis points below what Brainard would consider neutral. That's certainly not the way the majority of the FOMC thinks about this problem, as you can see from the last submitted projections. Most committee members think the fed funds rate will be above 2% by the end of 2018, and about 3% in the long run. Of course, the FOMC's actual policy interest rate has come in well below its forecasts for some time, and whether the FOMC now knows its own mind remains to be seen. Thus, if the low inflation readings we have seen this year turn out to be transitory, and the FOMC finds reasons, as it has in the past, to forego interest rate increases, things should be just fine (barring some unforeseen disaster, in which case inflation control is out the window anyway).

But, and this is critical, what should the Fed do if inflation continues on the low side or, alternatively, jumps to the high side of 2%? The views of the FOMC are summarized, for the most part, in this sentence from the last FOMC statement:
The stance of monetary policy remains accommodative, thereby supporting some further strengthening in labor market conditions and a sustained return to 2 percent inflation.
That's basically PC logic. According to the Committee, inflation may be low, but "accommodative" monetary policy will further tighten the labor market and, through a Phillips curve mechanism, make inflation come back to 2%. Why should the Fed continue to raise its nominal interest rate target? According to the Committee, that's preventative medicine. Tightening needs to occur in order to ward off excessive inflation, according to the majority of FOMC members, apparently.

Brainard appears to be disagreeing with that view. According to her, the Phillips curve mechanism is inoperative. But what is she recommending?
If, as many forecasters assume, the current shortfall of inflation from our 2 percent objective indeed proves transitory, further gradual increases in the federal funds rate would be warranted, perhaps along the lines of the median projection from the most recent SEP. But, as I noted earlier, I am concerned that the recent low readings for inflation may be driven by depressed underlying inflation, which would imply a more persistent shortfall in inflation from our objective. In that case, it would be prudent to raise the federal funds rate more gradually.
Basically, Brainard wants to see the inflation before increases in the policy rate occur. If inflation comes up, then she's in agreement with the rest of the committee. If if it doesn't come up, she would rather not have interest rate hikes. But, if the PC is inoperative, how will low nominal interest rates make inflation go up? How do low nominal interest rates cure the problem of "depressed underlying inflation" that she thinks exists?

Brainard suffers from Phillips curve confusion, and so does the rest of the FOMC, though in each case it's a different form of the disease. As I summarize in my recent paper, central bankers generally have inflation control wrong. Mainstream macroeconomic theory tells us that a central bank that raises its nominal interest rate target permanently raises the inflation rate - in the short run and in the long run. These models also tell us that a central banker armed with a Taylor rule and following the Taylor principle inevitably falls into a pit of frustration featuring low nominal interest rates and low inflation. That's in accord with the empirical evidence - with adjustments for factors other than monetary policy that matter for inflation and real interest rates. But central bankers aren't really interested in mainstream macroeconomic theory - for some reason they prefer to be led astray by undergraduate IS/LM/PC models. Why? Beats me.

Monday, June 26, 2017

The 2% Inflation Target

There's been a lot of talk recently about the 2% inflation target, and whether or not it would be a good idea to raise it, or change the nature of the target - to price level or nominal GDP targeting, for example. It's instructive, I think, to use as a starting point the letter addressed to Janet Yellen and the Board, and signed by some of my friends, acquaintances, and people I know of but have never met.

The authors of the letter argue that it's a good time to revisit the Fed's 2% inflation target. In case you haven't been following this, the Fed is a latecomer to inflation targeting. The Reserve Bank of New Zealand appears to have been the first inflation-targeting central bank, followed by the Bank of Canada, the Bank of England, the ECB, the Swedish Riksbank, the Swiss National Bank, and the Bank of Japan (not necessarily in that order, chronologically), among others. There are few deviants from the 2% inflation target, though central banks differ according to the price index they have chosen to measure inflation. The Fed stated its inflation targeting policy in January of 2012, in its "Statement of Longer-Run Goals and Monetary Policy Strategy," most recently amended in January 2016. The amended statement reads:
The inflation rate over the longer run is primarily determined by monetary policy, and hence the Committee has the ability to specify a longer-run goal for inflation. The Committee reaffirms its judgment that 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. Communicating this symmetric inflation goal clearly to the public helps keep longer-term inflation expectations firmly anchored, thereby fostering price stability and moderate long-term interest rates and enhancing the Committee’s ability to promote maximum employment in the face of significant economic disturbances.
Here's the key takeaway from that:

1) 2% inflation is a "longer run" goal, so we should expect to see deviations from 2% inflation in the short run. How long do we have to wait for the longer run? How large are the deviations the FOMC is willing to tolerate? Not specified.
2) The chosen price index that is used by the FOMC to measure inflation is the headline PCE. Not the CPI, the CPI excluding food and energy prices (core CPI), the core PCE, the Dallas trimmed mean index, etc. The headline PCE, dammit.
3) The inflation target is symmetric. The FOMC thus states that it's just as bothered by 3% inflation as by 1% inflation.

What's left out?

1) What's the time horizon? It makes a big difference whether the FOMC is interested in year-over-year inflation (last 12 months), or average inflation over the last 10 years. If it's the former, then past inflation quickly becomes a bygone - no need to make up for a period of low inflation with higher inflation in the future. If it's the latter, then the central bank has to be much more concerned about making up for previous misses.
2) How is the FOMC going to achieve its target? Will it use monetary aggregates as instruments, as in the 1980s or will it use as an instrument an overnight nominal interest rate, as is currently the case? Should there be a large central bank balance sheet or a small-footprint balance sheet? And given the instrument or instruments, which way does the FOMC move each instrument, and how much, in response to deviations in the inflation target?
3) Why 2%? Why not 10%, 0%, -2%, 5%?

The authors of the aforementioned letter first seem to want to argue that it's about time that the Fed's inflation target was revisited - after all it's been 10 years since the onset of the financial crisis. But, as should be clear from the above discussion, the Fed has not been at this game (inflation targeting) for long, and they have actually thought carefully about it as recently as last year (note the amendment to the Statement). Why is the issue so pressing? Is the FOMC missing its inflation target? Let's look:
That's a conventional inflation measure - 12-month headline PCE inflation. Inflation was fairly low in 2015, but from late last year the FOMC has been doing well. Inflation even exceeded the target early this year, and the last observation is 1.7%. To give us a ballpark idea how we might evaluate that performance, consider that the Bank of Canada (inflation targeters since 1991) sets a target range of 1% to 3% (though they look at a whole set of inflation measures). So, by the Bank of Canada's criterion, the FOMC hasn't been out of the 1-3% range very much since the last recession. So, the FOMC's inflation targeting performance, according to the goalposts it set up for itself, has been pretty good over the last 7 or 8 years.

But maybe, in order to accomplish so much on the inflation front, the FOMC has been sacrificing a lot on some other front. What does the FOMC think it is trying to achieve in terms of the second leg of its mandate? Again, back to the Statement of Longer Run Goals:
The maximum level of employment is largely determined by nonmonetary factors that affect the structure and dynamics of the labor market. These factors may change over time and may not be directly measurable. Consequently, it would not be appropriate to specify a fixed goal for employment; rather, the Committee’s policy decisions must be informed by assessments of the maximum level of employment, recognizing that such assessments are necessarily uncertain and subject to revision. The Committee considers a wide range of indicators in making these assessments. Information about Committee participants’ estimates of the longer-run normal rates of output growth and unemployment is published four times per year in the FOMC’s Summary of Economic Projections.
So, to paraphrase, the FOMC is worried about deviations from "normal" unemployment rates and rates of output growth, and cautions that there are forces outside the control of monetary policy that determine what those normal rates are.

So, what's the recent behavior of the unemployment rate? I'll even go one better and use a conventional measure of labor market tightness - the ratio of the number of job openings to the number of unemployed:
Since the BLS has been collecting job vacancy data, the only higher observation than the last one in April 2017 was in January 2001. Currently, what exists is an abnormally tight labor market. Real GDP growth, at about 2% per year since the last recession ended, is historically low, but it's well recognized that this ia due to low productivity growth - a factor outside the Fed's control. Some might argue that the employment/population ratio is abnormally low, or that U6 (including marginally attached workers, and part-time employed wanting full-time work) unemployment is somewhat abnormally high, but again it's hard to argue that's not due to factors (demographics, fiscal policy, skills mismatch) outside of the Fed's control.

Thus, in terms of the FOMC's own criteria, and qualifications to those criteria, there's nothing happening on the maximum employment front that somehow represents a sacrifice incurred in the fight to control inflation.

So what could the letter-writers be complaining about?
In years past, a 2 percent inflation target seemed to give ample leverage with which the Fed could lower real interest rates. But given the evidence that the equilibrium interest rate had fallen substantially even prior to the financial crisis, and that the Fed’s short-term policy rate remained at zero for seven years without sparking any large acceleration of aggregate demand growth, a reassessment of this target seems warranted. Such a reassessment is particularly appropriate when the lack of evidence that moderately higher inflation would harm Americans’ standard of living is juxtaposed with the tremendous evidence that a tighter labor market would improve Americans’ standards of living.
What's that about? First, as is widely recognized by now, real rates of return on safe government debt have been falling for some time, and that's a worldwide phenomenon. Here's a crude, but straightforward, measure of the overnight real interest rate - the nominal fed funds rate minus the PCE inflation rate (as a proxy for anticipated inflation):
I've used quarterly data to provide some smoothing. Even though this real rate measure is crude, I think it's about the best we can do. Some sophisticated measures that people have constructed require taking a stand on the theory, and the measure I've used is agnostic. Note that periods of low real interest rates are not uprecedented, but before the last recession, a low real interest rate tended to be temporary and associated with the tail end of a recession. A period of persistent negative real interest rates in a recovery period, as we've seen since 2009, is indeed unprecedented. The last observation (2017Q1) is -1.3%, and the average since the end of the last recession is -1.2%. Given what we know about the causes of low real rates (high demand and low supply of safe assets, low consumption growth), we have no reason to think that low real interest rates will not persist up to or beyond the time horizon that is relevant for monetary policy decisions. So, our first fact is:

1. The real overnight interest rate is persistently, and unprecedentedly, low. This could change, but there's no good reason to expect it to.

Then, as the letter-writers say, this means that the Fed no longer has "ample leverage" to "lower real interest rates." What could that mean? The Fed's key instrument is a nominal interest rate target. It's well-established that the Fed can lower real interest rates - but only in the short run - if it lowers its nominal interest rate target. So, the letter-writers must mean that, if the real interest rate is low, then with a 2% inflation target you can't lower the nominal interest rate target when you might want to. Why? Because it won't be very high, and there's an effective lower bound on how low the nominal interest rate can go (zero in the US under current rules - though that's subject to some debate). That's just basic Fisherian (or neo-Fisherian) logic, but I don't think I've ever seen an advocate of higher inflation targets say it that way. Something about using the word "Fisher," I guess. Go figure. Second fact:

2. A persistently low real interest rate implies that, to achieve a given inflation target - say 2% - the central bank must on average set its nominal interest rate target lower than was the case in days of yore when the real interest rate was higher.

So, with the current fed funds rate at 1.16%, if we suppose the real interest rate persists at about -1.2%, this should ultimately put inflation above its target, to about 2.4%, by Fisherian logic. In the last tightening cycle, the fed funds rate reached 5.25%, and the target was reduced beginning in September 2007, to essentially zero by the end of 2008. So, if we take seriously the power of monetary policy working through reductions in the nominal interest rate in bad times, then a fed funds rate of 1.16% (or possibly more appropriately 1%) doesn't give the FOMC much room to cut, should things go south. Of course, it's possible that the effects of changes in short-term nominal interest rates on real economic activity are small, even in the short run, and/or the key tool of the central bank in a crisis, for example, is lending to illiquid financial institutions. Unfortunately, as in much of macroeconomics we can't (perhaps surprisingly) say for sure.

But next, in the letter, it's stated: "...[as] the Fed’s short-term policy rate remained at zero for seven years without sparking any large acceleration of aggregate demand growth, a reassessment of this target seems warranted." First, "aggregate demand" is not something we observe - it's an undergraduate theoretical construct which, given its vagueness, shouldn't be bandied about by grownup economists. To be more precise, what the letter-writers have in mind, I think, is a Keynesian world with sticky wages and prices. In such a world "demand deficiency" is defined to be situations in which prices and/or wages are too high relative to efficient levels. So, (i) since the last recession (when the shock hit) is now going on 9 years in the rearview mirror, surely prices and wages have had time to adjust; (ii) the key symptom of "demand deficiency" is slack in the labor market. The chart above shows that the labor market is in fact unusually tight; (iii) I think the letter-writers think that a symptom of slack is inflation lower than the 2% inflation target. Low inflation is actually a symptom of persistently low short-term nominal interest rates. Ask, the Japanese about that (22 years with low interest rates and low inflation, and no sign of a sustained increase in inflation, even after throwing everything but the kitchen sink, i.e. higher nominal interest rates, at the problem), or read this accessible piece, or this one, which summarizes most of the more technical things I've written in blog posts. Basically, mainstream theory and the empirical evidence supports the neo-Fisherian view - that central bankers need to be more cognizant of the Fisher effect. That is, increasing (decreasing) the nominal interest rate makes inflation go up (down), and we can get this effect even in the short run.

The letter-writers recognize, implicitly, that the Fisher effect is important for inflation targeting. In fact, the crux of the argument is that a higher inflation target implies a nominal interest rate that is, on average, higher, implying that there is more room to cut interest rates in a recession. But, the letter-writers don't specify how we get from here to there. Seemingly, what they imagine is that, if the Fed keeps interest rates low, either by foregoing further tightening or even lowering the fed funds target, inflation will eventually take off. Then, supposedly, the Fed can get inflation under control by raising the nominal interest rate sufficiently to its new "normal" level, and we'll be set. If only the world worked that way. Again, persistently low nominal interest rates do not lead to persistently higher inflation, in theory or in practice. The way for a monetary policymaking committee to get around this, in the face of stubborn Phillips curve beliefs, is to raise the specter of incipient inflation - "horrendous inflation is just around the corner, and we have to tighten now to get ahead of the curve." It's not a lie as, by neo-Fisherian logic, it's self-fulfilling. Given the current policy debate, you can see how even that position is an uphill battle.

But, what about the 2% inflation target? Why keep it?

1. Many people have made this point, but it's the key one. The Fed has spent the time since Paul Volcker began his term in 1979 fighting for credibility. The view that the Fed will stick to 2% inflation forever is a strong belief - among financial market participants, economists, and lay people who are paying attention. We can't make a strong case for 2% vs. 4%, say, but we can make a very strong case that messing with the target is extremely dangerous, in terms of the potential for loss of credibility. And credibility is 90% of the game in the central banking business.
2. The Phillips curve model of inflation is basically a discredited theory. The parrot is dead. Admit it and move on. But, until that happens, people are being badly mislead by the dead parrot and its supporters. A central bank run by the letter-writers simply could not generate sustained 2% inflation, let alone anything higher, so they would be better off sticking with a low target, which they would undershoot anyway. The credibility problem again - better to miss by a little than a lot.

I'll leave you with one last chart.
This shows inflation averaged over the last x months, where x is measured on the horizontal axis. So, the time since the end of the last recession is 94 months, and average inflation over that period (again, measured by headline PCE) was about 1.5%. The price of crude oil fell at about 34 months back, and you can see that in the chart. Fed "tightening" began at 16 quarters back, at which time you can see cumulative inflation increasing. Aside from some volatility in the last couple of months (completely normal), that's consistent with a neo-Fisherian view of the world: supposed "tightening" makes inflation go up. It certainly ain't going down.