Showing posts with label interest rates. Show all posts
Showing posts with label interest rates. Show all posts

Tuesday, April 15, 2014

Interest, to Deficit, to Debt

What drives the federal government's near-term fiscal outlook is, to a surprising extent, interest payments rather than Medicare and Medicaid. They are set to grow faster than mandatory or discretionary spending over the next decade, from 1.3 percent of GDP to 2.6 percent of GDP.

The difference between rising debt over the next decade and keeping debt stable as a percentage of GDP is just one percentage point in the average interest rate on the U.S. public debt.

Paul Krugman has argued recently that the Congressional Budget Office's forecast for interest rates is too high -- and inconsistent with the odds that the economy remains somewhat depressed for some time to come. I figured it would be useful to do some math and test some of the assumptions in the latest CBO forecast.

First, I backed out its forecast for the average interest rate on U.S. public debt -- you can do this by dividing interest payments as a percentage of GDP by debt as a percentage of GDP. What you find is that the CBO expects this rate to reach 4.2 percent by 2024.

Is that reasonable? Well, it's hard to know without having a good sense of how the average interest rate on U.S. public debt behaves. It turns out that you can proxy for it very closely with the 10-year Treasury. I added the forecast line in green. The public debt interest rate in blue is estimated by taking the annual federal expenditure on interest payments and dividing it by the stock of total public debt.

That doesn't seem to be an impossible path for the average interest rate on public debt. In fact, we can use the 20-year Treasury and the 10-year Treasury to back out the 10-year, 10-year-forward rate -- the expected interest rate on the 10-year Treasury note in 2024. Given a current 10-year rate of 2.63 percent and a current 20-year rate of 3.35 percent, the 10, 10 forward rate is 4.08 percent.

But what if you assume that the interest rate will be 3 percent rather than 4.2 percent? How does the debt outlook change? Well, at that rate, debt stays constant for the next decade as a share of GDP, given the CBO's forecast for primary balance (the deficit ex-interest). Here's the graph comparing the two assumptions for the interest rate:

And here's the graph showing how this change in interest rates has a big impact on the near-term outlook for the federal debt:

I'm not making any claim that three percent is the correct assumption for the interest rate. In fact, I've presented some evidence as to why four percent is closer to market expectations. But it's always interesting to see how sensitive debt forecasts are to small changes in parameters like the interest rate. I guess this does illustrate Carmen Reinhart's view that highly-indebted governments almost always turn to financial repression.

Wednesday, July 17, 2013

Interest Rates: A Quick Update

As requested by David Beckworth, this is an update of my analysis on June 26. The red section of the graph indicates the new data since the original analysis. Wow. We live in interesting times.

For unfamiliar readers, I should note that the 10-year yield, as well as the yield curve across maturities, is about flat since June 26, but equity prices have recovered to levels seen prior to the jump in yields.

The marginal daily datapoint continues to indicate that rising rates are less a sign of an improving economy as opposed to a tighter monetary policy than 90 days ago, at the beginning of the sample interval. The last few weeks' worth of of data appears to be strongly negative in terms of the rate-equity association. We're about to cross zero any day now -- which roughly means that, over the past 90 days, monetary tightening has been as important to rates as has been macroeconomic strengthening. Since the tightening isn't 90 days old, that's pretty striking.

I've re-posted below a comment I just left on Scott Sumner's blog. It explains how I'm thinking about the market response to ongoing developments in forward guidance and clarification of the monetary-policy exit strategy.
I would have said with very high confidence that the major cause of the rise in Treasury yields was a change in future monetary policy. I think the last week forces me to revise down that confidence, even if it is still high. My sense is that the Fed has clarified one thing, and the market’s mind has changed on another: (1) the Fed will be conditional, and markets feared at first it wouldn’t, and conditionality improves the mean forecast by containing downside risks, (2) the market may have reassessed the sensitivity of NGDP growth to interest rate changes (or monetary policy changes) in the relevant range. I find (1) and (2) a much more persuasive story of why rates could stay high and equity prices could revive than anything else out there.

I’m still openminded on these questions. I don’t see myself as advocating for a particular point of view. I just saw a lot of writers who I respect getting way too cavalier last month about the changes in expected future interest rates. I’m excited for monetary policy to normalize — but, like you, I don’t see the super strong evidence (as much as I’d like to!) that the economy is suddenly stronger.As always, please leave a comment or send me an email if you have a better explanation or can poke a hole in mine. 
As always, please leave a comment or send me an email if you have a better explanation or can poke a hole in mine.

Note: It appears that my red line begins a little late, if you look at the original post.

Friday, June 21, 2013

Why Interest Rates Are Rising

There are two theories of why interest rates are rising. In the first, they are rising because of an improved economic outlook, which leads investors to anticipate a swifter exit for monetary policy. In the second, they are rising because of a change in investor expectations of the monetary exit, independent of economic conditions.

Fortunately, statistics has a way of answering these questions: correlation. (Or at least, helping us answer these questions.) I downloaded the daily time series data of the 10-year Treasury note yield and the S&P 500 stock index from June 2008 through the present. If on days that rates are rising, the stock index also rises, then we can assume that both are driven by changes in the economic outlook. If on days that rates are rising, the stock index is falling, then the "economic outlook" story doesn't hold up -- and a "monetary policy" story fits.

I calculated the 90-day correlation coefficient of their daily percentage changes. I find that it has been plummeting since May, which is when interest rates began to jump. See how it's falling off a cliff at the right end of the chart? That means the first story ("happy days are here again") is wrong, and the second story ("the Fed is tightening") is right. Here's the graph.

Oh, and if you're curious, the correlation coefficient is now near the lows of 2009 and 2010. Both of those times were major monetary easings, so rates were falling as stock prices were rising. You might also observe that though the first two big rallies in stocks were amid low correlation coefficients -- i.e. they were Fed-driven -- rallies since the start of 2012 have occurred amid relatively high correlation coefficients. On days that stocks have been doing well, in other words, rates have been rising.

Here's my editorial comment: If the Fed doesn't intend for all of its talk since the start of May to be perceived as pushing forward the schedule for monetary tightening, independent of the economic recovery, it needs to start clarifying its intentions. Now.

Tuesday, November 13, 2012

Fearing the Bond Viligantes

Paul Krugman posted on his blog an interesting write-up of a model which proposes that an "attack" by what he has called the "invisible bond vigilantes" is expansionary. In other words, an increase in the lending premium on sovereign debts should increase aggregate demand and thereby real GDP.

Krugman's mechanism makes a great deal of sense: (1) the increase in the risk premium generates depreciation of the currency for all domestic interest rates; (2) the lower exchange rate of the dollar causes an increase in net exports; and (3) thus we have a shifting to the left of the IS curve in the IS-LM model for all interest rates.

I agree with Krugman on several points, but in this post I want to propose a simple model which might make the best form of the counter-argument -- i.e. that such an increase in the risk premium would be contractionary. I also note a few areas in which his model and also my own make some assumptions which I, well, wouldn't bet very much on at all.

(Nick Rowe also has some brief comments on Krugman's model here, and so do Tyler Cowen, Brad deLong, David Beckworth and Scott Sumner.)

Let me first note the general areas of agreement. It's pretty obvious that a country with a floating exchange rate and an independent currency (like the U.S. or U.K.) is in a totally different situation than a country without either (like Greece or Spain) insofar as debt can create default risk. I also agree with some key components of the model -- you'll see me re-use much of his framework in a moment -- and with the insight that an increase in the risk premium should generate higher net exports and thereby, cet. par., higher real GDP in the short run.

But here's how I thought about this. In terms of intuition, an increase in the risk premium is a supply shock. A central bank which follows some sort of rule regarding price stability should be somewhat constrained as to how much devaluation they can allow. From this, one can reason that the sign on the effect to real GDP should always be negative, given that the central bank will split the impact between a decline in real GDP and an increase in the price level according to its preferences.

And that's what one sees come through in this little model.

First, start with the linearized demand function y = -ar + be, where r is the real interest rate, e is the nominal exchange rate in terms of the price of foreign currency, and a and b are constants. Note the signs of the terms mean that an increase in the real interest rate decreases real GDP and an increase in exchange rate increases real GDP -- i.e. when foreign currency is more valuable, our net exports increase.

Second, assume a real domestic interest rate determined by r = r* + p, where r* is the real risk-free rate of return and p is the risk premium. An increase in the risk premium increases the interest rate.

Third, assume that purchasing power parity (PPP) holds to some reasonable extent in some reasonably short time frame. That is to say, an identical tradable goods and services should cost roughly the same whether I'm buying them in dollars, yen, etc. We can write this out as P = ePf, where P is the domestic price level, e is (again) the exchange rate, and Pf is the foreign price level.

Fourth, assume some monetary policy rule. Here are three which I think characterize the broad swath of options, which I proceed to consider individually.

(1) price-level targeting: P = P*
(2) NGDP targeting: Py = N
(3) a Taylor-type rule: P + Ty = k, T > 0

To consider (1) with the assumptions explained above:

e = P* / Pf

y = -a(r* + p) + b(P* / Pf)

∂y/∂p = -a.

This means that real GDP will fall in response to an increase in the risk premium, due to its effect on real domestic investment, when the central bank is targeting the price level. (This should also be the response of an inflation-targeting central bank.) The strength of this effect will depend on the "a" parameter, which is the responsiveness of domestic investment to changes in the real interest rate.

To consider (2):

Again, this means that real GDP will fall, though less than under the previous monetary policy specification, due to the supply shock's effect on domestic investment.

To consider (3),

This finding should make a lot of sense. If T = 0, then there is no weight on output stabilization, and the Taylor-type rule becomes a price-level rule. As T rises, the effect on output is dampened -- though, naturally, by progressively larger increases in the price level.

Making some small and I believe acceptable assumptions -- the aggregate demand function, the determination of an interest rate, a soft PPP, and a monetary policy rule -- we see that an increase in the risk premium is likely contractionary. The intensity of the contraction, furthermore, depends on the willingness of the central bank to accept large increases in the price level to cushion output in the short run.

The major differences with Krugman's model in terms of structure are as follows. First, I assume that domestic investment will feel the sovereign's risk premium. My understanding is that this is consistent with the actual operation of debt markets; the debt of large companies will be knocked down in terms of credit rating when the sovereign's credit rating falls. Second, there are some important real-nominal distinctions in my model versus his; it's not clear why an independent central bank would tolerate the inflation Krugman's model builds in but never directly addresses. I think these explain the opposite findings.

Three further notes. First, I think the assumption of a fixed risk-free rate i* in the context of a run on US sovereign debt is highly strained, for the same reason that the small open economy model is not the same as the large open economy model. Second, when the risk premium rises, the increase in the real interest rate is likely not to capture the full effect on domestic investment -- there are other mechanisms, most importantly tighter lending standards, which will cause an even larger decrease in investment. Third, in the context of an increase in the risk premium on U.S. debt, the U.S. dollar is -- by our experience in the last recession -- likely to appreciate, unless global debt markets are sufficiently strong to withstand a global risk-off. Heavy capital flows into U.S. Treasuries will prevent devaluation for the time period Krugman's model expects an expansionary effect. It is worth noting that all three reasons suggest that an increase in the risk premium is likely to result in a decrease of real GDP in excess of what is predicted by my model.

Correction: I originally had "e" marked as the real exchange rate. It should have been the nominal exchange rate.

Saturday, June 2, 2012

What Volcker Did

I've been thinking a little bit about the interest rate targeting approach to monetary policy for which New Keynesians like John Taylor and Greg Mankiw advocate -- Taylor had an op-ed in the Wall Street Journal on Thursday which somehow led me to do some serious work on this.

In particular, I've been thinking about the inadequacies of such an approach, which strike me as awfully baked into the cake. If you're targeting the instrument to achieve a result, then you've introduced an intermediate item which is distracting if not misleading -- a sort of "monetary parallax" which distorts the field of vision of the central bank.

In the late 70s, this parallax effect confused the Burns and Miller Feds about the appropriate level of the fed funds rate given high inflation and nominal GDP growth, because such nominal interest rates seemed unreasonable even when real rates were below zero. In the productivity boom of 90s, the Greenspan Fed consistently feared that such real growth and unemployment below the "natural rate" would inevitably induce inflation and often considered rate hikes. Today, the Bernanke Fed is stuck with this parallax problem, struggling to see beyond the zero federal funds rate to the fall-off from the old NGDP path.

And I've been mulling over the Volcker Fed, which is credited, rightly so I think, for bringing about disinflation in the United States. I think Volcker succeeded because he saw beyond short-term interest rates -- he saw monetary growth and longer-term Fed behavior as critical. He avoided the parallax problem.

Allan Meltzer writes in  A History of the Federal Reserve that:
Paul Volcker's major contribution stands out. Unlike 1966, 1969, 1973, and other times, he persisted in an anti-inflation policy long enough to bring the inflation rate down permanently.
Greg Mankiw, in fact, has a version of the Taylor rule, which estimates the federal funds rate based on core inflation and the unemployment rate. It breaks several times, depending on your fitting parameters, and these breaks actually tell us a lot. (Moreover, that is a flaw with Mankiw's version of the rule, in that it's not clear what years you are supposed to sample from.)

Toying with Mankiw's model, we can see why Volcker's efforts succeeded where those before him had failed.

It wasn't because he raised interest rates up high in '79 and '80; it was because he kept them there in '83, '84, '85, and for the remainder of his term as chairman. That runs directly contrary to the Mankiw model's recommendation, which calls for a massive cut of the federal funds rate in the early 80s, even into the negative nominal territory -- impossible, I know -- but such cuts would have likely meant that the U.S. did not reduce inflation expectations as it did under Volcker.

Below is a graph of the nominal federal funds rate since '68, versus what one might call the "structural federal funds rate." To calculate it, you derive the Mankiw rule from the last ten years of data on core inflation, unemployment, and the federal funds rate, and then plug in an environment of 2 percent inflation and 5 percent unemployment (that is, a Mankiw indicator of -3).What you see is the signature of the Volcker disinflation: a massive and prolonged increase in the structural federal funds rate, which began in '82 lasted all the way into '94, when slow disinflation stopped and the Fed established its then de facto target of 2 percent inflation.

The change was massive. Until 1982, my measure of the structural federal funds rate floats around 4 percent, which sounds like a reasonable estimate of where the Fed would want the fed funds rate to be. Then comes Volcker. The structural fed funds rate goes to approximately 8 percent; Volcker committed to disinflation by keeping rates far higher even as inflation fell and unemployment rose. After 1994, the structural federal funds rate returned to 4 percent, until recently -- and correctly in my view, the Bernanke Fed has kept the structural federal funds rate at around 3 percent to support demand. (It's the reverse Volcker situation today.)

Notice how little the structural federal funds rate is correlated with the actual federal funds rate. Volcker's genius lies in, and his results came from, the decision to keep the federal funds rate high. The structural federal funds rate didn't budge in '79 or '80, which is why inflation did not descend like it did in '82. The increase in the structural federal funds rate in '82 is what produced the disinflation.

This is why it's hard to read interest rates as a sign of tight or loose monetary policy -- you've got to do the reading in the macroeconomic context. Using the Mankiw indicator to work backwards and find the structural rate shows how Volcker succeeded, and perhaps the path forward for resuscitating aggregate demand today.

Mysteries of Monetary Policy

I've been sitting on this post for a while, hoping that I could come up with an adequate explanation for this -- the movement of the federal funds rate within its quarter-percent to zero range, which has been established since the start of 2009.

Perhaps it is merely the by-product of the Fed's QE programs and Operation Twist, but it sure is interesting to try to see if there's something more systematic going on here, given that the Federal Reserve Bank of New York manages the rate within the range by trading from the System Open Market Account. Could it be that the Fed is signaling an easing-tightening bias?

I really have no idea, and given the fact that this is the first time the fed funds rate has been a range, the conduct going on within the range is interesting and worth asking about, worth bringing up. It is so easy to assume the fed funds rate away as somewhere inside the range, but this movement near zero is puzzling.

The only data that looks remotely related is quarterly real GDP growth, mainly because of the rise in 2010 and slowdown in 2011. Inflation doesn't fit the story, nor do equity prices. It doesn't appear to be random, although I suppose it could be a random walk. That seems unlikely, given the behavior of the data set and the involvement of the NY Fed.

Any ideas?

Wednesday, April 11, 2012

With Interest

Does NGDP targeting require interest rate volatility?

So I've been doing some serious thinking and research over the last few days into the variant-target monetary policies I wrote about in mid-March (see here, here, and here if you're a new reader of the blog).

I'd been interested, most critically, in what economists call the "loss function" of the central bank, with variance in real output growth and inflation from their trend rates representing relevant losses. One could look at the empirical data, I reasoned, and determine how the central bank assigned relative weights to inflation and real-output deviations.

My understanding has changed a little bit as I've gone forward, namely I've recognized that interest rate variability, since it would compromise the efficiency of investment allocation and capital markets, has costs, although I think it's pretty clear that it should be substantially lower weighted than, say, inflation or real output deviations.

I'll post more about my research (and hopefully get some suggestions and feedback) tomorrow, but I'll pose to you one of the questions with which I've been wrestling: if the central bank pursues NGDP level targeting, using futures markets and expectations, would you expect that to lead to more or less interest rate volatility?

There is, of course, a rather clear argument that it will lead to more. Since it entirely ignores the policy instrument -- unlike a Taylor rule, importantly, in this respect -- an NGDP target may send instrument measures all over the place as it aims to hit a target. One might argue that we saw this happen from 1978 through the early 1980s, when the Humphrey-Hawkins Act required the Fed to hit money supply growth targets.

Then I considered the counter-argument. An NGDP target better manages expectations for nominal growth, which should stabilize interest rates and prevent the need for sudden rate cuts due to nominal shocks. That would imply that an NGDP target would outperform discretionary policies and flexible inflation targets which assign lesser weights to real output.

And indeed, I found that it is the latter thesis which is supported by the data. Above, I've graphed the short-term interest rates in the United States, the United Kingdom, Australia, and Canada. I consider Australia an NGDP targeter this entire time span.  Also, I think it's fair to say that the UK maintained a de facto NGDP target up until 2008, at which point it assigned a substantially higher weight to inflation -- I've shown this in the past. Canada is more of a flexible inflation targeter, and the US is purely discretionary, but with the strongest weight on inflation.

The order I've just listed the countries -- Australia, the UK, Canada, and last the US -- is also the order, not coincidentally, from least to most interest rate volatility. It's clear that because NGDP targeting does a better job managing aggregate demand, that the outcomes for interest rate stability are far superior to the results of flexible inflation targeting or discretionary policies.

Oh, just a small note: the Australia data series is actually the RBA's discount rate, since FRED seems to be missing large chunks of the time series, but I looked at both data sets, and the discount rate seems to be a close-enough proxy.

Sunday, April 8, 2012

Below Zero

The Fed, the zero lower bound, and negative nominal interest rates?

Manuel Montori, like me a student at P.E.A very interested in economics, joins us as a guest blogger. (He was on the victorious YUEA team.) He's giving blogging a try, and if it works out, this blog may relocate in a month or so to another name, where he and I are both writers. We won't always agree, of course, but I see that many of the best econblogs are team efforts, with a handful of authors. More information if and when that time comes.

An interesting idea:

Some alternate Taylor rules (e.g., Mankiw & Krugman's) suggest that interest rates should still be substantially negative, but typically we say that the Federal Reserve faces a zero lower-bound on nominal interest rates. This comes out of a basic arbitrage argument. Since cash has a 0% nominal interest rate, lenders have no reason to ever dip below that rate.

Of course we can have negative real interest rates, but that implies inflation, and what central bank wants to promise high inflation and risk having an inflationary spiral on its hands? Certainly not the Fed. For a policy like this to work, management of inflation expectations would have to be spot-on. (One option here is price-level targeting, which also has quite a bit of potential).

Let's rewind. We've said that lenders have no reason to dip below zero and that is that, but there is one lender willing to go below zero: the Fed. Now it's likely the Fed would only pay a very slightly negative interest rate at first—maybe 25 basis points. The concept is simple: through some avenue, you borrow money from the Fed, and the Fed pays you to take this money and do with it what you will. More people take on the kinds of investment projects we need to boost our economy out of the post-recessionary blues, and everybody wins.

Is this a reasonable plan? There's some concerns, and managing them well would be important to avoid a fiasco: the arbitrage logic here is reversed: who wouldn't borrow when they're being paid to do so? You don't even have to do anything with the money, just hold it and make a tidy sum when it comes time to repay. If this happened on a large scale, the point of negative interest rates—to get people to invest that money—would fail.

An alternative is for the Fed to channel banks, and this seems more reasonable to me (though it's not perfect). In this case, the Fed would pay banks some sum of money for every dollar they lend, or maybe just for every dollar of excess reserves they pay. We can see a similar story arise here, where banks basically say, we'll lend you this money because it's going to make us more money than letting it sit, but don't go out and do anything crazy with it. That would be a risk-minimizing instead of a profit-maximizing situation, and people seeking to undergo large investment projects lose out again. But at least in this scenario, the Fed can exercise influence over banks and ensure their money is being used to lend to the kinds of lenders they want.

As a side note, this policy essentially enables the Federal Reserve to conduct fiscal policy, or at least a weird amalgam of fiscal and monetary policy. Our arbitrage logic suggests that if the Fed didn't regulate strictly who received the money involved in the negative nominal interest rate program, (almost) everyone would borrow money and pay back a slightly smaller sum. As long as the amount of money an individual could borrow was in some way capped, this essentially amounts to a subsidy. Individuals who choose to partake in the program are practically being handed the difference between what they borrowed and what they have to pay back.

Seems like a useful tool for a severe, liquidity trap recession with an uncooperative Congress. We're lucky nothing like that would ever happen in the real world.

Friday, March 30, 2012

Investment Starvation

The case for aggressive monetary policy now

The Austrians, my understanding is, like to talk about the need for savings to precede investment, and that we haven't recovered because we haven't worn our hair shirts saved for long enough, or we haven't repented for our sins liquidated our malinvestments.

I really wish they would learn to look at data.

The fact is, we've got a historically large private sector financial surplus as a percentage of gross domestic product -- all this gross private saving amid a shortage of gross private investment. 5.7 percent! It makes me want to tear my hair out in frustration sometimes, as this is what countercyclical monetary policy was created to correct.

We know that the level of savings is not sensitive to interest rates in the short run, due to income and substitution effects which run in opposite directions and cancel each other out. But investment is highly sensitive to real interest rates, yet as a component of GDP, private investment continues to lag well behind the rest of the recovery.

We're starving this recovery of private investment -- and, whether the Federal Reserve knows it or not, choosing to do so -- which is a simply terrible idea. Unlike Paul Krugman, who used our massive private financial surplus to argue for more government investment, I don't think that's the right way forward. First, I'm not as comfortable with the idea that there is no effective distinction between private and public investment. It was one of Keynes' fundamental policy recommendations that government socialize investment (I'm reading The General Theory), and it's one I don't think makes a lot of sense outside of the model, to put it baldly.

Roads and schools are important, but so are factories and offices. In public and private investment, neither one fully replaces the other. Yes, I would concede to Krugman that we've shortchanged ourselves to some extent on the former and would benefit from more state and local investment, but that won't come even close to making up for all of the investment we need. This is by in large a private-sector problem.

Nondefense public investment has consistently made up 2.5 percent of GDP. The gap we need to fill is more than twice that size, and I am not confident that this is a matter fiscal policy can solve, given the stimulus didn't push nondefense public investment above even 3 percent.

Most of the gross private saving is in corporate hands, and the surest way to incentivize investment, and to get this market to clear out the massive financial surplus, is to make investment cheaper by further depressing real interest rates.