PrefBlog

Assiduous Readers will know I often use the Interesting External Papers section of PrefBlog as my notepad when reviewing the literature for my own purposes. And that is exactly what this post is … not so much for readers’ information, but for mine, when I want to find this stuff again!

The Bank of Canada Review of Spring 2003 contained an essay by David Longworth, Deputy Governor and life-time employee of the Bank, titled Inflation Targeting and Medium Term Planning: Some Simple Rules of Thumb:

Real long-term bond rates typically average slightly above long-term real growth rates.

Footnote: This has tended to be the case in Canada over the last 20 years. Economic theory would suggest that the real rate of return on capital would exceed the real growth rate of the economy. As long as the risk premium on private capital relative to government bonds is not too large, we would also expect that the real yield on government bonds would be slightly higher than the real growth of the economy. All this is strictly true only in a closed economy. In a small open economy, this real interest rate would reflect the world real interest rate, which in turn would reflect the real growth rate of the world economy.

The Congressional Budget Office has published its December 2007 Background Paper: How CBO Projects the Real Rate of Interest on 10-Year Treasury Notes:

This background paper summarizes CBO’s methods for calculating the natural rate of interest and applying it in projections of the real and nominal interest rates on 10-year Treasury notes.

Estimating the natural rate of interest, either over history or for projections, is a two-step procedure. First, CBO estimates the real return on capital (adjusted for taxes on profits). That estimate is based on the agency’s view of the economy’s physical production process—how capital and labor are used to produce output and generate complementary income payments to capital and labor. Because all output simultaneously generates income, data from either the income side or the product (output) side of the national income and product accounts (NIPAs), compiled by the Bureau of Economic Analysis, can be used. Second, CBO estimates an adjustment for the risk in actually realizing the return on capital. Because part of the return on capital is compensation for the risk that some firms will default and inflict losses on investors, an estimate of the real rate based on income payments from capital is higher than the natural rate. Therefore, that risk premium must be removed to yield an estimate of the natural rate. That rate is comparable to the real rate on 10-year Treasury notes, which is also free of default risk. In particular, the risk premium is based on a weighted average of separate estimates of the risk of holding equity and debt claims on capital; it also includes an adjustment for the different tax treatment of profits and interest payments generated by businesses.

Over the next 10 years, CBO projects, the natural rate of interest will decline slightly, from an estimated level of about 3.6 percent in 2006 to about 3 percent. That decline stems from a projected decline in the return on capital, much of which reflects a projected slowdown in the growth of the labor force.

CBO uses two complementary approaches for estimating the return on capital, one from the income side and the other from the product, or production, side.1 The income-based approach measures the rate of return on capital as the ratio of capital income to the capital stock. Its construction has the advantage of being independent of assumptions about production relationships or determinations of whether the economy is in or out of equilibrium. It provides a relatively smooth estimate of the return on capital over the historical and projection periods.
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The income-side measure is estimated as the ratio of capital income to the capital stock (see Figure 2). Capital income is a domestic private-sector concept estimated as the sum of domestic corporate profits, people’s rental income, 35 percent of proprietors’ income, and interest paid by domestic businesses, using data from the NIPAs2,3 The private-sector capital stock, valued at the prices of newly produced investment goods, consists of businesses’ plant (that is, facilities) and equipment, software, inventories, housing, and land—all valued at current market prices.

The income-side measure of the return on capital has both cyclical and trend components. From 1960 to 1970 and from 1991 to 2001, the return rose during the recoveries from recessions and peaked during the expansions, before falling as the expansions matured. Across business cycles, the return has exhibited extended periods in which the underlying trend was falling (as from 1960 to 1980) and then rising (from 1980 to the late 1990s).
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The estimate of the natural rate of interest is obtained by adjusting the real return on capital (in this instance, the income-side measure) for both tax effects and the combined risk premium (see Figure 7).

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Thomas Laubach & John C. Williams, Measuring the Natural Rate of Interest:

A key variable for the conduct of monetary policy is the natural rate of interest – the real interest rate consistent with output equaling potential and stable inflation. Economic theory implies that the natural rate of interest varies over time and depends on the trend growth rate of output. In this paper we apply the Kalman filter to jointly estimate the natural rate of interest, potential output, and the trend growth rate, and examine the empirical relationship between these estimated unobserved series. We find substantial variation in the natural rate of interest over the past four decades in the United States. Our natural rate estimates vary about one-for-one with changes in the trend growth rate. We show that policymakers’ mismeasurement of the natural rate of interest can cause a significant deterioration in macroeconomic stabilization.

FRBSF Economic Letter, 2003-10-31:

Importantly, the natural rate of interest can change, because highly persistent changes in aggregate supply and demand can shift the lines. For example, in a recent paper, Laubach (2003) finds that increases in long-run projections of federal government budget deficits are related to increases in expected long-term real interest rates; in Figure 1, an increase in long-run projected budget deficits would be represented by a rightward shift in the IS curve and a higher natural rate. In addition, economic theory suggests that when the trend growth rate of potential GDP rises, so does the natural rate of interest (see Laubach and Williams (2003) for supporting evidence).

Econbrowser‘s Menzie Chinn wrote a recent post asking everybody to take a deep breath and calm down a little about inflation, titled High Anxiety (about Interest and Inflation Rates):

Of course, the United States in 2009 is different than Japan in 2001. One key difference is that Japan was, and remains, a net creditor. America is a big net debtor to the rest of the world, with extremely large holdings of US Treasurys by foreign private and state actors. And so, for me, I worry more about higher real interest rates (portfolio balance effects) than higher inflation. But even here, real yields according to TIPS seems fairly low in historical perspective (and roughly comparable to those prevailing during the period characterized as “the saving glut”).

My bottom line: Think, and recollect, before panicking.

In the post, he referenced a paper by Stefania D’Amico, Don H. Kim and Min Wei (all of the Fed’s Division of Monetary Affairs), Tips from TIPS: The Informational Content of Treasury Inflation-Protected Security Prices:

We examine the informational content of TIPS yields from the viewpoint of a general 3-factor no-arbitrage term structure model of inflation and interest rates. Our empirical results indicate that TIPS yields contained a “liquidity premium” that was until recently quite large (~ 1%). Key features of this premium are difficult to account for in a rational pricing framework, suggesting that TIPS may not have been priced efficiently in its early years. Besides the liquidity premium, a time-varying inflation risk premium complicates the interpretation of the TIPS breakeven inflation rate (the difference between the nominal and TIPS yields). Nonetheless, high-frequency variation in the TIPS breakeven rates is similar to the variation in inflation expectations implied by the model, lending support to the view that TIPS breakeven inflation rates are a useful proxy for inflation expectations.

This paper was cited by Grishenko & Huang (which has been discussed on PrefBlog), who emphasize:

In a related study, the long-run averages of inflation risk premium in D’Amico, Kim, and Wei (2006) can be positive or negative depending on the different series that they use to fit the three-factor term-structure model.

Footnote: See Figures 4 through 6 in their paper.

Back to D’Amico et al.:

Specifically, we model the dynamics of nominal yields, inflation, and TIPS yields in a general no-arbitrage term structure model setting, and examine the extent to which these data are consistent with each other. Furthermore, we seek to establish some basic facts about the real term structure and the inflation risk premia implicit in nominal bond yields and to obtain an estimate of the “liquidity premium” in TIPS yields.
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Our main results can be summarized as follows. In all the cases that we have examined, estimating the model taking TIPS yields at their face value fails to produce plausible estimates of inflation expectations or inflation risk premia. The difference between the observed TIPS yields and the model-implied real yields estimated without TIPS data indicates that the “liquidity premium” was quite large in the early years of TIPS’s existence, but has become smaller recently. This liquidity premium turns out to be difficult to account for within a simple rational pricing framework, suggesting that TIPS may not have been priced efficiently in their early years. Nonetheless, time variation in TIPS-based and model-implied breakeven rates are quite similar, suggesting that changes in the TIPS breakeven rates largely reflects changes in inflation expectations or in the investors’ attitude toward inflation risks, rather than being random movements.

They conclude:

The answer to the question of whether the TIPS breakeven rate can be taken as inflation expectation is more complicated. We find that the weekly changes in the model-implied 10-year inflation expectation tend to line up with the weekly changes in the 10-year TIPS breakeven rate. However, we also find that time variation in the inflation risk premium and the TIPS liquidity premium, the latter of which may also include other unaccounted-for effects, are often significant enough to drive a wedge between the qualitative behavior of the breakeven rates and inflation expectations. Our findings in this paper provide support for the use of TIPS breakeven rate information as a proxy for inflation expectations, but also provide a justification for caution. Indeed, in speeches that touch on inflation, policy makers often refer to the TIPS breakeven rate, but they also recognize that the interpretation of this measure is complicated by inflation risk premia and liquidity issues and then continue to monitor a large number of variables to gauge inflation expectations and underlying inflation pressures. More data and more work on TIPS modeling in the future will ndoubtedly shed more light on the informational content of TIPS prices.

The Anginer and Yıldızhan paper recently discussed on PrefBlog that attempted to corellate credit spreads with equity returns referenced a paper by Jing-zhi Huang and Ming Huang titled How Much of Corporate-Treasury Yield Spread is Due to Credit Risk?: A New Calibration, presented at the 14th Annual Conference on Financial Economics and Accounting:

No consensus has yet emerged from the existing credit risk literature on how much of the observed corporate-Treasury yield spreads can be explained by credit risk. In this paper, we propose a new calibration approach based on historical default data and show that one can indeed obtain consistent estimate of the credit spread across many different economic considerations within the structural framework of credit risk valuation. We find that credit risk accounts for only a small fraction of the observed corporate-Treasury yield spreads for investment grade bonds of all maturities, with the fraction smaller for bonds of shorter maturities; and that it accounts for a much higher fraction of yield spreads for junk bonds. We obtain these results by calibrating each of the models – both existing and new ones – to be consistent with data on historical default loss experience. Different structural models, which in theory can still generate a very large range of credit spreads, are shown to predict fairly similar credit spreads under empirically reasonable parameter choices, resulting in the robustness of our conclusion.

They note:

One common finding from these studies is that the average historical default loss rate for corporate bonds is typically much smaller than the observed corporate-Treasury yield spreads, and is only a small fraction of the yield spreads for investment-grade bonds. Figure 1 provides a visual summary of this finding.

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They point out:

This fact alone, however, should not lead one to automatically conclude that credit risk accounts for only a small fraction of the observed yield spreads for investment grade bonds. After all, the expected default loss rate is only part of the (promised) credit yield spread; the other part is the credit risk premium, defined as the difference between the expected realized return of a defaultable bond and that of a comparable Treasury bond. The credit risk premium is required by investors because the uncertainty of default loss should be systematic—bondholders are more likely to suffer default losses in bad states of the economy. Moreover, precisely because of the tendency for default events to cluster in the worst states of the economy, the credit risk premium can be potentially very large. In fact, some of the models considered in this paper can indeed generate credit risk premia that are large enough to explain the difference between the observed corporate yield spreads and historical default loss rate, provided that certain parameter choices are made. The key question, however, is whether any model can generate such large credit risk premia under empirically reasonable parameter choices. This question is the main focus of our paper.

They conclude:

We conclude that, for investment grade bonds (those with a credit rating not lower than Baa) of all maturities, credit risk accounts for only a small fraction—typically around 20%, and, for Baa-rated bonds, in the 30% range—of the observed corporate-Treasury yield spreads, and it accounts for a smaller fraction of the observed spreads for bonds of shorter maturities. For junk bonds, however, credit risk accounts for a much larger fraction of the observed corporate-Treasury yield spreads.