Statistical Implications of Inflation Targeting

11 The Bank of England’s Approach

Carol Carson, Claudia Dziobek, and Charles Enoch
Published Date:
September 2002
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The Basics of forward-looking market inflation measures are rather straightforward. Imagine that a government issues a very simple bond promising to pay £100 in a certain number of years. Imagine that it also issues another bond that pays off at the same time and pays £100 uplifted by the ratio of the price level when it pays off to the price level now. The relative price of the two bonds in the market will clearly be closely connected to what people think the price level will be when the bonds pay out, relative to now. If the nominal bond is yielding, say, 10 percent in the market, and the real yield on the indexed bond is, say, 3 percent, then there is an inflation rate of around 7 percent that equalizes the return on the two bonds. This is the break-even inflation rate.

Suppose that these two bonds pay off in two years, so that they give a view on the price level in two years. Suppose that the government issues another pair of bonds that pay off in three years, giving a view on the price level in three years. The result is a view on the forward inflation rate, the 12-month inflation rate from two to three years hence. That too can be an interesting number.

In practice the bonds one has to work with are not so neatly arranged. They generally don’t come in convenient pairs. They are not necessarily spread out at helpful intervals along the maturity spectrum. And for the most part they are not bullet bonds, with just one payoff at one point in the future, but coupon bonds that pay a bit of interest each year and then a lump sum at redemption. So the redemption yields that one observes in the market are muddy averages of rates from now to each of the payments due on the bond. Finally, indexed bonds are not perfectly indexed. Because of delays in the collection and publication of price statistics, the indexation of payments refers not to the contemporaneous price level, but to the price level of some previous period. Indeed in the United Kingdom the indexation lag is worse than that—it amounts to some eight months.

So to make the calculations that may be helpful to policymakers, one has to estimate curves. The Bank of England estimates spot yields, the yields that would apply to hypothetical zero-coupon bonds at an interesting range of maturities, including yields that would apply to perfectly indexed bonds. From hypothetical yield curves, given the cash flows of bonds actually trading in the market, one can estimate what the prices of these bonds would be. And the curves are fitted so that the estimated prices are close to the actual bond prices. For any part of the maturity spectrum where one can estimate these curves, the nominal, real, and implied inflation rates between any two points in the future can be worked out. (Figures 11.1 and 11.2 give some recent examples.)

Figure 11.1.United Kingdom: Spot Curves as of February 20, 2002


Source: Bank of England.

Figure 11.2.United Kingdom: Two-Week Forward Curves as of February 20, 2002


Source: Bank of England.

The ways of estimating curves can be important in practice. There are two main methods. One is to fit a curve defined by a relatively small number of parameters. The other is to fit a spline curve, a largish number of small curves that are spliced together in ways that follow certain rules as to the smoothness of the overall curve. Fashions change in these matters; in the author’s working life the Bank of England has moved from parametric curves to splines, back to parametric curves, and then to splines again. So there are no perfect answers here.

Until recently the Bank of England used a version of the parametric curve suggested by Lars Svensson in his 1994 IMF Working Paper (Svensson, 1994). In this approach a handful of parameters describe the yield curve (actually the forward curve). The parameters relate to the level of the curve, an exponential term that gives the overall slope and (in the Svensson case) two possible hump shapes or U-shapes built into the curve. In practice it was clear that the parameters were not very well estimated. The functional form of the curve was set up in a way that implied that the yield curve would asymptote at the long end. This was particularly troublesome because in practice the Bank of England’s curves often do not asymptote at the long end, and one can think of theoretical reasons why that might be so. The Bank estimates curves for every business day. A new set of prices gives a new set of estimated parameters. From day to day the estimates of the parameters shifted about, and so of course did the estimated curves. Quite tiny changes in the underlying data could on occasion generate quite marked changes in the estimated curves. When one is feeding information to policymakers, it is quite a disadvantage if the numbers are moving about as much—or more so—because of the estimation technique as because of developments in the underlying data.

So in the end the Bank of England went back to a spline technique, in which lots of little curves are spliced together to form one smooth curve, with no preconceptions about what general shape it should take. But how smooth should the curve be? Following some work by Waggoner (at the Federal Reserve Bank of Atlanta) on the U.S. market, the Bank allows greater curvature at the short end and requires greater smoothness at the long end of the curve. The idea is that markets may have a more detailed view of likely developments looking a few years ahead, say over a business cycle, but that it is implausible to suppose that they can take a very different view of events 29 years hence as opposed to 30 years hence. Apart from that, the smoothing parameters are chosen to maximize the out-of-sample fit of the curve. “Out-of-sample” has a particular meaning here. What the Bank does is leave each bond out of the sample one at a time and see how well the curve estimated without it “predicts” the price of the bond that has been left out. In practice, it is clear that spline-based curves are much less variable from day to day than the previous parametric curve. Another side benefit of spline methods is that they prevent the Bank from claiming to know more than it does. Once the parameters of a parametric curve have been estimated, it becomes possible to work out forward rates for any period from now to the infinite horizon. A spline curve actually needs some data to work with. If there are no bonds at a particular point in the maturity spectrum, there can be no estimated forward rates either. This enforced honesty is an advantage, even though inconvenient at times.

There are some other topics that should be mentioned. One is that in the United Kingdom one uses bonds indexed to the government’s retail prices index (RPI). This is not the same as the target variable the government has set for monetary policy. That is the RPIX, or the retail prices index less mortgage interest payments, which get built into the housing-cost part of the RPI. Mortgage interest payments in turn are closely related to the policy rate set by the Monetary Policy Committee. So the break-even inflation rates that one derives from market prices are a mixture of a forward look at the target inflation rate and something closely related to the change in the policy instrument. Of course, over long periods of time the average change in the policy instrument is quite small, and looking forward over 10 or 20 years one would not expect differences between RPI and RPIX to matter very much. But looking forward over the next two or three years, as policymakers tend to do, they can matter. (Figures 11.3 and 11.4 show RPI and RPIX inflation and the difference between them.)

Figure 11.3.United Kingdom: Annualized Growth Rates of Retail Prices1


Source: Office for National Statistics.

1 RPI, retail price index; RPIX, retail price index excluding mortgage interest payments.

Figure 11.4.United Kingdom: Year-on-Year Changes of Retail Price Indices and Policy Rate


Sources: Bank of England; and Office for National Statistics.

1RPI, retail price index; RPIX, retail price index excluding mortgage interest payments.

For policy analysis, forward rates are often of most interest. For example, it is forward inflation rates that the Bank’s Monetary Policy Committee plots in the famous fan charts of its Inflation Report. When providing the committee with market-based measures, the Bank staff usually has around 25 nominal bonds to work with and around 10 indexed bonds, spread over a maturity range of 25 or 30 years. It can have reasonable confidence about its estimates of the level of yields. But with that number of bonds it cannot be very confident about the precise slope of the curve, or therefore about the precise level of forward rates.

The Bank’s calculations, as described earlier, depend on finding a future inflation rate that equalizes the expected return from conventional and index-linked bonds. But what if investors are not interested only in expected returns? What if they are concerned with risk? Government bonds are essentially free of credit risk, but not from market risk—the price of bonds can change. And because conventional bonds are more susceptible to inflation shocks, investors may require a higher risk premium to hold conventional bonds. So part of the difference between the yield on conventional bonds and the yield on index-linked bonds may reflect not expected inflation, but an inflation risk premium, an extra reward for holding the riskier asset. This risk premium is not, of course, directly observable. Because inflation has come down over recent years and has stayed close to target, one might hope that the risk premium has come down, so that market-based inflation rates are less contaminated by the risk premium than they might have been in the past. (See Figure 12.4 in Chapter 12 for a comparison of the market-based forward inflation rates with expectations derived from surveys. It shows that they have come closer together, which is at least compatible with a fall in the inflation risk premium.)

Figure 11.5 gives a picture of the implicit 12-month inflation rate 7 years ahead. One can see the impact of the boom of the late 1980s, and also of the subsequent recession, and possibly of membership in the exchange rate mechanism (ERM); then the shock of leaving the ERM in 1992. Expectations stabilize at or above the top of the initial 1 percent to 4 percent target range. Then, in 1997, they drop by 50 basis points on the day the Bank was granted operational independence in monetary policy. Thereafter expectations drift down toward the new 2.5 percent target, and they have been around the target level ever since.

Figure 11.5.United Kingdom: Implied 12-Month Inflation Forward Rate, 7 Years Ahead


Source: Bank of England.

But Figure 11.6 shows that market-based inflation measures do not always behave so well. It again looks at implied inflation rates, but this time 5 and 15 years ahead. There is the same drop on independence day and the same drifting down toward the target. But then shorter-horizon market-based rates go back up to 4 percent, which was quite out of line with expectations taken from surveys. And longer-horizon market-based rates drop to an amazingly low 1 percent. What is happening?

Figure 11.6.United Kingdom: Implied 12-Month Inflation Forward Rates, 5 and 15 Years Ahead


Source: Bank of England.

In the United Kingdom, pension funds are important investors; they hold probably more than half of conventional and index-linked bonds. New pension fund legislation came into effect in 1997 requiring that defined benefit schemes value their nominal pension liabilities using the yield on a 15-year gilt and value their inflation-proofed pension liabilities using the yield on index-linked gilts of five years. Assets were to be marked to market, and the sponsoring employer had to make good any shortfall. This requirement gave funds a regulatory incentive to hold as assets conventional gilts of around 15 years’ maturity, but no incentive to hold index-linked gilts of that maturity in particular. The Bank thinks this additional demand for 15-year gilts had the effect of pulling down nominal yields at that maturity. The difference between nominal and indexed yields was also brought down, and the resulting implied inflation rate was reflecting these regulatory considerations over and above any actual inflation expectations. As the new legislation came under review and it became apparent that it was to be changed, these effects wore off. Clearly the details of this episode are not relevant to other countries, but there is a general message that bond prices can reflect prudential regulation as well as expectations about the macroeconomy.

How does this fit in with the general theme of this volume? Inflation targeting has not made for a complete change in the information considered by policymakers. For example, under monetary targeting they were never content to look at monetary data alone. But there has been a change of emphasis, and market-based measures of future inflation were taken seriously in the United Kingdom only after the introduction of an inflation target. In the United Kingdom, the Bank of England tries to operate the inflation target in a robust way. Clearly, different members of the Monetary Policy Committee have different points of view, so that policy actions are tested against different lines of thought. The Bank staff also tries not just to rely on the main forecasting model, but to offer analysis and forecasts based on a number of different approaches. There is a statistical counterpart to this. All statistics are likely to be imperfect. If policymakers look at a wide range of data, not as they would a checklist but trying to make sense of the whole picture, they are less likely to make mistakes than if they put a lot of weight on, say, monetary relationships and monetary data.

In that context it seems clear that market-based information has a role. The markets are forward looking, as is monetary policy. The markets look at many of the factors that interest policymakers. (But the markets do also consider the future actions of policymakers themselves, which can be a complicating factor.) In interpreting bond yields (or equity prices), one has to bear in mind that markets are concerned with risk as well as central expectations, and that they can be driven by regulation and other micro factors as well as by the macroeconomy. Nevertheless, the fact that market-based measures of future inflation are clustered around the target rate tells something about the credibility of policy. But one should never rely on those measures alone.


I am grateful to my colleague Cedric Scholtes for putting together a compendium of wisdom on this subject (see Chapter 12).

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