Statistical Implications of Inflation Targeting
Chapter

18 Usefulness of Private Inflation Forecasts in Inflation Targeting

Author(s):
Carol Carson, Claudia Dziobek, and Charles Enoch
Published Date:
September 2002
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Author(s)
TAKEDA MASAHIKO

OBTAINING A RELIABLE forecast of inflation over an appropriate time horizon—determined by the effectiveness lag of monetary policy—is the key to inflation targeting. As succinctly demonstrated by Svensson (1997), under certain assumptions inflation targeting implies using forecasted inflation as an intermediate target, rather than targeting future inflation itself. The theme of this volume, statistical implications of inflation targeting, is particularly relevant in this context—namely, which statistical data are most useful to central banks for forecasting inflation accurately?

To answer this question, one first has to have an inflation-forecasting model. The relevant statistical data are those the model requires as input. One big problem, though, is that there does not seem to be a definitive inflation-forecasting model that offers a reliable guide to central banks. Although many central banks publish their inflation forecasts regularly, few disclose the precise methodology by which they arrive at their forecasts. This indicates the absence of a model they feel confident and comfortable enough to disclose.

Given the difficulty of obtaining a reliable model, it would be nice if there were a good substitute for a model in the form of readily available statistics. One candidate for a substitute is the inflation expectations held by market participants. In many countries, inflation expectations by private forecasters are readily available. In those countries where indexed instruments are issued and actively traded, genuinely market-based inflation expectations, which aggregate views of market participants at large, can be calculated by comparing indexed and non-indexed yields. If the central bank could achieve its inflation target simply by adjusting its policy instrument so as to guide such market expectations to the target, the task of estimating the process through which inflation is generated, and ascertaining how the policy instrument affects variables that interact with the process, might be dispensed with.1

Unfortunately, Bernanke and Woodford (1997) have shown that a mechanism like this does not work, at least in its purest form. Their argument is as follows. Assume that market participants know the inflation-generating process, and also the value of a certain state variable that critically influences the actual realization of inflation. The central bank knows the process, but it cannot observe the state variable—namely, that statistical information is insufficient. Under these circumstances, if the central bank could extract information about the value of the state variable from market inflation expectations, inflation targeting would imply that the policy instrument would be adjusted, and the variable’s influence on inflation fully offset, so that the target would be achieved. This, in turn, would mean that, under rational expectations, market forecasts should be right on the target in the first place—in other words, that private forecasters should correctly predict that the central bank would hit the target, appropriately offsetting any disrupting influence of the state variable. But if the private forecasts were thus on target, it would be impossible for the central bank to extract any information from them about the value of the unobservable state variable. This is clearly a Catch-22 situation.

Targeting market inflation expectations was not what Svensson (1997) meant when he advocated inflation-forecast targeting. Rather, he was very explicit about targeting the central bank’s own inflation forecast. Bernanke and Woodford (1997) argue, however, that the problem can generalize to the case in which forecasts are generated by the central bank itself. As long as the section of the central bank in charge of forecasting inflation attempts to minimize forecasting errors, taking the central bank’s policy reaction into consideration, there is no difference from private forecasts. It follows that inflation forecasts that explicitly exclude the central bank’s policy reaction—for example, those estimated under the assumption of constant policy interest rates—have an important role to play for policy purposes. Such conditional forecasts usually are not available from the market, and hence each inflation-targeting central bank must develop an internal inflation-forecasting model suitable for conditional forecasting exercises.

Bernanke and Woodford’s insight—sometimes called a “monkey in the mirror” problem—is interesting, if somewhat extreme and exotic. This chapter does not dispute an important implication of their insight—that efforts should be made by central banks to develop good inflation-forecasting models of their own. What this chapter tries to do instead is to shed some positive light on the usefulness of market inflation expectations. That a central bank can improve its control of inflation by using market expectations was not denied by Bernanke and Woodford; rather, it is another important, but much less emphasized, implication of their paper. Their model is reviewed here to illustrate this point. This chapter also points out that once their assumption that the central bank is a pure inflation targeter is relaxed, the attractiveness of using market inflation expectations as a guide for monetary policy further increases.

The next section of this chapter examines a number of tools frequently used at the IMF and elsewhere for evaluating monetary policy and shows their problems and deficiencies, especially in the context of inflation targeting. Compared with them, market inflation forecasts seem to be much more suited for monetary policy surveillance under inflation targeting. Then the chapter reviews Bernanke and Woodford’s theoretical framework and their main findings. In their model, market inflation forecasts are more than a tool for policy evaluation; the central bank sets its policy instrument as a function of the forecasts. This chapter shows the mechanism that gives rise to the Catch-22 situation, and also the way that use of market forecasts nevertheless improves the conduct of monetary policy. Finally, it discusses how Bernanke and Woodford’s results are modified once their assumption of a purely inflation-targeting central bank is relaxed to include a “flexible” inflation targeter who cares about output fluctuations as well. The bottom line is that the Catch-22 situation is a consequence of their restrictive assumption, and that an alternative, more realistic assumption about the central bank’s cost function yields very different results.

Tools for Evaluating Monetary Policy

When IMF staff engage in country surveillance work, they ask themselves many questions, but, as far as macroeconomic policies are concerned, they all boil down to two. First, are policies too tight or too loose under the current and prospective economic conditions? Second, is there room for improving economic conditions by changing the mix of macroeconomic policies? The second one is not relevant in the present context, so the focus here is on the first.

There is an obvious and indisputably correct answer to that first question—to use a fully worked-out macro structural model to estimate the impact of a given macroeconomic policy setting on the target variables such as inflation and output. In reality, however, this answer only leads to a host of different questions. Various conceptual and practical problems arise in constructing and estimating macroeconometric models, which makes one hesitate to put faith in any particular model and the diagnosis derived from it. This approach is also very resource-intensive, which, together with its uncertain payoff, makes it worthwhile for the IMF to explore other, simpler methods of policy evaluation.

There are several such alternative methods of monetary policy evaluation based on readily available economic indicators, but none of them satisfactorily answers the question posed above. Here are some examples. The simplest indicator of all is nominal short-term policy interest rates. A rise or a fall in these rates clearly indicates the policy authorities’ intention to tighten or loosen monetary policy. Yet it is clear that this tells nothing about whether the policy is too tight or too loose, before or after the policy change. Translating nominal rates into real enables one to evaluate the policy impact on the economy somewhat better, but it does not fundamentally solve the problem. Another method, often used at the IMF, is to calculate the Monetary Conditions Index (MCI), which is a weighted sum of short-term interest rates and changes in the exchange rate. This again tells only about whether monetary conditions are tighter or looser relative to any reference point, and does not answer the question at all. It is also unclear what is really meant by “tighter” or “looser.” In the original work of the MCI, the relative weight between interest rates and exchange rate changes was chosen to reflect their relative impact on output. Thus, the MCI presumably measures how monetary conditions affect output. It seems no easy task to reinterpret or reconstruct the MCI as a tool for inflation targeting.

In sharp contrast, market inflation forecasts seem to have much better properties. They enable one to bypass all of the potential problems associated with econometric models. The forecasts are about future inflation, and thus they are very well suited for inflation targeting. They show whether monetary policy is too tight or too loose in a very straightforward way—just compare the forecasts with the target inflation rate, and if they are above (below) the target, the policy is too loose (too tight). And best of all, unlike other indicators mentioned above, the policy evaluation thus derived presumably takes the current and prospective economic conditions into account, as market participants see them.

All this sounds too good to be true, and there is indeed a problem. Use of the Bernanke-Woodford model shows the problem clearly.

Bernanke and Woodford Model and Main Findings

The Bernanke-Woodford model2 assumes that inflation is generated by the following simple process:

where π is inflation, s is a random state variable with mean zero and variance σs2, and u is the policy instrument.3 The realization of the state variable is observable by market participants, but not by the central bank. Market participants publish their inflation forecast, πƒ, which is observable by the central bank. The central bank sets its policy instrument, u, based on πƒ, hence:

where Φ is the reaction coefficient. Solving equations (18.1) and (18.2) under rational expectations, πƒ is given as follows:

Substituting this into equation (18.2) and then into (18.1), π is given as:

This means that π = πƒ—that is, the private forecast is always correct.4 The inflation-targeting central bank attempts to minimize the expected squared deviation of π around its target set equal to zero. From equation (18.4), the deviation is given as:

Bernanke and Woodford’s insight is derived from this simple model. In order to minimize 2, the central bank sets Φ equal to infinity, either positive or negative, violently reacting to any deviation of πƒ from the target of zero inflation. Such a policy will ensure that π is always equal to zero. If this policy is in fact followed, however, private forecasters will always announce that their inflation forecast is zero (see equation (18.3)), regardless of the realization of the state variable. But then the private forecast fails to reveal the unobservable value of the state variable to the central bank. Thus, this perfect foresight equilibrium collapses.

After making this point, the authors make another important point—that using market inflation expectations definitely helps. If the central bank does not use πƒ and if no other outside information is available, the best it can do is to assume that the value of the state variable is its mean (that is, zero), and to set its instrument equal to zero. In this case, the expected squared deviation of inflation from zero is equal to that of the state variable, σs2,. However, if the central bank uses a policy rule that links its instrument with πƒ, it can reduce the expected deviation of inflation below σs2,, as shown by equation (18.5). In fact, by choosing a finite, but arbitrarily large, value for Φ, the central bank can make Eπ2 arbitrarily close to zero.

Still, the model’s prediction that the central bank will choose a gigantic Φ is rather unattractive. Bernanke and Woodford offer one way to avoid this problem. Suppose the private forecast contains some random error, in which case πƒ will be expressed as follows:

where πe is the perfect foresight inflation rate derived from the model and υ is a random term with mean zero and variance σv2. Under this assumption, the same procedure as above gives the following expression for 2:

In this case, setting Φ equal to positive or negative infinity is not optimal, because it magnifies the error involved in the forecast. Bernanke and Woodford show that there are two minima to the expression given in equation (18.7) corresponding to two finite values of Φ, one positive and the other negative, and that the negative one gives the global minimum. It can be shown that the minimized value of equation (18.7) is necessarily smaller than σs2,, and thus, regardless of the size of the error variance, σv2, the right choice of Φ delivers a better outcome than the one obtained when the central bank disregards the private forecast.

Bernanke and Woodford have derived another interesting result. Suppose that, in addition to inflation forecasts, market forecasts of the central bank’s policy instrument are available. Then, the central bank can link its policy instrument with these two kinds of forecasts. Bernanke and Woodford have shown that this strategy drastically changes the nature of rational expectations equilibrium and allows the central bank to achieve its first best outcome. In many countries, market expectations about the most standard policy instrument, short-term interest rates, can be derived easily from the yield curve, or even from forward/futures interest rate markets in countries where such markets exist. Indeed, for many central banks this information may be much more accessible than market inflation expectations.

Why does this remarkable result obtain in the model? The policy reaction function is now expressed as follows:

where uƒ is the market forecast of the policy instrument. Applying rational expectations, equation (18.8) can be solved for uƒ as a function of πƒ, and plugging it back to the same equation, the policy instrument can be expressed as follows:

Using this expression together with equation (18.1), one can obtain the following solutions for π, πƒ, u, and uƒ:

From equation (18.10), Bernanke and Woodford’s result is immediate. By setting Φu equal to unity and choosing any nonzero Φπ, zero inflation will be achieved with probability one, which is the best possible outcome for these authors’s purely inflation-targeting central bank. Under these reaction coefficients, the policy instrument is set equal to -s, precisely offsetting the impact of the state variable. Unlike the previous case, the zero inflation outcome does not depend on the central bank’s violent reaction to a nonzero value of πƒ. The reason this is possible is that the information about the unobservable state variable is exactly revealed from the market forecast of the policy instrument. Although πƒ is always equal to zero in equilibrium, and hence is useless as an information variable, this does not cause any problem because the central bank has an alternative source of information.

One practical implication of this result might be the following. Market inflation forecasts are a potentially powerful tool for a central bank to use in justifying its policy action (inaction). If the forecasts are away from (on) the target, the central bank can cite this as a reason to change (keep unchanged) its policy. But this argument can be detrimental to the central bank under certain circumstances. It is possible that both the central bank and the market see a major price shock coming, but the market has full confidence in the central bank’s ability to counteract the shock. If so, πƒ does not deviate from the target. But then, anyone who is against a policy change might point out that inflation forecasts are still on the target, and argue that the central bank has no reason to change its policy. This problem can be solved if the central bank also cites the market’s instrument forecasts to explain its policy. The reason market participants expect that inflation will not deviate from the target is that they believe the central bank will appropriately adjust its policy instrument to counteract the price shock. This belief will be revealed in their forecasts of the instrument. Policy inaction is justified only when inflation forecasts are on the target and instrument forecasts are not indicating an imminent policy change.

In sum, apart from the Catch-22 paradox, the results derived from Bernanke and Woodford’s model are the following. First, the use of private forecasts can yield a better result in targeting inflation. Second, this does not mean, though, that the central bank should literally “target the inflation forecast.” As equations (18.3) and (18.10) show, πƒ generally deviates from the target of zero inflation in equilibrium (for any finite value of Φ in the case of equation (18.3)). However, it is suboptimal for the central bank to react to this deviation in order to force πƒ to converge to zero. This, in the authors’ view, is different from the policy of inflation-forecast targeting. They also argue that the fact that using instrument forecasts substantially improves the outcome is another reason to be cautious about targeting forecasted inflation. Focusing too much on inflation forecasts may result in the central bank’s failure to exploit the benefits of using other market forecasts/indicators in the conduct of monetary policy.

An Extension of the Model

As shown above, in one version of their model, Bernanke and Woodford introduced a forecast error to obtain an internal solution to the central bank’s reaction coefficient, Φ. This is a reasonable assumption; one can think of a variety of reasons why private forecasts should contain errors. But there is another important factor that explains why a central bank would not want to react violently to a deviation of inflation forecasts from the target. It is because adjusting the policy instrument violently has undesirable repercussions on other important economic variables, particularly output.

This observation leads us to a natural extension of the model—to modify the central bank’s cost function to include not only the deviation of inflation from the target, but also output fluctuations. This type of cost function is sometimes referred to as “flexible” inflation targeting.

The modification of the cost function yields a number of interesting results, most notably the following.5 First, as in the Bernanke and Woodford model, the use of market inflation forecasts in setting the policy instrument helps the central bank better achieve its policy objective. But in contrast to what happens with that model, it enables the central bank to achieve the full information, first best outcome, where “full information” refers to the situation in which the central bank can observe the realization of the state variable.

This result can be interpreted as follows. Even in the Bernanke and Woodford model, the value of the state variable was fully revealed by πƒ for any finite Φ (see equation (18.3)). But because of the Catch-22 situation, the full revelation was possible only if the central bank’s sole objective of price stability was compromised. Once the assumption of pure inflation targeting is relaxed, the central bank is ready to allow inflation to deviate from its target if it brings a larger benefit in terms of output stabilization. If inflation deviates from zero in equilibrium, πƒ fully reveals the value of the state variable. This, in turn, allows the central bank to pick the most desirable equilibrium for it—the one that best achieves its objective of inflation and output stabilization—by appropriately choosing the value of the reaction coefficient.

Second, the availability of instrument forecasts does not improve the outcome at all. This can be inferred from the first result above. The “flexible” central bank can achieve its first best without information about instrument forecasts. Hence, adding the latter information naturally does not improve the outcome. In other words, market inflation forecasts are a “sufficient” statistic for the central bank.6

These results imply that the Catch-22 situation, as well as the remarkable usefulness of instrument forecasts, are a consequence of Bernanke and Woodford’s restrictive assumption about the central bank’s policy objective. As long as the central bank cares also about output stabilization, which most central banks do, the strategy to link its policy instrument with market inflation forecasts, and market inflation forecasts alone, does not lead to a paradoxical situation, but in fact brings about the most desirable outcome.

Conclusions

Although this chapter contains nothing statistical, it has been strongly motivated by statistical considerations. Given the resource constraint the IMF faces, which, per country, is much more stringent than in any central bank, it is particularly useful to find a small set of critical statistics that enables the IMF to keep track of overall economic conditions or to evaluate macroeconomic policies. Market inflation expectations are a good candidate for such a statistic, and thus the IMF staff are naturally interested in their usefulness.

The conclusion is that, although interesting, the negative verdict delivered by Bernanke and Woodford on the use of market inflation forecasts may be exaggerated. Their model implies that market inflation forecasts do improve the policy outcome, and with a slight extension of their model it can be shown that these forecasts enable the central bank to achieve the full information, first best outcome.

Needless to say, the staff would never question the wisdom of using any available information to the policy authorities’ best advantage. But the conclusion of this chapter suggests that market inflation expectations might be of particular importance in inflation targeting. It therefore seems quite sensible and appropriate that some inflation-targeting central banks regularly publish market inflation expectations, in some cases conducting a survey in a controlled fashion. Maintaining, or even developing from scratch, a deep indexed bond market would also provide an excellent source of information.

Still, a large number of empirical issues need to be tackled to allow better evaluation of the practical usefulness of market inflation expectations. For example, Offenbacher and Sokoler (this volume) point out that market-based inflation expectations in Israel, where indexed instruments are widely available, are known to have a remarkably close relationship with past inflation, which strongly suggests their backward-looking nature. Although this evidence by itself does not necessarily imply that market expectations contain little information about the future or that they are any worse than predictions derived from central banks’ forecasting models, critical examinations should be made on the empirical value of market inflation expectations.

This is an example of reaction functions known as “forecast-based policy rules”; see Levin, Wieland, and Williams (2001) and citations therein.

Bernanke and Woodford present two models in their paper, one static and the other dynamic. This chapter focuses on their static model because their basic insight—the Catch-22 situation—and most of their other results do not require a dynamic setting. One important implication of their dynamic model is the possible indeterminacy of rational expectations equilibrium. This is a serious theoretical concern (see Levin, Wieland, and Williams, 2001, for more on this), but its empirical relevance needs to be further explored.

The Bernanke and Woodford model has one additional element, a random term on the right-hand side, which makes it impossible for market participants to fully predict the realization of inflation. It is disregarded here because it plays no substantive role in their framework. Otherwise, their model and notations are followed closely.

Because the random term in equation (18.1) is disregarded (see footnote 3), the assumption of rational expectations implies perfect foresight.

These and other results are derived from, and fully explained in, Takeda (2002).

This does not preclude the central bank’s use of a reaction function that takes the form of equation (18.8); it can achieve as good an outcome as when it uses only inflation forecasts. It can be shown, however, that linking the policy instrument only with instrument forecasts, thereby disregarding inflation forecasts, results in indeterminacy of rational expectations equilibrium. Hence, there is a clear asymmetry between these two types of forecasts, making inflation forecasts more important than instrument forecasts for the central bank.

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