19 Inflation Forecast Targeting in a Low-Income Country: The Case of Ghana

Andrew Berg, and Rafael Portillo
Published Date:
April 2018
  • ShareShare
Show Summary Details
Ali Alichi, Marshall Mills, Douglas Laxton and Hans Weisfeld 

1 Introduction

Over the past two decades, numerous monetary authorities have used inflation targeting to solve a chronic inflation problem.1,2 They announced numerical inflation reduction targets for the medium-term, and in some cases a long-run target, which may be interpreted as a price stability objective.

Although, in the end, most of these countries achieved the goal they sought, the disinflation phase was often uneven, with inflation outcomes outside the target range. Roger and Stone (2005) found that the frequency of outcomes outside the range for countries with inflation targets was 60 per cent. In retrospect, monetary policy in some cases responded too vigorously to these deviations in an attempt to get inflation quickly back to the target.

Indeed, early IT strategy put heavy emphasis on achieving annual reductions in the inflation rate on schedule, as a way to establish central bank commitment to price stability. This was an essential objective because monetary policy credibility had been badly eroded by high and persistent inflation, such as the Great Inflation of the 1970s and 1980s. Policymakers were also aware of the credibility problem implied by the theory of time-inconsistency in monetary policy. While this theory holds that short-run political time horizons create the time-inconsistency, the proposed solutions, e.g. by Barro and Gordon (1984) and Rogoff (1985), recommend that policymakers take a longer-run view. In practice, the focus on hitting short-run targets soon ran into difficulties, largely because of lags in the policy transmission mechanism. The effects of forceful policy reactions would stretch beyond their intended short-run purpose, pushing inflation to the other side of the target range and requiring actions to reverse it.

A lesson from this experience is that a modern approach to IT—which can be described as inflation forecast targeting (IFT)—should be more flexible and forward-looking as well as providing better communication. Credibility is not helped by policy actions that attempt to keep inflation within a target range every single year. Experience has shown that common shocks can be so large that such a goal may not be feasible, let alone desirable. Moreover, the objective of short-run output stability may influence policy actions, without harming credibility, as long as this influence is unbiased over time. A central bank can strengthen its credibility by openly focusing its policy on more than just hitting annual targets, recognizing that its actions involve short-run trade-offs and being mindful of undesired effects on output and employment. IFT instead emphasizes longer-term results, the framework committing monetary policy to a low-inflation goal, and accountability and transparent communications. Under IFT, central banks publish regular monetary policy reports that contain their forecast for inflation, associated macroeconomic variables, and at least a qualitative indication of the likely course of the policy interest rate; some have gone so far as to publish an explicit forecast for the policy interest rate.3 Each of the elements of the flexible approach requires that the policymakers have realistic, coherent models of the monetary policy process, from policy instruments to objectives.

While Ghana is one of several emerging market economies to adopt IT, it may be the first low-income country to have done so (IMF, 2008b). An important consideration for adopting an IT regime was that the existing framework, which was based on targeting monetary aggregates, proved to be increasingly infeasible as the demand for money changed rapidly in the wake of major structural transformation.

As a small, open low-income economy, Ghana faces several major challenges in its conduct of disinflation policy:

  • It is highly vulnerable to supply shocks.
  • Deviations from inflation targets tend to be larger during disinflation than with stable low targets.
  • Inflation expectations can be volatile and based on past experience.
  • The technical capacity of Bank of Ghana (BoG) is incipient, though still evolving.

Despite these challenges, the IFT approach can effectively deliver a program of inflation reduction for Ghana while limiting output loss.

To support this approach, we construct a model-based framework for disinflation under IT with the following features:

  • It explicitly models inflation expectation dynamics. Inflation expectations and policy responses depend on policy credibility.
  • It replaces the Taylor rule for interest rate setting with a time invariant objective function.
  • It avoids the shortcomings of inadequate communication strategies.
  • It generates plausible results for responding to shocks.

This approach offers responses to the questions facing any central bank thinking of disinflation:

  • What is an appropriate pace of disinflation?
  • Should a long-run target be announced?
  • Should the disinflation targets be revised following a shock? What sort of flexibility is appropriate in the execution of policy?

2 Inflation Trends in Ghana Through 2007

Ghana has historically experienced volatile and often high inflation rates (Figure 19.1). Ghana’s economy suffered bouts of high inflation in 1999–2000 and 2002–03, which were related to external shocks, unsustainable macroeconomic policies and exchange rate depreciation. A period of disinflation began in 2004 that brought inflation down to near 10 per cent in 2006, where it roughly stabilized until late 2007.

Figure 19.1.Ghana: CPI Inflation, 2000–2008 (Per cent year-on-year)

The BoG formally adopted IT in May 2007 after three years of informal IT management. It has been building the main institutional, analytical, and communications elements of this framework since 2002. With the enactment of the 2002 Bank of Ghana Act, the BoG had in place all of the key institutional components of modern central banking, especially independence and a statutory mission of price stability. In addition, central bank credit to the government each year is limited by law to 10 per cent of total revenue collected that year, but in practice the government has not resorted to any central bank financing for the last several years. The target range for CPI inflation is set jointly by the government and the BoG as part of the budget. Staff describe the current regime as ‘inflation-targeting lite’, because exchange rate stability is an important secondary objective and because operational transparency has not developed sufficiently to classify it as a fully fledged IT regime.

When the BoG formally launched IT, it established a large measure of goal transparency, aiming for disinflation over three years to achieve stability around 5 per cent, with a range of ±1 per cent. It also announced a fairly straight-line path of intermediate inflation targets to get to 5 per cent. In support of IT, the BoG has also developed a forecasting model and a detailed communication strategy. After each Monetary Policy Committee (MPC) meeting (every other month), it issues a press release and holds a press conference, chaired by the BoG Governor, at which it explains its decision. A detailed monetary policy report is then published.

In October 2007, inflation started to pick up again due to both demand shocks (from an expansionary fiscal policy and strong private sector credit growth) and supply shocks (from higher international fuel and food prices). The BoG has noted that core CPI inflation—which excludes energy and utilities—has been lower than the headline but has also begun to rise. In response, the BoG has raised the policy rate by a cumulative 350 basis points since November 2007. These inflation developments have posed an early challenge for the IT regime. The current straight-line disinflation path and communication strategy seem too rigid to respond well. As a result, the BoG credibility that was built up over the last four to five years may be at risk.

3 Standard Model

In the standard New Keynesian model in use at the Fund for several countries, the central bank sets an inflation target path dependent on current inflation and its long-run inflation objective and employs a Taylor-type rule to determine the policy (interest) rate, subject to the following behavioural equations:

  • an output gap equation (actual minus potential output—a gauge of excess demand—as a function of the interest rate, the exchange rate, and external demand);
  • an inflation rate equation (an expectations-augmented Phillips curve); and
  • an exchange rate equation (a relation embodying uncovered interest parity, a variable risk premium, and long-run purchasing power parity).

In the standard model, the central bank’s credibility is proxied by a parameter and is captured to some extent by the degree to which households form inflation expectations in a forward-looking rather than a backward-looking fashion. The standard model works reasonably well for countries that have already achieved low inflation rates, even though there is evidence that shows that a well-managed IT framework will over time strengthen central bank credibility.4 However, it is less appropriate for Ghana because during disinflation periods credibility is likely to change over time, which is not endogenously captured in the standard model.

4 Model for Disinflation Under Inflation Forecast Targeting

Our framework adds to the standard model three novel features relevant to a policy of inflation reduction:5

  • An endogenous credibility process. Starting from a situation in which agents initially expect inflation to remain high, policymakers may build credibility over time by providing a sufficient track record that anchors inflation to the target.
  • A monetary policy loss function that recognizes costs of fluctuations in output and interest rates, as well as costs of deviations of inflation from target—in place of a conventional interest rate reaction function for the policy interest rate. The advantage of the loss function approach over reaction functions is that the responsiveness of interest rates will change automatically over time and will be more aggressive in responding to shocks when credibility is low.
  • A non-linear Phillips curve. In practical terms, this means that the relationship of inflation and output gap depends on how big the output gap is. For very high output gap cases (high excess demand), small increases in output gap will translate into big increases in inflation. However, for reasonably low levels of excess demand, the relationship could be closer to a linear one. A non-linear Phillips curve serves to generate a number of important predictions and policy implications that are missing from linear models that presume high levels of policy credibility. First, the model suggests that it can be easier to lose credibility than it is to regain once lost, as it takes time and a period of significant slack in the economy to re-anchor inflation expectations. Second, this formulation strongly favours gradualism to prevent unnecessary cumulative output losses associated with disinflation.

Our simulation results based on this model suggest that monetary policy should enable the BoG to reduce inflation while limiting output losses. The model is calibrated on the basis of a wide range of international experience and is frequently refined using a continuing iterative feedback process. Note that these results are simply indicative; they do not constitute staff recommendations, but are merely one of several inputs into staff assessments.6 Model results should always serve as only one of several inputs into decision-making by monetary policymakers.

5 Simulation Results: Dynamic Responses to Shocks

We first study disinflation under imperfect and perfect credibility in the absence of shocks. Thereafter, we introduce supply and demand shocks and study both the policy reaction and the paths of all other economic variables.

5.1 Baseline—Disinflation under Imperfect Credibility

In the extended model, credibility is imperfect in the sense that people do not have full confidence that the central bank will achieve its announced objectives, and may not even believe that the bank will try to achieve them. In forming expectations of inflation, they give considerable weight to the recent history of inflation and to the risk that policymakers might have a covert high-inflation agenda. Monetary policy is assumed, however, to have some credibility: in the process of forming expectations; we set the initial weights at 0.4 on the announced low-inflation policy, and at 0.6 on the alternative possibility of a high-inflation policy. Furthermore, the central bank can earn an increased stock of credibility—moving the low-inflation weight towards unity—only by delivering an actual drop in inflation toward the official objective.

Monetary policy in the model follows a loss-minimizing strategy to get to the assumed ultimate inflation target of 5 per cent. We posit initial conditions similar to those prevailing in Ghana in the second quarter of 2008. The economy is experiencing excess demand pressures and has suffered an external price shock: inflation is high; growing fiscal deficits and easy monetary conditions are stimulating further inflation. In numerical terms, to start the model simulations we set the 2008 Q2 rate of inflation at 15.3 per cent, the annual output gap (excess demand) at 0.5 per cent; and the short-term rate of interest controlled by the central bank at 16 per cent.7 The initial real interest rate is below 1 per cent, and hence much less than the assumed natural equilibrium rate of about 3 per cent. We suppose that the central bank announces an ultimate target for the inflation rate of 5 per cent in 2008 Q3 and immediately starts implementing the loss-minimizing policy to this end.

The charts in Figure 19.2 show the simulated disinflation path. Given the level of inflation expectations at the outset and lags in the expectations process, the central bank has to raise the policy rate substantially to achieve the desired increase in the real interest rate. Optimal policy in the model—in the sense of achieving targeted disinflation with minimum loss in output—involves raising the interest rate to 19.6 per cent in 2008 Q3, and to a peak of 20 per cent in 2008 Q4.

Figure 19.2.Ghana: Baseline IT, 2008–2018a

a All variables are quarterly, except for Real GDP growth, which is annual because quarterly GDP data are not reported in Ghana.

b Increase represents depreciation of the cedi.

Source: IMF staff calculations.

This has an immediate impact on the nominal price of foreign exchange: the domestic currency appreciates against the US dollar. This combined with the higher domestic inflation rate compared to the United States implies that the real exchange rate appreciates by 12 per cent. The increased interest rate and reduced real price of foreign exchange (real appreciation of the domestic currency) both reduce demand for domestic output. This eliminates excess demand: the annual output gap declines from a +0.5 per cent to —1.5 per cent (indicating excess capacity) by 2008 Q4, and to a trough of —3.9 per cent in 2009 Q4. This excess capacity represents the short-run output sacrifice required for disinflation in the model.

Low credibility results in upward-biased expectations. During the inflation-reduction phase people expect a higher inflation rate than monetary policy actually delivers. Since expectations have a direct effect on actual inflation in the Phillips curve, monetary policy has to be tighter than if people had 100 per cent confidence in the objectives, and the loss of output and employment is greater. Thus, low credibility worsens the short-run inflation-output trade-off.

Excess productive capacity does reduce the rate of inflation though. In response, the public gradually revises downwards its expectations of future inflation and gives increased weight to the announced 5 per cent target. By mid-2011 actual inflation reaches this rate. Thus, monetary policy reduces the inflation rate by 10 percentage points over three years, an average reduction of just above 3⅓ per cent per year. The corresponding sacrifice ratio (the cumulative output loss divided by the inflation reduction) is just below one. By historical standards, despite the initial moderate credibility, this would represent a fairly rapid low-cost disinflation (Roger and Stone, 2005).

By 2014 the economy would be almost on its full long-run equilibrium path (barring new shocks). The stock of credibility is close to unity and the output gap is virtually zero. The real exchange rate stabilizes at its initial equilibrium value, but the nominal exchange rate continues to rise, reflecting the domestic-US inflation differential.

5.2 Disinflation under Perfect Credibility

This sub-section repeats the baseline but it assumes that the public has full confidence from the outset in the target announced by the central bank. This assumption implies the fastest path of disinflation consistent with loss minimization. The results show inflation declining to the 5 per cent range just six quarters after the announced policy takes effect (Figure 19.3). The reduction in expected inflation itself raises the real interest rate above the natural rate without an increase in the nominal rate. Indeed, the nominal rate declines through the disinflation phase, as the inflation premium goes down. The sacrifice ratio over the six-quarter inflation-reduction period is less than 0.1—almost negligible.

Figure 19.3.Ghana: Baseline with Full Credibility, 2008–2018a

Dotted = Full credibility; Solid = Endogenous credibility

a All variables are quarterly, except for Real GDP growth, which is annual because quarterly GDP data are not reported in Ghana.

b Increase represents depreciation of the cedi.

Source: IMF staff calculations.

5.2.1 Supply Shock

The first experiment here is a significant increase in the rate of inflation caused by an increase in world energy and food prices, which calls for a strong policy response. A stagflationary supply shock of this type clearly presents a very difficult problem for monetary policy in the absence of well-anchored inflation expectations. Policy has to guard against an inflationary spiral as the short-run increase in inflation may cause people to expect higher inflation in the future and to lose confidence in the announced 5 per cent objective. The loss-minimizing policy calls for considerable and repeated increases in the interest rate—by 450 basis points over eight quarters—relative to the baseline (Figure 19.4). In levels, the interest rate peaks at 24 per cent in 2008 Q4. This reaction, and the large, though short lived, appreciation of the exchange rate that accompanies it, does not prevent a prolonged divergence of inflation from target. Twelve quarters after the shock, inflation is still 3 percentage points above the baseline rate. The reasons for this are (i) the lagged response of the output gap to the interest rate and exchange rate; and (ii) the adverse, self-reinforcing, impact of the increase in inflation on expectations and credibility.

Figure 19.4.Ghana: Negative Supply Shock, 2008–2018a

Dotted = Negative shock; Solid = Baseline

a All variables are quarterly, except for Real GDP growth, which is annual because quarterly GDP data are not reported in Ghana.

b Increase represents depreciation of the cedi.

Source: IMF staff calculations.

The second experiment considers a supply shock of the opposite sign, against which BoG does not have to raise the interest rate as much to contain inflationary pressures (Figure 19.5). The inflation does fall below the baseline for an extended period, but this is in line with the announced policy objective, and boosts the stock of credibility. The potential size and duration of the effects of supply shocks on the inflation rate, even when a policy provides appropriate resistance, is a major reason for avoiding rigid adherence to short-run target ranges during the disinflation process.

Figure 19.5.Ghana: Positive Supply Shock, 2008–2018a

Dotted = Positive supply shock; Solid = Baseline

a All variables are quarterly, except for Real GDP growth, which is annual because quarterly GDP data are not reported in Ghana.

b Increase represents depreciation of the cedi.

Source: IMF staff calculations.

With full credibility, the central bank raises the interest rate, relative to baseline, by less than 100 basis points.8 The real price of foreign exchange shows a small, brief increase. The modest tightening, resulting in a small negative output gap, is sufficient to keep inflation close to 5 per cent, because public expectations of inflation are anchored firmly to the target. This result is in line with the experience of the past two decades in countries that have moved from high inflation to stable low inflation. In the 1970s and 1980s, unstable expectations transformed shocks that under good monetary policy regimes should only have price-level implications—e.g. energy price increases and currency depreciations—into inflation spirals. Monetary policy contained the problem eventually, but only with very tight monetary policies, and at the cost of a substantial output loss. Since the early 1990s, however, many central banks have re-established low-inflation and monetary policy credibility. The public now has confidence that the low-inflation policy objective will prevail, even after substantial price shocks. This in some cases has virtually eliminated the second- and third- round effects of such shocks on the price level. A beneficial supply shock where there is full monetary policy credibility has symmetric implications to the adverse shock (results not reported). The non-symmetries during the process of inflation-reduction and credibility-building are no longer present.

5.2.2 Demand Shock

The results for the expansionary shock, e.g., a change in government spending equivalent to 0.5 per cent of GDP (not reported) are similar to, but more pronounced than the baseline (not reported). This is because the baseline also was a situation of excess demand in the economy. For the expansionary shock, the appropriate policy reaction is a prompt sharp change in the interest rate, and hence in the exchange rate. Firm interest rate reaction effectively mitigates the impact on the goal variables, output and inflation. The contractionary shock requires a slightly more moderate policy reaction. One reason for the asymmetry between the effects of the two shocks is that in the case of the expansionary shock, unlike the contractionary one, the central bank has to offset the potential weak ening of credibility. In effect, the drop in demand in the second experiment does some of the disinflationary work for monetary policy.

5.2.3 Costs of Delaying Interest Rate Increase under Imperfect Credibility

Our simulations show that if policymakers delay their response shocks, serious inflationary consequences will follow. Suppose policymakers announce a 5 per cent inflation target in 2008 Q3, but put off the required large interest rate increases until 2009 Q2 out of concern to maintain the level of output. The simulated response shows serious inflationary consequences (Figure 19.6). For several years the deviation between the inflation and the baseline rate widens—to over 5 per cent in 2011. The inflation rate would rise from about 15 per cent currently and remain in double digits until 2011. After an initial hesitation, the interest rate has to play catch-up, and eventually rise far above the baseline—to above 25 per cent in 2009 Q4. From a historical perspective, this would not be unprecedented—e.g., in the early 1980s the US Federal Reserve and the Bank of Canada had to raise short-term interest rates above 20 per cent to stop double-digit inflation. Short-run low interest rate policy, in the face of inflation, eventually turns into a high interest rate policy.

Figure 19.6.Ghana: Positive Demand Shock with Delayed Policy Response, 2008–2018a

Dotted = Positive demand shock; Solid = Baseline

a All variables are quarterly, except for Real GDP growth, which is annual because quarterly GDP data are not reported in Ghana.

b Increase represents depreciation of the cedi.

Source: IMF staff calculations.

An erosion of credibility is, not surprisingly, a large part of the problem. The stock of credibility declines as the inflation rate fails to decline. Relative to baseline, the simulated loss in the stock of credibility has significant implications. The delay in raising the interest rate does keep demand high in the short run—excess demand intensifies for several quarters. But disinflation requires that a negative output gap eventually open up, and after two years, the gap is wider than in the baseline. Thus, the cost of the monetary policy delay is several years of stagflation.

5.3 Recommendations for Ghana

To respond to Ghana’s current challenges for disinflation, the BoG could shift to a more flexible IT regime presented above as IFT, drawing on a model like the one described. As noted, Ghana’s challenges are far from unique—IT often encounters problems in the disinflation phase. To respond to these difficulties, IFT is more forward-looking and flexible than the earlier form of IT; indeed, the inflation forecast should be used as an ideal intermediate target in these circumstances. Clearly, a solid forecasting model is an essential element of this approach, and the model presented above could provide a good starting point.

This approach stresses that the key to credibility lies not in hitting precise short-run targets but in a consistent record of policy actions that get the inflation rate back on target within two or three years—a critical difference that applies well to Ghana currently. Figure 19.7 contrasts a traditional ‘straight-line hard target’ approach to disinflation with a more flexible and modern IFT approach. The optimal path in the baseline scenario differs from the linear path (due to lags and concerns over output losses), and in the event of shocks, the optimal path diverges even further from the linear path. These divergences need not necessarily weaken credibility; a large body of evidence on IT—in countries with widely differing features and initial conditions—indicates that long-term expectations do gravitate over time to the low-inflation targets pursued by a committed monetary policy (which eventually earns strong credibility), despite short-term deviations.

Figure 19.7.Ghana: Linear versus Optimal Disinflationa 2008–2015 (year-on-year, per cent)

a The optimal disinflation paths are as follows: Baseline (no shocks), Positive supply shock (of 0.5 per cent of GDP), and Negative supply shock (of —0.5 per cent of GDP).

Source: IMF staff calculations.

Transparent communications are essential to build credibility in this flexible approach. Transparency is needed with respect both to policy objectives and to the way in which current policy actions are intended to achieve them—operational transparency. Ghana already has an element of goal transparency (the medium-term target of 5 per cent inflation), but could greatly strengthen its operational transparency. Doing so requires that the monetary policymakers have realistic, coherent models of the monetary policy process, from policy instruments to objectives, which they communicate openly.

In particular, the BoG can consider two new steps to strengthen communication:

  • publish its forecasts for inflation, the output gap, and the policy rate after each MPC meeting. These forecasts would be revised after each meeting, creating a continuous flow of information about the BoG’s reactions to developments; and
  • explain ex ante how it would react to different shocks (as in Figure 19.7), providing further transparency and predictability. Indeed, by ‘tying its own hands’ in advance, the BoG may even insulate itself more from political influence.

Operational transparency magnifies the impact of the central bank’s policy on expectations, which in turn reinforces its effectiveness. The Norges Bank has adopted this communication strategy with considerable success. It publishes model-consistent fan charts for all these forecasts, along with examples in the form of risk assessments explaining how it is likely to respond to future shocks. Market participants have begun to anticipate its policy moves, effectively enlisting them as allies in the monetary policy process. This anticipation can be seen in the muted reaction of market interest rates to MPC announcements after this policy was adopted. The impact of shifting to this approach could be enhanced considerably by publishing a policy paper explaining the new approach and including how it would likely react to different future shocks.

6 Conclusions

In adopting IT while still a low-income emerging-market economy, Ghana has been a trail-blazer. Its recent adverse inflation developments are reason not to abandon IT, but to improve the framework by adopting a more flexible and forward-looking approach to IT.

To support this approach, this paper presents a model that recognizes the difficulties facing Ghana, among them less than perfect credibility of announcements of inflation reduction and policymaker aversion both to movements of output from its potential level and to variability in the interest rate. The model emphasizes the importance of the BoG building credibility over time through consistent pursuit of a low-inflation goal. The nominal anchor is the ultimate target for low inflation; from this foundation, and for given initial conditions, a sequence of short-run inflation-forecast targets may be derived. A loss-minimizing monetary policy would not be locked into a rigid predetermined path of inflation reduction with fixed near-term targets.

The model simulations bear out some intuitive lessons about how monetary policy needs to react in response to shocks during disinflation. The effects of supply shocks on inflation can be large and of significant duration, even with an appropriate policy response—this is a reason to avoid rigid non-credible commitments to short-term inflation-reduction targets. Even so, the BoG must be prepared to raise interest rates to a level that dampens demand and visibley reduce in inflation. Any delay in responding (e.g., out of concern for near-term output losses) damages credibility, ultimately bringing on higher inflation and more prolonged output losses (in a word, stagflation).

The key to transparency and communications in this approach is ‘saying what you do and doing what you say’. By providing the public with its forecasts for inflation, output gap, and policy rates, the BoG could better shape expectations despite recent rises in inflation. Explaining ex ante how the BoG would react to different shocks would help market participants anticipate policy moves.

There are many aspects of this model that could be considered for other emerging low-income economies that wish to enhance their monetary policy framework, including incorporation of credibility as an endogenous variable and enhancing the operational transparency and communication strategy of the central bank. These could be useful not only for countries considering a move to IT but also for countries which wish to introduce a more formal and credible commitment to low inflation generally.

Appendix 19A: The Standard Model

The standard model, presented in Berg, Karam, and Laxton (2006a, b), has four behavioural equations, which feature variables both in terms of deviations from equilibrium values, i.e., as gaps, and in levels:9

  • Output gap equation The output gap equation is an IS curve that relates the output gap to expected and past output gaps, the real interest rate gap, the real exchange rate gap, and the foreign output gap:
  • where ygap is the output gap, RRgap is the real interest rate gap in percentage points, zgap is the real exchange rate (measured so an increase is a depreciation, in percentage points), and ygapu is the foreign output gap. The output gap is measured as the deviation, in percentage points, of actual output from a measure of the trend or equilibrium level of GDP (a positive number indicates that output is above trend). Economic agents are assumed to know the model and have rational expectations.
  • Phillips CurveThe Phillips curve relates inflation to past and expected inflation, the output gap, the exchange rate, and possibly key world market prices such as oil prices; the Phillips-curve equation may be split into two, one for overall inflation and one for core inflation:
    where π is the annualized month-on-month inflation rate, π4 is the four-quarter change in the CPI, and z is the real exchange rate.
  • Taylor Rule The variant of the Taylor rule chosen here determines the policy interest rate as a function of the output gap and expected inflation:
    where RS is the monetary authorities’ nominal interest rate and * denotes equilibrium values.
  • Exchange Rate Equation

The exchange rate equation imposes uncovered interest parity (IP), an arbitrage condition that says that real interest rates (on investments in different currencies) will be equalized across countries, up to a country risk premium. A real exchange rate definition is used to write the conventional IP condition as a real IP condition as follows:

where RRUS is the foreign real interest rate and ρ* is the equilibrium risk premium. The first two terms on the right hand capture agents’ real exchange rate expectations.

Equilibrium values are determined on the supply side. To preserve simplicity, the supply-side variables are assumed to follow simple stochastic processes not shown here for brevity. In practice this means that the analyst must make assumptions about equilibrium values, based on a variety of sources, including judgemental estimates or econometric analyses.

Appendix 19B: The Model

Our model of inflation with endogenous credibility has the following main components:

  • Inflation equation—an expectations-augmented Phillips curve.
  • Expectations process and credibility.
  • Non-linear output gap effect.
  • Output gap equation.
  • Exchange rate-real interest rate parity equation.
  • Monetary policy loss function.

We explain each of these components below.

Inflation Equation—An Expectations-Augmented Phillips Curve

The inflation equation is as follows:

where, π4te and π4t-1 are the forward-looking and backward-looking components of inflation, yt-1 is the output gap in period t — 1, ymax is the maximum output gap possible. z (in logs) is the real exchange rate (measured so an increase is a depreciation, in percentage points), and Δzt is changes in real exchange rate (zt) from last period’s level (zt-1). λ1, λ2, and λ3 are model parameters and ϵtπ is the supply shock.

The terms in the equation, from left to right, represent:

  • backward- and forward-looking components to the expectations process—with an endogenous credibility stock in the forward-looking component λ1*π4te+(1λ1)π4t1where,π4t=14i=14πt+iandπ4t=14i=14πti. We will characterize how inflation expectations—π4te—are formed in the next sub-section.
  • non-linear output gap effect (λ2*(yt1ymaxyt1ymax))
  • exchange rate pass-through (λ3*Δzt).

In line with the evidence, the equation contains a mechanism that changes the formation of expectations from a drifting, backward-looking, process to one which is anchored by the low-inflation target.

Expectations Process and Credibility

Inflation expectations are formed as follows:

The first two terms in the equation for expected inflation comprise a weighted average of a model—consistent forecast of the four-quarter inflation rate (forward-looking component) and the inflation rate observed last quarter (backward-looking component). The weight on the forward-looking component,γt, evolves between 0 (no credibility) and 1 (full credibility)—and is therefore a measure of the stock of credibility.

We use these scenarios to define a credibility coefficient. In order to define the evolution of the credibility stock, we postulate that the public sees a possibility for one of two inflation regimes—’L’ and ‘H’, for ‘Low’ and ‘High’ inflation. In the ‘L’ scenario, inflation would converge to the announced inflation target of πt*10. The ‘H’ scenario corresponds to a suspicion in the public mind that monetary policy might deliver an inflation rate much higher than the announced target—we suppose that rate to be very high, say 40 per cent. Under the H scenario, inflation would converge to 40 per cent. We use these scenarios to define a credibility coefficient:

The coefficient ηt gauges the extent to which inflation outcomes are seen as consistent with the ‘Low’ inflation scenario. Consider two extreme cases:11 in the ‘L’ case, inflation converges gradually to the inflation target and ηt converges to 1, since the term (π4tLπ4t) in the denominator of the equation above equals 0;12 in the ‘H’ case on the other hand, ηt equals 0, implying complete lack of credibility. Credibility is lost—people give increased weight to a suspected high inflation scenario—if inflation outcomes are above the announced target.13 The credibility stock (γt) then evolves in the following autoregressive form:

An increase in ηt results in a rise in the weight of the forward-looking component of expectations. This ties inflation more tightly to the target, such that the central bank has to do less in response to shocks and that convergence to the target rate is faster. Disturbance term ϵtγ represents a shock to central bank credibility, which may be positive or negative. bt, the inflation expectations ‘bias’ is simply defined as a proportion of the deviation of a weighted average of hypothetical inflation expectations from the inflation target, where the weights reflect the credibility stock (γt):

Based on this equation, as credibility approaches unity, the bias converges to zero, since π4te,L will tend to converge to the inflation target.

Under the no credibility scenario (βt = 0), the inflation bias is positive and is proportional to the difference between the high hypothetical inflation expectations and the target.14

Non-linear Output Gap

Empirical evidence suggests that the output gap effect on inflation is non-linear (e.g. Debelle and Laxton, 1997). In the Phillips curve we introduced an exponentially increasing impact on inflation, as follows: λ2*(yt1ymaxyt1ymax).

The parameter λ2 captures the marginal effect of inflation for small values of the output gap. This term implies that output gap cannot exceed a maximum value of ymax. We set ymax equal to 5 per cent in the model simulations. Thus, as the gap approaches 5 per cent, it has a diverging positive effect on the inflation rate (see Figure B.1). This puts a limit on the extent to which expansion of demand can stimulate an increase in output: at ymax, increases in demand result only in increasing inflation. Because of the non-linearity, an economy operating with an output gap near the maximum will subsequently have to incur long periods of negative output gaps to restore the desired inflation rate.

Figure 19B.1Non-linear Phillips Curve, an Example

Inflation (per cent); Output Gap (per cent of GDP)

Source: IMF staff calculations.

Output Gap Equation

Domestic output depends on the real interest rate, the real exchange rate, and demand in the rest of the world, represented by the United States.15

The equation is written in terms of deviations from equilibrium values. The output gap is the deviation, in percentage points, of actual output from a measure of the trend or equilibrium level of GDP (a positive number indicates that output is above trend). It is a function of the gap between the actual real interest rate and its equilibrium value, the real exchange rate gap, and the US output gap. Dynamics are added through the influence of past and future domestic output gaps, and lagged reactions to the interest rate and exchange rate:

where rr is the real interest rate in percentage points, ytUS is the U.S. output gap, and ‘-’ denotes the equilibrium value of a variable. The term ϵty represents a demand shock.

Exchange Rate-Real Interest Rate Parity Equation

We assume real uncovered interest parity (IP) holds, up to a country risk premium. The expected increase in the exchange rate is equal to the domestic-foreign interest differential plus the risk premium. The equation for the current exchange rate equation may thus be written (in logs) as:

where,rrtUS is the US real interest rate and δ is the equilibrium risk premium.

Expectations for the exchange rate are a weighted average of a forward-looking, model-consistent component, and a backward-looking component:

Portfolio preference shocks, e.g. exchange market disturbances, which can be large for emerging market economies, are in the term ϵtz.

Monetary Policy Loss Function

Under IT, almost by definition, the monetary policy loss function attaches a high cost to deviations of inflation from target. In the short run, monetary actions also affect interest rates and output, and policymakers are averse to fluctuations in output from potential and to variability of the interest rate from one period to the next. Aiming to keep output at its potential level—i.e. minimizing the amplitude of the business cycle—has an obvious justification since this is a fundamental objective of macroeconomic policy.

Aversion to interest rate variability, which is evident in the widely observed practice of central banks to adjust interest rates only gradually in response to changes in conditions, has a more technical rationale. Whereas the policy interest rate controlled by the central bank is a very short-term rate, the market interest rates that affect spending and output are not so short-term. Effective transmission of policy actions requires that these market rates respond predictably, in line with movements in the policy rate. With low variability in the policy rate, financial markets can project that a change this quarter will have some duration in the quarters ahead. Longer-term rates, which incorporate expectations of the future policy rate, then respond relatively strongly to policy actions.16

High quarter-to-quarter variability in the policy rate, on the other hand, reduces its impact on relevant market rates, and weakens the effectiveness transmission.

With these considerations in mind, the loss function in the model cumulates a weighted sum of:

  • squared deviations from the inflation target
  • squared output gaps, and
  • squared one-quarter changes in the policy interest rate

The weights (ωi) embody the costs policymakers attach to each of these items. The discount factor is denoted by υ. Monetary policy minimizes this loss function, subject to the constraints imposed by the structure of the model. Monetary policy has choices with respect to the path towards the inflation target. This may be fast, if the cost of misses is high relative to the costs of output and interest rate instability. Or it may be slow, if the cost of targeting errors is relatively low.

The quadratic loss function implies symmetric aversion to overshoots and undershoots with respect to the inflation target. One might argue that policymakers’ preferences would not be symmetric under a program of inflation reduction. They might regard an under-shoot as a benign, though unexpectedly rapid, approach to the low-inflation objective, but an overshoot as a serious threat to the program. Despite the symmetric loss function, the full model does not imply symmetric policy responses. For example, endogenous credibility encourages a stronger interest rate response to overshoots than to undershoots.


    Alichi, A.,Laxton, D.,Dagher, J.,Clinton, K.,Mills, M., andKamenik, O. (2010). A Model for Full-Fledged Inflation Targeting and Application to Ghana. IMF Working Paper 10/25. Washington, DC: International Monetary Fund.

    • Search Google Scholar
    • Export Citation

    Barro, R. andGordon, D. (1983). A Positive Theory of Monetary Policy in a Natural Rate Model. Journal of Political Economy, 91 (4), 589–610.

    • Search Google Scholar
    • Export Citation

    Berg, A.,Karam, P., andLaxton, D. (2006a). A Practical Model-Based Approach to Monetary Policy Analysis: Overview. IMF Working Paper 06/80. Washington, DC: International Monetary Fund.

    • Search Google Scholar
    • Export Citation

    Berg, A.,Karam, P., andLaxton, D. (2006b). A Practical Model-Based Approach to Monetary Policy Analysis: A How-To Guide. IMF Working Paper 06/81. Washington, DC: International Monetary Fund.

    • Search Google Scholar
    • Export Citation

    Debelle, G., andD.Laxton (1997). Is the Phillips Curve Really a Curve? Some Evidence for Canada, the United Kingdom, and the United States. IMF Staff Papers, 44(2) 249–82.

    • Search Google Scholar
    • Export Citation

    International Monetary Fund (2006). Country Report No. 06/229. Washington, DC: International Monetary Fund, pp. 12–17.

    International Monetary Fund. (2008a). Ghana: Selected Issues. Washington, DC: Inter national Monetary Fund.

    International Monetary Fund. (2008b). Regional Economic Outlook, Sub-Saharan Africa. Washington, DC: International Monetary Fund.

    Kamenik, O.,Kiem, H.,Klyuev, V., andLaxton, D. (2008). Why is Canada’s Price Level So Predictable?IMF Working Paper 08/25. Washington, DC: International Monetary Fund.

    • Search Google Scholar
    • Export Citation

    Laxton, D. andPesenti, P. (2003, July). Monetary Polciy Rules for Small, Open, Emerging Economies. Journal of Monetary Economics, 50, 1109–46.

    • Search Google Scholar
    • Export Citation

    Mishkin, F. andK.Schmidt-Hebbel. (2001). One Decade of Inflation Targeting in the World: What Do We Know and What Do We Need to Know?NBER Working Papers 8397. National Bureau of Economic Research.

    • Search Google Scholar
    • Export Citation

    Roger, S. andStone, M. (2005). On Target?: The International Experience with Achieving Inflation Targets. IMF Working Paper 05/163. Washington, DC: International Monetary Fund.

    • Search Google Scholar
    • Export Citation

    Rogoff, K. (1985). The Optimal Degree of Commitment to an Intermediate Monetary Target. The Quarterly Journal of Economics, 100 (4), 1169–89.

    • Search Google Scholar
    • Export Citation

    Smets, F. andWouters, R. (2003). An Estimated Stochastic Dynamic General Equilibrium Model of the Euro Area. Journal of European Economics, 49, 947–81.

    • Search Google Scholar
    • Export Citation

    Woodford, M. (2003). Optimal Monetary Policy Inertia. Review of Economic Studies, 70, 86–8.


This chapter is a slightly revised version of IMF (2008). See also Alichi et al. (2010). Though there have been some significant changes to Ghana’s inflation targeting framework since then, the analysis presented here remains informative for thinking about the ongoing (and recurrent) disinflation challenge in that country.


Examples of countries that have introduced inflation-reduction targets are Brazil, Canada, Chile, Colombia, Czech Republic, Hungary, Israel, Korea, Mexico, New Zealand, Peru, Poland, and the United Kingdom (Mishkin and Schmidt-Hebbel, 2001, Table 2).


Examples are the Reserve Bank of New Zealand, the Norges Bank, the Riksbank, and the Czech National Bank.


For details of the two models, see Appendices A and B, and Alichi et al. (2010).


The model was formulated in close cooperation with the authorities but is the sole responsibility of IMF staff; it does not reflect the conclusions of BoG analysis.


This was end-April 2008 inflation (year-on-year).


This was end-April 2008 inflation (year-on-year).


This appendix draws on Alichi et al. (2010).


The inflation target is defined as the mid-point of the targeting range.


We can think of inflation as specified in equations 6 and 7 to evolve according to a first-order, stationary autoregressive process, reverting in the long run to a targeted level of inflation in the ‘L’ case and 10.8% in the ‘H’ case. The parameter values on lagged inflation are indicative of the rate of convergence to the steady state, with high persistence values implying a longer time to converge.


This term is the expectation error of the low hypothetical inflation expectation.


The convergence rate parameter of the credibility stock was calibrated to 0.7, i.e., it takes 1.5–2.0 years for credibility to rebuild from some below-full level of initial credibility.


Clear evidence of inflation bias stemming from a credibility problem is seen in the behavior of the inflation premium in the UK bond market before 1997.


Representations such as this one are usually motivated with a first-order condition consistent with optimizing consumers with habit formation. See Smets and Wouters (2003) or Laxton and Pesenti (2003) for a linearized version of the Euler equation for consumption that depends on lagged and expected consumption, real interest rates, and a habit-persistence parameter. However, habit-persistence alone cannot account for a very large weight on the lagged output gap, which is resolved in DSGE models by adding investment to the model and significant adjustment costs associated with changing the levels of investment.


On these lines, Woodford (2003) argues that a strategy of gradual interest adjustment may be optimal.

    Other Resources Citing This Publication