In the world of inflation, the last six months have been more eventful than the preceding six years. After a decade of persistently below-target inflation, the US economy has witnessed price growth way above the central bank’s target, fuelled by strong consumer demand, supply constraints, and backlogs in logistics (Ball et al. 2021).

The debate over how the Federal Reserve should respond has hinged on the implementation of the new flexible average inflation targeting (AIT) framework announced in August 2020 (Powell 2020) and on the persistence of the inflationary spike. How can the Fed reconcile a commitment to make up for inflation shortfalls with the risk that persistent low rates could take them too far from their objective? In this column, we clarify a few important pieces of this puzzle.

The AIT framework implies that if inflation falls below the 2% target in a given year, the Federal Reserve should allow inflation to run above 2% in the following periods, so as to hit the target on average over time. Key questions for an AIT framework therefore concern (i) the time window over which inflation is averaged; and (ii) the weight this inflation average receives relative to some measure of output deviations from trend.

In a recent paper (Eggertsson et al. 2021), we document that the implied average inflation window, consistent with the Fed’s current and announced policy, is between three and five years, assuming the Fed starts to raise rates in the second quarter of this year. We also find that two alternative make-up strategies – a history-dependent nominal GDP target (HD-NGDPT) and a symmetric dual-objective targeting rule (SDTR) – would imply nominal rates similarly stuck at the zero lower bound. In contrast to AIT, these policy strategies explicitly take account of past shortfalls in both inflation and output.

A key conclusion from our exercise is that a lift-off of the Federal funds rate from zero in the first half of 2022 is consistent with the AIT framework outlined by the Fed, provided the averaging is over a period of around three to five years and that the Fed is giving equal weight to output deviations relative to average inflation.

These conclusions are derived solely using data and forecasts, and assuming the Fed follows the specified rules from 2022 onwards. Clearly, had those rules been implemented pre-pandemic, the data and projections would look very different, as the expectations of market participants would reflect the different course of action taken by the central bank. We therefore turn to a simple New Keynesian model to build counterfactual scenarios for a handful of policy strategies.

We find that the announced AIT strategy substantially mitigated (-40%) the recession that otherwise may have occurred under standard inflation targeting (i.e. the Taylor rule). Our more dovish rules that take explicit account of past misses of inflation and output targets would have provided even larger gains, mitigating the recession by 75%. Finally, we find that the expected lift-off of nominal rates does not seem to depend on the persistence of inflationary forces if they originate from shortcomings on the supply side. In addition, we find that being over-stimulative with respect to AIT introduces a trade-off, with output gains coming at the cost of higher inflation.

Despite its limitations in capturing all the facets of the recession relating to Covid-19, distributional consequences, or unconventional monetary policy such as quantitative easing, this is a useful baseline analysis for the forces at play when the economy is constrained by a zero lower bound on nominal interest rates.

## The window of average inflation

The Fed introduced the AIT framework in August 2020, making clear that they were not “tying [themselves] to a particular mathematical formula that defines the average” (Powell 2020). We therefore posit that, behind the scenes, the Fed has a flexible rule that accounts for deviations of average inflation from its target but also takes its employment-output mandate into consideration.

Given realised inflation and output in 2021 and central bank projections (Federal Reserve Board of Governors 2021), we obtain the implied interest rate lift-off dates for different time windows for average inflation and different weights for the dual mandate, shown in Figure 1. Consider, for example, the yellow line, for which there is equal weight on output and average inflation (which we consider a reasonable description of the Fed’s behaviour). If rates are lifted in the second quarter of this year – as it was plausible to assume as of the December 2021 policy meeting – the Fed is aiming at averaging inflation over a window of between three and five years.1 If lift-off falls in the third quarter of 2022, then the Fed is using an inflation window beyond six years. A window of three to five years is towards the lower end of the suggestions of Fed officials in 2021 (Buiter 2021). However, if the gap in output plays no role and the Fed only targets average inflation, the implied time window would be above eight years, as under narrower windows the Fed would already have increased the policy rate. This suggests that the US central bank is not following a pure average inflation targeting strategy.

**Figure 1** Implied time window for average inflation under three different assumptions on the welfare weight of output

*Note*: Blue dotted line implies no weight on output at all (strict average inflation targeting); Yellow solid line implies equal weights on deviations of inflation from target and the output gap, while red dashed line takes on an intermediate position. Projections for inflation and output start in 2022:Q1.

*Source*: US Bureau of Economic Analysis, Summary of Economic Projections, December 15, 2021, Federal Reserve Board of Governors, authors’ calculations.

## Make-up

The new policy of AIT was intended to signal commitment to making up for past shortfalls,2 following a decade of realised inflation consistently failing to hit the 2% target. In Eggertsson et al. (2021), we suggest two alternative indices to measure the extent of past misses: a cumulative shortfall of nominal GDP from its trend (what we call the Gamma index), and a summary of how both inflation and real output deviate from trend (the D index). The related policy rules (HD-NGDPT and SDTR, respectively) imply substantial accommodation even in the face of a strong recovery. We also show that they would have been more effective than AIT in mitigating the Great Recession (Eggertsson et al. 2020). Figure 2 (bottom right and centre panels) updates the analysis with the latest data release and suggests that, if the Fed started to follow either of our two strategies, lift-off would happen no earlier than 2024. We also consider a more conventional nominal GDP target, which only considers deviations of current nominal GDP from its trend. Under this rule, lift-off would already have happened in the second quarter of 2021 (bottom-left panel).

**Figure 2 **Data (solid line) and projections (dashed line) for selected macroeconomic variables

*Note*: Projections start in 2022:Q1. Real GDP is linearly detrended from 2012– 2019 output data.

*Source*: US Bureau of Economic Analysis, Summary of Economic Projections, December 15, 2021, Federal Reserve Board of Governors, authors’ calculations.

## What if?

So far, we have taken the path of the US economy as given by the data. To assess what would have happened under a different policy stance of the Fed during the pandemic, we need to build a proper counterfactual scenario, and for that we turn to a structural model.

To keep things simple and intuitive, we employ the canonical three-equation New Keynesian model (Galì 2008). We model the crisis as an unanticipated fall in the natural rate of interest, with some probability of reversal to the steady state (as in our toolkit paper referenced above). This is a convenient way to capture the aggregate uncertainty surrounding the end of the Covid-19 pandemic, while keeping long-run inflation expectations anchored. In addition, to incorporate the observed price increases, we also hit the economy with a deterministic cost-push shock that fades out over time following an AR(1) process.

The sizes of the shocks are calibrated so that the model replicates the realised path of inflation and real output from the outset of Covid-19 (2020:Q1) until the latest data release (2021:Q4), assuming the Fed has been following a four-year AIT rule throughout.3 We consider four alternative policy strategies: a standard Taylor Rule truncated at the zero lower bound (TTR), a nominal GDP target (NGDPT), and the previously mentioned HD-NGDPT and SDTR.

Figure 3 shows the response of real GDP and inflation to the two Covid-19 shocks. Had the Fed followed a Taylor rule, the output loss would have been much more severe (-20.2% with respect to trend, as opposed to the realised -11.5% contraction). However, the Fed would have done better to follow our two proposed rules or a nominal GDP target, in particular because they imply a stronger make-up component. The vertical bars in Figure 3 denote the expected date of lift-off of nominal interest rates as sociated with each policy rule. Unsurprisingly, the Taylor rule would have led to a lift in interest rates in 2021. Under all other rules, lift-off falls sometime this year or later.

**Figure 3** Counterfactual paths for real GDP and inflation under alternative Fed policy rules

*Note*: Average Inflation Targeting (AIT, blue solid), Taylor Rule (TTR, orange dashed), Nominal GDP Targeting (NGDPT, red dotted), History-Dependent Nominal GDP Targeting (HD-NGDPT, purple dash-dotted), Symmetric Dual-Targeting Rule (SDTR, green dashed). Shaded area denotes forecast. Vertical lines correspond to the expected date at which nominal interest rates are raised above zero.

While SDTR implies an expected lift-off date similar to that of AIT (2022:Q2), HD-NGDPT delays it until as late as the second half of 2023. The intuition above is thus confirmed: lift-off dates – and therefore economic stabilisation – largely depend on the policy rule followed, and more dovish policies that postpone the return to positive interest rates seem more effective at stabilising inflation and output.

## How persistent? It doesn’t matter

We further analyse the possibility of excessive dovishness under AIT in the face of the current inflationary pressures (D’Acunto and Weber 2021). In Figure 4, we provide some evidence that with the current policy strategy, the expected lift-off is unaffected by the persistence of inflation. Specifically, we compare the implied outcomes in the baseline economy under AIT, where the cost-push shock is set to peter out by 70% within a year, against the same economy in which the persistence of the shock implies that it would still be at 95% of its current size after a year. Given that the model must match the same realised data between the onset of Covid-19 and 2021year end, the implied shocks are characterised by a smaller – but more persistent – cost push and a more severe drop in demand. In the simulation, it turns out that the added inflation persistence does not add enough price pressure to raise rates earlier than the baseline. It should be noted that the assumption of a very persistent cost-push shock would imply, on average, a core inflation rate above 4% for at least three years into the future. This prediction is inconsistent with most current forecasts, suggesting that the current inflationary episode should be considered as transitory.

**Figure 4** Data (2020:Q1-2021:Q4) and predicted paths (shaded area) for real GDP and inflation

*Notes*: Persistent scenario implies that the cost push shock has persistence of 0.988. Shock size calibrated to match the same data under the two scenarios. Coloured markers indicate expected lift-off dates.

## Heating up: Not as simple as it looks

A second suspect for elevated inflation is simply a more dovish Fed. Using the same structural model, in Figure 5 we evaluate the costs of over-stimulating with respect to the AIT prescriptions on nominal interest rates. Suppose that, from the end of 2021 onwards, the Fed keeps interest rates at zero for four quarters beyond what the standard AIT rule would prescribe, under any possible future state of the world. The effects of this over-stimulation are increased output at the cost of higher inflation on average. Assessing the desirability of a more dovish policy therefore depends on how one views the trade-off between a stronger recovery and elevated inflation.

**Figure 5 **Data (2020:Q1-2021:Q4) and predicted paths (shaded area) for real GDP and inflation

*Notes*: Overstimulate scenario implies the Fed keeps nominal rates at zero for four additional quarters compared to what AIT prescribes in each state of the world. Vertical lines correspond to the expected date at which nominal interest rates are raised above zero.

*Authors’ note: The views expressed herein are those of the authors and do not necessarily represent the views of the Bank of Italy, the IMF, their respective management or Executive Boards.*

## References

Ball L, G Gopinath, D Leigh, P Mishra and A Spilimbergo (2021), “US inflation: Set for take-off?”, VoxEU.org, 7 May.

Buiter, W (2021), “The Fed must abandon average inflation targeting”, *Financial Times*, November 14.

D’Acunto, F and M Weber (2021), “Rising inflation is worrisome. But not for the reasons you think”, VoxEU.org, 4 January.

Eggertsson, G B, S K Egiev, A Lin, J Platzer and L Riva (2020), “The Fed’s new policy framework: A major improvement but more can be done”, VoxEU.org, 21 October.

Eggertsson, G B, S K Egiev, A Lin, J Platzer and L Riva (2021), “A toolkit for solving models with a lower bound on interest rates of stochastic duration”, *Review of Economic Dynamics* 41: 121-173.

Federal Reserve Board of Governors (2021), Summary of Economic Projections, December 15.

Galì, J (2008), *The Basic New Keynesian Model in Monetary policy, inflation, and the business cycle: an introduction to the new Keynesian framework and its applications*, Princeton University Press.

Powell, J H (2020), "Opening Remarks: New Economic Challenges and the Fed’s Monetary Policy Review".

## Endnotes

1 Most recent communication by the FOMC points to the possibility of a first rate hike towards the end of the first quarter of 2022. It is important to note that our analysis is conducted from the point of view of the latest available public release, which includes data up to December 2021.

2 The ECB also announced its new policy strategy in July 2021, to formally incorporate unconventional tools and to consider new challenges such as climate change. Their strategy differs from the Fed’s mainly because it is based on a symmetric inflation target.

3 To model changing expectations on the duration of the recession, we set the probability of exit from the crisis to a different value in each quarter, so that on average agents expect the crisis to revert in 2022:Q2. We report the estimated shocks in the table below. Results are robust to using a three- or five-year window for average inflation.

*Note*: Calibration of 3-equation New Keynesian model assuming the central bank follows a modified AIT. Shock process follows a 2-state martingale for rnand a deterministic AR(1) process for the cost push shock ut. β = 0.99875, µ changes every quarter (implied expected liftoff in 2022:Q2). Output data are percentage deviations from linear trend 2012:Q1-2019:Q4.

*Source*: U.S. Bureau of Economic Analysis, authors’ calculations.