Key interest rates have remained low since the Great Recession. The fact that rates have remained close to (or even below) zero has been a major policy issue for central banks worldwide. This situation has prompted policymakers and academics to speak of a ‘new normal’ in monetary policy. What is clear is that, in order to lower interest rates in future downturns, central banks face a ‘lack of room’ for manoeuvre in terms of monetary policy.

Raising the inflation target is a potential remedy to this problem and this has been proposed in recent work (Blanchard et al. 2010, Mishkin 2018, Cechetti and Schoenholtz 2017, Summers 2018). The idea is that raising the inflation target will raise the nominal interest rate, granting policymakers the room to lower interest rates again when needed. Not surprisingly, a wide literature has already emerged studying the question of what the ‘optimal inflation target’ *should* be (Coibion et al. 2012, Andrade et al. 2017, Adam and Weber 2019).

In this column we argue that the above policy remedy (as well as such normative analyses) disregards the importance of the constraints faced by the policymaker. These constraints kick in *after* the policymaker has actually decided to raise the target (and subsequently implements a change). The constraints follow from the fact that the manner in which the economy works varies when one changes a key policy parameter, such as the inflation target. Policy experiments should take this fact into account in order to correctly conduct analyses. Robert Lucas has once famously formulated this insight as the ‘Lucas critique’.

While there could conceivably be many changes to the workings of the economy when raising the inflation target, an obvious consideration is related directly to the phenomenon of inflation. Firms will change prices more frequently in a high-inflation environment compared to in a low-inflation environment. For example, one only needs to compare the inflation experience of Argentina versus Switzerland to realise this is a reasonable change to consider.

Ball et al. (1998) analysed the implications of this assumption early on. More recently, we present evidence on this key assumption using micro data. The complementary analysis in a modern quantitative framework found in Ball et al. (1998) is informative for this discussion. Their results suggest that the answer to the question of ‘how much extra room raising the inflation target can give’ may turn out to be ‘some, but less than intended’.

## Evidence on the inflation target and firm pricing behaviour

The key assumption that leads to this result is justified because there is a strong relationship between the inflation target and the frequency of price changes by firms.

In order to gauge this relationship, it is useful to consider measures of both variables, as we do for the US dataset (L’Huillier and Schoenle 2019). We use micro data on the frequency of price changes from Nakamura et al. (2018), as well as estimates of the inflation target. The former data are available from the Bureau of Labor Statistics for the period spanning 1978 to 2015. It is possible to draw estimates of the inflation target from various sources, including Fuhrer and Olivei (2017), Ireland (2007), Milani (2019), and Cogley and Sbordone (2008).^{1}

As is evident from the scatter plot in Figure 1, the frequency of price changes has a strong positive association with the annual inflation target. This result holds for all four measures of the inflation target. When estimating the relationship using regression analysis, we find that a one percentage point increase in the target is associated with at least a one percentage point increase in the frequency of price changes in the US. It is worth noting that this result also holds when the analysis is run from as late as 1984 (excluding the strong relation between frequency of price changes and inflation in the 1970s).

**Figure 1**

## The mechanics of the effective extra room gained by the policymaker

A first pass to understand the intuition for what will happen when the inflation target increases is to use a simple model, such as the canonical New Keynesian three-equation model. We illustrate this in our work by considering a world with 2% inflation where a demand shock causes the economy to contract. We then consider an identical world with 4% inflation and the same-sized demand shock but allow for the frequency of prices to be higher in response to the policy change.

In such a setting, the effective extra policy room turns out to equal the rise in the inflation target (4% – 2% = 2%), plus the product of two terms (the change in potency of monetary policy multiplied by the absolute value of the shock that hits the economy). Since this product is negative, the effective extra policy room is always less than the intended room of 2%. Why is this term negative? Figure 2 illustrates the intuition. The first arrow shows the economy with a 2% inflation target and a steady-state nominal interest rate of i_{1}. The arrow corresponds to the interest rate drop given a large enough demand shock to bring the nominal interest rate exactly to zero upon impact. Next, consider what happens when the policymaker raises the target to 4% but price flexibility remains the same. The economy moves to a nominal interest rate i_{2} in its new steady state. Upon the impact of the shock, the interest rate falls by the same amount as before, affording an unspent extra 2% of policy room compared to before.

**Figure 2**

Crucially, in the third, more realistic case, the economy also moves to a 4% target but price flexibility increases. In this case, the Phillips curve is steeper. As a result, prices fall by more in response to the demand shock. The interest rate also has to drop by more in order to accommodate the same-sized demand shock, suggesting that monetary policy has become less potent. The effective extra policy room is now less than the intended 2% for this reason. If the policymaker wanted to gain 2% extra room, they would have to move to an even higher target, such as 5%.

## Quantitative estimates and implications for the optimal inflation target

How large is the extra policy room gained in a more realistic scenario that takes into consideration the effect of the change in the target on price flexibility? We show how an estimated equation for the frequency of price changes can be readily used in many standard policy models. This is achieved by appropriately substituting it for the so-called ‘Calvo parameter’, which is frequently used in many policy models, and making it dependent on the inflation target.

An evaluation of several common New Keynesian models shows that the effects of allowing for increased price flexibility are economically significant when the inflation target increases. For example, by raising the target from 2% to 4%, the monetary authority only gains between 0.51 and 1.60 percentage points of policy room, rather than the intended two percentage points. (The exact figure depends on details of the model.) In order to achieve two percentage points additional policy room, the target needs to be raised to approximately 5%, as we conclude in our work.

Considering the higher price flexibility when the inflation target increases has quantitatively important implications for the optimal inflation target. This is especially true when the lack of room for monetary policy is an issue due to a low natural rate of interest (the prevailing current environment in most of the developed world). Indeed, following the approach by Andrade et al. (2019), our work shows that this consideration raises the optimal inflation by about one percentage point. For example, Andrade et al. (2019) find an optimal inflation target near 3% for a natural rate close to zero. Following their approach, we find an optimal target near 4% in our work when calibrating the increased price flexibility from the micro data.

## References

Adam, K and H Weber (2019), "Price trends over the product life cycle and the optimal inflation target," Discussion Papers 32/2019, Deutsche Bundesbank.

Adam, K and H Weber (2019), "Optimal Trend Inflation," *American Economic Review *109(2): 702-737.

Alvarez, F, M. Beraja, M Gonzalez-Rozada and P A Neumeyer (2018), “From Hyperinflation to Stable Prices: Argentina's Evidence on Menu Cost Models”, *Quarterly Journal of Economics* 134 (1): 451-505.

Andrade, P, J Gali, H Le Bihan and J Matheron (2017), “The optimal inflation target and the natural rate of interest”, *Brookings Papers*, forthcoming.

Blanchard, O, G Dell'Ariccia and P Mauro (2010), “Rethinking macroeconomic policy”, *Journal of Money, Credit and Banking* 42: 199-215.

Cechetti, S G and K L Schoenholtz (2017), “The case for a higher inflation target gets stronger”, Money and Banking.

Cogley, T and A M Sbordone (2008) “Trend inflation, indexation, and inflation persistence in the new keynesian phillips curve”, *American Economic Review *98 (5): 2101-2126.

Coibion, O, Y Gorodnichenko and J Wieland (2012) “The optimal inflation rate in new keynesian models: Should central banks raise their in targets in light of the zero lower bound?”, *The Review of Economic Studies* 79 (4): 1371-1406.

Fuhrer, J C and G P Olivei (2017), “Rules and discretion: An empirical Assessment”, Working paper, Federal Reserve Bank of Boston. Fuhr.

Ireland, P N (2007), “Changes in the Federal Reserve's Inflation Target: Causes and Consequences”, *Journal of Money, Credit and Banking* 39 (8): 1851-1882.

L’Huillier, J and R Schoenle (2019), "Raising the Inflation Target: How Much Extra Room Does It Really Give?", CEPR Discussion Paper 14142.

Milani, F (2019), “Learning and the evolution of the fed’s inflation target”, *Macroeconomic Dynamics* 1-20.

Mishkin, F (2018) Rethinking the inflation target. Slides.

Nakamura, E, J Steinsson, P Sun, and D Villar (2018), “The Elusive Costs of

Ination: Price Dispersion during the U.S. Great Inflation”, The Quarterly

Journal of Economics 133(4): 1933-1980.

## Endnotes

1 Alvarez et al. (2018) use inflation instead of the inflation target to establish a relation to the frequency of price changes in the case of Argentina. If we use their data, our subsequent analysis yields quantitatively very similar results. The reason is, once again, that the relationship between frequency and inflation also has a positive elasticity in the Argentina data. (Alvarez et al. also point out that this elasticity is relatively high for high inflation rates, say above 10%. However, even considering the elasticity at inflation close to zero is relevant for the question asked in this column.)