### Discussion Paper

## Abstract

Which level of inflation should Central Banks be targeting? The authors investigate this issue in the context of a simplified Agent Based Model of the economy. Depending on the value of the parameters that describe the micro-behaviour of agents (in particular inflation anticipations), they find a surprisingly rich variety of behaviour at the macro-level. Without any monetary policy, our ABM economy can be in a high inflation/high output state, or in a low inflation/low output state. Hyper-inflation, stagflation, deflation and business cycles are also possible. The authors then introduce a Central Bank with a Taylor-rule-based inflation target, and study the resulting aggregate variables. The main result is that too low inflation targets are in general detrimental to a CB-controlled economy. One symptom is a persistent under-realisation of inflation, perhaps similar to the current macroeconomic situation. This predicament is alleviated by higher inflation targets that are found to improve both unemployment and negative interest rate episodes, up to the point where erosion of savings becomes unacceptable. The results are contrasted with the predictions of the standard DSGE model.

## Comments and Questions

The authors use an Agent-Based Model to investigate the optimal level of inflation that a Central Bank should target. Their ABM is mainly populated by firms that produce, set prices and wages and hire workers. Other agents are a Central Bank determining baseline interest rates, a representative private bank setting ...[more]

... the interest rates on deposits and loans and a representative household that decides on the level of consumption given their expectations on inflation. The behavioral rules that determine the decisions of the agents are based on economic intuition – prices adjust to accommodate demand, firms hire workers and increase wages if they are not financially fragile, etc. The authors show that targeting a higher than 2% level of inflation reduces unemployment and the probability of negative nominal interest rates. This result is at odds with the prediction of a DSGE model specifically thought to address the same question of optimality of inflation targeting.

This is an important question that has not yet been studied within the ABM literature. (I would also suggest to the authors to look at the paper “Animal spirits and monetary policy” by Paul De Grauwe). The paper is methodologically sound, and the authors rightly acknowledge all limitations of their model. In addition to the weaknesses they mention, I would add that the behavioral rules are sometimes too rigid, and this can lead to unreasonable outcomes like 100% unemployment. The paper is generally well written, although minor revisions might improve readability (see below). One thing I did not understand is the negative real interest rate on deposits in Fig.3(d). First, it does not look reasonable that in the baseline parametrization interest rates are negative. Second, inflation targeting at 2% is actually better than at 3-5% in this case. Another thing the paper falls short is providing clear intuition in what drives some results, although this may be unavoidable in ABMs. For example, what drives the piebald phase diagram in Figure 2? Or the non-monotonicity in Fig. 4(a)?

Most importantly, I really like the idea of a neck and neck comparison with a DSGE model, for instance modelling consumption similarly (euler equation). As a main comment, I would suggest pushing this comparison even further. For example, can the results in Fig. 3(a) and 4(a) be compared with the New Keynesian Phillips Curve? Is the assumption that all firms produce a different good comparable to the Dixit-Stiglitz monopolistic competition? Is it possible to clearly identify a transmission mechanism that is absent in DSGE models? The reply to this paper from mainstream economists would be: nice to know that all these results are possible, but what have I learned from that in terms of economic intuition? Sorry to be vague on this last point.

Minor revisions:

- I would replace \ro by r, as is standard in the literature

- I would not use the acronyms HIHO and HILO in the captions or subsection headings

- Figures 1-2-5-6-7 should have larger axis and tick labels, bigger color bar and more explicative color bar title (e.g. unemployment and not <u>).

- I would replace “the authors” by “we” in the abstract

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This paper investigates the issue of optimal inflation targeting in a simple agent-based model with firms, households and a central bank. The authors take advantage of the flexibility of agent-based modeling to analyze the results of a highly non-linear model, in which boundedly rational agents adapt to the environment using ...[more]

... simple heuristics.

My comments are below.

1) In studying the optimal inflation targeting, a crucial role is played by the mechanism used by the agents to form expectations on future inflation. In this paper, agents use a constant linear combination between average past inflation and the inflation target of the central bank to form their expectation on future inflation (eq. 6). I believe that the assumption that the weights in eq. 6 are fixed is too strong, given the aim of the paper of investigating different inflation targets. This point is actually acknowledged by the authors themselves in the discussion session, and I think they are right. In particular:

a) A high inflation rate is usually associated with high inflation expectations. Do you think that your expectation formation mechanism is adequate to answer your research question? In figure 4 you show that when inflation target is high, inflation is high and in particular that inflation is higher than the target. In such situation, even a boundedly rational agent, would start doubting about the reliability of the inflation target, and increase the weight given to past inflation. I assume that this would further increase actual inflation, starting a hyper-inflation spiral. It would be interesting to analyze the model with adaptive weights in eq. (6).

b) The aim of the paper is not to study a change of the inflation target, but you mention the problem in the introduction. I believe that the model could try to give an answer also to the question about what happens if the CB changes the inflation target. Such point would be much more relevant to the policy debate, since the choice faced by central banks, and the policy discussion mentioned in the introduction of the paper, is about changing the inflation target. However, the effect of changing the inflation target must take into account the effect of such change on the expectation formation mechanism and in particular on “the trust of economic agents in the ability of the CB to enforce the target”. This would be possible by trying to make the weights in eq. (6) dependent on the actual ability of the CB to enforce the target.

2) What is rho_star? Why do you call it natural interest rate? Usually the natural interest rate is connected somehow to the structure of the economic system and to the shocks hitting the system.

3) In the abstract you write that you simulate the model without any monetary policy. This is slightly misleading, since what you actually simulate in Section III is a monetary policy which is not reacting to deviation of inflation from the target. Maybe you should write something like “without an active monetary policy”. What you call native state is influenced by the monetary policy, since it is influenced by the choice of rho_star, i.e. the interest rate set by the central bank.

4) Do you take into account a zero-lower bound? I guess that a zero lower bound should strengthen your results on the optimality of high inflation targeting, but it might have interesting effects in such a non-linear world.

5) Since you speak about optimality you should clearly state what the is criterion to define optimality. You should define some measure of social welfare and use it to evaluate optimality. I assume that you are implicitly taking employment as measure of social welfare (which is fine) but you should state it explicitly and argue in favor of the measure of welfare you want to use.

see attached file

The objective of the authors is to show how a simple agent-based model can be used to address the issue of the choice of the inflation target in a structured manner, i.e. by exploring first the different dynamical regimes of the economy and then by investigating for some regimes what ...[more]

... is the impact of different targets. I find the approach of great interest and the demonstration made by the authors convincing. Yet, an important open question from my point view is the extent to which the regimes identified by the authors and their determinants are canonical/generic. But this is clearly a question for future research. As far as the present paper is concerned, I think the authors could improve the paper by providing a more detailed interpretation of certain parameters/equations and a deeper discussion of certain conclusions. I am offering a few suggestion in this respect below.

- The authors emphasize in the introduction that there is no clear rationale for the choice of the 2% target. It would neve rtheless be interesting to give a brief historical account of the origin of this number.

- It would be good to give a few more details in the introduction about the building block of agents' behavior in the model, e.g in the paragraph starting with to our knowledge.

- It would probably be clearer to present first the firms' behavior because it is the part that gives the most insights about the model.

- On page 1, Our main conclusion is that in general, increasing the inflation target reduces unemployment and reduces the probability of negative rates. It would be good if the authors could provide an intuition of why this is the case.

- In part B. Households, the authors seem to employ the terms savings an investment in an interchangeable manner. This is confusing.

- In spirit, Eq. (5) is similar to the standard Euler equation of DSGE models (see e.g. [6, 23]). What dot he authors mean by "in spirit" ?

- In the "native" state of the economy, the "target" inflation rate is not really a target. It is more a constant term pushing the inflation expectation upwards if I am correct. More generally, the interpretation of equation 6 is not clear to me. Why do you need two parameters ? Why don't you write it rather in terms of the difference between the target and the realized inflation, i.e of the form \pi= tau^* \pi^* +tau (\pi^*-pi) ? Of course this formulation is mathematically equivalent to the one you have and it might not be better but the difficulty is to understand precisely what is the interpretation of the two parameters in the equation.

- Also in the native state of the economy, as tau*=rho* , it is not clear if it is the tau* or the rho* which is the governing parameter. Could you clarify this point or provide some sensitivity analysis in this respect ?

- The main policy conclusion of the authors is that 2% seem too low of a target. It is not completely clear from the paper that this conclusion is valid independently of the choice of parameters (certain parameters are kept fixed throughout) and, more fundamentally, that it is independent of the choice of the time-scale of the model, which seem at first sight arbitrary. I think this latter point should be discussed in more details.

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