Band or point inflation targeting? An experimental approach

Abstract

We conduct laboratory experiments with human subjects to test the rationale of adopting a band versus point inflation targeting regime. Within the standard New Keynesian model, we evaluate the macroeconomic performances of both regimes according to the strength of shocks affecting the economy. We find that when the economy faces small uncorrelated shocks, the level of inflation as well as its volatility are significantly lower in a band targeting regime, while the output gap and interest rate levels and volatility are significantly lower in a point targeting regime with tolerance bands. However, when the economy faces large uncorrelated shocks, choosing the suitable inflation targeting regime is irrelevant because both regimes lead to comparable performances. These findings stand in contrast to those of the literature and question the relevance of clarifying a mid-point target within the bands, especially in emerging market economies more inclined to large and frequent shocks.

Appendices

Appendix 1: Theoretical predictions: descriptive statistics

	Small shocks		Large shocks
	Point IT	No communication	Point IT	No communication
Mean
Inflation	4.80	4.31	4.89	4.62
Output	0.11	0.40	0.11	0.28
Interest rate	4.80	4.22	4.93	4.60
Variance
Inflation	0.51	1.28	0.66	1.22
Output	0.03	0.29	0.34	0.35
Interest rate	0.59	1.81	0.75	1.83

Appendix 2: Experiment: descriptive statistics

1.1 Band IT

Stat. by session (S)	BT with low variance of shocks					BT with high variance of shocks
	S1	S2	S3	S4	Avg	S1	S2	S3	S4	Avg
Inflation expectations
Mean	4.57	4.52	4.74	4.61	4.61	4.96	5.06	4.93	5.17	5.03
Median	4.60	4.58	4.77	4.65	4.66	4.96	5.05	4.97	5.24	5.06
SD	0.12	0.17	0.21	0.16	0.15	0.42	0.26	0.21	0.33	0.25
Inflation
Mean	4.58	4.54	4.72	4.62	4.62	4.96	5.06	4.94	5.15	5.03
Median	4.60	4.60	4.80	4.70	4.65	5	5.10	5	5.20	5.09
SD	0.18	0.20	0.23	0.20	0.18	0.51	0.43	0.41	0.45	0.42
Output gap
Mean	0.29	0.29	0.17	0.24	0.25	$-$0.03	$-$0.09	$-$0.01	$-$0.14	$-$0.07
Median	0.35	0.35	0.20	0.30	0.30	$-$0.05	$-$0.10	$-$0.05	$-$0.20	$-$0.13
SD	0.29	0.30	0.28	0.29	0.29	0.52	0.47	0.48	0.51	0.49
Interest rate
Mean	4.55	4.48	4.69	4.57	4.57	4.96	5.06	4.93	5.17	5.03
Median	4.60	4.60	4.80	4.70	4.65	5	5.20	5	5.30	5.14
SD	0.38	0.41	0.44	0.42	0.40	0.74	0.67	0.63	0.66	0.63

1.2 Point IT

Stat. by session (S)	PT with low variance of shocks					PT with high variance of shocks
	S1	S2	S3	S4	Avg	S1	S2	S3	S4	Avg
Inflation expectations
Mean	4.83	4.31	5.05	4.89	4.77	4.95	5.18	4.89	5.09	5.03
Median	4.84	4.52	5	4.92	4.81	5.03	5.16	4.93	5.09	5.07
SD	0.16	0.43	0.23	0.17	0.14	0.28	0.51	0.24	0.24	0.25
Inflation
Mean	4.80	4.37	4.99	4.85	4.75	4.97	5.16	4.91	5.08	5.03
Median	4.80	4.50	5	4.90	4.78	5	5.15	5	5.10	5.04
SD	0.19	0.39	0.25	0.22	0.19	0.44	0.64	0.42	0.43	0.45
Output gap
Mean	0.15	0.39	0.02	0.14	0.17	$-$0.03	$-$0.16	$-$0.01	$-$0.09	$-$0.07
Median	0.20	0.40	0.10	0.20	0.23	$-$0.10	$-$0.15	$-$0.05	$-$0.10	$-$0.10
SD	0.29	0.35	0.29	0.27	0.28	0.49	0.56	0.50	0.47	0.49
Interest rate
Mean	4.80	4.27	4.99	4.86	4.73	4.96	5.19	4.89	5.09	5.03
Median	4.90	4.50	5	4.95	4.83	5.10	5.25	5	5.20	5.16
SD	0.39	0.59	0.44	0.43	0.39	0.68	0.92	0.65	0.67	0.68

Appendix 3: Statistical tests results

In the following tables, p values are reported in brackets. ***, ** and * respectively indicate significance at 1, 5 and 10% conventional levels.

1.1 Pairwise comparison: band versus point IT with low variance of shocks

Macro. outcomes	Mann–Whitney–Wilcoxon test	Siegel–Tukey test
	Statistical equality betw. tr.?	Statistical equality betw. tr.?
Inflation	No*** (0.0001)	No* (0.0566)
Output gap	No*** (0.0010)	No* (0.0879)
Interest rate	No*** (0.0001)	No** (0.0118)

1.2 Pairwise comparison: band versus point IT with high variance of shocks

Macro. outcomes	Mann–Whitney–Wilcoxon test	Siegel–Tukey test
	Statistical equality betw. tr.?	Statistical equality betw. tr.?
Inflation	Yes (0.8583)	Yes (0.6785)
Output gap	Yes (0.9958)	Yes (0.7709)
Interest rate	Yes (0.8914)	Yes (0.5868)

Appendix 4: Inflation and inflation expectations series across sessions by treatment

See Figs. 5, 6, 7, and 8.

Fig. 5

Inflation, individual inflation expectations and average inflation expectations under band IT with low variance of shocks for four different sessions

Fig. 6

Inflation, individual inflation expectations and average inflation expectations under band IT with large variance of shocks for four different sessions

Fig. 7

Inflation, individual inflation expectations and average inflation expectations under point IT with low variance of shocks for four different sessions

Fig. 8

Inflation, individual inflation expectations and average inflation expectations under point IT with large variance of shocks for four different sessions

Appendix 5: Instructions

We present a translation from French to English of the instructions for inflation point targeting treatments. Instructions for other treatments are available from the authors upon request.

General information

Thank you for your participation to this economic experiment in which you can earn money. Your earnings will depend on both your actions and those of the other participants and will be paid in cash at the end of the experiment. From now until the end of the experiment, you are not allowed to communicate with each other. If you have any question, please raise your hand and we will come to you.

You are a group of 6 participants. The rules are the same for all participants. The experiment consists of 60 periods. Your role is to predict future values of a given economic variable. Your earnings will depend on the accuracy of your predictions. At each of the 60 periods, the economy will be characterized by the following variables: the inflation rate, the output gap, the interest rate, and the inflation target of the central bank.

Information about economic variables

To better understand the economic variables that you will use to make your decisions, we explain these variables as follows.

Inflation is defined as the generalized rise in prices in the economy. Inflation will depend in each period on agents’ average inflation forecasts in the economy (that is, both your forecast and the forecasts of the 5 other participants), on the output gap, as well as on a random shock affecting the economy.

The output gap describes the gap between the current output and the potential output (that is, the level of output the economy can achieve by using the maximum of its productive capacity). If the output gap is positive, the economy is producing beyond its potential level. Conversely, if the output gap is negative, the economy is producing below its potential level. The output gap also depends in each period on the agents’ average inflation forecasts (your prediction and the predictions of the 5 other participants), the lagged output gap, the interest rate as well as a random shock affecting the economy.

The interest rate is defined as the price of borrowing money for a period, and is set by the central bank of the economy. The interest rate mainly depends on inflation (and therefore indirectly on inflation forecasts), the output gap and the inflation target of the central bank.

The inflation target is clearly announced to all participants by the central bank in the form of a numerical target of 5% with a tolerance interval of ±1% around the target. The announcement of the inflation target reflects the central bank’s determination to guide current inflation towards its numerical target. So the central bank commits to reach its inflation target of 5%. However, given the various random shocks affecting the economy, the central bank allows itself a margin error of ±1% around its target. The inflation target then corresponds to a commitment of the central bank which has to ensure (via the interest rate) that inflation in the economy will converge towards this target.

The central bank has two goals: one primary, and the other secondary.

The primary goal the most important is for the central bank to stabilize inflation that is, to make as quickly as possible actual inflation converge towards its numerical target of 5%. The central bank uses the interest rate to stabilize inflation. Positive and significant deviations of actual inflation from the target (that is, actual inflation is not equal to the numerical target of 5%, and is above the upper band of the tolerance interval of 6%), force the central bank to increase the interest rate in order to lead actual inflation towards its target. By contrast, when the central bank notes that inflation is too low compared to its inflation target (that is, actual inflation is not equal to the numerical target of 5%, and is below the lower band of the tolerance interval of 4%) and penalizes the economic activity, it reduces the interest rate.

The secondary goal consists for the central bank in stabilizing the output gap that is, the gap between the current and potential output of the economy, by also using the interest rate. When the output gap is positive, the central bank tends to increase the interest rate, and when it is negative, the central bank tends to reduce the interest rate.

All these variables can be relevant for your inflation forecasts, but it is up to you to use them in your convenience to decide on your inflation expectations. The actual values of the different variables largely depend on your inflation forecasts and those of the others, but also on random shocks affecting the economy.

At the beginning of the experiment and before entering your inflation forecast for the first period in the computer, you observe on the screen initial values of the main economic variables (inflation, output gap and interest rate) at period 0. As stated earlier, the central bank implements an inflation targeting strategy by announcing to all participants its numerical target of 5% with tolerance interval of ±1%. By this announcement, the central bank commits to lead actual inflation towards its inflation target within a maximum of two periods. So you observe the central bank’s target within its tolerance interval. This target remains unchanged throughout the duration of the experiment. Based on these variables, you have to forecast inflation for the next period.

Once you have made your decision, a period ends and a new period starts where you observe the past and actual values of inflation, the output gap, the interest rate, and your inflation forecast made in the previous period. However, you do not observe the expectations of other participants in your group (you just indirectly observe them through actual inflation). All you observe in terms of expectations is your own time series forecasts. As time goes on, you get a large number of observations that allows you to evaluate the accuracy of your forecasts compared to actual values of inflation, as well as the inflation target of the central bank.

Information about your role in the economy

Throughout the 60 periods of the experiment, your role as an agent of the economy is simple. You have to forecast the actual value of future inflation. In other words, you have to predict in each period, the inflation that will prevail in the next period based on all information available to you when making your decision. You must then enter in the computer your inflation forecast. Suppose that on your computer screen, you observe at period 2, actual inflation. This observed inflation is not based on the forecasts that you and the other participants of your group have made at period 2, but the predictions you made in the previous period that is, those made in period 1 for period 2.

By choosing your inflation forecast, you seek to maximize your earnings. Your gain in each period depends on the accuracy of your inflation forecast relative to actual (realized) inflation. More specifically, your gain is given by:

$$\begin{aligned} \text {Your profit in ECU}=\max \Bigg \lbrace \dfrac{160}{1+f}-40,0\Bigg \rbrace , \end{aligned}$$

where $f=\mid \text {Inflation}-\text {Your forecast}\mid$. ‘Inflation’ indicates actual inflation, ‘Your forecast’ defines your inflation forecast made at previous period for the next,  f indicates in absolute value your forecasting error, and finally ‘ECU’ indicates the Experimental Currency Unit. The profit function above means that you get money every time your forecasting error is less than 3%. The smaller your forecasting error, the higher your payoff. For instance if f $=$ 0, you receive the maximum payoff of 120 units $(160/(1+0)-40)$. If your forecasting error is of 1.5%, you receive 24 units $(160/(1+1.5)-40)$. Otherwise if your forecasting error is of 3% or higher, then you receive 0 unit $(160/ (1+3) - 40)$. You can only choose your inflation forecasts within the interval [3, 16]. You can only choose whole numbers or numbers with one decimal digit (for instance, 5, 8.5, 4.6, etc). In addition, when making your decisions, you have to enter only numbers without the “%” symbol.

Once you have entered your decision in the computer, click on the ‘Submit’ button. Once all participants have done the same, the period ends and the profit for this period is written on the computer screen. Then, the next period starts. Once all the 60 periods are completed, the experiment ends. At each of the 60 periods of the experiment, at the top of each screen and on a graph, you can observe the entire history of economic variables as well as your earnings. You can then check at each period if your inflation forecast made in the previous period corresponds to actual inflation, and also whether it corresponds or converges towards the inflation target of the central bank. You will get informed about your gains period by period, and at the end of the experiment, your earnings will be added and will be paid in cash converted at the exchange rate of €1 $=$ 520 ECU. Note that you do not get money in the first period of the experiment because you will not have made any forecast for this period 1. So your potential gains start at period 2 of the experiment, because you will have made forecasts at period 1 for this period 2.

Questionnaire

At the beginning of the experiment, we ask you to fill out a questionnaire to make sure that you understand instructions. When all participants have correctly answered the questionnaire, the experiment will begin. At the end of the experiment, we ask you to complete a personal questionnaire on the computer. All requested information will remain strictly confidential and is used for the sole purpose of research.

If you have any questions, please ask them now!

Thank you for your participation!

Appendix 6: Examples of screens

We provide examples of screens (first screen: band IT; second screen: point IT).

Appendix 7: Formation of individual inflation expectations

Agents’ expectations influence macroeconomic outcomes. Following the LtFE literature that emphasizes expectation heterogeneity, we study the formation of individual inflation expectations owing to the collected times series data for all subjects. This allows us to evaluate the impact of point versus band IT regimes on subjects’ expectation formation process.

Following Pfajfar and Zakelj (2013, 2014), Assenza et al. (2013), and Cornand and M’baye (2016), we consider the main expectations formation models supported in the literature in order to find the best fit of each subject’s expectation series. We assume that subjects behave like econometricians and select both the given rule and its parameters to forecast inflation. We do not include exogenous shocks in the given expectation models, because they were not directly observable in the experiment.²⁸ The methodology we apply here is the following: for each subject of each session (each including 4 treatments), we estimate the coefficient(s) of interest of the given expectation model by performing the OLS techniques. Then and conditional on the significance of the estimated parameter(s), we compute for each treatment the percentage of subjects using such and such forecasting rule. Table 2 below presents the conclusions of our regressions.

1.1 Prediction models

Naive expectations model

$$\begin{aligned} \pi _{t+1/t}^{i}=\alpha _{0}+\alpha _{1}\pi _{t-1}, \end{aligned}$$

(M1)

where $\pi _{t+1/t}^{i}$ denotes subject i’s (where i $=$ 1, 2, $\ldots$, 96) inflation expectation made at time t for $t+1$, $\pi _{t-1}$ represents the past period inflation rate, and $\alpha _{0}$ and $\alpha _{1}$ are the estimating parameters. This forecasting rule implies that agents form their expectations for the next period conditional on the past period inflation rate.

AR(1) expectations model

$$\begin{aligned} \pi _{t+1/t}^{i}=\beta _{0}+\beta _{1}\pi _{t/t-1}^{i}, \end{aligned}$$

(M2)

where $\pi _{t+1/t}^{i}$ denotes subject i’s inflation expectation made at time t for $t+1$, $\pi _{t/t-1}^{i}$ represents its past period forecast, and $\beta _{0}$ and $\beta _{1}$ are the estimating parameters. Following this forecasting rule, agents form their next period expectations by only taking into account their former inflation forecasts.

Trend extrapolation model

$$\begin{aligned} \pi _{t+1/t}^{i}=\gamma _{0}+\pi _{t-1}+\gamma _{1}(\pi _{t-1}-\pi _{t-2}), \end{aligned}$$

(M3)

where $\gamma _{0}$ and $\gamma _{1}$ are the estimating parameters. In this case, agents form their inflation expectations based on past inflation and on the trend of past inflation.

Adaptive expectations model

$$\begin{aligned} \pi _{t+1/t}^{i}=\pi _{t-1/t-2}^{i}+\eta (\pi _{t-1}-\pi _{t-1/t-2}^{i}), \end{aligned}$$

(M4)

where $\eta \ge 0$ is the constant gain parameter. Agents revise their expectations based on the observed errors.

Table 2 Percentage of subjects using M1, M2, M3 and M4 expectation models for each treatment

1.2 Econometric results

Table 2 presents for each treatment the percentage of subjects using the given expectations model.

The relevance of subjects’ forecasting rule depends on the considered treatment. We find that Treatment 1 (band targeting with small shocks) is the one which has the highest proportion (87.5%) of subjects that use the naive expectations model (M1) to forecast inflation, while Treatment 2 (point targeting with small shocks) is associated with the lowest proportion (66.67%) of subjects that use this forecasting rule to form their expectations. We also explore whether the behavior of individual inflation expectations among treatments is consistent with the AR(1) model. We find that most subjects do not really use this forecasting rule to predict inflation. Finally, we find that both trend extrapolation (M3) and adaptive expectations (M4) prediction rules play an important role in the dynamics of inflation expectations formation as all subjects in each treatment use on average these models to forecast inflation. Treatments 2 and 3 are associated with the highest proportion (87.5%) of subjects using M3, while Treatments 1, 2 and 4 are associated with the highest proportion of subjects using adaptive learning rule to predict inflation. These results are consistent with those of Assenza et al. (2013), Pfajfar and Zakelj (2014), and Cornand and M’baye (2016) who find that subjects most use M3 and M4 to form their expectations. Moreover, we find that for the trend extrapolation model, the significant coefficient $\gamma _{1}$ is below 0 for a large proportion of subjects in all treatments, which suggests that on average and in all treatments, subjects using this rule expect that the upward (downward) movements in inflation in the current period will be followed by the downward (upward) movements in the next period.²⁹

We finally look for the prediction model that best explains the formation of average inflation expectations within each treatment. To do so, for each session of each treatment, we consider average inflation expectations and look at all prediction models to select the one that yields the highest adjusted $R^{2}$. After doing so, we select the most relevant forecasting rule for a whole treatment. We find that the trend extrapolation rule appears to be the forecasting model which best explains the formation of average inflation expectations in all treatments.