Name: Daria Minina Student number: 11648902
Study track: Behavioral Economics and Game Theory Number of ECTS: 15
Research supervisor: Stefanie J. Huber
MASTER THESIS
Inflation expectation formation: Laboratory experiment in high and low inflation environment
Statement of Originality
This document is written by Daria Minina who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
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Abstract
This thesis investigates if and how macroeconomic environment affects expectation formation. Based on a learning-to-forecast experiment conducted in Belarus and the Netherlands, the adaptive expectations model fitted the observed inflation forecasts best. Dividing the sample into two subperiods, the adaptive expectations were a better fit only for the period after the shock occurred. These results point to the heterogeneity in forecasting strategies depending on the environment. Contrary to the predictions, the updating parameter was not higher in the high-inflation treatment for the whole time period. However, when the adaptive expectations model was estimated for two subperiods, before and after the shock, the Belarus treatment had a significant increase in the updating parameter, while the UVA treatment did not. Hence, the results of the study suggest that macroeconomic environment, in particular, the level and stability of inflation, influences the way expectations are formed.
Key words: Laboratory Experiments, Learning-to-forecast Experiment, New Keynesian Model, Inflation Expectations, Rational Expectations Hypothesis, Adaptive Expectations Model.
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Contents
1. Introduction ………...………… 4
2. Literature review ………..……. 6
3. Experimental design ………...……….……. 18
4. Methodology of data analysis ………...………..…. 25
5. Experimental results ………. 27
6. Discussion ………...………. 36
7. Conclusions ………...………..………. 37
8. References ………...………. 39
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Introduction
Inflation represents one of the main macroeconomic variables, and maintaining price stability is in the mandate of almost every central bank. According to economic theory, inflation expectations are one of the main determinants of inflation. For instance, the Phelps-Friedman expectations augmented Phillips curve relates aggregate inflation expectations to the change in the actual price level. New Keynesian Phillips curve, which includes expectations as a determinant of inflation, is a crucial part of the modern macroeconomic models. Also, economic policymakers, for instance former Chairmen of the FED Ben Bernanke (2004, 2007), numerous times recognized the importance of inflation expectations in determining the actual inflation. Moreover, empirical research papers find evidence of the important role of expectations in determining the actual inflation. Galí, Gertler and López-Salido (2001), Taylor (2000) are the examples of such papers. To a greater or lesser extent, expectations of all economic agents influence inflation. Inflation expectations of consumers are of great importance, because they make decisions on how much to consume as well as what share of their income to keep in local currency. If consumers have high inflationary expectations, they lose confidence in the local currency which causes sharp currency depreciation. Moreover, inflation expectations influence the wage bargaining process. High inflation expectations of producers also have a significant effect on the economy. One example of this is when instead of making investment enterprises buy inflation-linked bonds.
Persistent high inflation expectations make the job of central banks very difficult because achieving targets requires managing inflation expectations besides influencing the economic fundamentals.
For the above described reasons, inflation expectations are an essential part of many macroeconomic models. Most of them assume expectations to be rational. Milani and Rajbhandari (2012) studied how sensitive the New Keynesian models are to the assumptions on expectation formation. The authors came to the conclusion that different mechanisms of expectation formation affect estimates of structural parameters of the models, properties of exogenous shocks, model fit and forecasting performance. So, if expectations follow a different rule, the New Keynesian models might require significant adjustments.
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Hence, understanding the formation of inflation expectations is a topic of great importance for monetary policy.
For the reasons described above, this thesis studies inflation expectation formation. In particular, the thesis presents an attempt to answer the following research questions:
• How are individual inflation expectations formed and adapted? • How are the aggregate inflation expectations formed?
In answering both questions, the thesis looks into the relationship between economic environment and the formation of expectations.
Empirical evidence of bounded rationality and violations of rational expectations motivated the research hypothesis that most agents use one rule – adaptive expectations but vary the updating parameter depending on the environment. Indeed, many research papers found evidence in favor of adaptive expectations.
Panic events, such as bank runs, queues in front of the exchange offices and in shops after minor changes in macroeconomic fundamentals in the countries with unstable economic situation motivate the hypothesis that people update their forecasts faster in such environments.
To sum up, the hypotheses of study are the following:
• Most people do not switch between forecasting rules. Instead, they use adaptive learning model (details in literature review) and change updating parameter in response to changes in the environment.
• Updating parameter will be bigger in high inflation environment because underprediction of inflation in unstable environment is more costly than overpredicting.
Inflation expectations are difficult to study because that they cannot be directly observed. Thus, measuring them accurately is also a complex task. There are two broad ways of measuring inflation expectations: direct and indirect. Direct measures use surveys as the main instrument, and indirect measures use financial instruments. For instance, the difference between nominal and real government bond yields gives an idea of investors’ inflation expectations. Inflation-linked securities, like inflation swaps, are also a tool for deriving inflation expectations.
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This thesis uses an alternative approach to measuring inflation expectations directly, namely a learning-to-forecast experiment. The experimental design section presents a discussion of the advantages of this method over survey expectations.
This study contributes to the field in two respects. First, the current body of research on learning-to-forecast experiments is mostly limited to individual expectation formation. This study makes a contribution to the field by researching the effects of environment on individual and aggregate expectation formation. In particular, the main idea of the thesis consists in conducting a learning-to-forecast experiment in 2 countries, one with persistent high inflation (Belarus) and the other with low inflation (Netherlands), and comparing the inflation expectations.
The second original idea of the study is the new rule of change in the parameter of the adaptive learning model. The thesis hypothesis states that the updating parameter depends on the phase of the cycle, because costs of underpredicting inflation are asymmetric. Additionally, the model will also include heterogeneity which means that people change this parameter at different pace. The results of the study showed that the adaptive expectations model was the best fit out of the estimated forecasting rules for most of the subjects. However, when the sample was divided into 2 subperiods, the results pointed to the heterogeneity in forecasting strategies depending on the environment. Contrary to the predictions of the thesis, the updating parameter was not higher in the high-inflation treatment for the whole time period, but the Belarus treatment showed a significant increase in the updating parameter in the subperiod after the shock, while the UVA treatment did not. Hence, the results of the study suggest that macroeconomic environment, in particular, the level and stability of inflation, influences the way economic agents form their expectations.
Literature review
This thesis deals with such topics as deviations from the rational expectations hypothesis, adaptive expectations, experimental macroeconomics and learning-to-forecast experiments. In the literature review, I will first define the rational expectations hypothesis, which is a standard approach to expectations in macroeconomics. Then, I will discuss empirical papers that found violations of this hypothesis. The description of the main approaches to modifying the rational expectations hypothesis, like information frictions, bounded rationality and the mixtures of the two, will follow.
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Next, I will discuss the adaptive expectations model, which is one of the most popular alternatives to the rational expectations hypothesis. Finally, I will give an overview of experimental macroeconomics focusing on the topic central to this thesis - learning-to-forecast experiments. Rational expectations hypothesis
The current consensus in the macroeconomic literature is still the rational expectations hypothesis (REH). This approach to expectations was suggested by Muth (1961) and developed by Lucas (1972, 1976) and Sargent and Wallace (1975). The rational expectations hypothesis in its strongest form assumes that individuals are perfectly rational, and they have complete information about the economy. The former assumption means that economic agents have perfect computational skills, hence they do not make systematic mistakes in their forecasts. The latter implies that agents use all the available information in forming expectations. Both assumptions are imperfect approximations of reality. According to numerous empirical papers, the rational expectations hypothesis fails to capture the patterns observed in laboratory experiments and surveys on inflation expectations.
Despite the compelling evidence of boundedly rational behavior, several research papers found evidence consistent with some form of rationality. For instance, Keane and Runkle (1990) studied individual inflation expectations of the professional forecasters from the ASA-NBER survey and obtained results supporting the rational expectations hypothesis.
Forsells and Kenny (2003) also found evidence of the intermediate form of rationality, meaning unbiasedness but incomplete information set, in the data from the European Commission’s Consumer Survey. In particular, consumers seemed to take into account the past inflation data but failed to fully incorporate other important macroeconomic variables, like monetary and financial indicators, in their calculations. Forsells and Kenny also found confirmation of increased forecasting efficiency in periods of low and stable inflation.
Another paper that could not reject rational expectations hypothesis for a significant percentage of consumers was Pfajfar and Santoro (2010). They looked into the data from the Michigan Survey of Consumers and detected 3 regions in the distribution of inflation forecasts: close to unbiased expectations in the middle range of the distribution, expectations exhibiting significant overreaction to the right of the median and expectations produced using incomplete information
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set to the left of the median. In particular, the left side of the distribution could be characterized by backward-looking rules, the data on the right side of the distribution was consistent with adaptive learning and rational inattention hypotheses and the central range possessed features of rational forecasts.
Many other papers demonstrated presence of features in the survey data that are inconsistent with the rational expectations hypothesis.
Figlewski and Wachtel (1981) studied inflation expectations data from the Levingston’s survey. They found the data to be inconsistent with rational expectations hypothesis due to significant downward bias and serially correlated forecast errors. Moreover, adaptive expectations model was the best fit to the data. Figlewski and Wachtel also found heterogeneity in the updating parameter both across individuals and across time. The adaptive coefficient was higher when uncertainty was higher but contrary to the finding of many research papers, the coefficient was lower when inflation was higher.
Ball and Croushore (1995) investigated whether inflation and output expectations from the Survey of Professional Forecasters, the Livingston and the Michigan surveys contradict the rational expectations hypothesis. The results of the research did not support complete rationality but were consistent with sticky prices and incomplete information. Ball and Croushore also found that individuals underreact when they receive new information.
De Brouwer and Ellis (1998) analyzed data from the Melbourne Institute survey of households and the Money Market Services survey of financial market economists and found that financial professionals tend to overestimate inflation when it is declining and underestimate when it is increasing, while households tend to overestimate inflation all the time. The study also found the forecasts of financial market economists to be less biased than the forecasts of households. The authors also conducted a formal test of REH and it was rejected.
Thomas (1999) studied the data from 3 surveys: Livingston, Michigan and the Survey of Professional Forecasters. He found inflation expectations to be biased when inflation is unstable, namely in periods of increasing inflation all forecasts underestimate the actual inflation and vice versa. Moreover, expectations failed the test on strong-form efficiency which means that agents did not utilize all the available information. The second finding of the paper was that inflation
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expectations exhibit adaptive behavior. Finally, respondents demonstrated significant long-run mean-reverting tendencies in their forecasts.
Mehra (2002) took the research of Thomas (1999) as a basis and addressed the limitations of the study. Namely, he applied cointegration to control for non-stationarity, Granger-causality to check the presence of a forward-looking component in the expectations and used real-time data to avoid the problem of data revision. The results of Mehra were similar to the ones obtained by Thomas (1999). In particular, forecasts were biased in different subperiods. Efficiency was also shown to be violated. However, when real-time data were used, evidence against efficiency was much weaker.
Mankiw, Reis and Wolfers (2003) found evidence against the rational expectation hypothesis in the data from the Michigan and the Livingston surveys. In particular, they showed consumer inflation expectations to be biased and inefficient. They also found substantial variance in the forecasts of consumers and professional economists.
Dias et al. (2010) studied survey data on inflation expectations released by the European Commission, and the rationality hypothesis did not hold for the euro area. Namely, inflation forecasts were biased, but efficiency results were mixed.
Long lasting effects of crises and shocks which have been documented by many research papers also give evidence against the rational expectations hypothesis.
Malmendier and Nagel (2009) investigate the long-term effects that experienced macroeconomic outcomes have on individual behavior. They found these effects to be significant even after several decades have passed. In particular, Malmendier and Nagel identified long lasting changes in risk attitudes after traumatic macroeconomic experiences, like stock market crashes. In their recent paper, Malmendier and Nagel (2016) extend the adaptive learning model with updating of expectations that depended on age of an agent. As in their earlier study, Malmendier and Nagel found that younger agents reacted to changes in macroeconomic indicators faster.
Galati et al. (2009) studied how the Great Recession affected long-run inflation expectations. In particular, they researched the anchoring of inflation expectations during and after the crisis. The theory predicts that well-anchored long-run expectations should not react to news about macroeconomic variables. The paper found a significant decrease in anchoring of the long-run
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inflation expectations after the crisis for the US, the UK and the euro area. This means that sensitivity to news about macroeconomic variables increased. However, in the UK and the euro area expectations remained relatively well anchored, while anchoring in the US was not firm both before and after the crisis.
Gnan et al. (2010) analyzed the data from the European Commission’s Business and Consumer Survey and the Survey of Professional Forecasters and demonstrated that the crisis of 2008-2009 significantly affected the inflation expectations of all economic agents. Their results give evidence in favor of both incomplete information and bounded rationality.
Another stream of literature, that gives evidence of REH violations, studies how various factors, sometimes unrelated to macroeconomy, affect expectations about macroeconomic indicators. For instance, Dohmen et al. (2006) provide evidence that not only crises but also events unrelated to macroeconomy can influence expectations about macroeconomic indicators. Using telephone surveys, they tested whether the FIFA World Cup 2006 affected economic expectations and perceptions in Germany. The paper found that unexpectedly good performance of the German team was associated with more positive perceptions of economic conditions and expectations of stronger improvements.
In similar vein, Brückner & Pappa (2015) examined the positive effects of hosting Olympic games. The authors concluded that hosting countries experienced increase in investment, consumption and GDP due to changes in expectations of economic agents.
Demographic characteristics have also been shown to affect expectations. The most often reported results indicate that women, people with lower income and lower level of education have an upward bias in inflation expectations.
One of the earliest research papers on the topic was written by Souleles (2004). He analyzed the Michigan Index of Consumer Sentiment and found inflation expectations to be biased and inefficient. Another important finding of the paper was that forecast errors were correlated with demographic characteristics of the respondents. Finally, Souleles indicated that aggregate shocks do not have the same effect on all consumers. So, he found aggregate shocks to be a source of heterogeneity.
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Pfajfar and Santoro (2008) studied consumer inflation expectations from the Michigan survey and found significant heterogeneity. Moreover, such demographic characteristics as income, gender and education were shown to influence the formation of expectations. In particular, respondents with greater income, higher level of education and males had smaller forecast errors and took into account the general price level instead of limiting attention to their consumption basket.
Burke and Manz (2014) conducted a learning to forecast experiment to research the effect of economic literacy on the accuracy of inflation expectations. They investigated two ways in which economic literacy may affect the forecasting errors: choice of information and use of information. Burke and Manz found that subjects with more economic literacy, in particular monetary and financial literacy, chose more relevant information and used it more efficiently. The authors also hypothesized that a significant share of demographic heterogeneity observed in inflation forecasts may come from heterogeneity in economic literacy.
Ehrman, Pfajfar and Santoro (2014) used panel data from the Michigan survey and demonstrated that besides demographic factors, like gender, education level and income, financial situation and attitudes of households matter for inflation expectations. The research found respondents with more pessimistic predictions of their future income to be more biased in the direction of overestimation. Ehrman, Pfajfar and Santoro also identified that obtaining more information, for example more extensive media coverage of inflation, significantly decreases this bias.
Abbas, Beg and Choudhary (2015) studied survey inflation expectations in Pakistan and demonstrated that forecasts of females, low-income, younger and less educated respondents were significantly biased upwards.
Dow Jr. (2016) studied data from the Survey of Consumer Finances of the United States and also found that demographic factors affected expectations of households about interest rates and economic growth.
Summarizing, the rational expectations hypothesis is the main approach to expectations currently used in macroeconomic models. In its strongest form, it assumes that economic agents are fully rational and possess all the necessary information to form expectations. The main conclusion from this subsection is that numerous research papers found violations of the rational expectations hypothesis in the aggregate and individual data. In particular, demographic characteristics,
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previously experienced crises and even events unrelated to macroeconomy were shown to influence long-run expectations of agents. This study complements the above described literature by showing that economic environment in which individuals are brought up affects the formation of expectations.
Modifications of the rational expectations hypothesis Information frictions
The evidence against the rational expectations hypothesis in its’ classical form had become overwhelming, and economists started exploring deviations from rationality. The first stream of research focused on relaxing the assumption of complete information while keeping the rationality assumption intact. Several research papers contributed to the stream by showing that deviations from the rational expectations hypothesis observed in the data can be explained by information frictions. One of such papers was Andolfatto et al. (2008). They question conclusions made in many papers that the bias observed in inflation expectations is evidence of boundedly rational behavior. The authors criticize the current stream of research rejecting the REH in several respects. First, Andolfatto et al. underscored small sample problem in many papers that found violations of the REH. Second, they show that adaptive expectations can be rational, for instance in the case of imperfect information. However, this is true only for small sample cases. In the population, forecasts should still be unbiased.
The authors prove their argument by constructing a New Keynesian model that rests on the assumption of rational expectations and testing inflation data generated by this model for unbiasedness. The key feature of their model is the Taylor rule with infrequent regime shifts and transitory shocks to interest rate which economic agents cannot disentangle. Decision-making in such conditions requires a forecasting rule similar to adaptive expectations. Andolfatto et al. showed that even in the data simulated by the model based on rational expectations unbiasedness was frequently rejected. However, two conditions need to be satisfied: limited information and relatively short sample.
In the stream of information frictions, the most influential alternatives to the rational expectations hypothesis are the sticky information hypothesis, suggested by Mankiw and Reis (2002), and the rational inattention hypothesis, invented by Sims (2003).
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In their model, Mankiw and Reis basically changed the New Keynesian Phillips curve. The modification to the curve consisted in replacing the inability to change prices every period with inability to obtain new information. So, in the model of Mankiw and Reis people update their information set infrequently.
Sims (2003) used an engineering approach and developed the rational inattention model. In his model, information is freely available, but agents have limited ability to process it. Individuals are solving an optimization problem to decide how much information to process. As a result, sometimes it is rational for agents to be inattentive to some information. That is why this model is called the rational inattention model.
Bounded rationality
The second stream of literature researches deviations from perfect rationality. In particular, it aims to explain the observed violations of the rational expectations hypothesis with psychological factors.
The findings of the empirical studies and economic experiments shed light on how agents make decisions and forecast economic outcomes. As a result, psychologists and behavioral economists categorized the observed patterns in decision-making into a number of rules of thumb that agents tend to use. These mental shortcuts are called heuristics.
Availability heuristic states that agents predict the likelihood of an event based on how easy a similar event comes to their mind. This heuristic explains why inflation expectations depend on the experience with inflation a particular individual had. A similar rule of thumb is simulation heuristic. It implies that individuals predict probability of an event depending on how easy they can imagine this event.
Another related rule of thumb is called representativeness heuristic. This mental shortcut explains why individuals might fail to take into account new information. In particular, agents estimate the probability of an event based on the probability of a similar event they have in mind. Applied to inflation, it helps explain why well-anchored long-run inflation expectations do not react to short-run changes in macroeconomic indicators.
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Under salience heuristic, individuals tend to pay more attention to information that stands out. For instance, in periods of high and volatile inflation, economic agents start actively taking into account the data on actual inflation because this information becomes more salient.
Confirmation bias refers to the selectivity of information processing. In particular, agents tend to ignore the information that does not confirm their prior beliefs.
Another heuristic, called anchoring and adjustment heuristic, was discovered by Kahnemann and Tversky (1974). Regarding inflation, this rule of thumb implies that expectations depend on the starting value of actual inflation (anchor).
Overconfidence bias also plays an important role in consumer inflation expectation. This phenomenon implies that agents overestimate the accuracy of their forecasts. Research (Thaler, 2000; Giordani and Söderlind,2003) confirmed the presence of overconfidence bias in consumers as well as professional forecasters.
Bounded rationality explains the observed consumer behavior pretty well, which is a significant advantage. On the other hand, imperfect rationality is difficult to model, and thus, including it into macroeconomic models is problematic. Nevertheless, there have been several attempts to include bounded rationality elements into the New Keynesian framework. Gabaix (2016) expanded the standard New Keynesian model with a myopia parameter. This parameter characterizes the inaccurate policy expectations of economic agents. The introduction of such a modification to the model leads to a number of important consequences, like determinacy of equilibrium even in the case of passive monetary policy and muted effects of forward guidance.
Adaptive expectations
Some theories combine information frictions with bounded rationality. One of them is adaptive expectations hypothesis which is the most widely used alternative to the rational expectations hypothesis. Adaptive expectations were first introduced by Cagan (1956) and well documented by Evans and Honkapohja (2001). This hypothesis assumes that expectations are adapted according to the following rule:
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where 𝜋𝑡𝑒 refers to expectation of inflation in period t, 𝛼 is the updating parameter and 𝜋𝑡 is the actual inflation in period t-1.
The parameter value 𝛼 depends on beliefs about the likely source of last period’s error. If agents believe the error was caused by a permanent shift in the process forming 𝜋, then 𝛼 is set to 1, so that 𝜋𝑡𝑒 = 𝜋𝑡−1. If last period’s error was just due to a random event, then 𝛼 = 0 and there is no adjustment.
An important development of adaptive expectations hypothesis is adaptive learning. It consists in changing the parameter of adaptive expectations model depending on the forecasting errors. Heterogeneity
Rational expectation and adaptive expectations find little empirical support in their pure form. Many researchers suggest that several types of agents co-exist in the markets. All these types form different expectations, thus expectations are heterogeneous. The most popular models of heterogeneous expectations are the following:
• Sticky information model of Mankiw and Reis (2003). This model is similar to Calvo pricing in that each period a fraction of people obtains new information and recomputes the forecast. This model, however, assumes that agents are fully rational which is not always true.
• Expectations switching of Anufriev and Hommes (2009, 2012). In this model, boundedly rational individuals choose from several forecasting rules, and the rational expectations hypothesis is one of the methods. The main idea of expectations switching is that sophisticated methods of forecasting are costly. Costs in this context can be interpreted as calculation time or costs related to acquiring information. So, the choice of a specific method depends on relative costs and successes of this method in the recent past.
• Heterogeneous expectations with behavioral rationality of Brock and Hommes (1997). This model assumes that agents choose from simple decision rules and they switch between rules based on evolutionary selection and learning.
Summing up, there are two main modification of the rational expectations hypothesis: information frictions and bounded rationality. The former assumes that agents are rational, but they do not have full information. The latter considers that agents have limited computational abilities, thus they
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make mistakes. Numerous research papers found confirmation of both features which suggests heterogeneity of forecasting rules.
One of the main alternatives to the rational expectations hypothesis is the adaptive expectations model. It combines features of information frictions with bounded rationality. This thesis contributes to the literature by testing how experimental data fits the adaptive expectations and researching the effects of environment on the updating parameter of the model.
In all research discussed above, inflation expectations were studied based on survey data. However, this is not the only method suitable for analyzing expectations. In the last 10-15 years experimental approach to macroeconomics has become increasingly popular.
Experimental macroeconomics
One of the first experiments on inflation expectations was conducted by Marimon and Sunder (1991, 1993). The experimental economy in their research was described by an overlapping generations (OLG) model. They found evidence in favor of agents’ adaptive behavior. Marimon and Sunder also studied the problem of indeterminacy of equilibria in OLG models and came to the conclusion that this problem is rare in the real economies compared to theoretical models. In particular, the experimental data of Marimon and Sunder converged to low-inflation steady state even in the hyperinflation treatment.
Currently, most experiments that study inflation expectations do not use the framework suggested by Marimon and Sunder. Instead, researchers use learning-to-forecast experiments with New Keynesian framework.
Learning-to-forecast experiments, where the simulated economy follows a New Keynesian model, were first conducted by Adam (2007). In such experiments subjects are typically asked to forecast inflation or output gap or both indicators at the same time. The New Keynesian model of a typical experimental economy consists of 3 equations (Woodford (2003)):
IS curve: 𝑦𝑡 = 𝐸𝑡∗𝑦
𝑡+1− 𝜑(𝑖𝑡− 𝐸𝑡∗𝜋𝑡+1) + 𝜀𝑡 (2)
New Keynesian Phillips curve: 𝜋𝑡 = 𝜆𝑦𝑡+ 𝛽𝐸𝑡∗𝜋
𝑡+1+ 𝑢𝑡 (3)
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where 𝑦𝑡, 𝜋𝑡, 𝑖𝑡 refer to actual output gap, inflation and nominal interest rate. 𝐸𝑡∗𝑦𝑡+1, 𝐸𝑡∗𝜋𝑡+1 are expectations of output gap and inflation for the period t+1 at time t. 𝜋̅ is the inflation target set by the central bank and 𝜀𝑡, 𝑢𝑡 denote mean-zero random shocks.
Expectations in such frameworks have feedback which means that inflation and output gap depend on forecasts of these variables.
As already mentioned above, the first paper that studied expectations in a simple New Keynesian model was Adam (2007). The author found that inflation expectations observed in experiments cannot be described by the rational expectations hypothesis. Instead, restricted perception equilibrium, which assumes that agents use simple forecasting rules by minimizing mean squared forecast error, explains the observed behavior.
In Assenza et al. (2010), subjects had to provide two-period ahead forecasts of inflation and output gap in an economy described by a simplified New Keynesian model. The authors found evidence that more aggressive monetary policy can stabilize inflation in experimental economies. They also distinguished 3 patterns of aggregate expectations: convergence to equilibrium, persistent oscillations, and oscillatory convergence.
In a similar setting, Petersen (2014) researched how subjects predict future inflation and output gap. The authors researched the effects of giving subjects salient information on their forecasting errors and the effects of learning. The main finding of the paper was that increasing the quality and availability of information on forecasting errors significantly improved coordination of the forecasts, and thus forecasting accuracy. The researchers also found that forecast errors of both inflation and output gap decrease with repetition but not in the treatment with salient forecast error information.
Pfajfar and Zakelj (2011, 2012) conducted a learning-to-forecast experiment to find out how inflation expectations react to different monetary policy environments. The experiment showed that inflation targeting was more successful than inflation forecast targeting in increasing forecasting accuracy and decreasing uncertainty. Aggressiveness of the monetary policy also improved accuracy and narrowed confidence intervals. Finally, the paper found evidence of overconfidence effect which is a common finding in psychological research.
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In another paper, Pfajfar and Zakelj (2016) explored how monetary policy design affects inflation expectation formation and thus inflation dynamics. They tested effectiveness of forward-looking and contemporaneous monetary policy rules as well as different levels of monetary policy aggressiveness, meaning a higher reaction coefficient in the monetary policy rule. The prior hypothesis of the paper that monetary policy reacting to contemporaneous data would lead to lower variance of inflation was supported by the experimental results. The researchers also confirmed the hypothesis that more aggressive monetary policy being more successful in stabilizing inflation. Another important finding of the paper was the varying share of different forecasting rules between treatments. This suggests that monetary policy rules influence which forecasting rules agents use. In particular, less aggressive monetary policy is susceptible to the emergence of forecasting rules that have destabilizing effects on inflation, i.e. trend extrapolation and adaptive expectations. Hommes and Makarewicz (2016) conducted a learning-to-forecast experiment to study the effects of different monetary policy rules on inflation and output gap expectations. They came to the conclusion that subjects coordinate on similar behavior and that specification of the Taylor rule plays crucial role on stabilizing inflation and output.
Concluding the section, experiments have become important tools for researching expectations. So far, the conducted learning-to-forecast experiments concentrated on individual expectations and did not research the role of the macroeconomic environment. This thesis contributes to the field by using a learning-to-forecast experiment to research expectation formation in different economic environments.
Experimental design
The experiment conducted in this thesis followed a learning-to-forecast design which means that subjects were paid according to the forecasting accuracy to incentivize them.
Before describing the experimental design, I will briefly give the reasons for using experiments instead of survey data. The first advantage of experiments over surveys is the presence of monetary incentives. Unincentivized subjects might report their expectations not truthfully and/or thoughtfully. As a result, when economic agents make decisions in real life situations, their expectations are different from what they reported in surveys. However, Armantier et at. (2012)
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showed that survey inflation expectations correlate with investment decisions made by the same subjects in an investment experiment.
The second reason is the small sample problem of some surveys. For instance, the surveys of professional economists usually include only 50-100 people.
Thirdly, panel survey databases are difficult to gather and maintain, while experiments provide 40-50 data points for every subject, so there is no need to control individual fixed effects.
Finally, in real economy several shocks might happen at the same time, so it is almost impossible to disentangle the effects of different shocks on expectations. Experiments, in turn, give the opportunity to manage shocks and information set of subjects.
The setup was similar to the ones in Adam (2007), Pfajfar and Zakelj (2011, 2013, 2014, 2016), Petersen (2014, 2015), Assenza et al. (2013). Subjects were not assigned roles of particular economic agents, instead they acted as professional forecasters. They were asked to provide their inflation forecasts at time t for time t+1 based on information from time t-1 (experimental instructions are given in Appendix 3). In particular, they were asked the following question: “During the next period, what do you expect inflation to be (negative value means decrease in prices, positive value refers to increase in prices and 0 denotes no change in prices)?” (Figure 1)
Figure 1. The screenshot of the experiment
In period t, subjects observed inflation, output growth, interest rate up to period t-1 in graphical and table form as well as their past forecasts, but they did not observe forecasts and performance of other participants. Additionally to the actual data and past forecasts, subjects were shown the
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payoff they received in the current period as well as the accumulated payoff. In period 1, subjects were asked to forecast inflation in period 2 without having actual inflation, GDP growth and interest rate data. Instead, they were given a range of possible values of the forecast: [-5;15]. Some research papers ask subjects to forecast inflation and output gap at the same time. Forecasting more than one variable may be difficult for participants, so a different method was applied in this thesis. It consisted in setting expectations of the output gap equal to its’ previous value. The same approach was used in many other learning-to-forecast experiments, such as Pfajfar and Zakelj (2011, 2013, 2014), Adam (2007).
Before the forecasting exercise began, participants were given information about the meaning of inflation, GDP growth and interest rate and the relationship between these variables. Subjects were also informed that their inflation forecast has an effect on all variables in the economy. Additionally, they were instructed that experimental economy can be hit by shocks that influence all variables in the system. It is worth noting that subjects did not know the model parameters and could not directly observe the shocks. Instead, they could only infer that a shock occurred from the data on inflation, output growth and interest rate.
A simplified forward-looking sticky price New Keynesian (NK) model was used to produce output gap, interest rate and inflation data in the experimental economy. The economy could experience random mean-zero supply and demand shocks. The NK model typically used in learning-to-forecast experiments (Petersen, 2014; Pfajfar and Zakelj, 2011) consists of the IS equation, the New Keynesian Phillips curve and the Monetary policy rule:
𝑦𝑡= 𝐸𝑡∗𝑦 𝑡+1− 𝜑(𝑖𝑡− 𝐸𝑡∗𝜋𝑡+1) + 𝜀𝑡 (5) 𝜋𝑡= 𝜆𝑦𝑡+ 𝛽𝐸𝑡∗𝜋𝑡+1+ 𝑢𝑡 (6) 𝑖𝑡 = 𝜙𝜋(𝐸𝑡∗𝜋𝑡+1− 𝜋̅) + 𝜋̅ (7) 𝜀𝑡 = 𝛼𝜀𝑡−1+ 𝜀̃ 𝑡 (8) 𝑢𝑡 = 𝛾𝑢𝑡−1+ 𝑢̃ 𝑡 (9)
where 𝑦𝑡, 𝜋𝑡, 𝑖𝑡 refer to actual output gap, inflation and nominal interest rate. 𝐸𝑡∗𝑦
𝑡+1, 𝐸𝑡∗𝜋𝑡+1 are expectations of output gap and inflation for the period t+1 at time t, and 𝐸𝑡∗𝑦
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mentioned above. 𝜋̅ is the inflation target set by the central bank, 𝜀𝑡, 𝑢𝑡 denote mean-zero random shock and 𝜀̃ , 𝑢𝑡 ̃ are independent white noises. 𝑡
IS curve characterizes the relationship between output gap, which refers to the difference between the actual output and its natural level, expected output gap and real interest rate. New Keynesian Phillips curve describes supply side of the economy. In particular, it expresses the relationship between current inflation, current output gap and expected inflation. Coefficient 𝛽 represents the discount rate. Monetary policy rule shows how the central bank sets interest rate based on expected inflation. In is worth noting that monetary authorities in this model do not care about output gap. Finally, shocks are assumed to be first-order autoregressive process.
Calibration of the model is performed in line with Pfajfar and Zakelj (2011) who, in turn, took it from McCallum and Nelson (1999): 𝜑 = 0.164, 𝜆 = 0.3, 𝛽 = 0.99.
Here we assume aggressive monetary policy which consists in applying the Taylor principle. In terms of the monetary policy rule, it means that 𝜙𝜋 is greater than 1. In particular, 𝜙𝜋 = 1.5 which is supported by empirical findings. Inflation target 𝜋̅ is set to 3, as was done in Pfajfar and Zakelj (2011). In line with Pfajfar and Zakelj and empirical evidence (for instance, Cooley and Prescott (1995)), autoregression coefficients in equations for shocks are set to 0.6 (𝛼 = 𝛾 = 0.6). In period 15 the experimental economy experienced an additional supply shock of magnitude 5.
So, the fully calibrated model takes the following form:
𝑦𝑡= 𝑦𝑡−1− 0.164(𝑖𝑡− 𝐸𝑡∗𝜋𝑡+1) + 𝜀𝑡 (10) 𝜋𝑡= 0.3𝑦𝑡+ 0.99𝐸𝑡∗𝜋𝑡+1+ 𝑢𝑡 (11) 𝑖𝑡 = 1.5(𝐸𝑡∗𝜋𝑡+1− 𝜋̅) + 𝜋̅ (12)
𝜀𝑡 = 0.6𝜀𝑡−1+ 𝜀̃ 𝑡 (13)
𝑢𝑡 = 0.6𝑢𝑡−1+ 𝑢̃ 𝑡 (14)
The sample consisted of 2 groups of 10 people, one of which were students from the University of Amsterdam and the other was comprised of students from the Belarusian State University. The experiment was conducted in 2 sessions (in Amsterdam and in Belarus), which lasted on average
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40 minutes. The instructions for students from UVA were written in English and for the Belarusian students they were translated into Russian.
Two treatments were tested in this experiment: stable and unstable inflation environment. Stable inflation environment refers to the group of UVA students and unstable inflation environment is researched on students from the Belarusian State University. Belarus has a long history of high inflation. In 2000-2017, the inflation rate in Belarus was below 10% only in 3 years. In 2011 the inflation rate amounted to 108%. Figure 2 shows the annual rates of inflation in Belarus and in the euro area respectively for comparison. High and persistent inflation in Belarus was caused by excess money emission to finance government expenditures coupled with 3-fold currency devaluation. Inflation expectation measured by surveys remained at extremely high levels until 2017. Expectations of currency devaluations were also persistent, and they remain in place even nowadays, in 2018.
Figure 2. Average annual CPI inflation in Belarus and the euro area
Both treatments had identical underlying models and the same supply shock in period 20 to ensure that differences observed between treatments can be attributed to the sample specifics.
Every group of 10 participants was divided into 2 subgroups of 5 people, each subgroup representing an independent fictitious economy. Each subject was assigned to only one group. After all group members filled in their forecasts for a period, the mean of these expectations was plugged into the above described New Keynesian model to produce actual inflation, output gap and interest rate data for the current period. The game was played for 30 rounds. The first 2 rounds
0 10 20 30 40 50 60 70 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 % Year CPI inflation
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were trial rounds in which subjects could not earn money. At the end of the experiment, subjects were paid in cash.
As was mentioned earlier, subjects’ possible payoffs depended on their forecasting accuracy. Here, the absolute forecast error was chosen as a measure of forecasting accuracy:
𝑒𝑟𝑟𝑜𝑟𝑡𝑘 = |𝜋𝑡− 𝜋𝑡|𝑡−1𝑘 | (15) 𝑒𝑟𝑟𝑜𝑟𝑡𝑘 – forecasting error of individual k at time t;
𝜋𝑡 – actual rate of inflation at time t;
𝜋𝑡|𝑡−1𝑘 – forecast of inflation in period t made by individual k based on information from period t-1 and earlier.
In every round subjects could earn up to 80 experimental points. The minimum number of points possible to earn was restricted to 0, so negative payoffs could not occur. Higher forecasting error translated into lower payoff for the period. The formula below describes how earnings in a period depended on the absolute forecasting error.
𝑝𝑜𝑖𝑛𝑡𝑠𝑡𝑘 = max { 100
1+𝑓𝑒𝑡𝑘− 20,0} (16)
where 𝑝𝑜𝑖𝑛𝑡𝑠𝑡𝑘 denotes the number of points subject k earned in period t.
This function was used in Pfajfar and Zakelj (2011, 2016) and similar functions were used in other learning-to-forecasting experiments, for instance Adam (2007). As can be seen from the formula, forecasting errors higher than 4 percentage points are heavily penalized, and the payoff in such case equals 0. Table 1 shows the points score for selected values of the forecasting error.
Table 1. Payoff for selected values of forecast error
𝑒𝑟𝑟𝑜𝑟𝑡𝑘 0 0.5 1 1.5 2 2.5 3 3.5 ≥ 4
𝑝𝑜𝑖𝑛𝑡𝑠𝑡𝑘 80 46.7 30 20 13.3 8.6 5 2.2 0
Points earned in every period accumulated and the total number of points after round 30 was converted to euro with the exchange rate 0.008 in the Netherlands and to rubles with the exchange rate 0.0065. It means that every 100 experimental points were worth 0.8 euro (or 80 euro cents) in the UVA experiment and 0.65 ruble in the BSU experiment. Additionally, every subject received
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7 euro (5 rubles) participation fee which did not depend on the forecasting performance. Forecasts with 0 error in every round could result in the payoff of 24.9 euro and 19.6 rubles respectively. The exchange rate of the Belarusian ruble is 2.4 rubles/euro, so payoffs in Belarus were approximately half as big as in the Netherlands due to differences in average income.
The average payoff amounted to 10 rubles (4 euro) in the Belarus treatment and 14 euro in the UVA experiment. In the CREED experiment, all payoffs obtained in the forecasting exercise were increased by 2 euro due to lower than average payments.
After the forecasting exercise, subjects were asked to fill in a short questionnaire about their socio-economic indicators and the forecasting strategy they used (see Appendix 4 for details).
The experiment was programmed in Z-TREE which is a free software for conducting economic experiments.
Methodology of data analysis
The data obtained in the learning-to-forecast experiment was first tested for compliance with the rational expectations hypothesis. Then I estimated the adaptive expectations model, general linear rule and trend extrapolation model and compared the fit of the models. Next, I tested whether subjects used one forecasting rule or switched between different rules. Finally, I studied the differences between treatments.
Testing the rational expectations hypothesis
Rational expectations hypothesis states that forecasts are unbiased and efficient. Unbiasedness means that inflation expectations are on average equal to the actual inflation. Efficiency, in turn, means that forecasters take into account all the available information when they make predictions. Under rational expectations, forecast errors should not be systematic which means that they should not be autocorrelated.
So, based on the above described characteristics of rational forecasts, several tests of rationality have been developed in the literature:
1. Unbiasedness is tested by performing the following regression:
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where 𝜋𝑡 is the actual inflation rate at time t and 𝜋𝑡𝑒 is the expected inflation at time t. Unbiasedness cannot be rejected if 𝛼 = 0, 𝛽 = 1 If, for instance, 𝛼 ≠ 0 , inflation expectations systematically under- or over-estimate the real inflation.
This test, however, assumes inflation and inflation expectations to be stationary which is often not the case. If these variables are not stationary, unbiasedness requires them to be cointegrated, and the cointegrating vector should be equal to [0 1].
2. Efficiency is the second property of rational expectations It means that forecasts take into account all the available information. Thus, in general form the test of efficiency consists in running the following regression:
𝜋𝑡− 𝜋𝑡𝑒 = 𝛼 + 𝛽Ω𝑡−1+ 𝑢𝑡, (18) where Ω𝑡−1 is the information set available to the forecaster at time t. If 𝛽 = 0 , expectations are efficient.
There is a distinction between strong-form and weak-form efficiency. The strong form implies that agents use all the publicly available information, while the weak form is limited to previous inflation data.
Testing for the strong-form efficiency consists in estimating the following regression: 𝜋𝑡− 𝜋𝑡𝑒 = 𝛼 + 𝛽𝜋𝑡−1+ 𝛾𝑦𝑡−1+ 𝛿𝑖𝑡−1+ 𝑢𝑡, (19) where 𝑦𝑡−1 refers to the output gap in period t-1 and 𝑖𝑡−1 denotes interest rate in period t-1.
In turn, the weak-form efficiency testing means estimating the following regression: 𝜋𝑡− 𝜋𝑡𝑒 = 𝛼 + 𝛽𝜋𝑡−1+ 𝑢𝑡, (20) If the coefficients in the above described regressions are statistically significant, we can reject the null hypothesis of efficiency.
3. Unpredictability of errors is another necessary condition for rationality. Under rationality, forecast errors do not contain a systemic element which means that they are random. Unpredictability can be tested by regressing the error on its previous values:
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If 𝛽1 is different from 0, the forecasting errors are predictable. Another way to test this condition is to look at the autocorrelation of forecasting errors. If errors are autocorrelated, unpredictability is violated.
Testing adaptive expectations hypothesis
Besides testing the experimental data on the compliance with the rational expectations hypothesis, I also tested the thesis hypotheses. The first hypothesis states that most people use adaptive expectations model to forecast inflation. I tested this assumption by estimating several most often used forecasting rules (adaptive expectations, general linear forecasting rule, trend extrapolation) and comparing the results.
Adaptive expectations model, as already stated in the literature review, assumes expectations to depend on previous expectations and the last available forecasting error:
𝜋𝑡𝑒= 𝛽0+ 𝛽1𝜋𝑡−1𝑒 + 𝛽3𝑓𝑒𝑡−2+ 𝜀𝑡 (22) General linear rule assumes that inflation expectations are a function of previous inflation, GDP and interest rate data:
𝜋𝑗,𝑡+1𝑒 = 𝛽0+ 𝛽1𝜋𝑡−2+ 𝛽2𝑦𝑡−2+ 𝛽3𝑖𝑡−2+ 𝜇𝑡 (23) Trend extrapolation implies that expected inflation is a function of the previous observed inflation and the previous observed change in inflation:
𝜋𝑗,𝑡+1𝑒 = 𝛽0+ 𝛽1𝜋𝑡−2+ 𝛽2(𝜋𝑡−2− 𝜋𝑡−3) + 𝜇𝑡 (24) Testing switching between rules
Another hypothesis is that most people do not switch between forecasting rules but instead, they change the updating parameter in the adaptive expectations model. This hypothesis can be tested by first, estimating the adaptive expectations model and then conducting a structural break test on the coefficients. An alternative way of testing the hypothesis is by estimating 2 regressions, one before the shock and the other after the shock and test the difference in the coefficients. I used the second approach and estimated adaptive expectations model (equation 22) for the two time intervals, periods 1-16 and periods 17-30. If the adaptive expectations model fits both time intervals but the updating parameter changes, then the experimental data will back up the hypothesis of the thesis. If, however, the adaptive expectations fit only one time period, there will be evidence against the hypothesis.
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The last hypothesis states that people from unstable inflation environment react faster to the changes of macroeconomic indicators. The test of this hypothesis consisted in comparing the updating parameter (𝛽3) from the adaptive expectations model (equation 22) in the UVA and Belarus treatment. The higher parameter in the Belarus treatment will support the hypothesis. The next section presents the results of the above described tests.
Experimental results Descriptive statistics
Before analyzing experimental data, I will describe the sample. The average age of the UVA group was 21.5 years, and the average age of the participants from Belarus was 19.8 years. The Amsterdam group consisted of 6 females and 4 males whereas the Belarus group was comprised of 8 females and 2 males. Regarding the average level of education, the treatments had no significant differences. The UVA group included 9 Economics and Business students and 1 student of Political Science, some of whom were Bachelor students and some Master students. This question was not in the questionnaire, so the exact composition is unknown. The Belarus group consisted of 10 third year Bachelor students specializing in Corporate Finance.
The first step in researching how subjects form inflation expectations is the analysis of descriptive statistics. Table 2 presents selected descriptives by group, and Table 3 gives selected descriptive statistics by subject in both treatments.
Table 2. Descriptives by group
Group UVA Belarus
1 starting_point = 3.46 mean_forecast = 4.47 mean_forecasting_error = 0.56 starting_point = 4.92 mean_forecast = 4.89 mean_forecasting_error = 0.1 2 starting_point = 5.2 mean_forecast = 4.27 mean_forecasting_error = 0.63 starting_point = -0.56 mean_forecast = 3.89 mean_forecasting_error = 1.1 Table 3. Descriptive statistics of individual forecasts
Subjects UVA Belarus
1 starting_point = 5 mean_forecast = 4.42 mean_forecasting_error = 0.59 country = USA *inflation_US = 1.3 starting_point = 7.5 mean_forecast = 5.52 mean_forecasting_error = -0.53 country = Belarus *inflation_BLR = 11.8 2 starting_point = 5.3 mean_forecast = 5.02 starting_point = 7 mean_forecast = 5.38
28 mean_forecasting_error = -0.01 country = Albania *inflation_Alb = 1.3 mean_forecasting_error = -0.24 country = Belarus *inflation_BLR = 11.8 3 starting_point = 2 mean_forecast = 4.50 mean_forecasting_error = 0.52 country = Netherlands *inflation_NL = 0.3 starting_point = 8 mean_forecast = 4.21 mean_forecasting_error = 0.92 country = Belarus *inflation_BLR = 11.8 4 starting_point = 0 mean_forecast = 3.82 mean_forecasting_error = 1.2 country = Germany *inflation_DE = 0.5 starting_point = 6 mean_forecast = 4.48 mean_forecasting_error = 0.66 country = Belarus *inflation_BLR = 11.8 5 starting_point = 5 mean_forecast = 4.6 mean_forecasting_error = 0.42 country = Latvia *inflation_LV = 0.1 starting_point = 2.1 mean_forecast = 4.89 mean_forecasting_error = 0.25 country = Belarus *inflation_BLR = 11.8 6 starting_point = 5 mean_forecast = 4.3 mean_forecasting_error = 0.44 country = Ukraine *inflation_UA = 13.9 starting_point = 0.7 mean_forecast = 4.26 mean_forecasting_error = 0.58 country = Belarus *inflation_BLR = 11.8 7 starting_point = 5 mean_forecast = 4.43 mean_forecasting_error = 0.31 country = Netherlands *inflation_NL = 0.3 starting_point = -5 mean_forecast = 4.75 mean_forecasting_error = 0.09 country = Belarus *inflation_BLR = 11.8 8 starting_point = 5 mean_forecast = 4.76 mean_forecasting_error = -0.06 country = Pakistan *inflation_PK = 3.8 starting_point = 0 mean_forecast = 3.87 mean_forecasting_error = 0.98 country = Belarus *inflation_BLR = 11.8 9 starting_point = 5 mean_forecast = 2.01 mean_forecasting_error = 2.73 country = Cuba *inflation_Cuba = 5.2 starting_point = 1.2 mean_forecast = 4.61 mean_forecasting_error = 0.23 country = Belarus *inflation_BLR = 11.8 10 starting_point = 6 mean_forecast = 5.15 mean_forecasting_error = -0.41 country = Sweden *inflation_SW = 1.0 starting_point = 1.5 mean_forecast = 1.29 mean_forecasting_error = 3.55 country = Belarus *inflation_BLR = 11.8
*inflation data was taken from the WorldBank website and latest available year was 2016. Inflation for Cuba was taken from tradingeconomics.com.
The first difference between groups that stands out is the higher dispersion of starting points in the Belarus treatment. Inflation forecasts in the first period ranged from -5 to 8. Negative and zero
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inflation forecasts in period 1 might indicate that participants did not fully understand the task. This effect vanished with learning in almost all subjects.
The mode of the starting points in the UVA treatment was 5 (the average of the possible interval of forecasts) while the mode in Belarus was 0. This raises concern that participants in Belarus did not understand the task, at least not in the beginning of the experiment. The choice of starting point 5 in the UVA treatment raises another concern. The midpoint of the interval of possible forecast values is exactly 5, so subjects might have performed the task technically without thinking about any economy in particular. This finding is in line with previous research (Mishkin and Schmidt-Hebbel, 2001 and 2007; Hubert, 2014) that showed the importance of focal points for expectation formation. Inflation target and forecasts of financial professionals often serve as anchors for the private sector. In the case of no available information on the experimental economy, the average of the forecasting interval might have served as a focal point for the UVA group. The effect, however, was not present in the Belarus treatment. One of the explanations for this finding is the lack of experience in forecasting experiments of the Belarusian subjects.
In the Belarus treatment, there were several starting points close to the past inflation in Belarus (7-8%), whereas in the UVA treatment the highest observed starting point was 6%. Moreover, subjects in the UVA treatment had only 2 starting points close to inflation level in the Euro area. It is worth noting that both treatments had one outlier. Subject 10 in the Belarus treatment most likely forecasted another variable or did not understand the task because the forecasts were significantly biased. Moreover, from time to time the subject switched to negative inflation forecasts while actual inflation was always positive and significantly higher than 0. Subject 9 in the Amsterdam treatment also had unusually high forecast errors.
In the first group of the high-inflation treatment the average forecast was almost unbiased, while the second group forecasted much worse. The average forecast errors of the biased participants were 2.83 and 3.64 percentage points respectively. As a result, the average expectation of group 2 is farther from the actual inflation. If outliers are excluded, the Belarus treatment has higher forecasting accuracy.
It is worth noting that the sample from UVA consisted of people from different countries, some of which have traditionally high inflation rates, like Cuba, Ukraine and Pakistan. These people,
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however, have lived in the euro area for a period of 1 year or more. Thus, it is difficult to predict what effect will dominate: high-instability home country experience or stable economy EU experience. Discussion section provides a more detailed analysis of this and other limitations of the study.
Next, we will proceed with visual analysis of the experimental data. Figures 3 depicts actual inflation and inflation forecasts by subject in the Belarus and Amsterdam treatments. The blue line denotes the realized inflation and the red line represents the individual inflation expectations.
Figure 3. Actual inflation and forecast in the Belarus and UVA treatments
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Based on the visual analysis, we can suggest that most of the forecasts depend on the previous inflation data. This is also confirmed by the answers to questionnaire where most participants specified “looking at previous inflation data” or “looking at the graph” as their forecasting strategy. Figure 4 provides the same graphs as Figure 3 but at a group level. As in the previous graphs, the blue line is the actual inflation and the red line is the forecast.
Figure 4. Actual inflation and forecast by group
Group UVA Belarus
1 0 5 10 15 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 % Period Actual vs forecast actual forecast 0 5 10 15 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 % Period Actual vs forecast actual forecast Amsterdam
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The group level data exhibits the same patterns as individual forecasts, namely the clear relationship between past inflation data and inflation forecasts.
Regression analysis
Next, individual and aggregate expectations were tested on the consistency with the rational expectations hypothesis. The regressions specified in the methodology sections are summarized in Table 4 and Appendix 1. All the models were estimated by the OLS. Appendix 1 presents the results of rationality tests of individual inflation forecasts and Table 4 describes the results for aggregate forecasts.
From the results of the formal tests (Appendix 1), perfect rationality of expectations is rejected for every subject. All forecasts in both treatments are biased. Most forecasts are weakly efficient, and only one is efficient in strong form. In particular, many subjects fail to take into account interest rate and GDP data in their forecasts. Some participants also do not fully use previous inflation data when forming expectations.
For the majority of subjects, the forecasting errors were also autocorrelated, which means that the unpredictability of errors was violated.
Table 4. Rational expectations hypothesis tests by group
Group UVA Belarus
1 • Biasedness: 𝜋𝑡 = 2.0 + 0.7𝜋𝑡𝑒+ 𝜀𝑡 (2.08**) (3.79***) • Weak-form efficiency: 𝑓𝑒𝑡 = 1.8 − 0.2𝜋𝑡−2+ 𝑢𝑡 (1.93) (-1.6) • Strong-form efficiency: • Biasedness: 𝜋𝑡 = 2.3 + 0.6𝜋𝑡𝑒+ 𝜀𝑡 (2.34**) (3.66***) • Weak-form efficiency: 𝑓𝑒𝑡 = 0.9 − 0.1𝜋𝑡−2+ 𝑢𝑡 (0.76) (-0.78) • Strong-form efficiency: 0 5 10 15 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 % Period Actual vs forecast actual forecast -5 0 5 10 15 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 % Period Actual vs forecast actual forecast
33 𝑓𝑒𝑡 = −0.2 − 0.7𝜋𝑡−2+ 1.1𝑦𝑡−1− 0.3𝑖𝑡−1+ 𝑢𝑡 (-0.4) (-2.26**) (4.78***) (-2.41**) • Predictability: 𝑓𝑒𝑡= 0.4 + 0.4𝑓𝑒𝑡−1+ 𝑢𝑡 (0.88) (1.93*) 𝑓𝑒𝑡= 1.4 − 0.6𝜋𝑡−2+ 1.0𝑦𝑡−2− 0.5𝑖𝑡−2+ 𝑢𝑡 (1.61) (-2.11**) (4.24***) (-4.04***) • Predictability: 𝑓𝑒𝑡 = 0.1 + 0.6𝑓𝑒𝑡−1+ 𝑢𝑡 (0.17) (3.63***) 2 • Biasedness: 𝜋𝑡 = 1.9 + 0.7𝜋𝑡𝑒+ 𝜀𝑡 (1.61) (3.09***) • Weak-form efficiency: 𝑓𝑒𝑡 = 1.6 − 0.2𝜋𝑡−2+ 𝑢𝑡 (1.51) (-1.17) • Strong-form efficiency: 𝑓𝑒𝑡 = 0.8 − 0.7𝜋𝑡−2+ 0.9𝑦𝑡−2− 0.3𝑖𝑡−2+ 𝑢𝑡 (1.15) (-2.39**) (4.31***) (-3.14***) • Predictability: 𝑓𝑒𝑡= 0.4 + 0.4𝑓𝑒𝑡−1+ 𝑢𝑡 (1.11) (1.85*) • Biasedness: 𝜋𝑡 = 2.5 + 0.6𝜋𝑡𝑒+ 𝜀𝑡 (3.28***) (3.24***) • Weak-form efficiency: 𝑓𝑒𝑡 = 2.0 − 0.2𝜋𝑡−2+ 𝑢𝑡 (2.42**) (-1.13) • Strong-form efficiency: 𝑓𝑒𝑡 = 0.3 − 0.04𝜋𝑡−2+ 0.5𝑦𝑡−2− 0.2𝑖𝑡−2+ 𝑢𝑡 (0.27) (-0.13) (1.33) (-0.93) • Predictability: 𝑓𝑒𝑡 = 0.6 + 0.4𝑓𝑒𝑡−1+ 𝑢𝑡 (1.27) (1.76*)
The numbers in the brackets refer to the t-statistics calculated using robust standard errors and the number of stars corresponds to the significance level (* - significant at 10%, ** - significant at 5%, *** - significant at 1% and no stars means significance at levels higher than 10%).
Tests of aggregate expectations confirm the results obtained from testing individual inflation expectations. Namely, forecasts are biased and efficient only in weak-form, and the forecast errors are autocorrelated. Only the second group in the Belarus treatment had strongly-efficient forecasts. Most individual and aggregate forecasts fail to fully account for the data on interest rate, inflation and output.
Next, we estimated 3 most popular forecasting rules in the literature: adaptive expectations, trend extrapolation and general linear rule. Table 5 presents the formulas for these forecasting rules. The results of estimation for individual and aggregate data are shown in Appendix 2 and Table 6 respectively.
Table 5. Description of the estimated forecasting rules
Forecasting rule Formula
General linear rule 𝜋𝑗,𝑡+1𝑒 = 𝛽0+ 𝛽1𝜋𝑡−1+ 𝛽2𝑦𝑡−1+ 𝛽3𝑖𝑡−1+ 𝜇𝑡
Trend extrapolation 𝜋𝑗,𝑡+1𝑒 = 𝛽0+ 𝛽1𝜋𝑡−2+ 𝛽2(𝜋𝑡−2− 𝜋𝑡−3) + 𝜇𝑡
Adaptive expectations 𝜋𝑡𝑒= 𝛽0+ 𝛽1𝜋𝑡−1𝑒 + 𝛽2𝑓𝑒𝑡−2+ 𝜀𝑡
Table 6. Estimated forecasting rules by group
Group UVA Belarus
