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Article Excerpt
DIFFERENCES IN AGENTS' beliefs and their importance to economic analysis has been emphasized by economists as early as Pigou (1927) and Keynes (1936). (1) A better understanding of the source of such disagreement has become increasingly important in view of the recent widespread use of macroeconomic models with heterogenous agents. Noting that disagreement about inflation is correlated with a host of macroeconomic variables, Mankiw, Reis, and Wolfers (2003, p. 2) go as far as suggesting that "disagreement may be a key to macro-economic dynamics." This view is consistent with the theoretical models of Lucas (1973) and Townsend (1983) where heterogeneity in agents' beliefs play a key role.
Inflation forecasting is an area where disagreements appear to be particularly significant. Strong differences in inflation forecasts are found even at short forecast horizons and among professional forecasters with access to many common sources of information. Among 29 forecasters that participated in the Survey of Professional Forecasters (SPF) in the third quarter of 2004, one-quarter-ahead forecasts of the annualized inflation rate ranged from 0.88% to 3.94% per annum. In the event, this range of 3 percentage points was one and a half times greater than the actual inflation rate of 1.98%. (2) Similar disagreements about future inflation have been found among different types of economic forecasters (professional economists versus lay consumers, Carroll 2003, Mankiw, Reis, and Wolfers 2003), for different commodity groups (Mankiw, Reis, and Wolfers 2003), and across different sample periods (Zarnowitz and Braun 1992).
A variety of explanations have been offered to explain these findings. Central to these is an assumption that agents have heterogenous information so that dispersion in beliefs reflects differences in information sets. Alternatively, differences may reflect heterogeneity in the rate at which agents update their beliefs. Mankiw and Reis (2002) and Carroll (2003) propose an elegant staggered updating model for expectations in which only a fraction of agents update their beliefs every period. Using this model, Mankiw, Reis, and Wolfers (2003) are able to account for a number of features of inflation, including the extent of the observed disagreement and a variety of properties of the median forecast error. Cukierman and Wachtel (1979) suggest that both differences in expectations about the future rate of inflation and most of the changes over time in the variance of inflation are driven by the variance of aggregate demand shocks, but their empirical results only refer to the relation between periods with large variances in the rate of inflation and periods with large variances in inflation expectations, without measuring the demand shocks. There is also a related literature on model uncertainty and heterogeneity. Brock and Hommes (1997) and, more recently, Branch (2007) study agents who choose between different forecasting models each period. Under a variety of model selection rules they are able to account for disagreement among agents and generate considerable time-variation in dispersion across agents' beliefs.
None of these explanations, however, can provide an entirely satisfactory explanation for the biases observed in inflation expectations and the positive relationships between the cross-sectional dispersion in inflation beliefs and the level of the inflation rate. This goes to the heart of how we model inflation expectations and the reason why they differ among agents. Modeling heterogeneity without addressing these empirical relations could introduce dynamics in economic models that are at odds with reality. The impact, in particular in macroeconomics and finance where inflation expectations play a key role, is potentially large, for instance, in models of the determination of the Phillips curve trade-off between unemployment and inflation (Mankiw and Reis 2002), the determination of aggregate demand through the effect on consumption and investment (Clarida, Gall, and Gertler 1999), and the determination of stock prices (Fama 1991).
This paper proposes a different explanation for how dispersion in inflation beliefs evolves overtime and why it is correlated with both the level and volatility of inflation. (3) Our explanation relies on three mechanisms, namely, asymmetric loss, heterogeneity in agents' loss functions, and a constant loss component. Asymmetric loss captures the idea that the cost of over- and underpredicting inflation may be very different. Suppose that for a particular agent the cost of underpredicting inflation is higher than the cost of overpredicting it. Then it is optimal for this agent to bias the forecast so that on average he overpredicts inflation, thereby reducing the probability of costly underpredictions. Furthermore, if costs are increasingly large, the larger in absolute value the forecast error (i.e., assuming loss is convex), then the optimal bias under rational expectations will be greater the higher the variance of the predicted variable. Finally, if the variance of the predicted variable is time varying, then the optimal bias also becomes time varying.
Turning to the second mechanism, heterogeneity in agents' loss functions means that periods with high degrees of macroeconomic uncertainty about the price level also coincide with periods where dispersions and biases in beliefs should be greater. Provided that there is heterogeneity across agents in their degree of loss asymmetry, such biases can drive dispersion across forecasters, giving rise to a positive relation between the variance of inflation and dispersion in beliefs. Moreover, if the variance of the inflation rate increases as the level of inflation goes up, then the dispersion in beliefs will also rise with the inflation rate. Both effects occur even if (i) agents are fully rational and their beliefs are updated every period and formed as conditional expectations (no belief distortions) and (ii) agents have access to identical information and have identical beliefs about the mean and variance of future inflation.
The effects of asymmetric loss and cross-sectional heterogeneity are explored under the assumption of rational expectations. However, these two mechanisms, on their own, fall short of explaining an important feature of the survey data, namely, the shift in the sign of the bias observed for a substantial portion of forecasters around 1982. We observe that many forecasters went from systematically underpredicting inflation prior to 1982 to overpredicting it in the period that followed. We show that the third mechanism, namely, a constant bias component, capturing agents' tendency to overpredict inflation, can help explain this. This constant tendency to overpredict inflation is held against the time-varying tendency of many agents to underpredict inflation which is induced by asymmetry in their loss function and which gets stronger, the higher the level of inflation volatility. Prior to 1982, inflation was very volatile and so the asymmetry effect dominated the constant bias component and the overall effect was for agents to underpredict inflation. After 1982, inflation volatility came down and so the constant bias component dominated and forecasters tended to underpredict inflation.
The rest of the paper proceeds as follows. After a brief discussion of sources of asymmetric loss, Section 1 presents a theory of forecasts under asymmetric loss and explores its implications for the cross-sectional distribution of beliefs. Empirical evidence of asymmetries in forecasters' loss functions and evidence in support of our theory on the relation between inflation forecasts and inflation uncertainty is presented in Section 2. After a discussion of alternative explanations for dispersion in inflation beliefs, we conclude the paper in Section 3.
1. INFLATION FORECASTING UNDER ASYMMETRIC LOSS
As pointed out by Mankiw and Reis (2002), an understanding of the microfoundations for agents' expectations is important to a theory of heterogeneity in expectation formation. For this reason we first briefly review three possible reasons for asymmetric loss, namely, a utility cost explanation, a psychological explanation and a strategic explanation--see Elliott, Komunjer, and Timmermann (2008) for a more detailed discussion. We then propose a simple model that captures asymmetric loss and explore its implications for the cross-section of inflation beliefs.
1.1 Why Asymmetric Loss?
The most obvious explanation of asymmetric loss comes from the underlying economic "primitives" of the decision problem that the inflation forecast is supposed to inform. Inflation forecasts matter for decisions on portfolio allocations, production levels, wage negotiations, etc., so asymmetries in the costs of these factors due to over- or underpredicting the inflation rate should also affect the properties of the optimal forecast. Elliott, Komunjer, and Timmermann (2008) show how to derive asymmetric loss functions based on constant absolute or relative risk aversion utility functions combined with relations linking the forecast to the decision maker's actions.
Turning to the second explanation of asymmetric loss, a large literature in psychology has studied how peoples' judgments are affected in situations with different consequences of overassessment as opposed to underassessment of a random event. In a comprehensive survey of this literature, Weber (1994, p. 228) argues that the "asymmetric-loss-function interpretation provides a psychological explanation for observed judgments and decisions under uncertainty and links them to other judgment tasks." This literature also finds that the direction of a "misestimate"--and thus the shape of the loss function--depends on the perspective of the forecaster in a way that reflects the consequences of a forecast error. For example, in experiments where individuals were asked to estimate the price of a car, when subjects took a buyer's perspective--a case where overestimates of the car's true price were more costly than underestimates--they tended to underestimate the price. Conversely, when subjects took the seller's perspective, the reverse happened and overestimates were more common (Birnbaum and Stegner 1979).
While some forecasters may overpredict and others underpredict a particular outcome, a given individual's perspective, as reflected in the tendency to overweight or underweight the outcome, appears to be quite stable over time. Weber and Kirsner (1997, p. 42) conclude that "individuals differ in the relative emphasis they put on outcomes at the low (security) end of the distribution or at the high (potential) end of the distribution, and that this tendency is a stable, dispositional, individual-difference characteristic. Security-minded individuals are assumed to overweight outcomes at the low end of the distribution whereas potential-minded individuals do the opposite." Psychological factors may thus explain why some forecasters overweight high inflation outcomes relative to low inflation outcomes when forming their beliefs.
Finally, strategic explanations (e.g., Ehrbeck and Waldmann 1996, Laster, Bennett, and Geoum 1999, Ottaviani and Sorensen 2006) argue that asymmetries in the information available to forecasters versus their clients can be responsible for biases. This class of models views professional forecasters as agents of end users (the principals) so the role of the better-informed agents is to generate signals that are used to inform the principals' actions. Forecasters are remunerated based on their clients' assessments of their skills and so the aim of the forecast is to affect the clients' views. Models of strategic behavior can give rise to biases and asymmetric costs as the forecaster takes into consideration how a forecast will affect her future career path.
Empirical evidence on asymmetric loss has been found in inflation forecasts and in forecasts of other economic variables. For example, Capistran (2008) finds that the Federal Reserve overpredicts inflation during the Volcker-Greenspan era as a result of the large costs...
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