Via email, Maurizio Bovi describes a paper of his on adaptive learning (M. Bovi (2012). "Are the Representative Agent’s Beliefs Based on Efficient Econometric Models?" Journal of Economic Dynamics and Control). A colleague of mine, George Evans -- a leader in this area -- responds:
Are you a good econometrician? No, I am British!, by Maurizio Bovi*: A typical assumption of mainstream strands of research is that agents’ expectations are grounded in efficient econometric models. Muthian agents are all equally rational and know the true model. The adaptive learning literature assumes that agents are boundedly rational in the sense that they are as smart as econometricians and that they are able to learn the correct model. The predictor choice approach argues that individuals are boundedly rational in the sense that agents switch to the forecasting rule that has the highest fitness. Preferences could generate enduring inertia in the dynamic switching process and a stationary environment for a sufficiently long period is necessary to learn the correct model. Having said this, all the cited approaches typically argue that there is a general tendency to forecast via optimal forecasting models because of the costs stemming from inefficient predictions.
To the extent that the representative agent’s beliefs i) are based on efficient (in terms of minimum MSE=mean squared forecasting errors) econometric models, and ii) can be captured by ad hoc surveys, two basic facts emerge, stimulating my curiosity. First, in economic systems where the same simple model turns out to be the best predictor for a sufficient span of time survey expectations should tend to converge: more and more individuals should learn or select it. Second, the forecasting fitness of this enduring minimum MSE econometric model should not be further enhanced by the use of information provided by survey expectations. If agents act as if they were statisticians in the sense that they use efficient forecasting rules, then survey-based beliefs must reflect this and cannot contain any statistically significant information that helps reduce the MSE relative to the best econometric predictor. In sum, there could be some value in analyzing hard data and survey beliefs to understand i) whether these latter derive from optimal econometric models and ii) the time connections between survey-declared and efficient model-grounded expectations. By examining real-time GDP dynamics in the UK I have found that, over a time-span of two decades, the adaptive expectations (AE) model systematically outperforms other standard predictors which, as argued by the above recalled literature, should be in the tool-box of representative econometricians (Random Walk, ARIMA, VAR). As mentioned, this peculiar environment should eventually lead to increased homogeneity in best-model based expectations. However data collected in the surveys managed by the Business Surveys Unit of the European Commission (European Commission, 2007) highlight that great variety in expectations persists. Figure 1 shows that in the UK the number of optimists and pessimists tend to be rather similar at least since the inception of data1 availability (1985).
In addition, evidence points to one-way information flows going from survey data to econometric models. In particular, Granger-causality, variance decomposition and Geweke’s instantaneous feedback tests suggest that the accuracy of the AE forecasting model can be further enhanced by the use of the information provided by the level of disagreement across survey beliefs. That is, as per GDP dynamics in the UK, the expectation feedback system looks like an open loop where possibly non-econometrically based beliefs play a key role with respect to realizations. All this affects the general validity of the widespread assumption that representative agents’ beliefs derive from optimal econometric models.
Results are robust to several methods of quantifications of qualitative survey observations as well as to standard forecasting rules estimated both recursively and via optimal-size rolling windows. They are also in line both with the literature supporting the non-econometrically-based content of the information captured by surveys carried out on laypeople and, interpreting MSE as a measure of volatility, with the stylized fact on the positive correlation between dispersion in beliefs and macroeconomic uncertainty.
All in all, our evidence raises some intriguing questions: Why do representative UK citizens seem to be systematically more boundedly rational than what is usually hypothesized in the adaptive learning literature and the predictor choice approach? What does it persistently hamper them to use the most accurate statistical model? Are there econometric (objective) or psychological (subjective) impediments?
*Italian National Institute of Statistics (ISTAT), Department of Forecasting and Economic Analysis. The opinions expressed herein are those of the author (E-mail email@example.com) and do not necessarily reflect the views of ISTAT.
 The question is “How do you expect the general economic situation in the country to develop over the next 12 months?” Respondents may reply “it will…: i) get a lot better, ii) get a little better, iii) stay the same, iv) get a little worse, v) get a lot worse, vi) I do not know. See European Commission (1997).
European Commission (2007). The Joint Harmonised EU Programme of Business and Consumer Surveys, User Guide, European Commission, Directorate-General for Economic and Financial Affairs, July.
M. Bovi (2012). “Are the Representative Agent’s Beliefs Based on Efficient Econometric Models?” Journal of Economic Dynamics and Control DOI: 10.1016/j.jedc.2012.10.005.
Here's the response from George Evans:
Comments on Maurizio Bovi, “Are the Representative Agent’s Beliefs Based on Efficient Econometric Models?”, by George Evans, University of Oregon: This is an interesting paper that has a lot of common ground with the adaptive learning literature. The techniques and a number of the arguments will be familiar to those of us who work in adaptive learning. The tenets of the adaptive learning approach can be summarized as follows: (1) Fully “rational expectations” (RE) are implausibly strong and implicitly ignores a coordination issue that arises because economic outcomes are affected by the expectations of firms and households (economic “agents”). (2) A more plausible view is that agents have bounded rationality with a degree of rationality comparable to economists themselves (the “cognitive consistency principle”). For example agents’ expectations might be based on statistical models that are revised and updated over time. On this approach we avoid assuming that agents are smarter than economists, but we also recognize that agents will not go on forever making systematic errors. (3) We should recognize that economic agents, like economists, do not agree on a single forecasting model. The economy is complex. Therefore, agents are likely to use misspecified models and to have heterogeneous expectations.
The focus of the adaptive learning literature has changed over time. The early focus was on whether agents using statistical learning rules would or would not eventually converge to RE, while the main emphasis now is on the ways in which adaptive learning can generate new dynamics, e.g. through discounting of older data and/or switching between forecasting models over time. I use the term “adaptive learning” broadly, to include, for example, the dynamic predictor selection literature.
Bovi’s paper “Are the Representative Agent’s Beliefs Based on Efficient Econometric Models” argues that with respect to GDP growth in the UK the answer to his question is no because 1) there is a single efficient econometric model, which is a version of AE (adaptive expectations), and 2) agents might be expected therefore to have learned to adopt this optimal forecasting model over time. However the degree of heterogeneity of expectations has not fallen over time, and thus agents are failing to learn to use the best forecasting model.
From the adaptive learning perspective, Bovi’s first result is intriguing, and merits further investigation, but his approach will look very familiar to those of us who work in adaptive learning. And the second point will surprise few of us: the extent of heterogeneous expectations is well-known, as is the fact that expectations remain persistently heterogeneous, and there is considerable work within adaptive learning that models this heterogeneity.
1) Bovi’s “efficient” model uses AE with the adaptive expectations parameter gamma updated over time in a way that aims to minimize the squared forecast error. This is in fact a simple adaptive learning model, which was proposed and studied in Evans and Ramey, “Adaptive expectations, underparameterization and the Lucas critique”, Journal of Monetary Economics (2006). We there suggested that agents might want to use AE as an optimal choice for a parsimonious (underparameterized) forecasting rule, showed what would determine the optimal choice of gamma, and provided an adaptive learning algorithm that would allow agents to update their choice of gamma over time in order to track unknown structural change. (Our adaptive learning rule exploits the fact that AE can be viewed as the forecast that arises from an IMA(1,1) time-series model, and in our rule the MA parameter is estimated and updated recursively using a constant gain rule.)
2) At the same time I am suspicious that economists will agree that there is a single best way to forecast GDP growth. For the US there is a lot of work by numerous researchers that strongly indicates that choosing between univariate time-series models is controversial, i.e. there appears to be no single clearly best univariate forecasting model, and (ii) forecasting models for GDP growth should be multivariate and should include both current & lagged unemployment rates and the consumption to GDP ratio. Other forecasters have found a role for nonlinear (Markov-switching) dynamics. Thus I doubt that there will be agreement by economists on a single best forecasting model for GDP growth or other key macro variables. Hence we should expect households and firms also to entertain multiple forecasting models, and for different agents to use different models.
3) Even if there were a single forecasting model that clearly dominated, one would not expect homogeneity of expectations across agents or for heterogeneity to disappear over time. In Evans and Honkapohja, “Learning as a Rational Foundation for Macroeconomics and Finance”, forthcoming 2013 in R Frydman and E Phelps, Rethinking Expectations: The Way Forward for Macroeconomics, we point out that variations across agents in the extent of discounting and the frequency with which agents update parameter estimates, as well as the inclusion of idiosyncratic exogenous expectation shocks, will give rise to persistent heterogeneity. There are costs to forecasting, and some agents will have larger benefits from more accurate forecasts than other agents. For example, for some agents the forecast method advocated by Bovi will be too costly and an even simpler forecast will be adequate (e.g. a RW forecast that the coming year will be like last year, or a forecast based on mean growth over, say, the last five years).
4) When there are multiple models potentially in play, as there always is, the dynamic predictor selection approach initiated by Brock and Hommes means that because of varying costs of forecast methods, and heterogeneous costs across agents, not all agents will want to use what appears to be the best performing model. We therefore expect heterogeneous expectations at any moment in time. I do not regard this as a violation of the cognitive consistency principle – even economists will find that in some circumstances in their personal decision-making they use more boundedly rational forecast methods than in other situations in which the stakes are high.
In conclusion, here is my two sentence summary for Maurizio Bovi: Your paper will find an interested audience among those of us who work in this area. Welcome to the adaptive learning approach.