Modeling Expectation Formation Involving Several Sources of Information

Abstract. Experimental studies of expectation formation of subjects are predominantly limited to the prediction of one single time series despite the practical relevance of expectations in situations with multiple sources of information. In this paper, we report on an experiment in which subjects are given time series (indicators) as additional information for the judgemental forecast of a stationary time series. The quality and the number of these indicators are varied in three versions of a forecasting experiment. We explore the effects on forecasting accuracy and we test the average forecasts of the subjects for consistency with the rational expectations hypothesis. A simple heuristic is presented that explains the average forecasting behavior better than the rational expectations if indicators are presented to the subjects. It is demonstrated by a simulation study that this result is representative for the considered stationary stochastic processes.     

Does purchasing power parity hold sometimes? Regime switching in real exchange rates

Standard unit root tests are not very powerful in drawing conclusions regarding the validity of Purchasing Power Parity (PPP). Rather than asking whether PPP holds throughout the whole sample period, we examine, in this study, if PPP holds sometimes by employing Hamilton-type (1989) Markov regime switching models. When at least one of multiple regimes is stationary, PPP holds locally within the regime. There are indeed various reasons that we should expect that the persistence of real exchange rates changes over time. Employing five real exchange rates spanning more than 100 years, we find herein strong evidence that the strength of PPP varies during the sample periods and that there exist stationary regimes in which PPP holds. Throughout the article, we also make comparisons to previous Markov regime switching estimation results by Kanas (2006) on the same data series. The new Markov switching model selection criterion of Smith et al. (2006), which is devised especially for discriminating Markov regime switching models, unambiguously indicates a preference for the Hamilton-type Markov regime switching model employed in this study. We also find that the evidence for PPP is not much different across different nominal exchange rate arrangements.     

The diversity of forecasts from macroeconomic models of the US economy

This paper investigates the accuracy and heterogeneity of output growth and inflation forecasts during the current and the four preceding NBER-dated US recessions. We generate forecasts from six different models of the US economy and compare them to professional forecasts from the Federal Reserve??s Greenbook and the Survey of Professional Forecasters (SPF). The model parameters and model forecasts are derived from historical data vintages so as to ensure comparability to historical forecasts by professionals. The mean model forecast comes surprisingly close to the mean SPF and Greenbook forecasts in terms of accuracy even though the models only make use of a small number of data series. Model forecasts compare particularly well to professional forecasts at a horizon of three to four quarters and during recoveries. The extent of forecast heterogeneity is similar for model and professional forecasts but varies substantially over time. Thus, forecast heterogeneity constitutes a potentially important source of economic fluctuations. While the particular reasons for diversity in professional forecasts are not observable, the diversity in model forecasts can be traced to different modeling assumptions, information sets and parameter estimates.     

Uncertainty and Learning in Stochastic Macro Models

Limits on information have deep economic impact and affect the conduct of economic policy. In the present paper we explore the effect of substantive uncertainty in a macro model, from both an analytical and methodological point of view. Agents are boundedly rational and make their forecasts according to different techniques and try to learn the values of the various parameters. In this context, a Markov regime switching rule, a VAR system, and recursive least square are considered and compared. As a result, we obtain a model which is mostly keynesian in nature that can be compared with the new neoclassical synthesis models. Simulations are carried out and show the possible appearence of endogenous and persistent fluctuations.     

Improving GARCH volatility forecasts with regime-switching GARCH

Many researchers use GARCH models to generate volatility forecasts. Using data on three major U.S. dollar exchange rates we show that such forecasts are too high in volatile periods. We argue that this is due to the high persistence of shocks in GARCH forecasts. To obtain more flexibility regarding volatility persistence, this paper generalizes the GARCH model by distinguishing two regimes with different volatility levels; GARCH effects are allowed within each regime. The resulting Markov regime-switching GARCH model improves on existing variants, for instance by making multi-period-ahead volatility forecasting a convenient recursive procedure. The empirical analysis demonstrates that the model resolves the problem with the high single-regime GARCH forecasts and that it yields significantly better out-of-sample volatility forecasts. First Version Received: November 2000/Final Version Received: August 2001     

Excessive Volatility is Also a Feature of Individual Level Forecasts

The excessive volatility of prices in financial markets is one of the most pressing puzzles in social science. It has led many to question economic theory, which attributes beneficial effects to markets in the allocation of risks and the aggregation of information. In exploring its causes, we investigated to what extent excessive volatility can be observed at the individual level. Economists claim that securities prices are forecasts of future outcomes. Here, we report on a simple experiment in which participants were rewarded to make the most accurate possible forecast of a canonical financial time series. We discovered excessive volatility in individual-level forecasts, paralleling the finding at the market level. Assuming that participants updated their beliefs based on reinforcement learning, we show that excess volatility emerged because of a combination of three factors. First, we found that submitted forecasts were noisy perturbations of participants’ revealed beliefs. Second, beliefs were updated using a prediction error based on submitted forecast rather than revealed past beliefs. Third, in updating beliefs, participants maladaptively decreased learning speed with prediction risk. Our results reveal formerly undocumented features in individual-level forecasting that may be critical to understand the inherent instability of financial markets and inform regulatory policy.     

中国通胀水平与通胀不确定性:马尔柯夫域变分析

本文使用中国1985年以来月度数据,基于马尔柯夫域变模型考察了通胀水平及其与不确定性的关系。我们将通胀的不确定性分解为两类成分:未来通胀冲击的不确定性和未来通胀均值域变的不确定性。研究结果表明,高的通胀水平伴随着这两类不确定性成分的同时增大,这意味着通胀成本很大程度上和不确定性的成本联系在一起,稳定价格和维持低通胀环境可能成为央行减少不确定性的重要手段。本文结果还表明,域变模型相对线性自回归模型以及ARCH模型更好地刻画了中国通胀率过程的特点。以往应用中忽略了这种域变特点可能导致通胀预测值相对于真实值的系统性偏差,或者通胀不确定性的错误估计。     

The evolution of inflation expectations in Canada and the US

We model inflation forecasts as monotonically diverging from an estimated long‐run anchor point towards actual inflation as the forecast horizon shortens. Fitting the model with forecaster‐level data for Canada and the US, we identify three key differences between the two countries. First, the average estimated anchor of US inflation forecasts has tended to decline gradually over time in rolling samples, from 3.4% for 1989–1998 to 2.2% for 2004–2013. By contrast, it has remained close to 2% since the mid‐1990 for Canadian forecasts. Second, the variance of estimates of the long‐run anchor is considerably lower for the panel of Canadian forecasters than US ones following Canada's adoption of inflation targets. And third, forecasters in Canada look much more alike than those in the US in terms of the weight that they place on the anchor. One explanation for these results is that an explicit inflation‐targeting regime (Canada) provides for less uncertainty about future monetary policy actions than a monetary policy regime where there was no explicit numerical inflation target (the US before 2012) to anchor expectations.     

Predicting U.S. recessions through a combination of probability forecasts

Recently De Luca and Carfora (Statistica e Applicazioni 8:123–134, 2010) have proposed a novel model for binary time series, the Binomial Heterogenous Autoregressive (BHAR) model, successfully applied for the analysis of the quarterly binary time series of U.S. recessions. In this work we want to measure the efficacy of the out-of-sample forecasts of the BHAR model compared to the probit models by Kauppi and Saikkonen (Rev Econ Stat 90:777–791, 2008). Given the substantial indifference of the predictive accuracy between the BHAR and the probit models, a combination of forecasts using the method proposed by Bates and Granger (Oper Res Q 20:451–468, 1969) for probability forecasts is analyzed. We show how the forecasts obtained by the combination between the BHAR model and each of the probit models are superior compared to the forecasts obtained by each single model.     

Conditional Markov regime switching model applied to economic modelling

In this paper we discuss the calibration issues of regime switching models built on mean-reverting and local volatility processes combined with two Markov regime switching processes. In fact, the volatility structure of these models depends on a first exogenous Markov chain whereas the drift structure depends on a conditional Markov chain with respect to the first one. The structure is also assumed to be Markovian and both structure and regime are unobserved. Regarding this construction, we extend the classical Expectation–Maximization (EM) algorithm to be applied to our regime switching model. We apply it to economic data (Euro/Dollar (USD) foreign exchange rate and Brent oil price) to show that such modelling clearly identifies both mean reverting and volatility regime switches. Moreover, it allows us to make economic interpretations of this regime classification as in some financial crises or some economic policies.     

Rationality tests in the presence of instabilities in finite samples

The importance of expectations in modern macroeconomic models and in particular of policy makers expectations for forward looking policy rules has generated a lot of interest in time series of professional forecasts (including central bank staff forecasts). This has spawned a large literature on the evaluation of forecasts that are not model based or where the model is unknown. Although, the available time series of historical forecasts are typically short, this literature has so far mostly disregarded the small sample properties of the proposed tests and estimators. In this paper we fill this gap in the literature, focusing on a set of recently proposed rationality tests for unstable environments. Using a Monte Carlo study we demonstrate that the asymptotic tests are substantially oversized in finite samples including any sample size that is practically available. We provide finite sample adjusted critical values, that allow those tests to be properly applied to sample sizes of typically available forecasts such as the Survey of Professional Forecasters, the Federal Open Market Committee. The critical values we provide will help to avoid false rejections using those data.     

Fixed exchange rate credibility with heterogeneous expectations

After disinflation has been achieved, agents who form more sophisticated forecasts have lower confidence in the sustainability of a peg compared to less sophisticated agents. Furthermore, sustained financial stability leads to a declining proportion of sophisticated agents. Thus, the credibility of a fixed exchange rate regime grows over time partly because fewer people pay attention to the workings of the monetary regime. These results are derived in a rules-versus-discretion model of a fixed exchange rate regime with heterogeneous agents. We provide unique supporting evidence using data on expectations and information about the monetary regime from Bulgaria’s currency board.     

Forecast performance,disagreement, and heterogeneous signal-to-noise ratios

We propose an imperfect information model for the expectations of macroeconomic forecasters that explains differences in average disagreement levels across forecasters by means of cross-sectional heterogeneity in the variance of private noise signals. We show that the forecaster-specific signal-to-noise ratios determine both the average individual disagreement level and an individuals’ forecast performance: Forecasters with very noisy signals deviate strongly from the average forecasts and report forecasts with low accuracy. We take the model to the data by empirically testing for this implied correlation. Evidence based on data from the Surveys of Professional Forecasters for the USA and for the Euro Area supports the model for short- and medium-run forecasts but rejects it based on its implications for long-run forecasts.     

An Evaluation of Alternative Methods of Forecasting Australian Inflation

The purpose of this paper is to evaluate the forecast of Australian inflation based on four alternative procedures: a univariate time series model, an interest rate model, an error correction model and a public survey of inflation forecasts. We derive estimates of expected and unexpected inflation from each of the methods and compare the out-of-sample forecasting results. Based on a range of evaluation criteria, the time series model dominates the other models, with the interest rate model, the error correction model and the survey forecasts following in that order.     

Rational expectations and fixed-event forecasts: An application to UK inflation

This paper tests a version of the rational expectations hypothesis using ‘fixed-event’ inflation forecasts for the UK. Fixed-event forecasts consist of a panel of forecasts for a set of outturns of a series at varying horizons prior to each outturn. The forecasts are the prediction of fund managers surveyed by Merrill Lynch. Fixed-event forecasts allow tests for whether expectations are unbiased in a similar fashion to the rest of the literature. But they also permit the conduct of particular tests of forecast efficiency - whether the forecasts make best use of available information - that are not possible with rolling-event data. We find evidence of a positive bias in inflation expectations. Evidence for inefficiency is much less clear cut.First version received: June 2002/ Final version received: November 2003We would like two anonymous referees and an editor for comments that have significantly improved the paper. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Bank of England.     

Forecasting tourism demand to Catalonia: Neural networks vs. time series models

The increasing interest aroused by more advanced forecasting techniques, together with the requirement for more accurate forecasts of tourism demand at the destination level due to the constant growth of world tourism, has lead us to evaluate the forecasting performance of neural modelling relative to that of time series methods at a regional level. Seasonality and volatility are important features of tourism data, which makes it a particularly favourable context in which to compare the forecasting performance of linear models to that of nonlinear alternative approaches. Pre-processed official statistical data of overnight stays and tourist arrivals from all the different countries of origin to Catalonia from 2001 to 2009 is used in the study. When comparing the forecasting accuracy of the different techniques for different time horizons, autoregressive integrated moving average models outperform self-exciting threshold autoregressions and artificial neural network models, especially for shorter horizons. These results suggest that the there is a trade-off between the degree of pre-processing and the accuracy of the forecasts obtained with neural networks, which are more suitable in the presence of nonlinearity in the data. In spite of the significant differences between countries, which can be explained by different patterns of consumer behaviour, we also find that forecasts of tourist arrivals are more accurate than forecasts of overnight stays.     

A vector error-correction forecasting model of the US economy

Any research or policy analysis in economics must be consistent with the time-series properties of observed macroeconomic data. Numerous previous studies reinforce the need to specify correctly a model’s multivariate stochastic structure. This paper discusses in detail the specification of a vector error correction forecasting model that is anchored by long-run equilibrium relationships suggested by economic theory. The model includes six variables––the CPI, the GDP price index, real money balances (M1), the federal funds rate, the yield on long-term (10-year) government bonds, and real GDP––and four cointegrating vectors. The accuracy of VECM model forecasts for individual, univariate time series during for the 1990s is comparable to forecasts made by government agencies and private forecasters, perhaps because many forecasters share a similar implicit, long-run steady-state growth model of the economy. Judged by multivariate statistics that account for forecast-error covariance, VECM forecasts are found to be somewhat more accurate than a naïve random-walk alternative.     

A dynamic factor model framework for forecast combination

A panel of ex-ante forecasts of a single time series is modeled as a dynamic factor model, where the conditional expectation is the single unobserved factor. When applied to out-of-sample forecasting, this leads to combination forecasts that are based on methods other than OLS. These methods perform well in a Monte Carlo experiment. These methods are evaluated empirically in a panel of simulated real-time computer-generated univariate forecasts of U.S. macroeconomic time series.     

Monetary policy regimes and beliefs*

This article investigates the role of beliefs over monetary policy in propagating the effects of monetary policy shocks within the context of a dynamic, stochastic general equilibrium model. In our model, monetary policy periodically switches between low and high money growth regimes. When individuals are unable to observe the regime directly, they form inferences over regime‐type based on historical money growth rates. For an empirically plausible money growth process, beliefs evolve slowly in the wake of a regime change. As a result, our model is able to capture some of the observed persistence of real and nominal variables following such a regime change.     

Forecasting development outcomes under alternative surplus labour assumptions

Economic forecasts are useful to policymakers both as aids to planning, and as baselines against which counterfactual scenarios can be compared. However, policy makers should be aware that assumptions relating to model structure can influence forecast results. We explore the sensitivity of forecasts to one aspect of model structure important in modelling developing economies: surplus agricultural labour. We outline a framework for modelling surplus agricultural labour that relies on average product remuneration. We embed this within a model of a developing economy (the Philippines) characterized by surplus agricultural labour. We compare the results of two forecasts that differ in their treatment of the agricultural labour market. In the first, the surplus labour theory is activated, establishing average product remuneration in agriculture. In the second, the surplus labour theory is not activated, creating a failure to recognize average product remuneration in agriculture. By comparing the two simulations, we show that failure to model the presence of average product remuneration, when it would be appropriate to do so, has an impact that would be material to economic planners, leading them to: under-estimate agricultural employment; over-estimate GDP growth; and, over-estimate important policy variables (like tax revenue) that are related to GDP growth.