Rational Expectations is not Generally Valid for Econometric Models: Evidence from Stock Market Data

In applying the rational expectations hypothesis to generate expectations in an econometric model it is assumed that (1) the model itself is capable of generating reasonable forecasts of all required expectations variables included in the model, and that (2) the economic agents whose behavior is being modeled act as if they form their psychological expectations as conditional mathematical expectations generated by the model. Both assumptions can be invalid, as demonstrated by the historical data on Hong Kong stock prices and by the successful application of the adaptive expectations hypothesis to explain panel data of prices of individual stocks and aggregate time series data on stock price indices of the United States and of Hong Kong.     

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.     

Macroeconomic forecasting in the Euro area: Country specific versus area-wide information

This paper compares several time series methods for short-run forecasting of Euro-wide inflation and real activity using data from 1982 to 1997. Forecasts are constructed from univariate autoregressions, vector autoregressions, single equation models that include Euro-wide and US aggregates, and large-model methods in which forecasts are based on estimates of common dynamic factors. Aggregate Euro-wide forecasts are constructed from models that utilize only aggregate Euro-wide variables and by aggregating country-specific models. The results suggest that forecasts constructed by aggregating the country-specific models are more accurate than forecasts constructed using the aggregate data.     

Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games

Most learning models assume players are adaptive (i.e., they respond only to their own previous experience and ignore others' payoff information) and behavior is not sensitive to the way in which players are matched. Empirical evidence suggests otherwise. In this paper, we extend our adaptive experience-weighted attraction (EWA) learning model to capture sophisticated learning and strategic teaching in repeated games. The generalized model assumes there is a mixture of adaptive learners and sophisticated players. An adaptive learner adjusts his behavior the EWA way. A sophisticated player rationally best-responds to her forecasts of all other behaviors. A sophisticated player can be either myopic or farsighted. A farsighted player develops multiple-period rather than single-period forecasts of others' behaviors and chooses to “teach” the other players by choosing a strategy scenario that gives her the highest discounted net present value. We estimate the model using data from p-beauty contests and repeated trust games with incomplete information. The generalized model is better than the adaptive EWA model in describing and predicting behavior. Including teaching also allows an empirical learning-based approach to reputation formation which predicts better than a quantal-response extension of the standard type-based approach. Journal of Economic Literature Classification Numbers: C72, C91.     

A heterogeneous agent exchange rate model with speculators and non-speculators

This paper constructs a heterogeneous agent exchange rate model of speculators and non-speculators from a simple monetary framework. The model replaces rational expectations with an adaptive learning rule that forecasts future exchange rates with an econometric model, and assumes two types of market participants, speculators and non-speculators, that differ by their forecasting model. Speculators employ a correctly specified forecasting model, are relatively short-term oriented, and are subject to momentum and herding effects via an expectation shock; non-speculators utilize a simple forecasting model, have no incentive to be short-term oriented, and are not subject to herding effects. Parameters are calibrated and estimated using the method of simulated moments, and simulation results show that the model is able to replicate foreign exchange market stylized facts better than a model of representative agent rational expectations. Furthermore, the dynamics of the model are shown to derive from both agent heterogeneity and the expectation shock.     

Macroeconomic expectations and time varying heterogeneity:evidence from individual survey data

ABSTRACT

The goal of this paper is to investigate forecast heterogeneity and time variability in the formation of expectations using disaggregated monthly survey data on macroeconomic indicators provided by Bloomberg from June 1998 to August 2017. We show that our panel of forecasters are not rational and are moderately heterogeneous and thus confirm that previously well-established results on asset prices hold for macroeconomic indicators. We propose a flexible hybrid forecast model defined at any time as a combination of the extrapolative, regressive, adaptive and interactive heuristics. Controlling for endogenous structural breaks, we find that experts adjust their forecast behaviour at any time with some inertia in extrapolative and adaptive profiles. Changes in the formation of expectations are triggered mostly by financial shocks, and uncertainty is dealt with by using complex processes in which the fundamentalist component overweighs chartist activity. Forecasters whose models combine different relevant rules and display high temporal flexibility provide the most accurate forecasts. Authorities can then stabilize the domestic markets by encouraging fundamentalists’ forecasts through increased transparency policy.     

Forecasting the aggregate stock market volatility in a data-rich world

ABSTRACT

In this article, we utilize the basic lasso and elastic net models to revisit the predictive performance of aggregate stock market volatility in a data-rich world. Motivated by the existing literature, we determine several candidate predictors that have 22 technical indicators and 14 macroeconomic and financial variables. Our out-of-sample results reveal several noteworthy findings. First, few macroeconomic and financial variables and most of technical indicators have superior performance relative to the benchmark model. Second, combination forecasts are able to significantly beat the benchmark and some signal predictors Third, the lasso and elastic models with all predictors can generate more accurate forecasts than the benchmark and some other predictors in both the statistical and economic sense. Fourth, the lasso and elastic models exhibit higher forecast accuracy during periods of expansions and recessions. Finally, our findings are robust to several tests, such as different forecasting windows, forecasting models, and forecasting evaluations.     

Heterogeneous expectations and the distribution of wealth

This study examines the extent to which heterogeneity of expectations affects wealth distribution, through the use of a standard heterogeneous agent model with uninsured idiosyncratic risk and aggregate uncertainty. A simple stylized model of heterogeneous expectations is considered to demonstrate that the impact of expectations’ heterogeneity on wealth inequality depends nonlinearly on the level and persistence of expectations’ dispersion. It is also shown that the heterogeneity of expectations generated by the empirically validated learning-from-experience model (Malmendier, Nagel, Q J Econ 2016) has a moderate but ambiguous impact on the distribution of wealth. The effect is sensitive to the calibration of the macroeconomic and learning parts of the model.     

On the uncertainty and risks of macroeconomic forecasts: combining judgements with sample and model information

Institutions which publish macroeconomic forecasts usually do not rely on a single econometric model to generate their forecasts. The combination of judgements with information from different models complicates the problem of characterizing the predictive density. This article proposes a parametric approach to construct the joint and marginal densities of macroeconomic forecasting errors, combining judgements with sample and model information. We assume that the relevant variables are linear combinations of latent independent two-piece normal variables. The baseline point forecasts are interpreted as the mode of the joint distribution, which has the convenient feature of being invariant to judgments on the balance of risks.     

Combining country-specific forecasts when forecasting Euro area macroeconomic aggregates

European Monetary Union member countries’ forecasts are often combined to obtain the forecasts of the Euro area macroeconomic aggregate variables. The aggregation weights which are used to produce the aggregates are often considered as combination weights. This paper investigates whether using different combination weights instead of the usual aggregation weights can help to provide more accurate forecasts. In this context, we examine the performance of equal weights, the least squares estimators of the weights, the combination method recently proposed by Hyndman et al.  (Comput Stat Data Anal 55(9):2579–2589, 2011) and the weights suggested by shrinkage methods. We find that some variables like real GDP and the GDP deflator can be forecasted more precisely by using flexible combination weights. Furthermore, combining only forecasts of the three largest European countries helps to improve the forecasting performance. The persistence of the individual series seems to play an important role for the relative performance of the combination.     

Learning and Equilibrium Selection in a Monetary Overlapping Generations Model with Sticky Prices

We study adaptive learning in a monetary overlapping generations model with sticky prices and monopolistic competition for the case where learning agents observe current endogenous variables. Observability of current variables is essential for informational consistency of the learning setup with the model setup but generates multiple temporary equilibria when prices are flexible and prevents a straightforward construction of the learning dynamics. Sticky prices overcome this problem by avoiding simultaneity between prices and price expectations. Adaptive learning then robustly selects the determinate (monetary) steady state independent from the degree of imperfect competition. The indeterminate (non-monetary) steady state and non-stationary equilibria are never stable. Stability in a deterministic version of the model may differ because perfect foresight equilibria can be the limit of restricted perceptions equilibria of the stochastic economy with vanishing noise and thereby inherit different stability properties. This discontinuity at the zero variance of shocks suggests one should analyse learning in stochastic models.     

A product diffusion model incorporating repeat purchases

A logistic-based model for forecasting the rate of product diffusion given aggregate time series data was constructed. The model differs from earlier models based on fitting the logistic to aggregate data in that it includes a submodel to separate replacement demand from first-time sales. We fit the theoretical model to data and show that forecasts will be significantly more accurate using this model instead of the logistic curve.     

The information content of regional employment data for forecasting aggregate conditions

We consider whether disaggregated data enhance the efficiency of aggregate employment forecasts. We find that incorporating spatial interaction into a disaggregated forecasting model lowers the out-of-sample mean squared error from a univariate aggregate model by 70% at a two-year horizon.     

Multi-horizon inflation forecasts using disaggregated data

In this paper we use multi-horizon evaluation techniques to produce monthly inflation forecasts for up to twelve months ahead. The forecasts are based on individual seasonal time series models that consider both, deterministic and stochastic seasonality, and on disaggregated Consumer Price Index (CPI) data. After selecting the best forecasting model for each index, we compare the individual forecasts to forecasts produced using two methods that aggregate hierarchical time series, the bottom-up method and an optimal combination approach. Applying these techniques to 16 indices of the Mexican CPI, we find that the best forecasts for headline inflation are able to compete with those taken from surveys of experts.     

DSGE model-based forecasting of modelled and nonmodelled inflation variables in South Africa

Inflation forecasts are a key ingredient for monetary policy-making – especially in an inflation targeting country such as South Africa. Generally, a typical Dynamic Stochastic General Equilibrium (DSGE) only includes a core set of variables. As such, other variables, for example alternative measures of inflation that might be of interest to policy-makers, do not feature in the model. Given this, we implement a closed-economy New Keynesian DSGE model-based procedure which includes variables that do not explicitly appear in the model. We estimate such a model using an in-sample covering 1971Q2 to 1999Q4 and generate recursive forecasts over 2000Q1 to 2011Q4. The hybrid DSGE performs extremely well in forecasting inflation variables (both core and nonmodelled) in comparison with forecasts reported by other models such as AR(1). In addition, based on ex-ante forecasts over the period 2012Q1–2013Q4, we find that the DSGE model performs better than the AR(1) counterpart in forecasting actual GDP deflator inflation.     

Improving the predictability of the oil–US stock nexus: The role of macroeconomic variables

In this study, we revisit the oil–stock nexus by accounting for the role of macroeconomic variables and testing their in-sample and out-of-sample predictive powers. We follow the approaches of Lewellen (2004) and Westerlund and Narayan (2015), which were formulated into a linear multi-predictive form by Makin et al. (2014) and Salisu et al. (2018) and a nonlinear multi-predictive model by Salisu and Isah (2018). Thereafter, we extend the multi-predictive model to account for structural breaks and asymmetries. Our analyses are conducted on aggregate and sectoral stock price indexes for the US stock market. Our proposed predictive model, which accounts for macroeconomic variables, outperforms the oil-based single-factor variant as well as the constant returns (historical average) model for both in-sample and out-of-sample forecasts. We find that it is important to account for structural breaks in our proposed predictive model, although asymmetries do not seem to improve predictability. In addition, we show that it is important to pre-test the predictors for persistence, endogeneity, and conditional heteroscedasticity, particularly when modeling with high-frequency series. Our results are robust to different forecast measures and forecast horizons and are useful for making effective hedging decisions in the US stock market.     

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.     

Do we need a global VAR model to forecast inflation and output in South Africa?

This study determines whether the global vector autoregressive (GVAR) approach provides better forecasts of key South African variables than a vector error correction model (VECM) and a Bayesian vector autoregressive (BVAR) model augmented with foreign variables. The article considers both a small GVAR model and a large GVAR model in determining the most appropriate model for forecasting South African variables. We compare the recursive out-of-sample forecasts for South African GDP and inflation from six types of models: a general 33 country (large) GVAR, a customized small GVAR for South Africa, a VECM for South Africa with weakly exogenous foreign variables, a BVAR model, autoregressive (AR) models and random walk models. The results show that the forecast performance of the large GVAR is generally superior to the performance of the customized small GVAR for South Africa. The forecasts of both the GVAR models tend to be better than the forecasts of the augmented VECM, especially at longer forecast horizons. Importantly, however, on average, the BVAR model performs the best when it comes to forecasting output, while the AR(1) model outperforms all the other models in predicting inflation. We also conduct ex ante forecasts from the BVAR and AR(1) models over 2010:Q1–2013:Q4 to highlight their ability to track turning points in output and inflation, respectively.     

Business cycle amplification with heterogeneous expectations

This paper studies the implications for business cycle dynamics of heterogeneous expectations in a stochastic growth model. The assumption of homogeneous, rational expectations is replaced with a heterogeneous expectations model where a fraction of agents hold rational expectations and the remaining fraction adopt parsimonious forecasting models that are, in equilibrium, optimal within a restricted class. Our approach nests the literature on rational expectations in business cycle models with a recent approach based on adaptive learning. We demonstrate that (i.) heterogeneous expectations can lead to substantial improvement in the internal propagation of equilibrium business cycle models and (ii.) the internal propagation depends on the degree of heterogeneity. A calibrated model with heterogeneity provides a closer fit to business cycle data than its representative agent, rational expectations counterpart.     

Inequality and the business cycle: evidence from U.S. survey data

ABSTRACT

We study the effects of macroeconomic shocks on measures of economic inequality obtained from U.S. survey data. To identify aggregate supply, aggregate demand, and monetary policy shocks, we estimate vector autoregressions and impose sign and zero restrictions on impulse response functions. We find that the effects of the macroeconomic shocks on inequality depend on the type of shock as well as on the measure of inequality considered. Contractionary monetary policy shocks increase expenditure and consumption inequality, whereas income and earnings inequality are less affected. Adverse aggregate supply and demand shocks increase income and earnings inequality, but reduce expenditure and consumption inequality. Our results suggest that different channels dominate in the transmission of the shocks. The earnings heterogeneity channel is consistent with the inequality dynamics after monetary policy shocks, but it appears to be less crucial when the economy is hit by either aggregate supply or aggregate demand shocks. Using variance decompositions, we find that although the macroeconomic shocks account for large shares of the variation in the macroeconomic variables, their contributions to the dynamics of the inequality measures are limited.