Assessment of the effect of the financial crisis on agents’ expectations through symbolic regression

Agents’ perceptions on the state of the economy can be affected during economic crises. Tendency surveys are the main source of agents’ expectations. The main objective of this study is to assess the impact of the 2008 financial crisis on agents’ expectations. With this aim, we evaluate the capacity of survey-based expectations to anticipate economic growth in the United States, Japan, Germany and the United Kingdom. We propose a symbolic regression (SR) via genetic programming approach to derive mathematical functional forms that link survey-based expectations to GDP growth. By combining the main SR-generated indicators, we generate estimates of the evolution of GDP. Finally, we analyse the effect of the crisis on the formation of expectations, and we find an improvement in the capacity of agents’ expectations to anticipate economic growth after the crisis in all countries except Germany.Peer ReviewedPostprint (author's final draft

Dynamic higher order expectations

In models where privately informed agents interact, agents may need to form higher order expectations, i.e. expectations of other agents' expectations. This paper develops a tractable framework for solving and analyzing linear dynamic rational expectations models in which privately informed agents form higher order expectations. The framework is used to demonstrate that the well-known problem of the infinite regress of expectations identified by Townsend (1983) can be approximated to an arbitrary accuracy with a finite dimensional representation under quite general conditions. The paper is constructive and presents a fixed point algorithm for finding an accurate solution and provides weak conditions that ensure that a fixed point exists. To help intuition, Singleton's (1987) asset pricing model with disparately informed traders is used as a vehicle for the paper.Dynamic Higher Order Expectations, Private Information, Asset Pricing

Optimal Monetary Policy When Agents Are Learning

Most studies of optimal monetary policy under learning rely on optimality conditions derived for the case when agents have rational expectations. In this paper, we derive optimal monetary policy in an economy where the Central Bank knows, and makes active use of, the learning algorithm agents follow in forming their expectations. In this setup, monetary policy can influence future expectations through its e ect on learning dynamics, introducing an additional tradeo between inflation and output gap stabilization. Specifically, the optimal interest rate rule reacts more aggressively to out-of-equilibrium inflation expectations and noisy cost-push shocks than would be optimal under rational expectations: the Central Bank exploits its ability to "drive" future expectations closer to equilibrium. This optimal policy closely resembles optimal policy when the Central Bank can commit and agents have rational expectations. Monetary policy should be more aggressive in containing inflationary expectations when private agents pay more attention to recent data. In particular, when beliefs are updated according to recursive least squares, the optimal policy is time-varying: after a structural break the Central Bank should be more aggressive and relax the degree of aggressiveness in subsequent periods. The policy recommendation is robust: under our policy the welfare loss if the private sector actually has rational expectations is much smaller than if the Central Bank mistakenly assumes rational expectations whereas in fact agents are learning.Optimal Monetary Policy, Learning, Rational Expectations

Anticipated Fiscal Policy and Adaptive Learning

We consider the impact of anticipated policy changes when agents form expectations using adaptive learning rather than rational expectations. To model this we assume that agents combine limited structural knowledge with a standard adaptive learning rule. We analyze these issues using two well-known set-ups, an endowment economy and the Ramsey model. In our set-up there are important deviations from both rational expectations and purely adaptive learning. Our approach could be applied to many macroeconomic frameworks

Anticipated Fiscal Policy and Adaptive Learning

We consider the impact of anticipated policy changes when agents form expectations using adaptive learning rather than rational expectations. To model this we assume that agents combine limited structural knowledge with a standard adaptive learning rule. We analyze these issues using two well-known set-ups, an endowment economy and the Ramsey model. In our set-up there are important deviations from both rational expectations and purely adaptive learning. Our approach could be applied to many macroeconomic frameworks.Taxation, expectations, Ramsey model.

The ECB's New Multi-Country Model for the Euro area: NMCM - with Boundedly Rational Learning Expectations*

Rational expectations has been the dominant way to model expectations, but the literature has quickly moved to a more realistic assumption of boundedly rational learning where agents are assumed to use only a limited set of information to form their expectations. A standard assumption is that agents form expectations by using the correctly specified reduced form model of the economy, the minimal state variable solution (MSV), but they do not know the parameters. However, with medium-sized and large models the closed-form MSV solutions are difficult to attain given the large number of variables that could be included. Therefore, agents base expectations on a misspecified MSV solution. In contrast, we assume agents know the deep parameters of their own optimizing frameworks. However, they are not assumed to know the structure nor the parameterization of the rest of the economy, nor do they know the stochastic processes generating shocks hitting the economy. In addition, agents are assumed to know that the changes (or the growth rates) of fundament variables can be modeled as stationary ARMA(p,q) processes, the exact form of which is not, however, known by agents. This approach avoids the complexities of dealing with a potential vast multitude of alternative mis-specified MSVs. Using a new Multi-country Euro area Model with Boundedly Estimated Rationality we show this approach is compatible with the same limited information assumption that was used in deriving and estimating the behavioral equations of different optimizing agents. We find that there are strong differences in the adjustment path to the shocks to the economy when agent form expectations using our learning approach compared to expectations formed under the assumption of strong rationality. Furthermore, we find that some variation in expansionary fiscal policy in periods of downturns compared to boom periods.

The role of price expectations in the UK housing market

Copyright University of HertfordshireThe objective of this paper is to explain and derive the non-linear, S-shaped diffusion path of price expectations and provide a forecasting model, three months ahead with the implications assessed. Bounded rationality means that various agents in the U.K. housing market, such as buyers,sellers, estate agents and chartered surveyors, play differing rôles in the overall formulation of expectations of prices. This is analogous to the logistic effect with a diffusion path of dis-equilibrium to the end-point of equilibrium. The empirical analysis makes use of the forwarding-looking price expectations data published by Royal Institution of Chartered Surveyors (RICS) with the actual observations produced by Mortgage lenders, the Halifax and the Nationwide

Learning to forecast and cyclical behavior of output and inflation

This paper considers a sticky price model with a cash-in-advance constraint where agents forecast inflation rates with the help of econometric models. Agents use least squares learning to estimate two competing models of which one is consistent with rational expectations once learning is complete. When past performance governs the choice of forecast model, agents may prefer to use the inconsistent forecast model, which generates an equilibrium where forecasts are inefficient. While average output and inflation result the same as under rational expectations, higher moments differ substantially: output and inflation show persistence, inflation responds sluggishly to nominal disturbances, and the dynamic correlations of output and inflation match U.S. data surprisingly well

Endogenous Persistence in an Estimated DSGE Model under Imperfect Information

We provide a tool for estimating DSGE models by BayesianMaximum-likelihood methods under very general information assumptions. This framework is applied to a New Keynesian model where we compare the standard approach, that assumes an informational asymmetry between private agents and the econometrician, with an assumption of informational symmetry. For the former, private agents observe all state variables including shocks, whereas the econometrician uses only data for output, inflation and interest rates. For the latter both agents have the same imperfect information set and this corresponds to what we term the 'informational consistency principle'. We first assume rational expectations and then generalize the model to allow some households and firms to form expectations adaptively. We find that in terms of model posterior probabilities, impulse responses, second moments and autocorrelations, the assumption of informational symmetry by rational agents significantly improves the model fit. We also find qualified empirical support for the heterogenous expectations model. JEL Classification: C11, C52, E12, E32.Imperfect Information, DSGE Model, Rational versus Adaptive Expectations, Bayesian Estimation

Endogenous Persistence in an Estimated DSGE Model under Imperfect Information

We provide a tool for estimating DSGE models by Bayesian Maximum-likelihood meth?ods under very general information assumptions. This framework is applied to a New Keynesian model where we compare the standard approach, that assumes an informa?tional asymmetry between private agents and the econometrician, with an assumption of informational symmetry. For the former, private agents observe all state variables including shocks, whereas the econometrician uses only data for output, inflation and interest rates. For the latter both agents have the same imperfect information set and this corresponds to what we term the ¡®informational consistency principle¡¯. We first assume rational expectations and then generalize the model to allow some households and firms to form expectations adaptively. We find that in terms of model posterior probabilities, impulse responses, second moments and autocorrelations, the assumption of informational symmetry by rational agents significantly improves the model fit. We also find qualified empirical support for the heterogenous expectations model.Imperfect Information, DSGE Model, Rational versus Adaptive Expectations, Bayesian Estimation.