The formation of wage expectations in the effort and quit decisions of workers

This study develops models in which workers form expectations of average wages in choosing levels of effort and on-the-job search. It is assumed that information on lagged average wages is available at a low fixed cost, whilst acquiring other information requires an additional variable cost. Under reasonable conditions, workers' expectations are at least partly adaptive, and may be a mixture of rational and adaptive expectations. Microeconomic parameters determine the degree to which expectations are adaptive and the weights placed on various lags of wages. As a result of partly adaptive expectations, nominal demand shocks may have real effects.     

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.     

Heterogeneous learning

There is by now a large literature characterising conditions under which learning schemes converge to rational expectations equilibria (REEs). It has been claimed that these results depend on the assumption of homogeneous agents and homogeneous learning. This paper analyses the stability of REEs under heterogeneous adaptive learning, for the class of self-referential linear stochastic models. Agents may differ in their initial perceptions about the evolution of the economy, the degrees of inertia in revising their expectations, or the learning rules they use. General conditions are provided for local stability of an REE. In general, it is not possible to show that stability under homogeneous learning implies stability under heterogeneous learning. To illustrate how to apply the results, several examples are provided.     

Rational expectations and M2 demand

This essay expands on existing studies of M2 money demand. It differs in that it applies a rational expectations approach to an adaptive expectation model. Unlike the adaptive expectations models, the author includes an explanatory variable for expectations of future inflation. The expectation variables used are: the actual inflation rate (t + 1) and the Livingston Survey from the Philadelphia Fed. By using the different measures of expectations the author is able to compare several adaptive expectations models that appear in the literature and the rational expectations models for fit and forecast ability. The empirical results are such that the importance of including the rational expectations variable is evident even though the overall fit of the equation is comparable to one of the existing adaptive expectations models.     

On capital accumulation paths in a neoclassical stochastic growth model

Summary. Boldrin and Montrucchio [2] showed that any twice continuously differentiable function could be obtained as the optimal policy function for some value of the discount parameter in a deterministic neoclassical growth model. I extend their result to the stochastic growth model with non-degenerate shocks to preferences or technology. This indicates that one can obtain complex dynamics endogenously in a wide variety of economic models, both under certainty and uncertainty. Further, this result motivates the analysis of convergence of adaptive learning mechanisms to rational expectations in economic models with (potentially) complicated dynamics. Received: June 21, 1996; revised version: October 31, 1996     

Modelling the business cycle of a small open economy: The Reserve Bank of New Zealand's DSGE model

We describe the underlying structure of the new forecast and policy model used at the Reserve Bank of New Zealand and evaluate its ability to explain New Zealand data. Unlike other estimated small-open-economy DSGE models, we find that more than one third of the domestic GDP growth is driven by foreign shocks. The elevated contribution of foreign shocks to the domestic economy is driven by our decision to exclude mapping export demand to data on world GDP. Estimating our model without any foreign demand data limits the response of exports to the real exchange variations. This feature makes exports and, consequently, domestic GDP much more sensitive to variations to foreign demand and raises the importance of foreign shocks to the domestic business cycle. Furthermore, our analysis suggests that a model with “adaptive” expectations is preferred by the data relative to the version of the model with “rational” expectations. In that case, the model explains nominal variables using on average much smaller shocks.     

Money, expectations, and interest rates

This paper employs a model of nominal interest rate determination in a framework of rational expectations of inflation. Hypotheses are developed with respect to relative impacts of predictable and unpredictable changes in money supply. These hypotheses are tested using quarterly Italian data from 1966–1975. The nominal monetary base is the measure of money employed and one private and two government bond rates measure nominal interest rates. The results are insensitive to variations in estimation procedure and specification of adjustment processes (and even predictive functions for the monetary base). The rational expectations formulation is well supported in every case.     

The influence of learning and price-level targeting on central bank forward guidance

This paper examines how the effectiveness of central bank forward guidance depends on two key channels: the expectations formation process and the monetary policy regime. The results show that rational expectations relative to an adaptive learning rule amplifies the positive benefits a price-level targeting central bank creates for forward guidance. Specifically, forward guidance generates greater amounts of output and inflation under a price-level than inflation targeting monetary policy regime, but rational expectations overstates these positive benefits compared to adaptive learning. The different responses of expectations between rational expectations and adaptive learning to forward guidance are driving this performance gap. Thus, policymakers should consider how expectations are modeled if forward guidance and price-level targeting are implemented in an economy.     

GENERALIZED STOCHASTIC GRADIENT LEARNING*

We study the properties of the generalized stochastic gradient (GSG) learning in forward‐looking models. GSG algorithms are a natural and convenient way to model learning when agents allow for parameter drift or robustness to parameter uncertainty in their beliefs. The conditions for convergence of GSG learning to a rational expectations equilibrium are distinct from but related to the well‐known stability conditions for least squares learning.     

Exchange Rates, Nominal Inertia and Inflation

This paper examines the use of the nominal exchange rate in achieving disinflation under managed exchange rate regimes. Most previous empirical studies have not explicitly identified expectations in the wage and price setting behaviour of their econometric models, despite the importance of expectations both during a disinflation and in correcting misalignments. This has meant that costs due to nominal inertia and non-neutralities have not been addressed separately from questions of credibility. We present results for the UK economy using both a theoretical and empirical model in which firms and workers form rational expectations, but where there is also nominal inertia. We identify costs in using the exchange rate to change the inflation rate, and also the costs involved in correcting any disequilibria in the real exchange rate.     

Expectation formation in the foreign exchange market: a time-varying heterogeneity approach using survey data

Using Consensus Economics survey data on JPY/USD and GBP/USD exchange rate expectations for the 3- and 12-month horizons over the period November 1989–December 2012, we first show that expectations fail the conventional tests of unbiasedness and do not exhibit a learning process towards rationality. Our approach is consistent with the economically rational expectations theory (Feige and Pearce, 1976), which states that information costs and agents’ aversion to misestimating future exchange rates determine the optimal amounts of information on which they base their expectations. The time variability of the cost/aversion ratios justifies at the aggregate level a representation of expectations as a linear combination of the traditional extrapolative, adaptive and regressive processes augmented by a forward market component, whose parameters are allowed to change over time. This mixed expectation model with unstable heterogeneity is validated by our Kalman filter estimation results for the two currencies and the two horizons considered. Although the relative importance of the ‘fundamentalists’ (‘chartists’) is found to increase (decrease) with the time-horizon, chartist behaviour appears to dominate fundamentalist behaviour for both horizons. Central bank intervention is then effective in stabilizing the foreign exchange markets if it encourages fundamentalist activity.     

Learning,estimation, and the stability of rational expectations

The stability of the rational expectations equilibrium of a simple asset market model is studied in a situation where a group of traders learn about the relationship between the price and return on the asset using ordinary least squares estimation, and then use their estimates in predicting the return from the price. The model which they estimate is a well-specified model of the rational expectations equilibrium, but a misspecified model of the situation in which the traders are learning. It is shown that for appropriate values of a stability parameter the situation converges almost surely to the rational expectations equilibrium.     

Fiscal Policy,Expectations, and Exchange-Rate Dynamics*

This paper uses the sticky-price monetary model to analyze the effects of fiscal policy on the exchange rate under alternative assumptions about exchange-rate expectations. the use of different expectations mechanisms-specifically the perfect-foresight model and the popular models tested by Frankel and Froot: regressive, adaptive, and distributed-lag-is based on recent empirical evidence suggesting that exchange-rate expectations may not be rational. the most surprising finding in the paper is that with adaptive and distributed-lag expectations, fiscal expansion has no initial impact on the exchange rate, and the same may be true for regressive expectations.     

Monetary Policy,Expectations and Commitment*

Commitment in monetary policy leads to equilibria that are superior to those from optimal discretionary policies. A number of interest‐rate reaction functions and instrument rules have been proposed to implement or approximate commitment policy. We assess these rules in terms of whether they lead to a rational expectations equilibrium that is both locally determinate and stable under adaptive learning by private agents. A reaction function that appropriately depends explicitly on private sector expectations performs particularly well on both counts.     

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.     

Heterogeneous expectations,indeterminacy, and postwar US business cycles

This paper estimates a New Keynesian model extended to include heterogeneous expectations: consumers and firms form either rational or boundedly-rational expectations. The inclusion of heterogeneous expectations alters the determinacy properties of the model, with the details of expectations potentially becoming more influential than the Taylor principle for equilibrium stability.The model is estimated with Bayesian techniques, using rolling windows and allowing the parameters to fall both in the determinacy and indeterminacy regions. The estimates reveal large shares of agents who depart from rational expectations. Heterogeneous expectations are decisively preferred by the data everywhere in the sample.Finally, the paper revisits the narrative that sees postwar US macroeconomic data as consistent with indeterminacy in the pre-1979 sample, with a switch to determinacy starting in the early 1980s, and it shows that it is overall robust to inclusion of heterogeneous expectations.     

Asset pricing with adaptive learning

We study the extent to which self-referential adaptive learning can explain stylized asset pricing facts in a general equilibrium framework. In particular, we analyze the effects of recursive least squares and constant gain algorithms in a production economy and a Lucas type endowment economy. We find that (a) recursive least squares learning has almost no effects on asset price behavior, since the algorithm converges relatively fast to rational expectations, (b) constant gain learning may contribute towards explaining the stock price and return volatility as well as the predictability of excess returns in the endowment economy but (c) in the production economy the effects of constant gain learning are mitigated by the persistence induced by capital accumulation. We conclude that in the context of these two commonly used models, standard linear self-referential learning does not resolve the asset pricing puzzles observed in the data.     

Limited information minimal state variable learning in a medium-scale multi-country model

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 that agents know the deep parameters of their own optimising frameworks. However, they are not assumed to know the structure nor the parameterisation 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 modelled 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 misspecified MSVs.Using a new multi-country euro area model with boundedly estimated rationality we show that this approach is compatible with the same limited information assumption that was used in deriving and estimating the behavioural equations of different optimising agents. We find that there are strong differences in the adjustment path to the shocks to the economy when agents form expectations using our learning approach compared to expectations formed under the assumption of strong rationality. Furthermore, we find some variation in expansionary fiscal policy in periods of downturns compared to boom periods.     

Unemployment and econometric learning

We apply well-known results of the econometric learning literature to the Mortensen and Pissarides real business cycle model. Agents can always learn the unique rational expectations equilibrium (REE), for all possible well-defined sets of parameter values, by using the minimum-state-variable solution to the model and decreasing gain learning. From this perspective the assumption of rational expectations in the model could be seen as reasonable. But using a parametrisation with UK data, simulations show that the speed of convergence to the REE is slow. This type of learning dampens the cyclical response of unemployment to small structural shocks.     

Learning process and rational expectations: An analysis using a small macro-economic model for New Zealand

The nature of expectations matters when conducting monetary policy. Models with a learning process can exhibit very different properties from models with other types of expectation rules. This paper draws on the work of Orphanides and Williams [Orphanides, A., Williams, J.C. 2002. Imperfect knowledge, inflation expectations and monetary policy, Federal Reserve Board Finance and Economics Discussion Series, 2002-27], extending it to allow for the possibility that the learning process may not be perpetual, but rather might be converging towards a rational expectations equilibrium. By modelling expectations using a learning process, we obtain that inflation expectations in New Zealand are moving towards rational expectations. The closer expectations are to rational, the more inflation can be reduced without costs, thus arguing for a rather tough policy aimed at anchoring expectations on the target.