Rational Expectations Model Research Articles

Saddle cycles: Solving rational expectations models featuring limit cycles (or chaos) using perturbation methods

Unlike linear ones, nonlinear business cycle models can generate sustained fluctuations even in the absence of shocks (e.g., via limit cycles/chaos). A popular approach to solving nonlinear models is perturbation methods. I show that, as typically implemented, these methods are incapable of finding solutions featuring limit cycles or chaos. Fundamentally, solutions are only required not to explode, while standard perturbation algorithms seek solutions that meet the stronger requirement of convergence to the steady state. I propose a modification to standard algorithms that does not impose this overly strong requirement.

A generalized approach to indeterminacy in linear rational expectations models

We propose a novel approach to deal with the problem of indeterminacy in linear rational expectations models. The method consists of augmenting the original state space with a set of auxiliary exogenous equations to provide the adequate number of explosive roots in presence of indeterminacy. The solution in this expanded state space, if it exists, is always determinate, and is identical to the indeterminate solution of the original model. The proposed approach accommodates determinacy and any degree of indeterminacy, and it can be implemented even when the boundaries of the determinacy region are unknown. Thus, the researcher can estimate the model using standard software packages without restricting the estimates to the determinacy region. We combine our solution method with a novel hybrid Metropolis–Hastings algorithm to estimate the New–Keynesian model with rational bubbles by Galí (2021) over the period 1982:Q4–2007:Q3. We find that the data support the presence of two degrees of indeterminacy, implying that the central bank was not reacting strongly enough to the bubble component.

Lucas’ Expectational Equilibrium, Price Rigidity, and Descriptive Realism

Robert Lucas’ 1972 article on the neutrality of money represented the first effective challenge to Samuelson’s neoclassical synthesis methodological separation between static microeconomic optimization and macroeconomic dynamics. Lucas rejected disequilibrium price dynamics, as expressed by the Walrasian tâtonnement and auctioneer mechanisms. Lucas’ new treatment of equilibrium as an expectational concept, determined by the rational behaviour of information processing agents, was not restricted to market clearing competitive economies. Lucas’ effort to compare alternative rational expectations models of price stickiness (including his 1972 original formulation) led him to stress the notion of “descriptive realism” of the models’ main assumptions, which played an important role in his original discussion of model robustness.

Solving linear rational expectations models in the presence of structural change: Some refinements

Solving linear rational expectations models in the presence of structural change: Some refinements

Persistent dynamics in (in)determinate equilibrium rational expectations models

Persistent dynamics in (in)determinate equilibrium rational expectations models

What Do Interest Rates Reveal About the Stock Market? A Noisy Rational Expectations Model of Stock and Bond Markets

We propose a novel theory and provide supporting empirical evidence that lower long-term interest rates (e.g., because of ``quantitative easing'') harm informational and allocative efficiency. We develop a noisy rational expectations equilibrium model with an endogenous interest rate that investors use to update their beliefs about economic fundamentals. The interest rate reveals information about discount rates, allowing investors to extract more information about cashflows from stock prices. The precision of the interest-rate signal and, hence, stock-price informativeness increase in the interest rate. As a result, informational and allocative efficiency rise with bond and money supplies and with policy transparency.

Spot Fishes at the Table: Tracking Retail Investors and Mutual Funds Return

We propose a new definition of mutual fund skill in tracking retail investors through characterizing trading synchronicity between mutual funds and retail flows. Firstly, we find robustness evidence that funds with low trading synchronicity significantly outperform funds with high trading synchronicity. Secondly, through a noisy rational expectations model with heterogeneous skills, we demonstrate the trading synchronicity captures mutual funds’ ability to explore noise retail flows, other than stock picking or market timing. These findings offer new evidence that some funds indeed track retail investors intentionally and that ability to explore retail flows could deliver excess return.

Research on the Factors of Competition in the Green Procurement Processes: A Case Study for the Conditions of Romania Using PLS-SEM Methodology

In this paper, starting from the conceptual model of the rational behavior theory developed by Icek Ajzen, the authors develop a behavioral model of rational expectations of the managerial decisions in order to determine the influence of the behavior of the undertakings on a competitive environmental market. The data were collected between 1 May 2019–30 June 2019 with the help of a questionnaire addressed to the employees and managers of the companies engaged in the green procurement processes in Romania. The sample volume was 160 and the data was analyzed with partial least square structural equation modeling (PLS-SEM) method and by using the statistical software Smart-PLS 3.2.8. Starting from the relevant economic literature in the field of rational behavior, the article identifies the behavioral indicators that underlie the decision to invest in this market. These indicators are the independent variables that model the impact of rational behavioral theory on managerial decisions. The conclusions of the study confirm the theoretical aspects presented in the article, emphasizing that the managerial decisions based on rational behavior theory are the direct result of the cooperation of several factors, such as the strategic vision, innovation, regulation, and the level of competences of the human factor.

Culture, learning and rational decision-making: evidence from a TV show

This paper analyzes the French and the Vietnamese versions of the TV game show “The Price is Right”, using data from 130 episodes. We focus on the bidding game, covering 434 rounds and 1,736 bids. We document that players deviate signifi cantly from what is predicted by the model of rational expectations, especially in the French population. Moreover, Vietnamese fourth bidders are found to win more frequently than their French counterparts in spite of using strategic bids less often. We attribute these results to cultural reasons. Contestants from the collectivistic, uncertainty-tolerant culture (i.e., Vietnam) are more reluctant to engage in strategic bidding than individuals from the individualistic, uncertainty-avoidant culture (i.e., France). However, Vietnamese contestants pay more attention to the estimates of the previous players and thus make a better use of the informational advantage inherent to the sequential nature of the game. Overall, our evidence suggests that culture is an important omitted variable in studies that examine cross-country differences in decision-making.

The Optimized Monetary Policy ZLB Mandate in NK Behavioural and RE Models Compared

In this paper, we extend the basic ‘workhorse’ New Keynesian model by relaxing the rationality assumption in favor of bounded rationality. We broadly follow (Gabaix, 2020) whereby agents are unable to anticipate macroeconomic developments perfectly and assumed to be both partially myopic and inattentive. In my set-up, we assume that agents form beliefs over the future infinite time horizon of aggregate states and prices which are exogenous to their decisions. we then directly apply agents’ inattentiveness on these exogenous market factors into their infinite-time-horizon decision rules. This approach produces identical decision rules as the “sparse agent” approach of Gabaix. Most importantly, with my method we can derive a fully non-linear form of my model, which is necessary to provide a correct welfare rankings in my mandate study. Results by the standard linear Bayesian estimation technique in this paper show that the boundedly rational expectation (BR) model outperforms the fully rational expectation model (RE). In the BR model, introducing the zero-lower-bound (ZLB) episode results in a higher welfare cost compared to the RE model. As a result, the optimal steady state inflation level of the BR model is higher given a probability of the nominal interest hitting the ZLB. Optimized interest rate rules for the RE and BR models closely mimics a price-level targeting rule. However, under the RE model, the nominal interest rate reacts more aggressively to the price inflation.

Persistent dynamics in (in)determinate equilibrium rational expectations models

Equilibrium indeterminacy in rational expectations models is often claimed to produce higher time series persistence relative to determinacy. Proceeding by means of a simple linear stochastic model, I formally show that, for reasonable parameter configurations, there exists an uncountable (continuously infinite) set of indeterminate equilibria in low-order AR(MA) representation, which exhibit strictly lower persistence than their determinate counterpart. Implications for empirical studies concerned with, e.g., testing for indeterminacy and macroeconomic forecasting are discussed.

Remeasuring and decomposing stochastic trends in business cycles

This paper is motivated by the fact that the standard deviation of cyclical TFP derived from the standard approach under the stochastic trend is not even close to the real-world data. The main part of the paper devotes to developing a new method to apply geometric Brownian motion to characterize TFP in continuous time and converting it to an estimated process of random walk with drift. As a result, the drift estimate together with the lagged TFP in the random walk process are the stochastic trend of TFP and the stochastic error term in the random walk with drift process is the cyclical component of TFP. I then have two findings: the first one is that the standard deviation of cyclical TFP derived from the new approach is much closer to the real-world data; the second one is that stochastic trend of TFP can be decomposed into three parts: an initial value, a deterministic trend, and a term involved with Weiner process. Moreover, this paper argues that, by recalculating the business cycle statistics based on a rational expectations model, if we remeasure the stochastic trend and cyclical component of TFP using the new approach, then the ability of real business cycle model to mimic real-world economic fluctuations will be significantly improved.

Parallel Extended Path Method for Solving Perfect Foresight Models

We parallelize the extended path method for solving rational expectations models, and apply it to compute perfect foresight competitive equilibrium for the global economy with multiple goods, regions, industries, and households. At each iteration, first intertemporal variables are updated, then equations for intra-temporal variables are solved in parallel. We compare serial, and parallel, versions of the extended path method in high-performance computing environments based on scenarios with long time horizons that include future populations, economic growth, energy use, and carbon dioxide emissions. Relative to the serial version, the speedup factor for the parallel extended path method grows almost linearly up to about 30 times with 18 cores, and computing times reduced from over 10 h for the serial version down to about 20 min for the parallel version.

Sunspot-driven fat tails: A note

Empirical growth-rate distributions of major macroeconomic aggregates are typically non-Normal and exhibit fat tails. We advance the idea that indeterminacies in standard rational expectations models can qualify as a source of high-frequency extreme macroeconomic outcomes. In a univariate setup, we demonstrate the emergence of fat-tailed behavior for an endogenous variable even though structural and sunspot shocks both follow Normal distributions.

Do Firms’ Inflation Expectations Matter in Their Employment and Wages? A Causal Evidence

This paper investigates how the difference between firms' inflation expectations, measured by the loan amounts they demand, and actual inflation affects their employment. In addition, it examines the relationship between firms' inflation expectations and wages in an individualistic bargaining model. Theoretically, the model shows that a firm's actual labor demand meets its expected labor demand if the firm has a rational expectation regarding inflation. On the other hand, the firm's actual labor demand deviates from its expected labor demand if the firm cannot forecast inflation correctly. Empirically, using firm-level data from a province in Iran between 2004 and 2011, the model's predictions have been tested. The empirical results confirm that there is a specific loan amount for which firms' expected employments meet their actual ones. In contrast, there is a gap between firms' expected employments and their actual ones for any other loan amount. Furthermore, the result indicates that there is a positive and significant relationship between the loan amounts demanded by firms and wages. These results can be explained by firms' inflation expectations that show they are not consistent with full-information rational expectations models, though they are not far away from them.

Stationary bubble equilibria in rational expectation models

A linear rational expectation model with current expectations admits a unique linear stationary dynamic equilibrium only under specific restrictions on the parameter values. This paper shows that, in general, there is a multiplicity of stationary dynamic equilibria due to the existence of nonlinear stationary equilibria. These nonlinear stationary equilibria are consistent with the self-fulfilling prophecies that characterize the rational expectation equilibria, and can display speculative bubbles, volatility induced mean reversion and/or stochastic autoregressive patterns. They are also compatible with the transversality conditions when the model involves intertemporal optimization. The stationary nonlinear dynamic equilibria are economically relevant. Their analysis requires revised methods of identification for the stationary equilibrium, impulse response analysis, and estimation techniques, which are presented in this paper. Standard econometric and economic methods, which ignore the nonlinear stationary solutions provide misleading outcomes, which may affect the validity of an economic policy or portfolio strategy.

ETFs, Learning, and Information in Stock Prices

This paper studies how the introduction of ETFs, and the growth of ETF ownership, can change investors' learning behavior. I develop a rational-expectations model where agents decide (1) whether they want to become informed or not and (2) if informed, how to allocate their limited attention between learning about individual stocks and a systematic risk-factor. Introducing an ETF does not universally increase or decrease learning about systematic risk. If the volatility of the systematic risk-factor is large, risk aversion is high, or the cost of becoming informed is high, introducing the ETF leads investors to devote more attention to the systematic risk-factor. Otherwise, the ETF may lead investors investors to learn more about the individual stocks. I decompose the effect of introducing the ETF into 2 channels: (1) Changes in the share of agents who decide to become informed (2) Re-allocation of attention among informed investors. I then extend the model, allowing an intermediary to buy the underlying stocks and create more shares of the ETF. Finally, I link the model's predictions to empirical evidence on the growth of ETF ownership and less informative stock prices.

New Tests of Expectation Formation with Applications to Asset Pricing Models

We develop new tests for expectation formation in financial and macroeconomic models under various informational assumptions. Survey data suggests stock price forecasts are not anchored by consumption forecasts and rejects this aspect of the formation of stock price expectations in a wide range of asset pricing models. The evidence casts some doubt on the modeling of expectation formation in the asset pricing models which assume agents possess the knowledge of the equilibrium pricing function as in Rational Expectations and Bayesian Rational Expectations models. Relaxing this knowledge appears necessary for models to reconcile the survey evidence and potential resolutions are discussed.

A Matter of Perspective: Mapping Linear Rational Expectations Models into Finite-Order VAR Form

This paper considers the characterization of the reduced-form solution of a large class of linear rational expectations models. I show that under certain conditions, if a solution exists and is unique, it can be cast in finite-order VAR form. I also investigate the conditions for the VAR form to be stationary with a well-defined residual variance-covariance matrix in equilibrium, for the shocks to be recoverable, and for local identification of the structural parameters for estimation from the sample likelihood. An application to the workhorse New Keynesian model with accompanying Matlab codes illustrates the practical use of the finite-order VAR representation. In particular, I argue that the identification of monetary policy shocks based on structural VARs can be more closely aligned with theory using the finite-order VAR form of the model solution characterized in this paper.

Delayed Crises and Slow Recoveries

We present a rational expectations model of credit-driven crises, providing a new perspective to explain why credit booms can lead to severe financial crises and aftermath slow economic recoveries. In our model economy, banks can operate in two types of business a la Minsky's narratives. They are sequentially aware of the deterioration of fundamentals of the speculative business and decide whether to continue credit extension in that business or liquidate capital and move into the traditional business. However, because individual banks face uncertainty about how many of their peers have been aware, they rationally choose to extend credit in the speculative business for a longer time than is socially optimal, leading to an over-delayed crisis and consequently more banks being caught by the crisis. This in turn renders the financial crisis more severe and the subsequent economic recovery slower. Within a standard textbook macroeconomic growth setting, our model generates rich dynamics of economic booms, slowdowns, crashes, and recoveries.