Rational Expectations Model Research Articles

The Unavoidability of Low Inflation–Low Output Traps

Abstract Since the collapse of the Bretton Woods monetary system, the monies of the developed world have been unbacked by any formal promise of convertibility. Yet, inflation has typically undershot, not overshot, central bank targets over the past couple decades. The low, while generally positive, inflation rate has (more arguably) been associated with low output and low growth. In this article, I consider these observations through the lens of a class of representative agent rational expectations models with nominal (price-setting) frictions and the possibility of firm entry/exit. I show that for any level of nominal frictions (no matter how small) and for any monetary policy rule that satisfies a set of weak restrictions, there is a large set of equilibria that exhibit permanently low inflation, low output, and low nominal interest rates. These equilibria can only exhibit positive long-run inflation if growth is low and the specification of nominal frictions (i.e. the Phillips curve) takes an unconventional but nonetheless empirically plausible form.

Lucas’ expectational equilibrium, price rigidity, and descriptive realism

ABSTRACT Robert Lucas' ([1972b] 1981a) article on the neutrality of money represented the first effective challenge to Samuelson’s neoclassical synthesis methodological separation between static microeconomic optimisation 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.

Rational Expectations Models with Multiplicative Noise

Rational Expectations Models with Multiplicative Noise

Predictable Forecast Errors in Full-Information Rational Expectations Models with Regime Shifts

Predictable Forecast Errors in Full-Information Rational Expectations Models with Regime Shifts

Analytic policy function iteration

We propose an approach to solving and analyzing linear rational expectations models with general information frictions. Our approach is built upon policy function iterations in the frequency domain. We develop the theoretical framework of this approach using rational approximation, analytic continuation, and discrete Fourier transform. Conditional expectations, which are difficult to evaluate in the time domain, can be calculated efficiently in the frequency domain. We provide the numerical implementation accompanied by a flexible object-oriented toolbox. We demonstrate the efficiency and accuracy of our method by studying four models in macroeconomics and finance that feature asymmetric information sets, endogenous signals, and higher-order expectations.

Risk matters: Breaking certainty equivalence in linear approximations

In this paper we use the property that certainty equivalence, as implied by a first-order approximation to the solution of stochastic discrete-time models, breaks in its equivalent continuous-time version. We derive a risk-sensitive first-order perturbation solution for a general class of rational expectations models. We show that risk matters economically in a real business cycle (RBC) model with habit formation and capital adjustment costs, and that neglecting risk leads to substantial pricing errors. A first-order perturbation provides a sensible approximation to the effects of risk in continuous-time models. It reduces pricing errors by around 90% relative to the certainty equivalent linear approximation.

Lapse-Based Insurance

Most individual life insurance policies lapse, with lapsers cross-subsidizing non-lapsers. We show that policies and lapse patterns predicted by standard rational expectations models are the opposite of those observed empirically. We propose two behavioral models consistent with the evidence: (i) consumers forget to pay premiums and (ii) consumers understate future liquidity needs. We conduct two surveys with a large insurer. New buyers believe that their own lapse probabilities are small compared to the insurer’s actual experience. For recent lapsers, forgetfulness accounts for 37.8 percent of lapses while unexpected liquidity accounts for 15.4 percent. (JEL D91, G22, G52)

How do firms form inflation expectations? Empirical evidence from the United States

Inflation expectations of firms affect their micro-decision-making behaviors and therefore impact the macro-economy. Thus, a deep understanding of how firms form inflation expectations benefits the achievement of central bank’s policy objectives on macro-economic sustainability and development. In this paper, we focus on the inflation expectations of firms from surveys. Specifically, the Naïve Expectation, Adaptive Expectation, Rational Expectation, VAR, and Heterogeneous Static Expectation formation models are adopted to test the models being used by firms to form inflation expectations. Empirically, this paper reveals the heterogeneity between the formation mechanisms of households and firms. Then, empirical results reject the rational expectation hypothesis of firms’ inflation expectations, which means that they are not perfectly rational. Finally, we find that the inflation perception is a non-negligible factor in forming firms’ inflation expectations. Therefore, central banks’ monetary policies that aiming to formulate firms’ inflation perceptions can be a useful tool in regulating their inflation expectations, which are expected to benefit the stability of the macro-economy.

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. Dynamic equilibrium economies computational methods nonlinear solution methods limit cycles chaos C63 C68 E37

The more myopic, the more chaos? How the degree of traders’ short-termism affects the financial market equilibrium

We investigate the impact of the extent of investors’ short-termism on the market equilibrium in a dynamic rational expectations model. We show that multiple equilibria always arise irrespective of the degree of traders’ myopia, and that short-termism alone may not be the cause of equilibrium multiplicity, but it does significantly affect the market quality of all equilibria. The liquidity, price efficiency and expected trading volume under the high trading intensity equilibrium (HTIE) are higher than those under the low trading intensity equilibrium (LTIE) no matter how myopic the informed traders are. As the extent of investors’ short-termism increases, the difference between the HTIE and LTIE becomes larger. Interestingly, an increase in the degree of investors’ myopia in the market on the one hand mitigates the instability of the unstable equilibrium --- the HTIE (upon market perturbations a higher degree of investors’ myopia slows down the deviation from the original equilibrium under an HTIE), but on the other hand also dampens the stability of the stable equilibrium --- the LTIE (upon market perturbations a higher degree of investors’ myopia slows down the converging process to the original equilibrium under an LTIE).

Private Information, Securities Lending, and Asset Prices

Abstract We study the role of private information in the equity lending market in a rational expectations model with endogenous loan fees. When all investors are privately informed, an increase in information precision reduces the fee by increasing trade aggressiveness and decreasing demand dispersion. However, when some investors are uninformed, the information asymmetry tends to increase the fee, and, thus, the overall effect of an increase in precision is ambiguous. We show that the fee can be incrementally informative given the stock price and that fee opaqueness tends to increase the fee but has an ambiguous effect on the stock price.

Stackelberg solution for a two-agent rational expectations model

In this paper, we derive the Stackelberg solution associated with a leader–follower rational expectations model. By solving the dynamic rational expectations optimization problem subject to forward and backward stochastic difference equations (FBSDEs), we obtain the Stackelberg strategy of the leader with an adapted open-loop information structure, in terms of the FBSDEs. Furthermore, we solve the associated FBSDEs by establishing a nonhomogeneous relationship between backward and forward stochastic processes. This leads to an explicit form of the Stackelberg strategy of the leader.

Determinacy and classification of Markov-switching rational expectations models

In a general class of Markov-switching rational expectations models, this study derives necessary and sufficient conditions for determinacy, indeterminacy and the case of no stable solution. Classification of the models into these three mutually disjoint and exhaustive subsets is completely characterized by only one particular solution known as the minimum of modulus solution in the mean-square stability sense. The rationale behind this result comes from the novel finding that the solution plays the same role as what the generalized eigenvalues do for linear rational expectations models. Moreover, the solution has its own identification condition that does not require examining the entire solution space. The accompanying solution procedure is therefore computationally efficient, and as tractable as standard solution methodologies for linear rational expectations models. The proposed methodology unveils several important implications for determinacy in the regime-switching framework that differ from the linear model counterpart.

Optimal Policy with Occasionally Binding Constraints: Piecewise Linear Solution Methods

This paper develops a piecewise linear toolkit for optimal policy analysis of linear rational expectations models, subject to occasionally binding constraints on (multiple) policy instruments and other variables. Optimal policy minimises a quadratic loss function under either commitment or discretion. The toolkit accounts for the presence of ‘anticipated disturbances’ to the model equations, allowing optimal policy analysis around scenarios or forecasts that are not produced using the model itself (for example, judgement-based forecasts such as those often produced by central banks). The flexibility and applicability of the toolkit to very large models is demonstrated in a variety of applications, including optimal policy experiments using a version of the Federal Reserve Board’s FRB/US model.

Noise traders incarnate: Describing a realistic noise trading process

We estimate a realistic process for noise trading to help theorists derive predictions from noisy rational expectations models. We characterize the trades of individual investors, who are natural candidates for the role of noise traders because their trades are weakly correlated with fundamentals, in line with how such models define noise trading. Data from a retail brokerage house, small and price-improved trades in TAQ, and flows to retail mutual funds yield consistent estimates. The properties of noise trading are highly sensitive to the frequency considered, with the common assumption of i.i.d.-normal noise appropriate only at monthly and lower frequencies.

Adaptive Learning, Social Security Reform, and Policy Uncertainty

AbstractI develop an adaptive learning model to study the welfare effects of Social Security policy uncertainty in an aging economy. Agents combine full knowledge of the political process (which Social Security reforms are possible and when they could occur) with limited knowledge about the structure of the economy. The adaptive learning amplifies cyclical dynamics along the transition path to the new steady state. This magnifies the welfare effects of policy uncertainty, compared to a standard rational expectations model. The ex ante consumption equivalent variation that equates the expected utility of consumption (with policy uncertainty) to the utility of expected consumption (across the possible policies without uncertainty) ranges between −0.29% and 0.21% of lifetime consumption in the adaptive learning model compared to −0.012% to −0.018% in the standard model. The welfare cost to future generations is also larger in the adaptive learning model compared to the rational model.

The stabilizing effects of economic policies in Spain in times of COVID-19

Purpose This paper aims to analyse the stabilizing macroeconomic effects of economic policies during the COVID-19 crisis in Spain. Design/methodology/approach The contribution of the structural shocks that explain the behaviour of the main macroeconomic aggregates during 2020 are estimated, and the effects of economic policies are simulated using a dynamic stochastic general equilibrium (DSGE) model estimated for the Spanish economy. Findings The results highlight the importance of supply and demand shocks in explaining the COVID-19 crisis. The annual fall in gross domestic product (GDP) moderates at least by 7.6 points in the most intense period of the crisis, thanks to these stabilizing policies. Finally, the potential effects of Next Generation EU in the Spanish economy are estimated. Assuming that Spain may receive from the EU between 1.5 and 2.25 percentage points (pp) of GDP, activity could increase to between 2 and 3 pp in 2024. Originality/value To the best of the authors’ knowledge, the exercises and findings are original. All these results show the usefulness of a DSGE model, such as the estimated rational expectation model for Spain, as a practical tool for the applied economic analysis, the macroeconomic assessment of economic policies and the understanding of the Spanish economy.

Identifiability of structural singular vector autoregressive models

We generalize well‐known results on structural identifiability of vector autoregressive (VAR) models to the case where the innovation covariance matrix has reduced rank. Singular structural VAR models appear, for example, as solutions of rational expectation models where the number of shocks is usually smaller than the number of endogenous variables, and as an essential building block in dynamic factor models. We show that order conditions for identifiability are misleading in the singular case and we provide a rank condition for identifiability of the noise parameters. Since the Yule–Walker equations may have multiple solutions, we analyse the effect of restricting system parameters on over‐ and underidentification in detail and provide easily verifiable conditions.

How do Investors React to Biased Information? Evidence from Chinese IPO Auctions

We study how institutional investors utilize potentially biased information by analyzing the effect of IPO underwriters' earnings forecasts on investors' bidding behaviors in Chinese IPO auctions. Despite the presence of upward biases in underwriters' earnings forecasts, we nd that investors' bid prices are higher in IPOs with higher earnings forecasts. The investors' positive reaction to biased information can be explained in a rational expectation model where the underwriter has valuable information about the IPO but has a biased incentive in presenting the information to investors. Consistent with the model's predictions, we find that an investor's bid price is more sensitive to the underwriter's earnings forecast when the forecast bias is expected to be smaller, when the relative precision of the underwriter's information over the investor's information is higher, and when the investor has a higher valuation of the IPO.

Recursive equilibria in dynamic economies with bounded rationality

This paper provides a general framework to model bounded rationality in dynamic stochastic general equilibrium models with infinitely lived heterogeneous agents. A boundedly rational agent is associated with an information set $I$ and an extra parameter $\epsilon$, which can be interpreted as the ``level of irrationality''. To make decisions, the boundedly rational agent forms a belief of a stationary joint distribution of the exogenous and endogenous variables and uses the marginal distribution (conditional on $I$) to form forecasts. If the equilibrium distribution stays within $\epsilon$ of the forecasted next-period distribution, the agent would consider it as $\epsilon$-stationary. In equilibrium, each agent maximizes utility with an $\epsilon$-stationary belief and markets clear. The main theorem of this paper shows that for any strictly positive $\epsilon$, a recursive equilibrium exists. With a quantifiable ``level of irrationality'', the model incorporates many behavioral economics models as well as rational-expectations models with computational approximations into a unified framework. An illustration example is presented to show that the boundedly rational recursive equilibrium may substantially enrich the asset pricing dynamics of the rational-expectations model even for small $\epsilon$.