A New Keynesian model with staggered price and wage setting under learning

This paper provides a study of the implications for economic dynamics when the central bank sets its nominal interest rate target in response to variations in wage inflation. I provide results on the existence, uniqueness, and stability under learning of rational expectations equilibrium for alternative specifications of the manner in which monetary policy responds to economic shocks when nominal rigidities are present. Monopolistically competitive producers set prices via staggered price contracts, and households set nominal wages in the same fashion. In this setting, the conditions for determinacy and learnability of rational expectations equilibrium differ from a model where only prices are sticky. I find that when the central bank responds to wage and price inflation and to the output gap, a Taylor principle for wage and price inflation arises that is related to stability under learning dynamics. In other words, a moderate reaction of the interest rate to wage inflation helps to avoid instability under learning and indeterminacy.     

Competitive market equilibrium under asymmetric information

This paper studies the existence of a competitive market equilibrium under asymmetric information. There are two agents involved in the trading of the risky assets: an “informed” trader and an “ordinary” trader. The market is competitive and the ordinary agent can infer the insider information from the price dynamics of the risky assets. The insider information is considered to be the total supply of the risky assets. The definition of market equilibrium is based on the law of supply-demand as described by a rational expectations equilibrium of the Grossman and Stiglitz (Am Econ Rev 70:393–408, 1980) model. We show that equilibrium can be attained by linear dynamics of an admissible price process of the risky assets for a given linear supply dynamics.      

On the behavior of commodity prices when speculative storage is bounded

This paper investigates the implications of bounded speculative storage, storage bounded from below at zero and above at a capacity, on commodity prices. Binding capacity mirrors the non-negativity constraint on storage and leads to negative price spiking and higher volatility when the market is in deep contango, i.e. low current prices at high stock levels. With bounded storage there is no need to restrict storage to be costly to ensure a rational expectations equilibrium. This allows the model to cover a wide range of storage technologies, including free and productive storage. We also provide an alternative expression for speculative prices that highlights the key role of the storage boundaries. The competitive equilibrium price is the sum of discounted future probability weighted boundary prices. The boundary prices can be viewed as dividends on commodities in storage reflecting the realization of economic profits from storage.     

Solving DSGE portfolio choice models with dispersed private information

Noisy rational expectations models, in which agents have dispersed private information and extract information from an endogenous asset price, are widely used in finance. However, these linear partial equilibrium models do not fit well in modern macroeconomics that is based on non-linear dynamic general equilibrium models. We develop a method for solving a DSGE model with portfolio choice and dispersed private information. We combine and extend existing local approximation methods applied to public information DSGE settings with methods for solving noisy rational expectations models in finance with dispersed private information.     

Systematic Price Differences Between Successive Auctionsare no Anomaly

Identical cases of wine are often auctioned one immediately after another. Ashenfelter (1989) reports that on average, the later lots fetch less. Such a systematic price difference seems anomalous, the more so because it is shown here that rational expectations imply not equal, but rising, prices. Risk aversion is an obvious way of reconciling the evidence with rational behavior. There is an alternative explanation. The auctions observed by Ashenfelter involved a buyer's option, whereby the first-round winner could purchase further cases at the same price. It is shown that this feature may both account for the observed price trajectory and raise seller revenue.     

Trend inflation,sticky prices,and expectational stability

Micro evidence indicates that each period a fraction of prices is kept unchanged under a positive trend inflation rate. In a sticky price model based on this evidence, recent research shows that high trend inflation is a serious cause for indeterminacy of rational expectations equilibrium under the Taylor rule. This paper examines implications of trend inflation for expectational stability of the equilibrium. An empirically plausible calibration of the model demonstrates that a fundamental rational expectations equilibrium is likely to be expectationally stable even in cases of indeterminacy induced by high trend inflation.     

Evolution of heterogeneous beliefs and asset overvaluation

I analyze a model in which different agents have different non-rational expectations about the future price and cash flows of a risky asset. The beliefs in the society evolve according to a very general class of evolution functions that are monotone; that is if one type has increased its share in the population then all types with higher profit should also have increased their shares. I show that the price of the risky asset converges to the risk-neutral fundamental price even though all agents in the economy are risk-averse. The risky asset thus becomes overvalued as compared to the equilibrium with rational expectations. The overvaluation is a result of the evolution of beliefs and does not rely on such asymmetric assumptions as short-sale constraints or optimistic bias.     

Random Advertising and Monopolistic Price Dispersion

We investigate the role of price advertising in a market where consumers are imperfectly informed about prices. We consider a monopolist whose demand depends on price and advertising expenditure. This demand function is derived from optimizing behavior of consumers. Uninformed consumers may pay a cost to visit the seller and obtain price information. Advertising enables the monopolist to increase the number of informed consumers. In equilibrium the uninformed consumers form rational price expectations, and the seller necessarily adopts a random pricing and advertising strategy.     

An Econometric Analysis of Polish Inflation Dynamics with Learning about Rational Expectations

Rational expectations modelling has been criticized for assuming that economic agents can learn quickly about and compute rational price expectations. In response, various authors have studied theoretical models in which economic agents use adaptive statistical rules to develop price expectations. A goal of this literature has been to compare resulting learning equilibria with rational expectations equilibria. The lack of empirical analysis in this literature suggests that adaptive learning makes otherwise linear dynamic models nonlinearly intractable for current econometric technology. In response to the lack of empirical work in this literature, this paper applies to post-1989 monthly data for Poland a new method for modelling learning about price expectations. The key idea of the method is to modify Cagan’s backward-looking adaptive-expectations hypothesis about the way expectations are actually updated to a forward-looking characterization which instead specifies the result of learning. It says that, whatever the details of how learning actually takes places, price expectations are expected to converge geometrically to rationality. The method is tractable because it involves linear dynamics. The paper contributes substantively by analyzing the recent Polish inflation, theoretically by characterizing learning, and econometrically by using learning as a restriction for identifying (i.e., estimating wth finite variance) unobserved price expectations with the Kalman filter. This revised version was published online in July 2006 with corrections to the Cover Date.     

Market analysis with rational expectations: Theory and estimation

In a dynamic market structure the rational expectations hypothesis implies the existence of a ‘fixed point’ or‘equilibrium’ price sequence. For a prototype market structure we develop the This approach displays the relationships between exogenous structure, expectations, and behavior. The resulting framework suggests effective estimation procedures and clarifies analysis. Results for an application are presented and discussed.     

The dynamic annihilation of a rational competitive fringe by a low-cost dominant firm

A low-cost dominant firm will drive all competitive fringe firms out of the market if all firms have rational expectations; however, the dominant firm will not predate (price below marginal cost). Since a dominant firm will not drive out fringe firms if they have myopic expectations, it may be in the dominant firm's best interests to inform the fringe. The effects of governmental intervention on the optimal path and welfare are presented.     

Modelling oil price expectations: Evidence from survey data

Using Consensus Forecast survey data on WTI oil price expectations for 3- and 12-month horizons over the period November 1989 to December 2008, we find that the rational expectation hypothesis is rejected and that none of the traditional extrapolative, regressive and adaptive processes fits the data by itself. We suggest a mixed expectation model defined as a linear combination of these traditional processes, which we interpret as the aggregation of individual mixing behavior and of heterogenous groups of agents using these simple processes. This approach is consistent with the economically rational expectations theory. We show that the target oil price included in the regressive component of this model depends on the long-run marginal cost of crude oil production and on short term macroeconomic fundamentals whose effects are subject to structural changes. For the two horizons, estimation results provide evidence for our mixed expectation model incorporating this break-dependent target price.     

Switching from complete to incomplete information

We construct an elementary mechanism [Dutta, B., Sen, A., Vohra, R., 1995. Nash implementation through elementary mechanisms in economic environments. Review of Economic Design 1, 173–203] that Nash implements the constrained Walrasian correspondence. We extend it to incomplete and non-exclusive information economies by enlarging the message space of agents. In addition, measurability restrictions on allocations with respect to prices proper to constrained rational expectations equilibria are imposed in the outcome function. We show that by imposing such restrictions, the mechanism Bayesian implements the constrained rational expectations equilibrium correspondence. This result shows game-theoretic connections between these two market equilibrium concepts. However, these connections are obtained at the price of strong restrictions on the behavior of agents.     

Equilibrium in incomplete markets: II : Generic existence in stochastic economies

We model multiperiod securities markets with differential information. A price system that admits no free lunches is related to martingales when agents have rational expectations. We introduce the concept of resolution time, and show that a better informed agent and a less informed agent must agree on the resolution times of commonly marketed events if they have rational expectations and if there are no free lunches. It then follows that if all elementary events are marketed for a less informed agent then any price system that admits no free lunches to a better informed agent must eliminate any private information asymmetry between the two. We provide an example of a dynamically fully revealing price system that is arbitrage free and yields elementarily complete markets.     

Multiperiod security markets with differential information: Martingales and resolution times

We model multiperiod securities markets with differential information. A price system that admits no free lunches is related to martingales when agents have rational expectations. We introduce the concept of resolution time, and show that a better informed agent and a less informed agent must agree on the resolution times of commonly marketed events if they have rational expectations and if there are no free lunches. It then follows that if all elementary events are marketed for a less informed agent then any price system that admits no free lunches to a better informed agent must eliminate any private information asymmetry between the two. We provide an example of a dynamically fully revealing price system that is arbitrage free and yields elementarily complete markets.     

From General Equilibrium to Schumpeter

A simple model of cost innovation in a monetary economy is presented that illustrates the essentially dynamic model of Schumpeter involving breaking the circular flow of capital is logically consistent with the General Equilibrium (GE) model of an exchange and production economy. The GE model as presented by Arrow, Debreu and McKenzie is a non-process model; and the original theory deals with the non-constructive proofs of existence of competitive equilibria (CEs). To associate this theory with GE it is necessary to recast the basic model as a process model. The GE model is enlarged and specified as a playable game by adding rules to describe the mechanisms that carry process.Although we believe that GE was a great intellectual achievement, it strangled dynamics and the type of low dimensional equilibrium dynamics of the rational expectations school is profoundly misleading. It turns out that, by remodeling GE as a process model even with only one or two strategic moves, Pandora׳s Box of mechanisms appears and the functions of markets, money and default conditions all emerge as logical necessities.It is shown that the opportunity for process innovation can be described minimally and formally modeled by considering the availability of a new process as a function of a controlled stochastic variable where success depends on chance modified by the level of investment. The Schumpeterian concept of “breaking the circular flow of capital” appears naturally as a disequilibrium phenomenon where the extra resources are captured by a strategic disequilibrating allocation of money.     

The forward method as a solution refinement in rational expectations models

This paper generalizes the standard forward method of recursive substitution to a general class of linear rational expectations models with potentially multiple fundamental solutions. It is shown that the existence and uniqueness of the well-known forward solution are preserved in a general context. We also propose a key property embedded in the forward solution - the no-bubble condition - as an economically sensible solution refinement in the class of fundamental solutions. In the literature, the no-bubble condition has been assumed to rule out non-fundamental bubble solutions. We show that the forward solution is the only rational expectations equilibrium satisfying the no-bubble condition and consequently, it is the most relevant fundamental solution within the class of fundamental equilibria. Several economic examples are provided where the fundamental solutions obtained by other solution methods and refined by other solution selection criteria violate the no-bubble condition.     

Competition among mechanism designers in a common value environment

A competitive economy is studied in which sellers offer alternative direct mechanisms to buyers who have private information about their own private use value for the commodity being traded. In addition the commodity has a common value to all buyers, perhaps represented by the future resale value of the commodity. A competitive equilibrium in mechanisms is described. In every such equilibrium it is shown that sellers must offer mechanisms that are allocationally equivalent to English ascending price auctions. The reservation prices that sellers set are shown to be below their ex post cost of trading the commodity. Received: 24 April 1998 / Accepted: 8 March 1999     

Descending price multi-item auctions

We propose a simultaneous descending price auction mechanism to sell multiple heterogeneous items, each owned by a distinct seller, to a number of buyers. Each buyer has known private valuations on items, and wants at most one item. We show that if the sellers follow a descending price offer procedure and the buyers follow a greedy strategy for accepting the offers, the auction results in a nearly efficient allocation, and terminates close to a competitive equilibrium price vector. The descending price offer strategy of the sellers is close to a Nash equilibrium. However, we show that the buyers are better off waiting in our auction. There is a maximum limit (corresponding to the minimum competitive equilibrium price vector) till which they can wait without running into the risk of not winning any item. If the buyers wait within this limit, the prices can be brought arbitrarily close to a uniquely defined competitive equilibrium price vector.     

Learning from experience in the stock market

New evidence suggests that individuals “learn from experience,” meaning they learn from events occurring during their lives as opposed to the entire history of events. Moreover, they weigh more heavily recent events compared to events occurring in the distant past. This paper analyzes the implications of such learning for stock pricing in a model with finitely lived agents. Individuals learn about the rate of change of the stock price and of dividends using a weighted decreasing-gain algorithm. As a result of waves of optimism and pessimism, the stock price exhibits stochastic fluctuations around the rational expectations equilibrium. Conditional on the historical path of dividends, the model produces a price–dividend ratio which is in line with the evidence for the last century, except for the “dot-com” bubble in the 1990s.