Instability and concentration in the distribution of wealth

We consider a setup in which infinitely lived households face idiosyncratic investment risk and show that in this case the equilibrium distribution of wealth becomes increasingly right-skewed over time until wealth concentrates entirely at the top. The households in our setup are identical in terms of their patience and their abilities, and we assume that there are no redistributive mechanisms—neither explicit in the form of government tax or fiscal policies, nor implicit in the form of limited intergenerational transfers. Our results demonstrate that the presence of such redistributive mechanisms alone ensures the stability of the distribution of wealth over time.     

Determination of general equilibrium with incomplete markets and default penalties

This paper is concerned with the existence and computation of general equilibrium with incomplete asset markets and default. Due to the incompleteness of asset markets, the excess demand functions are typically not continuous at prices and delivery rates for which the assets have redundant nominal deliveries. This discontinuity results in a serious problem for the existence and computation of general equilibrium. We show that this problem can be resolved by replacing the nominal delivery matrix with a constant-rank one and restricting the macro variables in a subset of the domains. With this approach, the economies with incomplete markets and default penalties can be analyzed with differentiable homotopy techniques, and thus in the same framework as standard general equilibrium models. As a by-product, the existence of equilibrium is ensured for generic economies. Several computational examples demonstrate the effectiveness of the algorithm and show some quantitative features of equilibria in the model with default penalties.     

A simple method for computing equilibria when asset markets are incomplete

The problem of computing equilibria for general equilibrium models with incomplete real asset markets, or GEI models for the sake of brevity, is reconsidered. It is shown here that the rank-dropping behavior of the asset return matrix could be dealt with in rather a simple fashion: We first compute its singular value decomposition, and then, through this decomposition, construct, by the introduction of a homotopy parameter, a new matrix such that it has constant rank before a desired equilibrium is reached. By adjunction of this idea to the homotopy method, a simpler constructive proof is obtained for the generic existence of GEI equilibria. For the purpose of computing these equilibria, from this constructive proof is then derived a path-following algorithm whose performance is finally demonstrated by means of three numerical examples.     

A remark on rational expectation equilibria with incomplete markets and real assets

In this note, I established the existence, for a generic set of endowments, of a fully revealing rational expectation equilibrium (REE) in an economy characterized by incomplete markets and real assets.     

Game contingent claims in complete and incomplete markets

A game contingent claim is a contract which enables both the buyer and the seller to terminate it before maturity. For complete markets Kifer [Finance and Stochastics 4 (2000) 443–463] shows a connection to a (zero-sum) Dynkin game whose value is the unique no-arbitrage price of the claim. But, for incomplete markets one needs a more general approach. We interpret the contract as a generalized non-zero-sum stopping game. For the complete case this leads to the same results as in Kifer [Finance and Stochastics 4 (2000) 443–463]. For the general case we show the existence of an equilibrium point under the condition that both the seller and the buyer have an exponential utility function. For other utility functions such a point need not exist in the context of incomplete markets.     

The relation between sunspot effects and multiplicity in incomplete markets models with numeraire assets

This paper considers the necessity and sufficiency of multiple certainty equilibria for sunspot effects, and shows that neither implication is valid. This claim is made for models with incomplete markets and numeraire assets. First, I prove that a multiplicity of certainty equilibria is neither necessary nor sufficient for sunspot effects by way of two counter-examples. Second, I verify over an entire subset of economies that equilibrium with sunspot effects can never be characterized as a randomization over multiple certainty equilibria.     

Arbitrage and price revelation with asymmetric information and incomplete markets

This paper deals with the issue of arbitrage with differential information and incomplete financial markets, with a focus on information that no-arbitrage asset prices can reveal. Time and uncertainty are represented by two periods and a finite set S of states of nature, one of which will prevail at the second period. Agents may operate limited financial transfers across periods and states via finitely many nominal assets. Each agent i has a private information about which state will prevail at the second period; this information is represented by a subset S_i of S. Agents receive no wrong information in the sense that the “true state” belongs to the “pooled information” set ∩_iS_i, hence assumed to be non-empty.Our analysis is two-fold. We first extend the classical symmetric information analysis to the asymmetric setting, via a concept of no-arbitrage price. Second, we study how such no-arbitrage prices convey information to agents in a decentralized way. The main difference between the symmetric and the asymmetric settings stems from the fact that a classical no-arbitrage asset price (common to every agent) always exists in the first case, but no longer in the asymmetric one, thus allowing arbitrage opportunities. This is the main reason why agents may need to refine their information up to an information structure which precludes arbitrage.     

Adaptive learning,endogenous uncertainty,and asymmetric dynamics

I present a simple model where forecasting confidence affects aggregate demand. It is shown that this model has similar stability properties, under statistical and evolutionary learning, as a model without a confidence affect. From this setup, I introduce “Expectational Business Cycles” where output fluctuates due to learning, heterogeneous forecasting models and random changes in the efficient forecasting model. Agents use one of two forecasting models to forecast future variables while heterogeneity is dictated via an evolutionary process. Increased uncertainty, due to a shock to the structure of the economy, may result in a sudden decrease in output. As agents learn the equilibrium, output slowly increases to its equilibrium value. Expectational business cycles tend to arrive faster, last longer and are more severe as agents possess less information.     

Adaptive learning and monetary exchange

This paper investigates three classic questions in monetary theory: How can an intrinsically worthless asset, such as fiat money, maintain value as a medium of exchange? What are the short-run and long-run effects of a change in the money supply? What is the social cost of inflation? I answer these questions using a microfounded model of monetary exchange that replaces the rational expectations assumption with an adaptive learning rule. First, I show that monetary exchange is a robust arrangement in the sense that agents are able to learn the stationary monetary equilibrium while the non-monetary equilibrium is unstable under learning. Second, an unanticipated monetary injection has real effects in the short-run because learning the value of money takes time. In the long run, agents successfully learn the value of money, hence money is neutral. Third, under a constant money growth policy, an increase in the growth rate of money increases output in the short-run producing a short-run Phillips curve. A ten percent increase in the money growth rate has a social cost of 0.41 percent of output per year. Alternatively, a ten percent decrease in the money growth rate has a social benefit of 0.37 percent of output per year.     

Recursive equilibrium in stochastic OLG economies: Incomplete markets

We prove generic existence of recursive equilibrium for overlapping generations economies with uncertainty and incomplete financial markets. Generic here means in a residual set of utilities and endowments. The result holds provided there is sufficient intragenerational household heterogeneity, and transition probabilities and the asset payoff matrix satisfy mild regularity conditions. The paper also provides a new methodological technique to establish comparative statics, or perturbation, properties in such environments.     

Predictability dynamics of Islamic and conventional equity markets

This study undertakes the challenging task of comparing the weak form efficiency of conventional and Islamic equity markets. Using 12 different Dow Jones indexes that cover 16 years of daily data, we compare the time-varying non-linear predictability patterns of conventional market indexes and their Islamic counterparts at country and continent level by using permutation entropy. Accordingly, we find that all indexes in our analysis have different degrees of time-varying predictability and all conventional markets are found to be more efficient compared to their Islamic counterparts. However, in some of the cases, this difference in efficiency is almost indistinguishable. Our findings reveal that compared to their conventional counterparts, Islamic markets do not necessarily need to carry a more deterministic or predictable structure since efficiency in these markets depends mostly on liquidity, market quality, institutional characteristics and the country/continent specific investment behavior.     

Speculative behavior and the dynamics of interacting stock markets

We develop a simple agent-based financial market model in which heterogeneous speculators apply technical and fundamental analysis to trade in two different stock markets. Speculators׳ strategy/market selections are repeated at each time step and depend on predisposition effects, herding behavior and market circumstances. Simulations reveal that our model is able to explain a number of nontrivial statistical properties of and between international stock markets, including bubbles and crashes, fat-tailed return distributions, volatility clustering, persistent trading volume, coevolving stock prices and cross-correlated volatilities. Against this background, our model may be deemed to have been validated.     

Taxing capital is a good idea: The role of idiosyncratic risk in an OLG model

We investigate an overlapping generations (OLG) model in which agents who live for two periods receive idiosyncratic productivity shocks when they are old. We show that, around zero tax equilibria, we can always construct a combination of a small capital tax and a lump-sum transfer that are Pareto-improving. As Dávila et al. (Econometrica (2012)) show, a capital reduction in one period raises the welfare level of agents who are old in that period, but lowers that of the young agents, because it reduces their wages. We show that the government can compensate for these wage losses by additionally taxing the old agents, such that their welfare gains remain positive. Our result is unchanged when earnings are uncertain at young age.     

Adaptive learning forecasting,with applications in forecasting agricultural prices

We introduce a new forecasting methodology, referred to as adaptive learning forecasting, that allows for both forecast averaging and forecast error learning. We analyze its theoretical properties and demonstrate that it provides a priori MSE improvements under certain conditions. The learning rate based on past forecast errors is shown to be non-linear. This methodology is of wide applicability and can provide MSE improvements even for the simplest benchmark models. We illustrate the method’s application using data on agricultural prices for several agricultural products, as well as on real GDP growth for several of the corresponding countries. The time series of agricultural prices are short and show an irregular cyclicality that can be linked to economic performance and productivity, and we consider a variety of forecasting models, both univariate and bivariate, that are linked to output and productivity. Our results support both the efficacy of the new method and the forecastability of agricultural prices.     

Cobweb dynamics and price dispersion in illicit drug markets

Extreme price dispersion is a hallmark of illegal drug markets, and this apparent contradiction to the law of one price has long puzzled drug market economists. We propose a novel explanation for this dispersion: the coupling of dealers’ unwillingness to hold inventory with dealers’ imperfect foresight concerning future prices and/or random lead times when “ordering” drugs from higher-level suppliers. Unwillingness to hold inventory means drug markets might operate consistent with a cobweb model. The classic cobweb model was inspired by the observation of cyclic (typically annual) fluctuations in commodity prices. However, with minor changes that make the model more realistic the resulting price trajectories can be highly variable or even chaotic, not just periodic. Cobweb dynamics can also amplify the variability created by supply chain disruptions.     

Failure of the index theorem in an incomplete market economy

Recently, it was proved that the index of an economy with incomplete real asset markets is typically +1$+1$ when the degree of incompleteness, which is defined as the difference between the number of states and the number of securities, is an even number. This paper considers the case where the degree of incompleteness is an odd number and proves that any odd number can be realized as the index of such an economy.     

Alliances and negotiations: an incomplete information example

We study a bargaining game between an individual and an ‘alliance’ in the sense of Manzini and Mariotti (J Econ Theory 121:128–41, 2005), in which the opponent of the alliance is incompletely informed about the relative strengths of its members. The best equilibrium outcome for the alliance under a unanimity rule is not attainable with a non-unanimity rule. However, unlike in the complete information model, less than optimal outcomes and delays may occur with positive probability even under unanimity, depending on the prior beliefs and the preferences of the agents. We are grateful to a careful referee for comments. We wish to thank Clara Ponsati for useful comments.     

Competitive equilibrium fraud in markets for credence-goods

This is a study of the nature and prevalence of persistent fraud in a competitive market for credence-quality goods. We model the market as a stochastic game of incomplete information in which the players are customers and suppliers and analyze their equilibrium behavior. Customers characteristics, idiosyncratic search cost and discount rate, are private information. Customers do not possess the expertise necessary to assess the service they need either ex ante or ex post. We show that there exists no fraud-free equilibrium in the markets for credence-quality goods and that fraud is a prevalent and persistent equilibrium phenomenon.     

Exchange rate dynamics and US dollar-denominated sovereign bond prices in emerging markets

Using data on Brazil, Colombia, Mexico, the Philippines, Russia and Turkey, our empirical results show that the exchange rates of their currencies have adequate explanatory power in explaining their US dollar-denominated sovereign bonds, particularly in the post-global financial crisis period. We develop a two-factor pricing model with closed-form solutions for the sovereign bonds in which the correlated factors are foreign exchange rates and US risk-free interest rates that follow a double square-root process relevant in the low interest rate environment. The numerical results and associated error analysis show that the model credit spreads can broadly track the market credit spreads.     

Irreversible investment and capacity choice with Bayesian learning

This paper incorporates information incompleteness into the standard capacity choice model. The firm dynamically updates its belief about the expected growth rate based on the realization of demand shocks. First, the firm’s expansion decision becomes more conservative in the dynamic updating case. Moreover, a myopic firm always overestimates the marginal value of capital but underestimates firm value. When we decompose the firm value into the value of assets in place and growth opportunities, dynamic learning significantly increases the value of growth opportunities rather than that of assets in place. Finally, the implications for the user cost of capital is also examined.