Lucas Tree Research Articles

Regret-sensitive equity premium

In a static Lucas tree economy, we propose a model that the representative agent is sensitive to regret, that is, the agent is affected by not only the actual outcome but also value-differences between actual and foregone consequences. Our model generalizes the classical simple regret model pioneered by Bell (1982) and Loomes and Sugden (1982), and makes it possible to derive the equilibrium asset price and to see when the regret effect decreases the price. To verify that our model predicts sufficient decreases of the equilibrium price to explain the empirically high risk premium, we analyze the data of U.S. stock market and GDP growth rates during 1871–2018. The numerical calculation indicates that the estimated equilibrium price is small enough to explain the equity premium puzzle.

Comovement and return predictability in asset markets: An experiment with two Lucas trees

Abstract Using a laboratory experiment, we investigate whether comovement can emerge between two risky assets, despite their fundamentals not being correlated. The ‘Two trees’ asset pricing model developed by Cochrane et al. (2007) guides our experimental design and its predictions serve as our source of hypotheses. The model makes time-series and cross-section return predictions following a shock to one of the two assets’ dividend distributions. As the model predicts, we observe (1) positive contemporaneous correlation between the two assets, (2) positive autocorrelation in the shocked asset, and (3) time-series and cross-sectional return predictability from the dividend-price ratio. In line with the rational foundations of the model, the model's predictions have stronger support in markets with relatively sophisticated agents.

Contagion and Return Predictability in Asset Markets: An Experiment With Two Lucas Trees

Using a laboratory experiment, we investigate whether comovement can emerge between two risky assets, despite their fundamentals not being correlated. The ‘Two trees’ asset pricing model developed by Cochrane et al. (2007) guides our experimental design and its predictions serve as our source of hypotheses. The model makes time-series and cross-section return predictions following a shock to one of the two assets’ dividend distributions. As the model predicts, we observe (1) positive contemporaneous correlation between the two assets, (2) positive autocorrelation in the shocked asset, and (3) time-series and cross-sectional return predictability from the dividend-price ratio. In line with the rational foundations of the model, the model's predictions have stronger support in markets with relatively sophisticated agents.

Asset pricing with index investing

We theoretically analyze how index investing affects financial markets using a dynamic exchange economy with heterogeneous investors and two Lucas trees. We identify two effects of indexing: lockstep trading of stocks increases market volatility and stock return correlations but reduction in risk sharing decreases them. Overall, indexing decreases market volatility but has an ambiguous effect on the correlations. Also, index investing decreases an investor’s welfare, but indexing by other investors partially offsets the loss. When the introduction of index trading opens financial markets for new investors, the improved risk sharing makes market returns more volatile and stock returns more correlated.

An Experimental Comparison of Two Exchange Economies: Long-Lived Asset vs. Short-Lived Asset

The Lucas tree model [Lucas RE Jr (1978) Asset prices in an exchange economy. Econometrica 46(6):1429–1445.] lies at the heart of modern macrofinance. At its core, it provides an analysis of the equilibrium price of a long-lived asset in an exchange economy where consumption is the objective and the sole purpose of the asset is to smooth consumption through time. Experimental tests of the model use a particular instantiation of the Lucas model. Here we adopt a different instantiation to the first two, extending their analyses from a two-period oscillating world to a three-period cyclical world; this is partly to test the robustness of their results. We also go one step further and compare this solution (to a consumption-smoothing problem), in which consumption claims are traded via the long-lived asset, with the alternative solution provided by a market, in which agents can directly trade (short-lived) consumption claims between periods. We find that the latter exchange economy is more efficient in encouraging consumption smoothing than the economy with the long-lived asset. We find evidence of uncompetitive trading in both markets. This paper was accepted by Yan Chen, decision analysis.

Solving the Equity Premium Puzzle by unifying Economics and Finance

The Equity risk-premium and volatility puzzle - is it possible to have a high equity premium and a low risk-free rate with a plausible risk aversion- have received a great deal of attention but beyond this question, the fundamental issues of that puzzle are the followings: what are the economic representations that can provide such results? What are the relevant links between finance and economics? And what should be the consequences for economic decisions makers? The classic ways to model the financial economy with a representative agent placed in a Lucas tree model, i.e. maximizing consumption-based utility, where fruit is equivalent to dividend and consumption, failed to explain a high equity premium and a low risk free rate. Even more, simple changes in reasoning failed to provide a consistent macroeconomic and finance representation that sticks to reality. This paper presents a new eco-financial approach based on three major changes: the definition of Wealth and wealth increment and their utility for any agent instead of consumption, a permanent change of equilibrium theory, a more realistic model in which the agents fear much more crises than ordinary fluctuations. This model borrows two key principles from the model developed in Modigliani and Miller’s seminal papers: firstly an economy with investment opportunities in the market of goods and services and secondly an economy where rational agents always prefer more wealth to less and are indifferent as to whether a given increment to their wealth takes the form of dividend or growth in value .Main changes come from, we generalized this wealth approach to any agent, in a changing of equilibrium world, where crises are much more dreaded than ordinary negative events. We will show that it is a way to solve the equity premium and to make consistent: macro, micro, finance and reality.

An Experimental Comparison of Two Exchange Economies: Long-Lived Asset Versus Short-Lived Asset

The Lucas (1978) Tree Model lies at the heart of modern macro-finance. At its core, it provides an analysis of the equilibrium price of a long-lived asset in an exchange economy where consumption is the objective, and the sole purpose of the asset is to smooth consumption through time. Experimental tests of the model are mainly confined to Crockett et al (2018), Asparouhova et al (2016) and Halim et al (2016), all of them using a particular instantiation of the Lucas Model. Here we adopt a different instantiation to the first two, extending their analyses from a two-period oscillating world to a three-period cyclical world; this is partly to test the robustness of their results. We also go one step further, and compare this solution (to a consumption-smoothing problem), in which consumption claims are traded via the long-lived asset, with the alternative solution provided by a market, in which agents can directly trade (short-lived) consumption claims between periods. We find that the latter exchange economy is more efficient in encouraging consumption smoothing than the economy with the long-lived asset. We find evidence of uncompetitive trading in both markets.

Asset prices in segmented and integrated markets

This paper evaluates the effect of market integration on prices and welfare, in a model where two Lucas trees grow in separate regions with similar investors. We find equilibrium asset price dynamics and welfare both in segmentation, when each region holds its own asset and consumes its dividend, and in integration, when both regions trade both assets and consume both dividends. Integration always increases welfare. Asset prices may increase or decrease, depending on the time of integration, but decrease on average. Cross-asset correlation is zero or negative before integration, but significantly positive afterwards, explaining some effects commonly associated with financialisation.

Information Frictions and Stock Returns

The purpose of this paper is to assess the impact of ambiguity on financial analyst forecast incentives and the associated abnormal stock returns. I present a model incorporating ambiguity aversion into a two-period Lucas tree model. The resulting model confirms the role of ambiguity in the determination of asset returns. In particular, the model with ambiguity aversion generates a lower price and a higher required rate of returns compared to the classical model without ambiguity concern. I construct a measure of ambiguity and provide empirical evidence showing that the incentive of analysts to misrepresent information is a function of ambiguity. Analysts are more likely to bias their forecasts when it is more difficult for investors to detect their misrepresentation. Under ambiguity, analysts’ optimistic forecasts for good/bad news tend to deteriorate. Moreover, stock returns are positively related with ambiguity. Under ambiguity neither good nor bad news is credible. Investors systematically underreact to good news forecast and overreact to bad news forecast when ambiguity exists.

Internet Appendix for 'The Oligopoly Lucas Tree: Consumption Risk and Industry-Level Risk Exposure'

This is the supplemental material to the paper titled The Oligopoly Lucas Tree. It includes additional empirical, theoretical, and quantitative results. It also includes illustration for the numerical algorithm for our model solution.

Preferences with taste shock representations: Price volatility and the liquidity premium

If price volatility is caused in some part by taste shocks, then it should be positively correlated with the liquidity premium. Our argument is based on Krishna and Sadowski (2014), who provide foundations for a representation of dynamic choice with taste shocks, and show that volatility in tastes corresponds to a desire to maintain flexibility. To formally connect volatile tastes to price volatility and preference for flexibility to the liquidity premium, we analyze a modified simple Lucas tree economy with two otherwise identical assets, where one provides more liquidity because its output can be traded on an auxiliary international market, and where the representative agent is uncertain about his degree of future risk aversion. We show that a representative agent with a higher degree of uncertainty about his future risk aversion implies a higher liquidity premium (ie, a higher price for the more liquid asset) and more price volatility.

Lipschitz recursive equilibrium with a minimal state space and heterogeneous agents

This paper analyzes the Lucas tree model with heterogeneous agents and one asset. We show the existence of a minimal state space Lipschitz continuous recursive equilibrium using Montrucchio (1987) results. The recursive equilibrium implements a sequential equilibrium through an explicit functional equation derived from the Bellman Equation. Our method also allows to prove existence of a recursive equilibrium in a general class of deterministic or stochastic models with several assets provided there exists a Lipschitz selection on the demand correspondence. We provide examples showing applicability of our results.

Undefeated equilibria of the Shi–Trejos–Wright model under adverse selection

Decentralized markets where assets are useful as media of exchange are also usually subject to private information. To analyze the liquidity and prices of such assets, I adapt the Shi (1995), Trejos and Wright (1995) model with Lucas trees under adverse selection. While most studies focus on either a pooling or separating equilibrium, I apply the undefeated equilibrium refinement by Mailath et al. (1993) to make the selection based on fundamentals. Under pooling, the high-quality asset holder accepts a pooled price, and under separating signals quality through asset retention. Applying the refinement results in a regime switch from no-information (pooling) to information revelation (separating) following a negative shock to the quality or quantity of lemons. This change leads to a discontinuous fall in aggregate welfare.

Asset Prices in Segmented and Integrated Markets

This paper evaluates the effect of market integration on prices and welfare, in a model where two Lucas trees grow in separate regions with similar investors. We find equilibrium asset price dynamics and welfare both in segmentation, when each region holds its own asset and consumes its dividend, and in integration, when both regions trade both assets and consume both dividends. Integration always increases welfare. Asset prices may increase or decrease, depending on the time of integration, but decrease on average. Correlation in assets' returns is zero or negative before integration, but significantly positive afterwards, explaining some effects commonly associated with financialization.

Uncertainty and Economic Activity: A Multi-Country Perspective

Measures of economic uncertainty are countercyclical, but economic theory does not provide definite guidance on the direction of causation between uncertainty and the business cycle. This paper proposes a new multi-country approach to the analysis of the interaction between uncertainty and economic activity, without a priori restricting the direction of causality. We develop a multi-country version of the Lucas tree model with time-varying volatility and show that in addition to common technology shocks that affect output growth, higher-order moments of technology shocks are also required to explain the cross country variations of the realized volatility of equity returns. Using this theoretical insight, two common factors, a ‘real’ and a ‘financial’ one, are identified in the empirical analysis assuming different patterns of cross-country correlations of country-specific innovations to real GDP growth and realized stock market volatility. We then quantify the absolute and the relative importance of the common factor shocks as well as country-specific volatility and GDP growth shocks. The paper highlights three main empirical findings. First, it is shown that most of the unconditional correlation between volatility and growth can be accounted for by the real common factor, which is proportional to world growth in our empirical model and linked to the risk-free rate. Second, the share of volatility forecast error variance explained by the real common factor and by country-specific growth shocks amounts to less than 5 percent. Third, shocks to the common financial factor explain about 10 percent of the growth forecast error variance, but when such shocks occur, their negative impact on growth is large and persistent. In contrast, country-specific volatility shocks account for less than 1-2 percent of the growth forecast error variance.

Learning, leverage and stability

I construct and analyse a simple general equilibrium model with an active credit market in which borrowers and lenders form expectations adaptively. Except for expectation formation the model is a small open economy variant of the standard Lucas (1978) tree model. To abstract from institutional detail there is just a representative investor/borrower and a representative lender (rest of the world), both of whom are learning from experience. The point is to show that even in this fairly standard model financial crises can occur, and to examine the conditions, with respect to policy, institutions and other aspects of the environment, that affect the likelihood of crises in the model.

Decentralizing constrained-efficient allocations in the Lagos–Wright pure currency economy

This paper offers two ways to decentralize the constrained-efficient allocation of the Lagos–Wright (2005) pure currency economy. The first way has divisible money, take-it-or-leave-it offers by buyers, and a transfer scheme financed by money creation. If agents are sufficiently patient, the first best is achieved for finite money growth rates. If agents are impatient, the equilibrium allocation approaches the constrained-efficient allocation asymptotically as the money growth rate tends to infinity. The second way has indivisible money, take-it-or-leave-it offers by buyers, and no government intervention. We discuss the strict implementation of constrained-efficient allocations and the applicability of our scheme to economies with Lucas trees, endogenous participation, match-specific heterogeneity, and sequential competitive markets.

Preferences with Taste Shock Representations: Price Volatility and the Liquidity Premium

If price volatility is caused in some part by taste shocks, then it should be positively correlated with the liquidity premium. Our argument is based on Krishna and Sadowski (2014), who provide foundations for a representation of dynamic choice with taste shocks, and show that volatility in tastes corresponds to a desire to maintain flexibility. To formally connect volatile tastes to price volatility and preference for flexibility to the liquidity premium, we analyze a modified simple Lucas tree economy, where the representative agent is uncertain about his degree of future risk aversion, and where the productive asset cannot be traded in every period, while rights to output can. We show that a representative agent with a higher degree of uncertainty about his future risk aversion implies a higher liquidity premium (i.e., a lower price for the illiquid asset) and more price volatility.

Asset Pricing with Index Investing

We provide a theoretical analysis of how index investing affects capital market equilibrium. We consider a dynamic exchange economy with heterogeneous investors and two Lucas trees and find that the introduction of index trading increases volatilities and correlation of stock returns. Contrary to conventional wisdom, these effects mainly result from improved risk sharing rather than from lockstep trading of stocks implied by indexing. Despite the residual market incompleteness, index investing increases welfare of investors previously excluded from financial markets so that it becomes close to its first-best level in the economy in which all investors trade individual assets.

Lucas Trees with Exponential Utility

This paper examines the behavior of the market equilibrium in an endowment economy in continuous time, in which a representative investor with exponential utility consumes the dividends generated by multiple risky assets. The dividends are assumed to be mutually independent and belong to a class of non-negative stochastic processes including square root processes, increasing Levy processes, and non-Gaussian OU processes. We then characterize expected returns and volatilities on the assets as well as interest rates. Based on these quantities, we construct the CAPM in an infinitesimal time period and investigate the impacts of dividend fluctuations and the risk aversion of the investor to the market equilibrium. It is shown that even if the dividends are independent, the asset returns may have strong positive correlations. Moreover, heterogeneous dividend processes generate Jensen's alpha that can be interpreted as the small cap premium.