Trade policy with asset markets: The role of financial structure for time consistency

The present study uses a two-country, two-good, stochastic general equilibrium trade model to analyze the implications of optimal trade policy under uncertainty in the presence of financial markets. Using such a framework, I demonstrate that the policy-active home government, acting to maximize domestic welfare, will always have incentive to revise the previously announced import tariff policy once an asset position is taken by the representative agent in each country engaged in trade. The resulting time-consistent solution will be sensitive to the composition of asset income. Since the fiancial contracts can be combined in an infinite number of ways to yield the same optimal level of asset income, there will exist multiple time-consistent solutions, one for each financial structure. Using a specific log utility function, I also show that for certain financial structures, precommitment solutions will be replicated by time-consistent solutions, a result which marks a significant departure from the standard deterministic framework.     

The Structure of Sunspot Equilibria: The Role of Multiplicity

This paper examines the structure of sunspot equilibria in a standard two period exchange economy with real assets. We show that for a generic choice of utility functions and endowments, there exists an open set of real asset structures whose payoffs are independent of sunspots such that the economy with this asset structure has a regular sunspot equilibrium. An important implication of our result is that the multiplicity of non-sunspot equilibria is not necessary for the existence of sunspot equilibria. Our technique is general and can be applied to show the existence of sunspot equilibria in other frameworks.     

Uniqueness of asset prices in an exchange economy with unbounded utility

Summary. This paper studies conditions under which the price of an asset is uniquely determined by its fundamental value – i.e., no bubbles can arise – in Lucas-type asset pricing models with unbounded utility. After discussing Gilles and LeRoy's (1992) example, we construct an example of a two-period, representative agent economy to demonstrate that bubbles can arise in a standard model if utility is unbounded below, in which case the stochastic Euler equation may be violated. In an infinite horizon framework, we show that bubbles cannot arise if the optimal sequence of asset holdings can be lowered uniformly without incurring an infinite utility loss. Using this result, we develop conditions for the nonexistence of bubbles. The conditions depend exclusively on the asymptotic behavior of marginal utility at zero and infinity. They are satisfied by many unbounded utility functions, including the entire CRRA (constant relative risk aversion) class. The Appendix provides a complete market version of our two-period example. Received: January 22, 1996; revised version: February 18, 1997     

WELFARE GAINS AND LOSSES IN SUNSPOT EQUILIBRIA*

We study a standard two period exchange economy with one nominal asset. As is well known, there is a continuum of sunspot equilibria around each efficient equilibrium. A sunspot equilibrium is inefficient but some households may gain in sunspot equilibria relative to the efficient equilibrium. We show that a household's equilibrium utility level is either locally maximized or locally minimized at the efficient equilibrium, and derive a condition which identifies whether or not a household's utility is locally minimized or maximized.     

Taste-homogeneity of optimal jurisdictions in a Tiebout economy with crowding types and endogenous educational investment choices

We examine a local public goods economy with differentiated crowding. The main innovation is that we assume that the crowding effects of agents are a result of choices that agents make. For example, agents may be crowded (positively or negatively) by the skills that other members of their jurisdiction possess and these skills may be acquired through utility maximizing educational investment choices made in response to equilibrium wages and educational costs. In such an environment, we show that taste-homogeneous jurisdictions are optimal. This contrasts with results for both the standard differentiated crowding model and the crowding types model. We also show that the core and equilibrium are equivalent, and that decentralization is possible through anonymous prices having a structure similar to cost–share equilibrium prices.     

Existence and efficiency of equilibrium in infinite economies with finite aggregate wealth

Summary. We prove the existence and efficiency of equilibrium in economies with infinitely many consumers in which there are finitely many agents who own a positive portion of the aggregate endowment. We prove existence for commodity spaces which are employed in the general equilibrium asset pricing models and use incomplete and intransitive preferences. We discuss the importance of existence of finitely many agents who own a positive portion of the aggregate endowment in obtaining efficient equilibrium. For general equilibrium asset pricing applications we require forward properness only at individually rational Pareto optimal allocations. We provide an Arrow-Debreu model for these economies. We also give an application of our approach and results by employing Stochastic Differential Utility as the utility of each consumer in an infinite horizon model.     

Risky arbitrage,asset prices,and externalities

We introduce a no-risky-arbitrage price condition (NRAP) for asset market models allowing both unbounded short sales and externalities such as trading volume. We then demonstrate that NRAP is sufficient for the existence of competitive equilibrium in the presence of externalities. Moreover, we show that if all risky arbitrages are utility increasing, then NRAP characterizes competitive equilibrium in the presence of externalities. We are indebted to an anonymous referee for helpful comments on an earlier version of this paper. Page and Wooders are especially grateful to CERMSEM and EUREQua for their support and hospitality which made possible our collaboration.     

Insecure property rights and growth: the role of appropriation costs, wealth effects, and heterogeneity

Summary. We extend the model from Tornell and Velasco [13] and Tornell and Lane [12] by adding three features: (i) extracting the common property asset involves a private appropriation cost, (ii) agents derive utility from wealth as well as from consumption, and (iii) agents can be heterogeneous. We show that both an increase in the appropriation cost and, when appropriation costs vary across agents, an increase in the degree of heterogeneity of these costs reduce the growth rate of the public capital stock. We also show that, in the interior equilibrium, the private asset can have either a lower or a higher money rate of return than the common property asset.Received: 22 June 2004, Revised: 20 April 2005, JEL Classification Numbers: C73, O40.This research is supported by SSHRC, FQRSC, and the Austrian Science Fund (FWF). Thanks are due to Hassan Benchekroun, Parkash Chander, Gerard Gaudet, Basant Kapur, Kim Long, Colin Rowat, Koji Shimomura, and an anonymous referee for comments and discussions.     

On the generic existence of fully revealing price equilibria

In an asset trading model, the generic existence of rational expectations equilibrium established by Radner requires an assumption which is not shown to be generic. A regularity condition is imposed on the relative risk aversion of the utility function to eliminate the assumption.     

Welfare-improving financial innovation with a single good

Summary. We show that at any equilibrium of almost every single-good incomplete markets economy, it is possible to find an asset which when introduced makes every agent better-off. Diamond (1967) has shown, however, that such economies are constrained suboptimal, so it is of course impossible to find a new asset which makes all agents worse-off. This contrasts with the case of multiple consumption goods, for which Cass and Citanna (1995) and Elul (1995) demonstrate that equilibrium utilities may be arbitrarily perturbed via financial innovation. Proving our result requires us to exploit not changes in equilibrium prices, but rather the gains to trading the new asset. In particular, we find an asset which when introduced does not change the existing asset prices even though it is traded by every agent – by a revealed preference argument it must therefore make everyone better-off. Received: May 28, 1997; revised version: July 1, 1997     

Search and endogenous concentration of liquidity in asset markets

We develop a search-based model of asset trading, in which investors of different horizons can invest in two assets with identical payoffs. The asset markets are partially segmented: buyers can search for only one asset, but can decide which one. We show the existence of a “clientele’’ equilibrium where all short-horizon investors search for the same asset. This asset has more buyers and sellers, lower search times, and trades at a higher price relative to its identical-payoff counterpart. The clientele equilibrium dominates the one where all investor types split equally across assets, implying that the concentration of liquidity is socially desirable.     

Credit risk in general equilibrium

This paper contributes to the literature on default in general equilibrium. Borrowing and lending takes place via a clearing house (bank) that monitors agents and enforces contracts. Our model develops a concept of bankruptcy equilibrium that is a direct generalization of the standard general equilibrium model with financial markets. Borrowers may default in equilibrium and returns on loans are determined endogenously. Restricted to a special form of mean variance preferences, we derive a version of the capital asset pricing model with bankruptcy. In this case, we can characterize equilibrium prices and allocations and discuss implications for credit risk modeling.     

Endogenous market incompleteness without market frictions: Dynamic suboptimality of competitive equilibrium in multiperiod overlapping generations economies

In this paper, we show that within the set of stochastic three-period-lived OLG economies with productive assets (such as land), markets are necessarily sequentially incomplete, and agents in the model do not share risk optimally. We start by characterizing perfect risk-sharing and find that it requires state-dependent consumption claims which depend only on the exogenous shock realizations. We show then that the recursive competitive equilibrium of any overlapping generations economy with weakly more than three generations is not strongly stationary. This then allows us to show directly that there are short-run Pareto improvements possible in terms of risk-sharing and hence, that the recursive competitive equilibrium is not Pareto optimal. We then show that a financial reform which eliminates the equity asset and replaces it with zero net supply insurance contracts (Arrow securities) will implement to Pareto optimal stochastic steady-state known to exist in the model. Finally, we also show via numerical simulations that a system of government taxes and transfers can lead to a Pareto improvement over the competitive equilibrium in the model.     

Efficient ‘myopic’ asset pricing in general equilibrium: A potential pitfall in excess volatility tests

Excess volatility tests for financial market efficiency maintain the hypothesis of risk neutrality. This permits the specification of the benchmark efficient market price as the present discounted value of expected future dividends. By departing from the risk neutrality assumption in a stripped-down version of Lucas's general equilibrium asset pricing model, I show that asset prices determined in a competitive asset market and efficient by construction can nevertheless violate the variance bounds established under the assumption of risk neutrality. This can occur even without the problems of non-stationarity (including bubbles) and finite samples. Standard excess volatility tests are joint tests of market efficiency and risk neutrality. Failure of an asset price to pass the test may be due to the absence of risk neutrality rather than to market inefficiency.     

Existence and local indeterminacy of periodic equilibrium paths in infinite horizon models with external effects

Summary. It is expected that every periodic equilibrium path may exist even under standard assumptions such as low discounting and the concavity of utility functions in infinite horizon models with external effects. Nevertheless, until now no such example has been presented. In this note we will first construct a bounded growth model that has an external effect and every periodic equilibrium path under any discount factor. Next we will study the conditions under which periodic equilibrium paths have a local indeterminacy. Received: December 23, 1998; revised version: April 19, 1999     

Comparative dynamics in a productive asset oligopoly

We build a subgame perfect Nash equilibrium of a common property productive asset oligopoly and analyze separately the impact of a change in the implicit growth rate of the asset and a change in the number of firms exploiting the asset. We show that the steady state level of asset can be a decreasing function of the asset's implicit growth rate. This phenomenon arises when the initial stock of asset is below a certain threshold. In the short-run we show that firms’ exploitation rate can be a decreasing function of the implicit growth rate. We study the impact of a change in the number of firms that share access to the asset. Reducing the number of firms can result, in the long-run, in higher industry production. In the short-run, it can result in an increase of the industry's exploitation and a decrease of the level of the asset's stock.     

Social Welfare Analysis in a Financial Economy with Risk Regulation

In the last years, regulating agencies of many countries in the world have adopted VaR‐based risk regulation to control market risk of financial institutions. This paper investigates the consequences of such kind of regulation to social welfare and soundness of financial institutions through an equilibrium model. We show that the optimum level of regulation for each financial institution (the level that maximizes its utility) depends on its appetite for risk and that some of them can perform better in a regulated economy. In addition, another important result asserts that under certain market conditions the financial fragility of an institution can be greater in a regulated economy than in an unregulated one.     

Rational inattention,long-run consumption risk,and portfolio choice

This paper explores how the introduction of rational inattention (RI) – that agents process information subject to finite channel capacity – affects optimal consumption and investment decisions in an otherwise standard intertemporal model of portfolio choice. We first explicitly derive optimal consumption and portfolio rules under RI and then show that introducing RI reduces the optimal share of savings invested in the risky asset because inattentive investors face greater long-run consumption risk. We also show that the investment horizon matters for portfolio allocation in the presence of RI, even if investment opportunities are constant and the utility function of investors is constant relative risk aversion. Second, after aggregating across investors, we show that introducing RI can better explain the observed joint dynamics of aggregate consumption and the equity return. Finally, we show that RI increases the implied equity premium because investors under RI face greater long-run consumption risk and thus require higher compensation in equilibrium.     

Time-varying beta: a boundedly rational equilibrium approach

The conditional CAPM with time-varying betas has been widely used to explain the cross-section of asset returns. However, most of the literature on time-varying beta is motivated by econometric estimation using various latent risk factors rather than explicit modelling of the stochastic behaviour of betas through agents’ behaviour, such as momentum trading. Misspecification of beta risk and the lack of any theoretical guidance on how to specify risk factors based on the representative agent economy appear empirically challenging. In this paper, we set up a dynamic equilibrium model of a financial market with boundedly rational and heterogeneous agents within the mean-variance framework of repeated one-period optimisation and develop an explicit dynamic behaviour CAPM relation between the expected equilibrium returns and time-varying betas. By incorporating the two most commonly used types of investors, fundamentalists and chartists, into the model, we show that there is a systematic change in the market portfolio, risk-return relationships, and time varying betas when investors change their behaviour, such as the chartists acting as momentum traders. In particular, we demonstrate the stochastic nature of time-varying betas. We also show that the commonly used rolling window estimates of time-varying betas may not be consistent with the ex-ante betas implied by the equilibrium model. The results provide a number of insights into an understanding of time-varying beta.     

Mortgage contracts in a general equilibrium model when there are inflation shocks

This paper examines the general equilibrium effects of anticipated and unanticipated inflation shocks when an asset such as housing is financed by long-term contracts. Unlike other analyses of housing and mortgage finance, this model specifies that financial markets are fully integrated. Within a simple three-period overlapping generations model, agents obtain a mortgage in the first period and maximize utility under the constraint that no borrowing for consumption is allowed. Following inflation shocks, transition paths of endogenous interest rates, house prices, and welfare can be traced in simulations of the economy under the assumption of rational expectations. When nominal contracts prevail, an unexpected increase in the inflation rate causes a decline in the real rate of interest, owing to adjustments in the loanable funds market. Thus, real effects emerge even in the absence of tax distortions or explicit modelling of uncertainty. I contrast these real effects, given loans in the form of adjustable rate mortgages, with the absence of such effects when loans are price-level-adjusted mortgages.