تنظیمات ناهمگن و حجم معاملات تعادلی
|کد مقاله||سال انتشار||تعداد صفحات مقاله انگلیسی||ترجمه فارسی|
|11441||2007||32 صفحه PDF||سفارش دهید|
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Financial Economics, Volume 83, Issue 3, March 2007, Pages 719–750
The representative-agent Lucas model stresses aggregate risk and hence does not allow us to study the impact of agents’ heterogeneity on the dynamics of equilibrium trading volume. In this paper, we investigate under what conditions non-informational heterogeneity, i.e., differences in preferences and endowments, leads to nontrivial trading volume in equilibrium. We present a non-informational no-trade theorem that provides necessary and sufficient conditions for zero equilibrium trading volume in a continuous-time Lucas market model with heterogeneous agents, multiple goods, and multiple securities. We explain in detail how no-trade equilibria are related to autarky equilibria, portfolio autarky equilibria, and peculiar financial market equilibria, which play an important role in the literature on international risk sharing.
The main focus of the representative-agent Lucas model (Lucas, 1978) is on equilibrium prices and returns. Agents in this model are identical by assumption. As a consequence, the equilibrium sharing rule is linear and can be implemented without trade in financial securities. The representative-agent Lucas model is therefore valuable as a tool to study aggregate market risk, but at the same time, does not provide any testable hypotheses for equilibrium trading volume. In order to generate nontrivial trading volume in a Lucas-type model, one needs to model heterogeneity among agents. Heterogeneity can be introduced in terms of either information,1 preferences or endowments. While it is well understood that in symmetric information models the degree of heterogeneity of endowments, preferences, and beliefs determines the equilibrium trading volume, necessary and sufficient conditions for trade in a dynamic model are still unavailable. The main result of this paper fills this gap. It comes in the form of a no-trade theorem that provides necessary and sufficient conditions for zero trading volume in a Pareto-efficient Lucas economy with multiple goods, multiple securities, symmetric information, and homogeneous beliefs. We illustrate this result in a number of examples that include most of the classical multi-good utility functions used in financial economics. These examples show that the existence of a no-trade equilibrium does not necessarily require that agents have identical preferences. In particular, we show that such an equilibrium can exist when agents have log-linear preferences but assign different weights to each good in their consumption bundle. As shown by Cass and Pavlova (2004) in a continuous-time model with multiple stocks, markets are not necessarily complete in equilibrium even if the number of risky securities equals the number of sources of risk. In order to circumvent the difficulties arising in the study of inefficient equilibria, we restrict our attention to Pareto-efficient equilibria and use the resulting proportionality of the utility gradients to infer the characteristics of preferences and endowments that do not generate trade in equilibrium. In contrast, in finite dimensional models, it is possible to choose the aggregate dividend in such a way that markets are necessarily dynamically complete in equilibrium. Such a model is studied in Judd, Kubler, and Schmedders (2003), where the aggregate dividends are given as an irreducible, stationary Markov chain. They show that in this case, the optimal consumption policies inherit the time homogeneity of the aggregate dividend, and they conclude that no trading occurs after the initial period in equilibrium irrespective of the agents’ preferences. This is a striking result, but one should bear in mind that stationarity and irreducibility are strong assumptions. In particular, they imply that all information about future dividends is revealed at the initial time and prevent the introduction of dividend growth into the model. Furthermore, Bossaerts and Zame (2005) show that the no-trade result of Judd, Kubler, and Schmedders (2003) fails to hold as soon as individual endowments are nonstationary, even if stationarity is preserved at the aggregate level. Our study complements this discussion by allowing for general arbitrarily growing dividend processes in continuous time. However, this generalization comes at a cost, as it then becomes impossible to assume market completeness a priori. A natural context in which our results can be applied is that of international finance, where each agent is interpreted as being representative of a country and the relative prices of goods represent the terms of trade. A very active area of research in this field is the analysis of international capital flows. In particular, Souriounis (2003) and Hau and Rey (2005) show that equity returns and portfolio rebalancings are an important source of exchange rate dynamics. Given these empirical findings, it is surprising that many of the theoretical asset pricing models in the international finance literature2 consider preference specifications which satisfy the conditions of our theorem and thus fail to produce realistic international capital flows. Our result describes the structure of preferences for which a no-trade equilibrium prevails, and thus characterizes the minimal level of preference heterogeneity required to generate nontrivial portfolio rebalancings in equilibrium. The no-trade equilibria introduced in this paper are related to autarky and portfolio autarky equilibria which are prominently featured in international financial economics. A no-trade equilibrium is an autarky equilibrium if initial endowments are individually optimal. Lucas (1982) uses such equilibria to study interest rates and currency prices in a general preference setting. He derives a perfectly pooled equilibrium assuming that investors have identical preferences and symmetric endowments. It follows from our main result and examples that such perfect pooling is not necessary: autarky equilibria are not necessarily symmetric and can exist even if agents are not identical. In a multi-good Lucas model, intertemporal risk sharing occurs through two channels. First, as in a single-good economy, agents can trade Arrow-Debreu securities synthesized from risky assets to finance their consumption plans. At the same time, relative price movements and the possibility of trade in the spot market for goods provide additional means for consumption smoothing. The importance of this second channel for international trade has been stressed by Cole and Obstfeld (1991), Zapatero (1995), Serrat (2001), and Pavlova and Rigobon (2003). In particular, Cole and Obstfeld study the welfare gains associated with the existence of international financial markets and show that for identical Cobb–Douglas preferences, there exists a Pareto-efficient equilibrium for which optimal consumption plans can be financed without trades in financial assets. Such an equilibrium is referred to as a portfolio autarky equilibrium. Interestingly, and as demonstrated by our examples, for this class of preferences there exists a no-trade equilibrium which yields the same consumption allocation and prices. It turns out that, in general, the consumption allocation of an efficient no-trade equilibrium can be implemented with portfolio autarky if and only if all investors have unit elasticity of substitution. This condition is necessary and sufficient provided that the no-trade equilibrium is not already an autarky equilibrium which by definition is also a portfolio autarky equilibrium. If the same allocation can be achieved either by trading once in the financial markets and never after that, or by trading continuously in the goods market, financial markets are redundant and agents are indifferent with respect to their portfolio holdings. We formalize this intuition by showing that when efficient no-trade equilibria and efficient portfolio autarky equilibria coincide, the equilibrium is necessarily peculiar in the sense that all but one of the risky assets are redundant. Cass and Pavlova (2004) introduce peculiar equilibria and prove their existence in a model with log-linear preferences. Our results show that the property of logarithmic preferences which implies the existence of peculiar financial market equilibria is their unit elasticity of substitution. This property implies that the terms of trade are inversely proportional to the ratio of aggregate dividends, and thus stock prices are linearly dependent. The rest of the paper is organized as follows. Section 2 introduces our multi-good economy and defines the different types of equilibria to be studied in the paper. Section 3 presents some simplifying notation and preliminary results. Section 4 contains our main result and shows its application in a number of examples prominently featured in international asset pricing. Section 5 discusses the economic relevance of no-trade equilibria and their relation to linear sharing rules, fund separation, and international risk sharing. Section 6 shows that no-trade equilibria are non-robust with regard to extensions of the basic model that introduce heterogeneous beliefs and random endowments. Proofs of all results are provided in the Appendix.
نتیجه گیری انگلیسی
In this paper we investigate under what conditions non-informational heterogeneity among agents leads to positive trading volume in equilibrium. We provide necessary and sufficient conditions for the existence of an efficient no-trade equilibrium in a continuous- time economy with multiple goods, multiple securities, symmetric information, and homogeneous beliefs. We illustrate our results with numerous examples that include most of the classic multi-good utility functions. Relations with linear sharing rules, fund separation, autarky, and portfolio autarky equilibria are also addressed. No-trade equilibria are computationally tractable and thus attractive for future empirical studies of the connections between financial markets, exchange rates, and spot markets for goods. In contrast to portfolio autarky equilibria they cannot necessarily be implemented by trades only in the spot market of consumption goods. Financial markets are non-redundant and, contrary to peculiar financial market equilibria, asset volatilities are non-degenerate in general. If extended to an overlapping generation setting where one cohort of investors is always in their initial period, these equilibria can potentially be used to derive tractable efficient equilibria with trade in both the spot market for consumption goods and the financial markets. The study of such a model would overcome some of the deficiencies of the classic international asset pricing models and is left for future research.