A characterization of inefficiency in stochastic overlapping generations economies

In this paper, we provide a characterization of interim inefficiency in stochastic economies of overlapping generations. With respect to the established body of results in the literature, we allow for sequentially incomplete markets and we remove the hypothesis of two-period horizons, by considering longer, though uniformly bounded, horizons for generations. The characterization exploits a suitably Modified Cass Criterion, based entirely on observable prices and independent of the length of the horizons of generations. For sequentially incomplete markets, we introduce a notion of unambiguous inefficiency, separating the inefficient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous inefficiency reduces to inefficiency when markets are sequentially complete. Furthermore, our analysis shows that the hypothesis of two-period horizons is purely heuristic in establishing a criterion for inefficiency.     

Efficiency and prices in economies of overlapping generations

In a general economy of overlapping generations, I introduce a notion of uniform inefficiency, corresponding to the occurrence of a Pareto improvement with a small uniform destruction of resources [G. Debreu, The coefficient of resource utilization, Econometrica 19 (1951) 273-292]. I provide a necessary and sufficient condition for uniform inefficiency in terms of prices at a competitive equilibrium: an allocation is uniformly inefficient if and only if the relative price of the aggregate endowment in a given period into the aggregate endowment up to that period does not vanish over periods of trade, a sort of Modified Cass Criterion [D. Cass, On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization, J. Econ. Theory 4 (1972) 200-223]. Minimal assumptions on fundamentals are needed for such a complete characterization. Furthermore, proofs reduce to simple and short direct arguments. Finally, I verify that uniform inefficiency is preserved under perturbations, a property that might fail for the canonical notion of inefficiency. Remarkably, an allocation is uniformly inefficient if and only if a non-vanishing redistribution, like a social security mechanism, is welfare improving.     

On the empirics of risk-sharing across MENA countries

In this article, we compute the potential welfare gains and the realized gains from risk-sharing among Middle East and North African (MENA) countries, including the oil-rich Gulf region and the resource-scarce economies. We find that the overall potential welfare gains across MENA countries are positive for all countries under the assumption of full risk-sharing. The potential welfare gains among the six Gulf Cooperation Council (GCC) countries are positive even though the magnitudes are smaller compared to those of the rest of the MENA region. We also quantify the extent of risk-sharing for the MENA region and show that it is significant for the MENA region and its subgroups; however, we could not find any sign of inter-temporal smoothing across the same groups. Decomposing the aggregate output shocks shows that the extent of risk-sharing is significant when only positive output shocks exist across the resource-scarce MENA economies. However, we observe that GCC countries share output risks with each other even under negative output shocks.     

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     

The Cass criterion, the net dividend criterion, and optimality

Abel, Mankiw, Summers, and Zeckhauser [Assessing dynamic efficiency: theory and evidence, Rev. Econ. Stud. 56 (1989) 1-20] propose the net dividend criterion as an easy to use sufficient condition for optimality in general stochastic overlapping generations economies with production. We provide examples based on the criterion due to Cass [On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization, J. Econ. Theory 4 (1972) 200-223] and its extensions, the usual tools for such problems, to show that the net dividend criterion need not give the right answer. We identify the flaw in their proof. We also provide an alternative condition which, by an argument unrelated to theirs, is a sufficient condition for optimality when dividends are nonnegative and then argue that the condition is not innocuous since it cannot be verified in actual economies.     

Crowding out and crowding in: When does redistribution improve risk-sharing in limited commitment economies?

When the risk of default constrains financial contracts, public insurance policies can significantly affect private risk-sharing. This is because by changing income expectations and volatility, redistribution changes the attractiveness of default and thus endogenous borrowing constraints. Extending results by Krueger and Perri (2011) [8], this paper analyses the conditions under which redistribution can improve private insurance by making default less attractive to the income-rich, whose income it reduces. I first explain why public redistribution typically crowds out private insurance in the two-income economy, and identify the role of income persistence and saving after default. Second, I show how, in endowment economies with three income states or more and in economies with capital, redistributive taxes can improve, or “crowd in”, private consumption insurance. Finally, in a quantitative exercise using a realistic income process calibrated to US micro-data, moderate redistribution crowds in private insurance with production but not in an endowment economy.     

Waste not,want not: The efficiency of health expenditure in emerging and developing economies

Public health spending is low in emerging and developing economies relative to advanced economies and health outputs and outcomes need to be substantially improved. Simply increasing public expenditure in the health sector, however, may not significantly affect health outcomes if the efficiency of this spending is low. This paper quantifies the inefficiency of public health expenditure and the associated potential gains for emerging and developing economies using a stochastic frontier model that controls for the socioeconomic determinants of health, and provides country‐specific estimates. The results suggest that African economies have the lowest efficiency. At 2009 spending levels, they could boost life expectancy up to about 5 years if they followed best practices.     

Economies with observable types

We study economies of asymmetric information with observable types. Trade takes place in lotteries. Individuals face a standard budget constraint, while the incentive compatibility constraints are imposed on the production set of the intermediaries. This formalization encompasses moral hazard, as in [Jerez, 2003] and [Jerez, 2005], and private information economies. Equilibrium allocations are constrained efficient, but, contrary to what stated for example in Jerez (2005), the set of equilibrium allocations may be empty and the Second Welfare Theorem may fail. This happens for two reasons. First, constrained efficient allocations may violate the necessary and sufficient conditions of price supportability for the individuals. Second, even when constrained efficient allocation are price supportable, they may fail to be a profit maximizing choice of the firm at the individual supporting prices. To restore existence of an equilibrium the firm has to be restricted to supply allocations with support in the set of incentive compatible contracts.     

Financial markets,the structure of long-term investments and labour income risks

The paper develops a model to analyse the feedback between financial markets, long-term capital investments and the risk of labour incomes. We study a situation where firms are owned by entrepreneurs, who are able to share and diversify their income risk by trading on financial markets. Workers, in contrast, cannot short-sell the flows from future labour endowments and thus do not have the same opportunities. We derive two central results. Firstly, even if financial markets offer perfect risk-sharing opportunities for entrepreneurs, the participation restriction for labour incomes leads to a constrained inefficient market allocation. The constrained inefficiency arises because the effect of long-term investments on the risk of wages is not internalized by state prices. Secondly, we show that in general it is not true that workers indirectly benefit when we go from a situation with no financial markets to a situation with perfect financial markets for entrepreneurs but restricted participation for workers. The results suggest that a policy solution might require either to close some financial markets or to create new ones. We argue why there is a strong case for the creation of new markets rather than for closing existing ones.     

Decentralizing lottery allocations in markets with indivisible commodities

Summary In economies with indivisible commodities, consumers tend to prefer lotteries in commodities. A potential mechanism for satisying these preferences is unrestricted purchasing and selling of lotteries in decentralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev.25, 1–20]. However, this paper shows in several examples that such lottery equilibria do not always exist for economies with finitely many consumers. Other conditions are needed. In the examples, equilibrium and the associated welfare gains are realized if consumptions are bounded or if lotteries are based upon a common sunspot device as defined by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ.91, 193–227]. The paper shows that any lottery equilibrium is either a Walrasian equilibrium or a sunspot equilibrium, but there are Walrasian and sunspot equilibria that are not lottery equilibria.This paper is based on Chapter 3 of my doctoral dissertation, written while I was a student at Cornell University. I thank Larry Blume, Yue Yun Chen, David Easley, Aditya Goenka, John Marshall, Bruce Smith, John Wooders and an anonymous referee. I am particularly grateful to Karl Shell and Cheng-Zhong Qin. I thank the Academic Senate at UCSB for financial support.     

Idiosyncratic risk and financial policy

In economies subject to uninsurable idiosyncratic risks, competitive equilibrium allocations are constrained inefficient: reallocations of assets support Pareto superior allocations. This is the case even if the asset market for the allocation of aggregate risks is complete.     

Efficient assignment respecting priorities

A widespread practice in assignment of heterogeneous indivisible objects is to prioritize some recipients over others depending on the type of the object. Leading examples include assignment of public school seats, and allocation of houses, courses, or offices. Each object comes with a coarse priority ranking over recipients. Respecting such priorities constrains the set of feasible assignments, and therefore might lead to inefficiency, highlighting a tension between respecting priorities and Pareto efficiency. Via an easily verifiable criterion, we fully characterize priority structures under which the constrained efficient assignments do not suffer from such welfare loss, and the constrained efficient rule (CER) is indeed efficient. We also identify the priority structures for which the CER is singleton-valued and group strategy-proof.     

Implications of Endogenous Group Formation for Efficient Risk-Sharing

The existing literature on sub-game perfect risk-sharing suffers from a basic inconsistency. While a group of size n is able to coordinate on a risk-sharing outcome, it is assumed that deviating subgroups cannot. I relax this assumption and characterise the optimal contract among all coalition-proof history-dependent contracts. This alters the predictions of the standard dynamic limited commitment model. I show that the consumption of constrained agents depends on both the history of shocks and its interaction with the current income of other constrained agents. From this, I derive a formal test for the presence of endogenous group formation under limited commitment.     

The type-agent core for exchange economies with asymmetric information

The type-agent core is a new solution concept for exchange economies with asymmetric information. It coincides with the set of subgame-perfect equilibrium outcomes of a simple competitive screening game. Uninformed intermediaries help the agents to cooperate in an attempt to make some profit. The paper extends the work of Perez-Castrillo [Cooperative outcomes through non-cooperative games, Games Econ. Behav. 7 (1994) 428-440] to exchange economies with non-transferable utility and asymmetric information. The type-agent core is a subset of Wilson's coarse core [Wilson, Information, efficiency, and the core of an economy, Econometrica 46 (1978) 807-816]. It is never empty, even though it may be a strict subset of Wilson's fine core. In addition, it converges towards the set of constrained market equilibria as the economy is replicated.     

Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually—so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.     

A portfolio model of capital flows to emerging markets

Since the crises of the late 1990's, most emerging market economies have built up substantial positive holdings of US dollar treasury bills, while at the same time experiencing a boom in FDI capital inflows. This paper develops a DSGE model of the interaction between an emerging market economy and an advanced economy which incorporates two-way capital flows between the economies. The novel aspect of the paper is to make use of new methods for analyzing portfolio choice in DSGE models. We compare a range of alternative financial market structures, in each case computing equilibrium portfolios. We find that an asymmetric configuration where the emerging economy holds nominal bonds and issues claims on capital (FDI) can achieve a considerable degree of international risk-sharing. This risk-sharing can be enhanced by a more stable monetary policy in the advanced economy.     

Environmental Taxation and Induced Structural Change in an Open Economy: The Role of Market Structure

Abstract. Studies of structural change induced by environmental taxation usually proceed in a perfect-competition framework and typically find structural change to be quite moderate under realistic emission reduction scenarios. By observing that some of the industries affected are likely to operate under imperfect rather than perfect competition, additional mechanisms emerge which may amplify structural change beyond the extent identified as yet. Especially, changes in economies of scale may arise which weaken or strengthen the competitive position of industries over and above the initial cost effect. Using a computable general equilibrium model for Germany to examine the effects of a unilaterally introduced carbon tax, we find that induced structural change is more pronounced under imperfect competition than under perfect competition. At the macroeconomic level, we find that aggregate losses in economies of scale are larger than aggregate gains, implying that the total costs of environmental regulation are higher under imperfect competition than under perfect competition.     

Equilibrium theory with asymmetric information and with infinitely many commodities

The traditional deterministic general equilibrium theory with infinitely many commodities cannot cover economies with private information constraints on the consumption sets. We bring the level of asymmetric information equilibrium theory at par with that of the deterministic one. In particular, we establish results on equilibrium existence for exchange economies with asymmetric (differential) information and with an infinite dimensional commodity space. Our new equilibrium existence theorems include, as a special case, classical results, e.g. Bewley [Existence of equilibria in economies with infinitely many commodities, J. Econ. Theory 4 (1972) 514-540] or Mas-Colell [The price equilibrium existence problem in topological vector lattices, Econometrica 54 (1986) 1039-1053].     

Edgeworth's conjecture with infinitely many commodities: commodity differentiation

Summary. Convergence of the cores of finite economies to the set of Walrasian allocations as the number of agents grows has long been taken as one of the basic tests of perfect competition. The present paper examines this test in the most natural model of commodity differentiation: the commodity space is the space of nonnegative measures, endowed with the topology of weak convergence. In Anderson and Zame [12], we gave counterexamples to core convergence in L ¹, a space in which core convergence holds for replica economies and core equivalence holds for continuum economies; in addition, we gave a core convergence theorem under the assumption that traders' utility functions exhibit uniformly vanishing marginal utility at infinity. In this paper, we provide two core convergence results for the commodity differentiation model. A key technical virtue of this space is that relatively large sets (in particular, closed norm-bounded sets) are compact. This permits us to invoke a version of the Shapley-Folkman Theorem for compact subsets of an infinite-dimensional space. We show that, for sufficiently large economies in which endowments come from a norm bounded set, preferences satisfy an equidesirability condition, and either (i) preferences exhibit uniformly bounded marginal rates of substitution or (ii) endowments come from an order-bounded set, core allocations can be approximately decentralized by prices. Received: July 29, 1996; revised version: January 14, 1997     

Money, credit and banking

In monetary models where agents are subject to trading shocks there is typically an ex post inefficiency since some agents are holding idle balances while others are cash constrained. This problem creates a role for financial intermediaries, such as banks, who accept nominal deposits and make nominal loans. In general, financial intermediation improves the allocation. The gains in welfare come from the payment of interest on deposits and not from relaxing borrowers’ liquidity constraints. We also demonstrate that when credit rationing occurs increasing the rate of inflation can be welfare improving.