Continuity properties of the private core

Let be a sequence of differential information economies, converging to a limit differential information economy (written as ). Denote by the set of all ε-private core allocations, ε ≥ 0 (for ε=0 we get the private core of Yannelis (1991), denoted by ). Under appropriate conditions, we prove the following stability results

The price of anarchy of serial, average and incremental cost sharing

We compute the price of anarchy (PoA) of three familiar demand games, i.e., the smallest ratio of the equilibrium to efficient surplus, over all convex preferences quasi-linear in money. For any convex cost, the PoA is at least in the average and serial games, where n is the number of users. It is zero in the incremental game for piecewise linear cost functions. With quadratic costs, the PoA of the serial game is , and for the average and incremental games. This generalizes if the marginal cost is convex or concave, and its elasticity is bounded.      

Asymptotical behavior of finite and possible discontinuous economies

We consider a finite economy in which the data are depending on an exogenous parameter and the utilities satisfy a condition, previously introduced by the authors and called sequential pseudocontinuity, weaker than sequential lower semicontinuity and than sequential upper semicontinuity. We show that the economy has a nice asymptotical behavior, that is: for any sequence (x _n ) _n of exogenous parameters converging to x _o , any convergent subsequence of a sequence of approximate competitive equilibria of converges to an exact equilibrium of .      

Eco-Efficiency and Convergence in OECD Countries

This paper assesses the convergence in eco-efficiency of a group of 22 OECD countries over the period 1980–2008. In doing so, three air pollutants representing the impact on the environment of economic activities are considered, namely, carbon dioxide ( ${\text{ CO}}_{2}$ ), nitrogen oxides ( ${\text{ NO}}_\mathrm{X}$ ) and sulphur oxides ( ${\text{ SO}}_\mathrm{X}$ ); furthermore, eco-efficiency scores at both country and air-pollutant-specific level are computed using Data Envelopment Analysis techniques. Then, convergence is evaluated using the recent approach by Phillips and Sul Econometrica 75:1771–1855 (2007), which tests for the existence of convergence groups. First, we find that eco-efficiency has improved over the period, with the exception of ${\text{ NO}}_\mathrm{X}$ emissions. Second, Switzerland is the most eco-efficient country, followed by some Scandinavian economies, such as Sweden, Iceland, Norway and Denmark. In contrast, Southern European countries such as Portugal, Spain and Greece, in addition to Hungary, Turkey, Canada and the United States, are among the worst performers. Finally, we find that both the most eco-efficient countries and the worst tend to form clubs of convergence.     

The asymptotic shapley value for a simple market game

We consider the game in which b buyers each seek to purchase 1 unit of an indivisible good from s sellers, each of whom has k units to sell. The good is worth 0 to each seller and 1 to each buyer. Using the central limit theorem, and implicitly convergence to tied down Brownian motion, we find a closed form solution for the limiting Shapley value as s and b increase without bound. This asymptotic value depends upon the seller size k, the limiting ratio b/ks of buyers to items for sale, and the limiting ratio of the excess supply relative to the square root of the number of market participants. This work was sponsered in part by NSF Grant DMS-03-01795.     

More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model

Summary. This paper studies monotone risk aversion, the aversion to monotone, mean-preserving increase in risk (Quiggin [21]), in the Rank Dependent Expected Utility (RDEU) model. This model replaces expected utility by another functional, characterized by two functions, a utility function u in conjunction with a probability-perception function f. Monotone mean-preserving increases in risk are closely related to the notion of comparative dispersion introduced by Bickel and Lehmann [3,4] in Non-parametric Statistics. We present a characterization of the pairs (u,f) of monotone risk averse decision makers, based on an index of greediness G _u of the utility function u and an index of pessimism P _f of the probability perception function f: the decision maker is monotone risk averse if and only if . The index of greediness (non-concavity) of u is the supremum of taken over . The index of pessimism of f is the infimum of taken over 0 < v < 1. Thus, , with G _u = 1 iff u is concave. If then , i.e., f is majorized by the identity function. Since P _f = 1 for Expected Utility maximizers, forces u to be concave in this case; thus, the characterization of risk aversion as is a direct generalization from EU to RDEU. A novel element is that concavity of u is not necessary. In fact, u must be concave only if P _f = 1.Received: 10 April 2001, Revised: 18 November 2003, JEL Classification Numbers: D81. Correspondence to: Michéle CohenAlain Chateauneuf, Michéle Cohen, Isaac Meilijson: We are most grateful to Mark Machina, Peter Wakker and two anonymous referees for very helpful suggestions and comments.     

Existence of Sparsely Supported Correlated Equilibria

We show that every N-player K ₁ × ... × K _N game possesses a correlated equilibrium with at least zero entries. In particular, the largest N-player K × ... × K games with unique fully supported correlated equilibrium are two-player games. We thank an anonymous referee for most useful comments. The first author acknowledges financial support from Spanish Ministry of Science and Technology, grant SEJ2004-03619, and in form of a Ramón y Cajal fellowship. The second author acknowledges support by the PASCAL Network of Excellence under EC grant no.506778, as well as from Spanish Ministry of Science and Technology and FEDER, grant BMF2003-03324. Both authors also acknowledge financial support from BBVA grant “Aprender a jugar.”     

Stationary measures for some Markov chain models in ecology and economics

Summary. Let continuous, exists in for x in . Let be an i.i.d. sequence from F and X₀ be a nonnegative random variable independent of . Let be the Markov chain generated by the iteration of random maps by . Such Markov chains arise in population ecology and growth models in economics. This paper studies the existence of nondegenerate stationary measures for {X_n}. A set of necessary conditions and two sets of sufficient conditions are provided. There are some convergence results also. The present paper is a generalization of the work on random logistics maps by Athreya and Dai (2000).Received: 20 March 2002, Revised: 4 December 2002, JEL Classification Numbers: C22, D9.The author wishes to thank Professor Mukul Majumdar and the referees for several useful suggestions.     

On the hellwig method of feasible portfolio construction

The work feasible portfolio is built into the work, that is, the k-dimensional Q column vector with components q_i where q_i 0 for i=1,...,k and q₁+...+q_k=1. We define i=1,...,k in the following way:

Voting in assemblies of shareholders and incomplete markets

Summary. An economy with two dates is considered, one state at the first date and a finite number of states at the last date. Shareholders determine production plans by voting - one share, one vote - and at -majority stable stock market equilibria, alternative production plans are supported by at most percent of the shareholders. It is shown that a -majority stable stock market equilibrium exists if where S is the number of states at the last date and J is the number of firms. Moreover, an example shows that -majority stable stock market equilibria need not exist for smaller s.Received: 23 December 2002, Revised: 14 June 2004, JEL Classification Numbers: D21, D52, D71, G39. Correspondence to: Hervé CrésThe authors are grateful to an anonymous referee for helpful comments and suggestions. Financial support from the Danish Research Councils and hospitality of HEC is gratefully acknowledged by Mich Tvede and support from Fondation HEC is gratefully acknowledged by Hervé Crés.     

The (S,s) Policy is an Optimal Trading Strategy in a Class of Commodity Price Speculation Problems

This paper introduces a model of commodity price speculation and proves that the optimal trading strategy is of the (S,s) form when a no expected loss condition holds. A strong form of this condition is that the retail price charged to consumers at time t exceeds the expected wholesale price of the commodity at time t+1, i.e. , where β ∈(0,1) is the speculator’s discount factor. We are extremely grateful to Herbert Scarf for pointing out an important error in a previous draft of this paper and for suggesting the key argument in a revised proof that fixed the problem. We also benefited from helpful feedback from an anonymous referee, William Brainard, Zvi Eckstein, participants of seminars at Yale, the Operations Research Center at MIT, and the Econometric Society Winter School at the Indian Statistical Institute, New Delhi.     

The nature of the steady state in models of optimal growth under uncertainty

Summary. We study a one-sector stochastic optimal growth model with a representative agent. Utility is logarithmic and the production function is of the Cobb-Douglas form with capital exponent . Production is affected by a multiplicative shock taking one of two values with positive probabilities p and 1-p. It is well known that for this economy, optimal paths converge to a unique steady state, which is an invariant distribution. We are concerned with properties of this distribution. By using the theory of Iterated Function Systems, we are able to characterize such a distribution in terms of singularity versus absolute continuity as parameters and p change. We establish mutual singularity of the invariant distributions as p varies between 0 and 1 whenever . More delicate is the case . Singularity with respect to Lebesgue measure also appears for values such that . For and Peres and Solomyak (1998) have shown that the distribution is a.e. absolutely continuous. Characterization of the invariant distribution in the remaining cases is still an open question. The entire analysis is summarized through a bifurcation diagram, drawn in terms of pairs .Received: 9 April 2002, Revised: 29 October 2002, JEL Classification Numbers: C61, O41.Correspondence to: Tapan MitraThis research was partially supported by CNR (Italy) under the "Short-term mobility" program and by M.U.R.S.T. (Italy) National Group on "Nonlinear Dynamics and Stochastic Models in Economics and Finance" . We are indebted to Rabi Bhattacharya for providing us with the reference to Solomyak's (1995) paper. The present version has benefitted from comments by Mukul Majumdar and two anonymous referees.     

The Welfare Impact of Self-supplied Water Pricing in Canada: A Computable General Equilibrium Assessment

This paper uses a computable general equilibrium model to assess the welfare cost of changing the method of water allocation in Canada towards one that uses prices to ration demand. We model the introduction of a price on both water that is abstracted as well as water that is consumed (that is abstracted, and not returned to the source). We estimate that reducing water consumption by 25 % would require imposition of a price on water consumption of around $$\$0.21/\text{ m }^{3}$$ . Similarly, introduction of a water abstraction charge of about $$\$0.013/\text{ m }^{3}$$ would be sufficient to reduce water abstraction by 25 %. We find that if revenues from water pricing are returned in lump sum to households, the introduction of water pricing would result in a modest welfare loss. When revenues from water pricing are used to offset existing taxes, we find a gain in welfare corresponding to a ‘strong double dividend.’     

Quantifying knowledge exchange in R&amp;D networks: a data-driven model

We propose a model that reflects two important processes in R&D activities of firms, the formation of R&D alliances and the exchange of knowledge as a result of these collaborations. In a data-driven approach, we analyze two large-scale data sets, extracting unique information about 7500 R&D alliances and 5200 patent portfolios of firms. These data are used to calibrate the model parameters for network formation and knowledge exchange. We obtain probabilities for incumbent and newcomer firms to link to other incumbents or newcomers able to reproduce the topology of the empirical R&D network. The position of firms in a knowledge space is obtained from their patents using two different classification schemes, IPC in eight dimensions and ISI-OST-INPI in 35 dimensions. Our dynamics of knowledge exchange assumes that collaborating firms approach each other in knowledge space at a rate μ for an alliance duration τ. Both parameters are obtained in two different ways, by comparing knowledge distances from simulations and empirics and by analyzing the collaboration efficiency \(\mathcal {\hat {C}}_{n}\). This is a new measure that takes in account the effort of firms to maintain concurrent alliances, and is evaluated via extensive computer simulations. We find that R&D alliances have a duration of around two years and that the subsequent knowledge exchange occurs at a very low rate. Hence, a firm’s position in the knowledge space is rather a determinant than a consequence of its R&D alliances. From our data-driven approach we also find model configurations that can be both realistic and optimized with respect to the collaboration efficiency \(\mathcal {\hat {C}}_{n}\). Effective policies, as suggested by our model, would incentivize shorter R&D alliances and higher knowledge exchange rates.     

Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach

In this paper, we make use of the Sobolev space to derive at once the Pontryagin conditions for the standard optimal growth model in continuous time, including a necessary and sufficient transversality condition. An application to the Ramsey model is given. We use an order ideal argument to solve the problem inherent to the fact that L ¹ spaces have natural positive cones with no interior points. The paper was written when Cuong Le Van was visiting CORE, Université catholique de Louvain, and Cagri Saglam was a research fellow of the Economics Department of the same university. The authors are indebted to an anonymous referee and Takashi Kamihigashi for very useful comments. R. Boucekkine acknowledges the support of the Belgian research programmes PAI P4/01 and ARC 03/08-302.     

Offsetting Versus Mitigation Activities to Reduce $$\hbox {CO}_{2}$$ Emissions: A Theoretical and Empirical Analysis for the U.S. and Germany

This paper studies the voluntary provision of public goods that is partially driven by a desire to offset for individual polluting activities. We first extend existing theory and show that offsets allow a reduction in effective environmental pollution levels while not necessarily extending the consumption of a polluting good. We further discuss the impact of an increased environmental preference on purchases of offsets and mitigation activities. Several theoretical results are then econometrically tested using a novel dataset on activities to reduce \(\hbox {CO}_{2}\) emissions for the case of vehicle purchases in the U.S. and Germany. We show that environmental preference triggers the stated use of \(\hbox {CO}_{2}\) offsetting and mitigation channels in both countries. However, we find strong country differences for the stated purchase of \(\hbox {CO}_{2}\) offsets. While such activities are mainly triggered by a high general awareness of the climate change problem in the U.S., the perception that road travel is responsible for \(\hbox {CO}_{2}\) emissions to a large extent is more important for driver’s license holders in Germany.     

Controlling Episodic Air Pollution with a Seasonal Gas Tax: The Case of Cache Valley,Utah

Using daily data spanning 10 years, we establish a statistical relationship between episodic particulate-matter \((\hbox {PM}_{2.5})\) concentrations and vehicle trips in Cache Valley, Utah, and estimate an average gas-price elasticity for the region. We also estimate the benefits and costs associated with a seasonal gas tax set to reduce vehicle trips during the winter-inversion season and thereby lower health costs through concomitant decreases in the \(\hbox {PM}_{2.5}\) concentrations. We find a strong positive relationship between vehicle trips reduced and associated reductions in \(\hbox {PM}_{2.5}\) concentrations. Further, we estimate a mean gas price elasticity of approximately \(-\)0.3 in what we call a “high price variability environment.” Incorporating these results, cost-benefit analysis suggests that the social net benefit for Cache Valley associated with the imposition of a seasonal gas tax during the winter-inversion season is highly dependent upon the type of benefit estimation method used.     

Shaping the Relationship Between Economic Development and Carbon Dioxide Emissions at the Local Level: Evidence from Spatial Econometric Models

The debate over the correlation between economic growth and environmental pollution has attracted a great deal of attention from academic researchers and policy makers in recent years. There has been excessive use of spatial econometric models and too much emphasis on statistical procedures in empirical studies. In this study, we contribute to the existing literature by conducting a more rigorous analysis of the relationship between economic growth and \(\hbox {CO}_{2}\) emissions in Chinese cities using spatial Durbin models. Our results show that \(\hbox {CO}_{2}\) emissions increase monotonically in relation to economic growth at the city level and that the driving effects of economic growth are slightly smaller in central China than in eastern and western China. In addition to economic growth, industry’s share of the economy is a major driver of \(\hbox {CO}_{2}\) emissions, while technological improvement, measured by energy intensity per unit of gross domestic product (GDP), and the effectiveness of environmental governance flatten the shape of the environmental Kuznets curve. We provide evidence of local spillover effects of explanatory variables on \(\hbox {CO}_{2}\) emissions. Economic competition as well as technological diffusion are found to exist in Chinese cities in relation to \(\hbox {CO}_{2}\) emissions. We also find carbon leakage between cities only if the per capita GDP of a given city is less than $493 (in 2010 constant dollars). Results hold when robustness checks are performed. Policy makers should carefully consider regional differences and the inherent spatial interactions between factors when formulating carbon reduction policies.     

Fractional Integration Versus Structural Change: Testing the Convergence of $$\hbox {CO}_{2}$$ Emissions

This paper assesses the stochastic convergence of relative \(\hbox {CO}_{2}\) emissions within 28 OECD countries over the period 1950–2013. Using the local Whittle estimator and some of its variants we assess whether relative per capita \(\hbox {CO}_{2}\) emissions are long memory processes which, although highly persistent, may revert to their mean/trend in the long run thereby indicating evidence of stochastic convergence. Furthermore, we test whether (possibly) slow convergence or the complete lack of it may be the result of structural changes to the deterministics of each of the relative per-capita emissions series by means of the tests of Berkes et al. (Ann Stat 1140–1165, 2006) and Mayoral (Oxford Bull Econ Stat 74(2):278–305, 2012). Our results show relatively weak support for stochastic convergence of \(\hbox {CO}_2\) emissions, indicating that only between 30 and 40% of the countries converge to the OECD average in a stochastic sense. This weak evidence disappears if we enlarge the sample to include 4 out of the 5 BRICS, indicating that our results are not robust to the inclusion of countries which are experiencing rates of growth which are far larger than those of the OECD members. Our results also decisively indicate that a slow or lack of convergence is not the results of a structural break in the relative \(\hbox {CO}_{2}\) emissions series.     

Technical Synergies and Trade-Offs Between Abatement of Global and Local Air Pollution

In this paper, we explore the synergies and tradeoffs between abatement of global and local pollution. We build a unique dataset of Swedish combined heat and power plants with detailed boiler-level data 2001–2009 on not only production and inputs but also on emissions of \(\hbox {CO}_{2}\) and \(\hbox {NO}_{\mathrm{x}}\). Both pollutants are regulated by strict policies in Sweden. \(\hbox {CO}_{2}\) is subject to the European Union Emission Trading Scheme and Swedish carbon taxes; \(\hbox {NO}_{\mathrm{x}}\)—as a precursor of acid rain and eutrophication—is regulated by a heavy fee. Using a quadratic directional output distance function, we characterize changes in technical efficiency as well as patterns of substitutability in response to the policies mentioned. The fact that generating units face a trade-off between the pollutants indicates the need for policy coordination.