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

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.     

Fiscal Policy and $$\hbox {CO}_{2}$$ Emissions of New Passenger Cars in the EU

To what extent have national fiscal policies contributed to the decarbonisation of newly sold passenger cars? We construct a simple model that generates predictions regarding the effect of fiscal policies on average \(\hbox {CO}_{2}\) emissions of new cars, and then test the model empirically. Our empirical strategy combines a diverse series of data. First, we use a large database of vehicle-specific taxes in 15 EU countries over 2001–2010 to construct a measure for the vehicle registration and annual road tax levels, and separately, for the \(\hbox {CO}_{2}\) sensitivity of these taxes. We find that for many countries the fiscal policies have become more sensitive to \(\hbox {CO}_{2}\) emissions of new cars. We then use these constructed measures to estimate the effect of fiscal policies on the \(\hbox {CO}_{2}\) emissions of the new car fleet. The increased \(\hbox {CO}_{2}\)-sensitivity of registration taxes have reduced the \(\hbox {CO}_{2}\) emission intensity of the average new car by 1.3 %, partly through an induced increase of the share of diesel-fuelled cars by 6.5 percentage points. Higher fuel taxes lead to the purchase of more fuel efficient cars, but higher diesel fuel taxes also decrease the share of (more fuel efficient) diesel cars; higher annual road taxes have no or an adverse effect.     

Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case

In 1961, Vickrey posed the problem of finding an analytic solution to a first-price auction with two buyers having valuations uniformly distributed on ${[\underline{v}_{1}, \overline{v}_{1}]}$ and ${[\underline{v}_{2}, \overline{v}_{2}]}$ . To date, only special cases of the problem have been solved. In this paper, we solve this general problem and in addition allow for the possibility of a binding minimum bid. Several interesting examples are presented, including a class where the two bid functions are linear.     

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.     

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.      

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.”     

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.     

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.     

Is the Green Solow Model Valid for $$\hbox {CO}_{2}$$ Emissions in the European Union?

This paper addresses the \(\hbox {CO}_{2}\) emission patterns of the European Union from 1950 to 2010, and examines the validity of the Green Solow model, which simulates \(\hbox {CO}_{2}\) emissions growth by including only Solow forces and assuming emission intensity growth to be exogenous and constant. This study verifies that an environmental Kuznets curve (EKC) trajectory exists for per capita \(\hbox {CO}_{2}\) emissions in the European Union, that emission intensity growth is decreasing over time, and that the decreasing intensity growth reflects variations of the dependent variable in the specifications of the Green Solow model. The critique by Stefanski (On the mechanics of the Green Solow model. OxCarre Research Paper 47, OxCarre & Laval University, Oxford, 2013) of the Green Solow model assumption of exogenous and constant intensity growth is validated. The EKC is defined as the emissions plotted against income and emission intensity is defined as the ratio of emissions to income. The EKC and emission intensity share identical definitions and similar transition trajectories over time. The transition of the EKC trajectory and decline in emission intensity growth began before worldwide attention was focused on global warming.     

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.     

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 .      

Specification and Aggregation Errors in Environmentally Extended Input–Output Models

This article considers the specification and aggregation errors that arise from estimating embodied $\text{ CO }_{2}$ emissions and embodied water use with environmentally extended national input–output (IO) models, instead of with an environmentally extended international IO model. Model specification errors result from the use of domestic environmental and domestic technology coefficients to estimate emissions or resources that are embodied in international trade. For $\text{ CO }_{2}$ footprints, unacceptably large overestimations arise from using domestic emission coefficients, which are only partly canceled out by using domestic technology coefficients. For water use footprints both specification errors are smaller, but hardly cancel out. Sectoral aggregation errors occur when combining the 129 EXIOPOL industries to 59 EU industries and 10 broad sectors. The latter aggregation creates the largest errors. Spatial aggregation errors arise from combining 43 individual EXIOPOL countries in four broad regions and “the rest of the world”. Substantial, unacceptable errors occur again, now especially in relation to water use.     

Shadow prices of $$\hbox {CO}_{2}$$ emissions at US electric utilities: a random-coefficient,random-directional-vector directional output distance function approach

We estimate the shadow prices of \(\hbox {CO}_{2}\) emissions of electric utilities in the US over the period from 2001 to 2014, using a random-coefficient, random-directional-vector directional output distance function (DODF) model. The main feature of this model is that both its coefficients and directional vector are allowed to vary across firms, thus allowing different firms to have different production technologies and to follow different growth paths. Our Bayes factor analysis indicates that this model is strongly favored over the commonly used fixed-coefficient DODF model. Our results obtained from this model suggest that the average annual shadow price of \(\hbox {CO}_{2}\) emissions ranges from $61.62 to $105.72 (in 2001 dollars) with an average of $83.12. The results also suggest that the firm-specific average shadow price differs significantly across electric utilities. In addition, our estimates of the shadow price of \(\hbox {CO}_{2}\) emissions show an upward trend for both the sample electric utilities as a whole and the majority of the individual sample electric utilities.     

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.     

Restrictions and identification in a multidimensional risk-sharing problem

We consider $H$ expected utility maximizers that have to share a risky aggregate multivariate endowment $X\in {\mathbb {R}}^{N}$ and address the following two questions: does efficient risk-sharing imply restrictions on the form of individual consumptions as a function of $X$ ? Can one identify the individual utility functions from the observation of the risk-sharing? We show that when $H\ge \frac{2N}{N-1}$ efficient risk sharings have to satisfy a system of nonlinear PDEs. Under an additional rank condition, we prove an identification theorem.     

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.     

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.     

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.     

Nonparametric measures of efficiency in the presence of undesirable outputs: a by-production approach

In empirical research on productivity measurement adjusted for undesirable outputs on the side, the good and the bad outcomes are treated as joint products of the underlying production process. In the present paper, following Murty, Russell, and Levkoff, we conceptualize the good output as technologically separable from the bad output. Joint disposability is assumed between the bad output and the polluting input, rather than weak disposability and null jointness between the good and bad outputs. Moreover, we set up an integrated DEA optimization problem over the intersection of these two subtechnologies to measure the efficiency of a firm that produces a bad output alongside the good output. In an empirical illustration of our methodology, we use country-level data for an unbalanced panel of 64 countries over the years 1986 through 2011 where per capita GDP is the good and per capita \(\hbox {CO}_{2}\) emission is the bad output. We then utilize our DEA results to compute opportunity costs of a targeted reduction in \(\hbox {CO}_{2}\) emission in terms of required dollar amounts of reduction in per capita GDP for the individual countries in selected years.