Semantics for intuitionistic epistemic logics of shallow depths for game theory

Epistemic logic of shallow depths has been developed by Kaneko–Suzuki using classical logic. In this paper, we adopt intuitionistic logic as the base logic to limit each player’s reasoning to constructive one. The resulting logical system is denoted by IG $_{EF}$ , and we introduce epistemic possible world semantics for IG $_{EF}$ . We show the soundness and completeness of IG $_{EF}$ with respect to this semantics for it. We also show some applications to game theoretical decision making.     

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.     

Essential data, budget sets and rationalization

According to a minimalist version of Afriat’s theorem, a consumer behaves as a utility maximizer if and only if a feasibility matrix associated with his choices is cyclically consistent. An “essential experiment” consists of observed consumption bundles $(x_{1}, \ldots , x_{n})$ and a feasibility matrix $\varvec{\alpha }$ . Starting with a standard experiment, in which the economist has access to precise budget sets, we show that the necessary and sufficient condition for the existence of a utility function rationalizing the experiment, namely, the cyclical consistency of the associated feasibility matrix, is equivalent to the existence, for any budget sets compatible with the deduced essential experiment, of a utility function rationalizing them (and typically depending on them). In other words, the conclusion of the standard rationalizability test, in which the economist takes budget sets for granted, does not depend on the full specification of the underlying budget sets but only on the essential data that these budget sets generate. Starting with an essential experiment $(x_{1}, \ldots , x_{n}; \varvec{\alpha }$ ) only, we show that the cyclical consistency of $\varvec{\alpha }$ , together with a further consistency condition involving both $(x_{1}, \ldots , x_{n})$ and $\varvec{\alpha }$ , guarantees the existence of a budget representation and that the essential experiment is rationalizable almost robustly, in the sense that there exists a single utility function which rationalizes at once almost all budget sets which are compatible with $(x_{1}, \ldots , x_{n}; \varvec{\alpha }$ ). The conditions are also trivially necessary.     

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.     

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 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.’     

Getting Cars Off the Road: The Cost-Effectiveness of an Episodic Pollution Control Program

Ground-level ozone remains a serious problem in the United States. Because ozone non-attainment is a summer problem, episodic rather than continuous controls of ozone precursors are possible. We evaluate the costs and emissions reductions of a program that requires people to buy permits to drive on high-ozone days. We estimate the demand function for permits based on a survey of 1,300 households in the Washington, DC, metropolitan area. Assuming that all vehicle owners comply with the scheme, the permit program would reduce nitrogen oxides ( $\text{ NO }_{\mathrm{x}}$ ) by 42 tons per Code Red day at a permit price of $75. Allowing for non-compliance by 15 % of respondents reduces the effectiveness of the scheme to 33 tons of $\text{ NO }_{\mathrm{x}}$ per day. The cost per ozone season of achieving these reductions is approximately $9 million (2008 USD). Although year-round measures, such as the Tier II emissions standards, might be preferred on benefit-cost grounds, an episodic permit system might be considered as an interim measure before the Tier II emissions standards are fully reflected in the vehicle fleet.     

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.     

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.     

Marginal WTP and Distance Decay: The Role of ‘Protest’ and ‘True Zero’ Responses in the Economic Valuation of Recreational Water Quality

We evaluate the sensitivity of distance decay in individuals’ stated willingness to pay (WTP) for water quality improvements in eutrophied lakes. We extend the standard model of contingent valuation (CV) by allowing individuals to adopt a sequential evaluation process consisting of two decision stages. In the first stage respondents decide whether they are ‘protesters’, have a WTP   \(=\)   ‘true zero’ or a \(\hbox {WTP}>0\) . Conditioned on a strictly positive WTP, we use Lee’s selectivity-corrected model to determine the magnitude of their WTP in the second stage. Using CV survey data from Norway we find significant distance decay in the first stage classification of respondents as ‘protesters’, ‘true zero’ WTP, or positive WTP. In the second stage model for positive WTP responses, we find little or no significant relationships when correcting for selection. Results suggest that previous findings of significant distance decay in contingent valuation of lake and river water in Europe may be driven by the definition of ‘protest’ and ‘true zero’ respondents. We find that WTP for water quality may be more useful as a qualitative indicator of political support for user financed water quality measures, than as a cardinal measure of marginal utility of water quality improvements.     

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.     

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.     

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.     

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.     

How Much Does Wind Power Reduce $$\text {CO}_{2}$$ Emissions? Evidence from the Irish Single Electricity Market

This paper evaluates the effect of wind generation on \(\text {CO}_{2}\) emissions using 2008–2012 historical data for the Irish Single Electricity Market. Wind generation displaces \(\text {CO}_{2}\) emissions, as expected, in line with the average system emissions. Over the whole period, wind generation avoided about 8.8 million tons of \(\text {CO}_{2}\), equivalent to about 12% of total system emissions. To understand what drives the level of abatement we evaluate the results by technology and determine that wind generation has similar effects on total emissions from CCGT and coal plants, due to the higher carbon content of coal. Each MWh of wind, however, replaces more generation from CCGTs than from coal plants, in proportion to their generation. We also test the hypothesis that as wind displaces baseload plants it pushes them to generate less efficiently, but find no evidence of a strong negative effect of wind on CCGT or coal plant efficiency. Finally wind displaces about 2.5% fewer emissions when the pumped storage plant is on outage, suggesting that wind is more effective when paired with a flexible system.     

Outsourcing versus technology transfer: Hotelling meets Stackelberg

We consider a Hotelling duopoly with two firms $A$ and $B$ in the final good market. Both can produce the required intermediate good, firm $B$ having a lower cost due to a superior technology. We compare two contracts: outsourcing ( $A$ orders the intermediate good from $B$ ) and technology transfer ( $B$ transfers its technology to $A$ ). An outsourcing order is equivalent to building an endogenous capacity and it generates a Stackelberg leadership effect for firm $A,$ which is absent in technology transfer. We show that compared to the situation of no contracts there are always Pareto improving outsourcing contracts (making both firms better off and all consumers at least weakly better off), but no Pareto improving technology transfer contracts. It is also shown that if firm $B$ has a relatively large bargaining power in its negotiations with $A,$ then both firms prefer technology transfer while all consumers prefer outsourcing.     

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.     

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.