the ellsberg paradox and risk aversion an anticipated utility approach the paper describes a decision process under which it is rational to prefer a lottery with known probabilities to a similar ambiguous lottery where the decision maker does not know the exact values of the probabilities the ellsberg paradox this is done by modeling ambiguous lotteries as two stage lotteries by assuming the independence axiom without the reduction of compound lotteries axiom and by using the anticipated utility functional this paper also gives conditions under which less ambiguity is preferred and presents some comparative statics analysis as well as some inter personal comparisons finally it proves that within the anticipated utility framework risk and ambiguity are almost identical copyright 1987 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

second best carbon taxation in the global economy the green paradox and carbon leakage revisited acceleration of global warming resulting from a future carbon tax is large if the price elasticities of oil demand are large and that of oil supply is small the fall in the world interest rate weakens this weak green paradox effect especially if intertemporal substitution is weak still social damages from greenhouse gases drop if the fall in oil supply and cumulative emissions is strong enough if the current carbon tax is set too low the second best future carbon tax is set below the first best too to mitigate adverse green paradox effects unilateral second best optimal carbon taxes exceed the first best taxes due to an import tariff component the intertemporal terms of trade effects of the future carbon tax increase current and future tariffs and those of the current tax lower the current tariff finally carbon leakage and globally altruistic and unilateral second best optimal carbon taxes if non kyoto oil importers price carbon too low are analysed in a three country model of the global economy

individual option prices for climate change mitigation abstract willingness to pay for climate change mitigation depends on people s perceptions about just how bad things will get if nothing is done individual subjective distributions for future climate conditions are combined with stated choices over alternative climate policies to estimate individual option prices the appropriate ex ante welfare measure in the face of uncertainty for climate change mitigation we find statistically significant sensitivity of estimated option prices to both expected future conditions and uncertainty about future conditions

uncertainty and risk in financial markets this paper considers a general equilibrium model in which the distinction between uncertainty and risk is formalized by assuming agents have incomplete preferences over statecontingent consumption bundles as in bewley 1986 without completeness individual decision making depends on a set of probability distributions over the state space a bundle is preferred to another if and only if it has larger expected utility for all probabilities in this set when preferences are complete this set is a singleton and the model reduces to standard expected utility in this setting we characterize pareto optima and equilibria and show that the presence of uncertainty generates robust indeterminacies in equilibrium prices and allocations for any specification of initial endowments we derive comparative statics results linking the degree of uncertainty with changes in equilibria despite the presence of robust indeterminacies we show that equilibrium prices and allocations vary continuously with underlying fundamentals equilibria in a standard risk economy are thus robust to adding small degrees of uncertainty finally we give conditions under which some assets are not traded due to uncertainty aversion

non additive beliefs and strategic equilibria abstract this paper studies n player games where players beliefs about their opponents behaviour are modelled as non additive probabilities the concept of an equilibrium under uncertainty which is introduced in this paper extends the equilibrium notion of dow and werlang 1994 j econom theory 64 305 324 to n player games in strategic form existence of such an equilibrium is demonstrated under usual conditions for low degrees of ambiguity equilibria under uncertainty approximate nash equilibria at the other extreme with a low degree of confidence maximin equilibria appear finally robustness against a lack of confidence may be viewed as a refinement for nash equilibria journal of economic literature classification numbers c72 d81

dynamically consistent beliefs must be bayesian abstract experimental evidence such as the ellsberg paradox contradicts the savage model of decision making under uncertainty since the representation of beliefs underlying preferces by a single probability measure leaves no room for the degree of imprecision in information to affect decisions proceeding axiomatically this paper shows that the existence of a bayesain prior is implied even if savage s sure thing principle is deleted if preferences i are based on beliefs and ii admit dynamically consistent updating in response to new information the result raises questions about the appeal of models of preference that feature a separation of tastes and beliefs journal of economic literature classification number d81

a dynamic ellsberg urn experiment two rationality arguments are used to justify the link between conditional and unconditional preferences in decision theory dynamic consistency and consequentialism dynamic consistency requires that ex ante contingent choices are respected by updated preferences consequentialism states that only those outcomes which are still possible can matter for updated preferences we test the descriptive validity of these rationality arguments with a dynamic version of ellsberg s three color experiment and find that subjects act more often in line with consequentialism than with dynamic consistency

intertemporal price speculation and the optimal current account deficit abstract the paper studies the effects of terms of trade fluctuations in an infinite horizon optimizing model of a small open economy while the current account response to a transitory terms of trade shock is in part explicable by intertemporal smoothing an important additional factor is the effect of anticipated future terms of trade shifts on the ral value of the external debt in terms of the home consumption basket when foreign borrowing is indexed to the import good a temporary worsening of the terms of trade creates the expectation of a decline in the real value of external debt this fall in the relevant real interest rate leads households to increase consumption while export prices are low and to decrease consumption sharply once the terms of trade recover if an adverse price shock is of sufficiently brief duration instantaneous utility will rise initially

attitudes to risk and attitudes to uncertainty experimental evidence in a series of experiments the interactions among individual attitudes towards risk and uncertainty the sign of the outcome domain and the way uncertainty is represented are tested this is done in a unified framework eliciting individual values by means of a second price auction results confirm the presence of the well known fourfold pattern of risk attitude risk aversion for gains and risk seeking for losses at high probability and risk seeking for gains and risk aversion for losses at low probability and show that this pattern can also be extended to uncertainty in the valuation of losses the modal pattern is decreasing risk and uncertainty aversion as the probability of loss increases while increasing risk and uncertainty aversion is observed for gains moreover it is found that the size of reaction to uncertainty does not depend on the outcome domain and that it persists in the face of an incentive compatible mechanism to elicit preferences

ambiguity aversion and incompleteness of financial markets it is widely thought that incomes risks can be shared by trading in financial assets but financial assets typically carry some risk idiosyncratic to them hence disposing incomes risk using financial assets will involve buying into the inherent idiosyncratic risk however standard theory argues that diversification would reduce the inconvenience of idiosyncratic risk to arbitrarily low levels this argument is less robust than what standard theory leads us to believe ambiguity aversion can exacerbate the tension between the two kinds of risks to the point that classes of agents may not want to trade some financial assets thus theoretically the effect of ambiguity aversion on financial markets is to make the risk sharing opportunities offered by financial markets less complete than it would be otherwise

welfare effects of changes in environmental quality under individual uncertainty about use we adapt the theoretical state preference model to value nonmarket public goods under individual uncertainty about use illustrating with an assessment of willingness to pay to prevent acid rain lake damage in the northeast united states individual usage uncertainty is modelled via probabilities of participation in trout fishing changes in environmental quality are valued using a random utility model to explain yes no responses to a contingent valuation question we produce quantitative welfare measures individual fitted and simulated passiveand active use values individual expected consumer surplus option price option value and complete individual willingness topay loci

an exact solution method for binary equilibrium problems with compensation and the power market uplift problem abstract we propose a novel method to find nash equilibria in games with binary decision variables by including compensation payments and incentive compatibility constraints from non cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization or relaxation of integrality conditions the reformulation offers a new approach to obtain and interpret dual variables to binary constraints using the benefit or loss from deviation rather than marginal relaxations the method endogenizes the trade off between overall societal efficiency and compensation payments necessary to align incentives of individual players we provide existence results and conditions under which this problem can be solved as a mixed binary linear program we apply the solution approach to a stylized nodal power market equilibrium problem with binary on off decisions this illustrative example shows that our approach yields an exact solution to the binary nash game with compensation we compare different implementations of actual market rules within our model in particular constraints ensuring non negative profits no loss rule and restrictions on the compensation payments to non dispatched generators we discuss the resulting equilibria in terms of overall welfare efficiency and allocational equity

a theory of subjective compound lotteries abstract we develop a savage type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries our theory permits issue preference that is agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues hence we establish subjective foundations for the anscombe aumann framework and other models with two different types of probabilities we define second order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second order risk which implies issue preference and behavior consistent with the ellsberg paradox

transmission and wind power investment this paper jointly considers wind power investment and transmission reinforcement the proposed model is a mathematical program with equilibrium constraints mpec that seeks to identify the optimal wind projects to be developed and the required network reinforcements under the transmission system operator perspective this mpec seeks to minimize consumer payments and is constrained by investment conditions and the equilibria of the market under different operating conditions an array of subsidies is considered to promote independent wind power investment an example and two case studies illustrate the characteristics of the proposed model

auction choice for ambiguity averse sellers facing strategic uncertainty abstract the robustness of the bayes nash equilibrium prediction for seller revenue in auctions is investigated in a framework of interdependent valuations generated from independent signals seller expected revenue may fall well below the equilibrium prediction even though the individual payoff consequences of suboptimal bidding may be small for each individual bidder this possibility would be relevant to a seller who models strategic uncertainty as ambiguity and who is ambiguity averse in the sense of gilboa and schmeidler it is shown that the second price auction is more exposed than the first price auction to lost revenue from the introduction of bidder behavior with small payoff errors

consumption opportunities and the real value of the external debt abstract developing countries have in the period since the oil shock of 1973 1974 built up large external indebtedness at the same time world inflation has in good part eroded the real value of existing debts but the measurement of the inflation effects on real debt depend critically on which among a number of deflators is selected the deflators proposed in this context have traditionally been export prices import prices or prices in world trade this paper argues that the correct deflator is the domestic consumer price index using the consumer price index as a debt deflator it is readily shown that conventional results in trade theory are recovered in the presence of external indebtedness the income effect of an export price increase is proportional to the level of exports the income effect of an import price increase is proportional to the level of imports real income using a comprehensive income measure is equal to the value of domestic output less the real value of real interest payments on external debt

a theory of anticipated utility abstract a new theory of cardinal utility with an associated set of axioms is presented it is a generalization of the von neumann morgenstern expected utility theory which permits the analysis of phenomena associated with the distortion of subjective probability

renewable energy investments under different support schemes a real options approach abstract this paper adopts a real options approach to analyze investment timing and capacity choice for renewable energy projects under different support schemes the main purpose is to examine investment behavior under the most extensively employed support schemes namely feed in tariffs and renewable energy certificate trading we consider both multiple sources of uncertainty under each support scheme and uncertainty with respect to any change of support scheme and we obtain both analytical when possible and numerical solutions in a nordic case study based on wind power we find that the feed in tariff encourages earlier investment nevertheless as investment has been undertaken renewable energy certificate trading creates incentives for larger projects in our baseline scenario and taking the fixed feed in tariff as a base the revenue required to trigger investments is 61 higher with renewable certificates at the same time investment capacity is 61 higher

evaluating change in objective ambiguous mortality probability valuing reduction in ambiguity size and risk level this article develops a valuation model to evaluate mortality probability changes under objective ambiguity where multiple mortality probabilities are exogenously given we construct the valuation model based on upalpha maxmin expected utility to evaluate the reduction in ambiguity size and risk level as well as estimate the subjects ambiguity attitude our model can bring an interesting policy implication if the subjects are ambiguity averse a reduction in ambiguity size with a constant risk level can increases welfare thus even if risk level cannot be lowered reduction in ambiguity size can also be used as a measure toward increasing welfare our model can empirically estimate this welfare change resulting from the reduction in ambiguity size to demonstrate how our model works we apply it to survey data on a public program that reduces mortality probability in accidents caused by wildlife

uncertainty and measurement error in welfare models for risk changes abstract most welfare models of environmental or mortality risk reductions assume that risks are exogenously determined and known with certainty however a growing body of research suggests that uncertainty about risks can affect choices over risky prospects i present a decision weighted random utility model that decomposes welfare losses into those attributable to an increase in the deterministic component of risk and those attributable to uncertainty about risk i apply the model to an illustrative dataset of subjects perceived mortality risk and willingness to accept the risk of nuclear waste transport i estimate the model using lewbel s 2000 strictly exogenous regressor approach to account for endogeneity bias and measurement error subjects display aversion to both risk and uncertainty about the risk of a transport accident so that increases in either leads to social welfare losses roughly 12 of the external cost of nuclear waste transport is attributable to the public s uncertainty about transport risk

market power in renewable portfolio standards abstract renewable portfolio standard rps which requires a certain percentage of electricity production from renewables has received considerable attention one emerging issue is the possibility of strategic behavior in the renewable energy certificate credit rec market and its spillover effects on the electricity market this paper develops dominant firm competitive fringe models that account for market power we show that market power could have significant impacts on the rec and power prices in particular when a nonrenewable generator is a dominant firm and a renewable generator is a competitive fringe the nonrenewable firm has a strong incentive to lower the rec price even to zero for avoiding rec costs the zero rec price would negate price impacts in the power market thereby mitigating market power of the dominant firm however this could lead to an underinvestment in renewables in the long run as subsidies received by renewables in form of recs vanish therefore regulatory agencies need to carefully oversee the market performance to ensure a healthy development of renewable industries under the rps policies

does renewable energy generation decrease the volatility of electricity prices an analysis of denmark and germany although variable renewable energy vre technologies with zero marginal costs decrease electricity prices the literature is inconclusive about how the resulting shift in the supply curves impacts price volatility because the flexibility to respond to high peak and low off peak prices is crucial for demand response applications and may compensate for the losses of conventional generators caused by lower average prices there is a need to understand how the penetration of vre affects volatility in this paper we build distributed lag models with danish and german data to estimate the impact of vre generation on electricity price volatility we find that in denmark wind power decreases the daily volatility of prices by flattening the hourly price profile but in germany it increases the volatility because it has a stronger impact on off peak prices our analysis suggests that access to flexible generation capacity and wind power generation patterns contribute to these differing impacts meanwhile solar power decreases price volatility in germany by contrast the weekly volatility of prices increases in both areas due to the intermittency of vre thus policy measures for facilitating the integration of vre should be tailored to such region specific patterns

nash equilibrium under knightian uncertainty breaking down backward induction abstract we define nash equilibrium for two person normal form games in the presence of knightian uncertainty using the formalization of schmeidler and gilboa we show that nash equilibrium exists for any degree of uncertainty aversion that maxmin behaviour can occur even when it is not rationalizable in the usual sense and that backward induction breaks down in the twice repeated prisoners dilemma we relate these results to the literature on cooperation in the finitely repeated prisoners dilemma and the literature on epistemological conditions underlying nash equilibrium the knowledge notion implicit in this model of equilibrium does not display logical omniscience journal of economic literature classification numbers c72 d81

preference reversals for ambiguity aversion this paper finds preference reversals in measurements of ambiguity aversion even if psychological and informational circumstances are kept constant the reversals are of a fundamentally different nature than the reversals found before because they cannot be explained by context dependent weightings of attributes we offer an explanation based on sugden s random reference theory with different elicitation methods generating different random reference points then measurements of ambiguity aversion that use willingness to pay are confounded by loss aversion and hence overestimate ambiguity aversion this paper was accepted by teck ho decision analysis

decision theory under ambiguity we review recent advances in the field of decision making under uncertainty or ambiguity we start with a presentation of the general approach to a decision problem under uncertainty as well as the standard bayesian treatment and issues with this treatment we present more general approaches choquet expected utility maximin expected utility smooth ambiguity and so forth that have been developed in the literature under the name of models of ambiguity sensitive preferences we draw a distinction between fully subjective models and models incorporating explicitly some information we review definitions and characterizations of ambiguity aversion in these models we mention the challenges posed by some of the models presented we end with a review of part of the experimental literature and applications of these models to economic settings

sustainable transmission planning in imperfectly competitive electricity industries balancing economic and environmental outcomes abstract we explore the role of a transmission system operator tso that builds a transmission line to accommodate renewable energy in order to lower emissions as required by government policy in contrast to central planning a tso in a deregulated electricity industry can only indirectly influence outcomes through its choice of the transmission line capacity via a bi level model we show that this results in less transmission capacity and with limited emissions control in a perfectly competitive industry vis a vis a benchmark centrally planned system a carbon charge on industry that fully accounts for the cost of pollution damage leads to a perfect alignment of incentives and maximised social welfare only under perfect competition by contrast a carbon charge may actually lower social welfare under a cournot oligopoly as the resulting reduction in consumption facilitates the further exercise of market power

subjective beliefs and ex ante trade we study a definition of subjective beliefs applicable to preferences that allow for the perception of ambiguity and provide a characterization of such beliefs in terms of market behavior using this definition we derive necessary and sufficient conditions for the efficiency of ex ante trade and show that these conditions follow from the fundamental welfare theorems when aggregate uncertainty is absent our results show that full insurance is efficient if and only if agents share some common subjective beliefs our results hold for a general class of convex preferences which contains many functional forms used in applications involving ambiguity and ambiguity aversion we show how our results can be articulated in the language of these functional forms confirming results existing in the literature generating new results and providing a useful tool for applications

international capital markets oil producers and the green paradox a rapidly rising carbon tax leads to faster extraction of fossil fuels and accelerates global warming we analyze how general equilibrium effects operating through the international capital market affect this green paradox in a two region two period world with identical homothetic preferences and without investment the global interest rate falls and the green paradox weakens with investment or a relatively more impatient oil importing region the green paradox may be strengthened because the future oil demand function shifts downward or because the interest rate rises if the oil importing region is very much more patient than the oil exporting region the green paradox may be reversed but in our calibrated model the effects are tiny with exploration and endogenous initial oil reserves a future carbon tax lowers cumulative oil extraction in partial equilibrium if the boost to current oil extraction is weakened strengthened or reversed in general equilibrium so is the fall in cumulative extraction a partial and general equilibrium welfare analysis of a future carbon tax both for full and partial exhaustion is given the effects of stock dependent extraction costs are separately discussed in an appendix

do generation firms in restructured electricity markets have incentives to support social welfare improving transmission investments this paper examines the incentives that generation firms have in restructured electricity markets for supporting long term transmission investments in particular we study whether generation firms which arguably play a dominant role in the restructured electricity markets have the incentives to fund or support incremental social welfare improving transmission investments we examine this question in a two node network and explore how such incentives are affected by the ownership of financial transmission rights ftrs by generation firms in the analyzed two node network we show both i that the net exporter generation firm has the correct incentives to increase the transmission capacity incrementally up to a certain level and ii that although a policy that allocates ftrs to the net exporter generation firm can be desirable from a social point of view such a policy would dilute the net importer generation firm s incentives to support transmission expansion moreover if all ftrs were allocated or auctioned off to the net exporter generation firm then it is possible to increase both consumer surplus and social welfare while keeping the net exporter generation firm revenue neutral

a definition of uncertainty aversion a definition of uncertainty or ambiguity aversion is proposed it is argued that the definition is well suited to modelling within the savage as opposed to anscombe and aumann domain of acts the defined property of uncertainty aversion has intuitive empirical content behaves well in specific models of preference multiple priors and choquet expected utility and is tractable tractability is established through use of a novel notion of differentiability for utility functions called eventwise differentiability

evaluating the effect of alternative risk communication devices on willingness to pay results from a dichotomous choice contingent valuation experiment two versions of a contingent valuation questionnaire that differ only in the device used to communicate risks from hazardous waste were sent to california households both risk communication devices provide wtp functions which vary in a statistically significant fashion with the absolute risk reduction however these empirical results also demonstrate that different risk communication devices produce statistically different logit equations and hence estimates of willingness to pay wtp for reductions in exposure to hazardous waste the pros and cons of using each risk communication device in cvm surveys is also discussed

linear complementarity models of nash cournot competition in bilateral and poolco power markets two cournot models of imperfect competition among electricity producers are formulated as mixed linear complementarity problems lcps and a simple example is presented to illustrate their application the two models simulate bilateral markets the models include a congestion pricing scheme for transmission but other transmission pricing approaches can also be represented in this framework the two models differ from each other in that one has no arbitrage between nodes of the network while in the other model arbitragers erase any noncost based differences in price the latter bilateral model turns out to be equivalent to a cournot model of a poolco the models differ from other cournot market models in that they include both of kirchhoff s laws via a dc approximation can include arbitragers possess unique solutions and are readily solved by efficient lcp algorithms the key assumption that permits their formulation as lcps is that each producer naively assumes that its output will not affect transmission prices