Finding a Nash equilibrium in spatial games is an NP-complete problem

Summary. We consider the class of (finite) spatial games. We show that the problem of determining whether there exists a Nash equilibrium in which each player has a payoff of at least k is NP-complete as a function of the number of players.Received: 15 September 2002, Revised: 9 March 2003, JEL Classification Numbers: C72.Correspondence to: H. HallerWe thank a referee for helpful comments. The hospitality of the Institute of Economics, University of Copenhagen, and the Institute for Advanced Studies, Vienna, is gratefully acknowledged by the third author.     

Does Increased Extraction of Natural Gas Reduce Carbon Emissions?

Without an international climate agreement, extraction of more natural gas could reduce emissions of CO₂ as more clean natural gas may drive out dirty coal and oil. Using a computable equilibrium model for the Western European electricity and natural gas markets, we examine whether increased extraction of natural gas in Norway reduces global emissions of CO₂. We find that both in the short run and in the long run total emissions are reduced if the additional quantity of natural gas is used in gas power production in Norway. If instead the additional quantity is exported directly, total emissions increase both in the short run and in the long run. However, if modest CO₂-taxes are imposed, increased extraction of natural gas will reduce CO₂ emissions also when the additional natural gas is exported directed.earlier version of this paper was presented at the 25th Annual IAEE International Conference in Aberdeen June 2002.     

Sequencing and the Adding-up Property in Contingent Valuation of Endangered Species: Are Contingent Non-Use Values Economic Values?

This paper presents tests of the theoretical validity of the contingent valuation (CV) method. The validity of CV is especially a concern when involving environmental goods with a predominant non-use value. One test of theoretical validity is the adding-up property that implies that a specific good should be equally valued irrespectively of it is being valued directly or built-up sequentially. In this CV study four independent sub-samples stated willingness to pay for the same composite good, or package, using different sequences. One sub-sample valued the composite good directly, while two sub-samples faced built-up sequences valuing first subsets of this composite good. A fourth sub-sample valued the composite good from a dividing-out approach, facing first the valuation of a larger multi-package. Theoretically expected sequencing effects were observed; the subset goods obtained higher values earlier in a sequence, and the dividing-out approach decreased the stated value for the composite good. Most importantly, these CV data did pass the tests of the adding-up property.     

Distribution Dynamics of CO<Subscript>2</Subscript> Emissions

This paper uses nonparametric methods to examine the convergence in CO₂ emissions per capita on a sample of 100 countries for the period 1966–1996. Industrial countries show a convergence pattern. However, there is little evidence of convergence for the whole sample.     

Joseph A. Schumpeter’s contributions in the area of fiscal sociology: a first approximation

Fiscal sociology deals with the ramifications of the fiscal activities of the state into areas which are not their primary target. These effects may occur in sectors not directly affected such as related markets, but they may also occur outside the economic sphere proper, such as in politics, culture, religion, or society at large. Schumpeter contributed to the research project of fiscal sociology throughout his life. In this first approximation, his contribution is discussed in terms of his appreciation of three important scholars who all made landmark contributions to fiscal sociology: Franz Oppenheimer, Werner Sombart, and Gustav (von) Schmoller.JEL Classification: B15, H39     

Double Dividend with Involuntary Unemployment: Efficiency and Intergenerational Equity

This paper analyzes the double dividend and distributional issues within an overlapping generations model framework with involuntary unemployment. We characterize the necessary conditions needed to obtain a double dividend, when the revenue of the environmental tax is recycled by a variation of the labor tax rate. We show that an employment dividend may occur without any efficiency dividend and that the young generation is not always harmed by the fiscal reform, even without any intergenerational transfers. Therefore, three dividends (environmental, efficiency and intergenerational equity) can occur simultaneously.     

Pricing-to-market tests in instrumental regressions: Case of the transportation equipment industry

Pricing-to-market (PTM) theory suggests that exporting monopolistic firms adjust their destination-specific mark-ups in the face of exchange rate shocks. A large proportion of the existing evidence for PTM comes from Wald tests applied to OLS- and IV-estimated parameters of single-equation models. Such tests can seriously over-reject in the presence of endogeneity and weak instruments so that some of the available results supporting PTM could be spurious. In this paper we revisit the PTM evidence for Japanese and German exporting firms in the transportation equipment industry. Using the model of Marston (1990), we apply exogeneity and LR-LIML-based tests for which the error probability is controlled irrespective of the quality of the available instruments. Our results show right-hand-side endogeneity in almost all of the examined PTM equations. In addition, we find that statistical decisions often differ depending on whether they are based on the traditional Wald test or on our proposed test.The authors would like to thank Philippe Barla, Jean-Thomas Bernard, Christos Constantatos, Larry Schembri, seminar participants at the Bank of Canada, and two anonymous referees for useful comments and suggestions. Thanks also to Richard Marston for providing data. Finally, a special thanks to Marjorie Santos for excellent research assistance. All remaining errors are our own and should not be attributed to the Bank of Canada.First version received: May 2002/Final version received: December 2002     

Art as an investment: Short and long-term comovements in major painting markets

This paper examines the short and long-term price linkages among major art and equity markets over the period 1976–2001. The art markets examined are Contemporary Masters, French Impressionists, Modern European, 19^th Century European, Old Masters, Surrealists, 20^th Century English and Modern US paintings. A global equity index (with dividends and capitalisation changes) is also included. Multivariate cointegration procedures, Granger non-causality tests, level VAR and generalised variance decomposition analyses based on error-correction and vector autoregressive models are conducted to analyse short and long-run relationships among these markets. The results indicate that there is a stationary long-run relationship and significant short and long run causal linkages between the various painting markets and between the equity market and painting markets. However, in terms of the percentage of variance explained most painting markets are relatively isolated, and other painting markets are generally more important than the equity market in explaining the variance that is not caused by innovations in the market itself. This suggests that opportunities for portfolio diversification in art works alone and in conjunction with equity markets exist, though in common with the literature in this area the study finds that the returns on paintings are much lower and the risks much higher than in conventional financial markets.The authors would like to thank delegates to the 14th Australasian Finance and Banking Conference, University of New South Wales, seminar participants at the Queensland University of Technology and Massey University, Masaki Katsuura, and two anonymous referees for helpful comments on earlier versions of this paper. The financial assistance of a Queensland University of Technology, Faculty of Business Research Initiative Grant is also gratefully acknowledged.     

Commodity price cycles and heterogeneous speculators: a STAR–GARCH model

We propose an empirical commodity market model with heterogeneous speculators. While the power of trend-extrapolating chartists is constant over time, the symmetric impact of stabilizing fundamentalists adjusts endogenously according to market circumstances: Using monthly data for various commodities such as cotton, sugar or zinc, our STAR–GARCH model indicates that their influence positively depends on the distance between the commodity price and its long-run equilibrium value. Fundamentalists seem to become more and more convinced that mean reversion will set in as the mispricing enlarges. Commodity price cycles may thus emerge due to the nonlinear interplay between different trader types. The paper represents the authors’ personal opinion and does not necessarily reflect the views of the Deutsche Bundesbank.