On the inconsistency of certain axioms on solution concepts for non-cooperative games

The mutual compatibility of four recently discussed axioms on solution concepts for extensive form games is explored. Two subsets of the axioms are shown to be inconsistent. Our results underline the importance of the information lost in moving from the extensive form to the normal (or agent-normal) form of a game.     

A note on the “size” of determinacy and indeterminacy

Summary. It is shown in this note that in an incomplete markets economy with uncountably many states of the world there may be uncountably many isolated equilibria as well as uncountably many non-isolated equilibria. Moreover, both subsets can be simultaneously of second category. Therefore, none of the subsets can be considered negligible with respect to the other, neither from a cardinality point of view nor from a topological one. Unfortunately, this fact prevents from claiming that these economies may have “typically” determinate equilibria – even though uncountably many of them – as would have been desirable for comparative statics exercises. Received: May 19, 1995; revised version: March 24, 1997     

V-Branch: A generalized utility function

Much of the work in demand theory is restricted by the functional form of the relationship The S-Branch utility function, which is a generalization of the linear expenditure system, corrects many of the restrictions. Many faults, however, still exist. The Allen partial elasticities of substitution are equal and constant for all commodities from different subsets of the function. The V-Branch utility function corrects many of these faults. The Allen partial elasticities of substitution are not restricted to be constant or equal either within or between commodity subsets. They vary according to the amount consumed of each commodity.     

Global stability condition on the plane: A general law of demand

It is well known that global stability of competitive equilibrium obtains only under quite stringent restrictions. This paper identifies a set of restrictions which may be interpreted as a very weak form of the so-called Law of Demand and shows how this may imply global stability for motion on the plane. It is also of some interest that this condition is satisfied by a perturbed version of the celebrated Scarf example which does not satisfy existing conditions for global stability.     

The role of fiscal policy in Britain's Great Inflation

We investigate whether the Fiscal Theory of the Price Level (FTPL) can explain UK inflation in the 1970s. We confront the identification problem involved by setting up the FTPL as a structural model for the episode and pitting it against an alternative Orthodox model; the models have a reduced form that is common in form but, because each model is over-identified, numerically distinct. We use indirect inference to test which model could be generating the VECM approximation to the reduced form that we estimate on the data for the episode. Neither model is rejected, though the FTPL model substantially outperforms the Orthodox. But by far the best account of the period assumes that expectations were a probability-weighted combination of the two regimes. Fiscal policy has a substantial role in this weighted model in determining inflation. A similar model accounts for the 1980s but this role of fiscal policy is much diminished.     

Edgeworth's conjecture with infinitely many commodities: commodity differentiation

Summary. Convergence of the cores of finite economies to the set of Walrasian allocations as the number of agents grows has long been taken as one of the basic tests of perfect competition. The present paper examines this test in the most natural model of commodity differentiation: the commodity space is the space of nonnegative measures, endowed with the topology of weak convergence. In Anderson and Zame [12], we gave counterexamples to core convergence in L ¹, a space in which core convergence holds for replica economies and core equivalence holds for continuum economies; in addition, we gave a core convergence theorem under the assumption that traders' utility functions exhibit uniformly vanishing marginal utility at infinity. In this paper, we provide two core convergence results for the commodity differentiation model. A key technical virtue of this space is that relatively large sets (in particular, closed norm-bounded sets) are compact. This permits us to invoke a version of the Shapley-Folkman Theorem for compact subsets of an infinite-dimensional space. We show that, for sufficiently large economies in which endowments come from a norm bounded set, preferences satisfy an equidesirability condition, and either (i) preferences exhibit uniformly bounded marginal rates of substitution or (ii) endowments come from an order-bounded set, core allocations can be approximately decentralized by prices. Received: July 29, 1996; revised version: January 14, 1997     

The pricing of protected areas in nature-based tourism: A local perspective

This paper extends the literature on optimal pricing of recreation in protected areas by introducing price discrimination between groups of visitors and, given that the agency charges different prices to subsets of visitors, by including a distributional dimension that is particularly relevant for a national park agency receiving visitors from different origins. Other issues related to optimal entrance fees, including negative ecological impacts and positive spillover effects on local communities resulting from changes in visitation, are also discussed. Based on this model, the paper provides an estimation of optimal entrance fees and revenues for the Costa Rican system of protected areas.     

Between cointegration and multicointegration: Modelling time series dynamics by cumulative error correction models

This study proposes a cumulative error correction model where the summing weights follow a geometrically decreasing function of prior deviations from the equilibrium and are estimated from the data. It is shown that this approach nests both the traditional error correction model – where no weight is given to deviations from the steady state prior to the most recent period – and the error correction model based on the idea of multicointegration.The form of accumulation presented here does not change the order of integration of the series, as is the case in the multicointegration approach of Granger and Lee (1989). Furthermore, it is very parsimonious as only one or two parameters more have to be estimated. The assumption of geometrically decreasing weights can be tested by estimating the model in its unrestricted form.Based on this new model type, the relationship between private consumption and real disposable income of private households in the US is estimated. The short-term forces which set off the most recent period's deviations are much smaller than would be suggested by a VEC and a conventional single equation ECM, and the income elasticity is lower as well. The proposed model outperforms the other two with respect to its forecasting power.     

Nearly compact and continuous normal form games: characterizations and equilibrium existence

Normal form games are nearly compact and continuous (NCC) if they can be understood as games played on strategy spaces that are dense subsets of the strategy spaces of larger compact games with jointly continuous payoffs. There are intrinsic algebraic, measure theoretic, functional analysis, and finite approximability characterizations of NCC games. NCC games have finitely additive equilibria, and all their finitely additive equilibria are equivalent to countably additive equilibria on metric compactifications. The equilibrium set of an NCC game depends upper hemicontinuously on the specification of the game and contains only the limits of approximate equilibria of approximate games.     

Global sunspots in OLG models: Theory and computational analysis

This paper discusses sunspots equilibria in a context that is general in the sense that: (i) the evolution of the system takes place in a general state space (i.e., a space which is not necessarily finite or even countable); and (ii) the orbits of the unperturbed, deterministic component of the system converge to subsets of the state space which can be more complicated than a stationary state or a periodic orbit, i.e., they can be aperiodic or chaotic. This problem is represented mathematically as a system of stochastic difference equations the invariant probability distributions of which correspond to stationary sunspots equilibria. The conditions for stochastic stability are recalled and the theoretical results are applied to a model of overlapping generations with individuals living three periods. A computational analysis of this model is provided, covering the basic different cases suggested by the theory.     

SCREENING FOMC MEMBERS FOR THEIR BIASES AND DEPENDABILITY

This paper develops conjectures regarding the process by which the President as a principal selects Federal Reserve Governors and Bank Presidents as his agents on the Federal Open Market Committee (FOMC). It first establishes that FOMC members can be grouped into sets which are marked by ease and tightness biases in voting behavior. It then identifies certain career characteristics of FOMC members which are correlated with each of these biases. The paper goes on to isolate reliable partisan subsets within the ease and tightness sets and identifies a career characteristic which is highly correlated with membership in these subsets; that characteristic is a career as an economist.     

Exploring causal relationships in an innovation program with Robust Portfolio Modeling

Many countries seek to foster the commercial exploitation of science-based research results through selective policy instruments. Typically, these instruments involve processes of follow-up data collection where the results of ex ante and ex post assessments are systematically recorded. Yet, several factors – such as the presence of multiple objectives, predominance of qualitative data and missing observations – may complicate the use of such data for adjusting the management practices of these instruments. With the aim of addressing these challenges, we adopt Robust Portfolio Modeling¹ (RPM) as an evaluation framework to the analysis of longitudinal data: specifically, we (i) determine subsets of outperforming and underperforming projects through the development of an explicit multicriteria model for ex post evaluation, and (ii) carry out comparative analyses between these subsets, in order to identify which ex ante interventions and contextual characteristics may have contributed to later performance. We also report experiences from the application of RPM-evaluation to a Finnish innovation program and outline extensions of this approach that provide further decision support to the managers of innovation programs.     

A simple model for study of the determination of the price level and the interaction of monetary and fiscal policy

Summary A representative-agent model with money holdings motivated by transactions costs, a fiscal authority that taxes and issues debt, no production, and a convenient functional form for agents' utility is presented. The model can be solved analytically, and illustrates the dependence of price determination on fiscal policy, the possibility of indeterminacy, even stochastic explosion, of the price level in the face of a monetary policy that holdsM fixed, and the possibility of a unique, stable price level in the face of a monetary policy that simply pegs the nominal interest rate at an arbitrary level.In a rational expectations, market-clearing equilibrium model with a costlessly-produced fiat money that is useful in transactions, the following things are true under broad assumptions.- A monetary policy that fixes the money stock may (depending on the transactions technology) be consistent with indeterminacy of the price level—indeed with stochastically fluctuating, explosive inflation.- A monetary policy that fixes the nominal interest rate, even if it holds the interest rate constant regardless of the observed rate of inflation or money growth rate, may deliver a uniquely determined price level.- The existence and uniqueness of the equilibrium price level cannot be determined from knowledge of monetary policy alone; fiscal policy plays an equally important role. Special case models with interest-bearing debt and no money are possible, just as are special cases with money and no interest-bearing debt. In each the price level may be uniquely determined.Determinacy of the price level under any policy depends on the public's beliefs about what the policy authority would do under conditions that are never observed in equilibrium.These points are not new. Eric Leeper [1991] has made most of them within a single coherent model. Woodford [1993], in a representative agent cash-in-advance model, has displayed the possibility of indeterminacy with a fixed quantity of money and the possibility of uniqueness with an interest-rate pegging policy. Aiyagari and Gertler [1985] use an overlapping generations model to make many of the points made in this paper, without discussing the possibility of stochastic sunspot equilibria. Sargent and Wallace [1981] and Obstfeld [1983] have also discussed related issues.This paper improves on Leeper by moving beyond his analysis of local linear approximations to the full model solution, as is essential if explosive sunspot equilibria are to be distinguished from explosive solutions to the Euler equations that can be ruled out as equilibria. It improves on the other cited work by pulling together into the context of one fairly transparent model discussion of phenomena previously discussed in isolation in very different models.We study a representative agent model in which there is no production or real savings, but transactions costs generate a demand for money. The government costlessly provides fiat money balances, imposes lump-sum taxes, and issues debt, but has no other role in the economy. We make restrictive assumptions about the form of the utility function and the form of a transactions cost term in the budget constraint.The model could be extended to include production, capital accumulation, non-neutral taxation, productive government expenditure, and a more general utility function without affecting the conclusions discussed in this paper. Indeed the model I informally matched to data in an earlier paper [1988] makes some such extensions. While such an extended model is more realistic, it is harder to solve. The version in my earlier paper [1988] was solved numerically and simulated. The bare-bones model of this paper allows an explicit analytic solution that may make its results easier to understand.This paper improved following comments from participants at seminars at Yale and the Atlanta Federal Reserve Bank. Eric Leeper and James Robinson were particularly helpful. Comments from Michael Woodford led to important corrections and clarifications.     

A Dynamic Analysis of the Market for Wide-Bodied Commercial Aircraft

This paper uses an empirical dynamic oligopoly model of the commercial aircraft industry to analyse industry pricing, industry performance, and optimal industry policy. A novel feature of the model with respect to the previous literature is that entry, exit, prices, and quantities are endogenously determined in Markov perfect equilibrium (MPE). We find that many unusual aspects of the aircraft data, such as high concentration and persistent pricing below static marginal cost, are explained by this model. We also find that the unconstrained MPE is quite efficient from a social perspective, providing only 10% less welfare on average than a social planner would obtain. Finally, we provide simulation evidence that an anti-trust policy in the form of a concentration restriction would be welfare reducing.     

Proof of the law of diminishing returns

Based on a general mathematical model of a technology, implying certain properties for the production function, weak and strong forms of a physical law of diminishing returns are derived. It is also shown that the classical forms of this law hold if the technology is homogeneous (degree one) and the production possibility sets of the technology are strictly convex, but the latter property violates an essential property of a technology, namely that these sets have bounded efficient subsets.Dedicated to my friend Oskar Morgenstern who called this issue to my attention and urged me to work on it.     

Biased Technical Change and the Aggregate Production Function

This paper offers a classical model of biased technical change in the MarxRicardo tradition as a framework for theoretical and applied studies of growth. The observable data it generates would appear to an unsuspecting economist to be well-described by a neoclassical model with a static Cobb-Douglas production function, when in fact this production function describes only the technological history of the economy. The CobbDouglas form results from the capital-using, labour-saving bias of technical change. The model's trajectory in wage-profit space will lie along the displaced image of the neoclassical factor price frontier, in contradiction to marginal productivity theory. The Solow residual can be reinterpreted by the classical theory as a measure of the size of this displacement.     

On the location of public bads: strategy-proofness under two-dimensional single-dipped preferences

In a model with finitely many agents who have single-dipped Euclidean preferences on a polytope in the Euclidean plane, a rule assigns to each profile of reported dips a point of the polytope. A point $x$ of the polytope is called single-best if there is a point $y$ of the polytope such that $x$ is the unique point of the polytope at maximal distance from $y$ . It is proved that if the polytope does not have either exactly two single-best points or exactly four single-best points which form the vertices of a rectangle, then any Pareto optimal and strategy-proof rule is dictatorial. If the polytope has exactly two single-best points, then there are non-dictatorial strategy-proof and Pareto optimal rules, which can be described by committee voting (simple games) between the two single-best points. This also holds if there are exactly four single-best points which form the vertices of a rectangle, but in that case, we limit ourselves to describing an example of such a rule. The framework under consideration models situations where public bads such as garbage dumping grounds or nuclear plants have to be located within a confined region.     

Cost-Padding in Profit-Regulated Firms*

When entry into an industry is restricted, economic regulation of that industry is often directed at preventing existing firms from monopoly pricing behaviour. One form of such regulation is to set prices so as to control the level of profits earned by these firms. This paper briefly reviews the relevant economic literature and presents a model of the regulated firm in which such price-setting procedures provide an incentive to inflate costs above minimum levels. The welfare cost of this form of regulation can then exceed that occurring at the unconstrained monopoly outcome. The setting of air fares under the Two-Airline Policy and the regulation of natural gas in NSW are discussed in the context of this analysis.     

An Extended Analytical Approach to Credit Risk Management

Among the 'reduced form models' for measuring the credit risk of a bank's portfolio is CreditRisk+, which provides a closed–form solution for calculating the portfolio loss distribution based on an actuarial approach. The limitations of this model are well known, but they are often misinterpreted as being deeply embedded within the model. Dismantling the mathematical components of the model allows one to modify and extend it in several ways while remaining within an analytical approach. One of the most unattractive features is the orthogonality of the background factors or sectors as it hinders any resemblance to real–world macroeconomic indexes or industrial sectors and geographical areas. Among other extensions, which we mention briefly, we present in more detail how the original model can be amended to consider correlations among default risk sectors and among severity risk segments. These extensions are applied to real–life data, based on mortality rate data produced by the Italian Central Bank.
(J.E.L.: C00, C51).