A quantile approach to US GNP

In this paper we fitted a quantile self-exciting threshold autoregressive (QSETAR) time series model to the growth rate of real US GNP. We also presented a forecasting method for QSETAR models. This forecasting method makes it possible to obtain the predictive quantiles and predictive distribution function of x_t+m given x_t for m > 0, and hence any quantities of interest can be derived. Therefore, this new approach allows us to study the US GNP from a distribution point view, rather than from a mean point of view. The results obtained in this paper show that the method works very well in practice.     

A game of timing and visibility

We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x_i in the interval [0,1], and a player's payoff is the distance from its point x_i to the next larger point, or to 1 if x_i is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games.     

Estimation of the value of the marginal product of emission in a country where emissions output is regulated — an empirical study

Emissions resulting from the production process can be characterized as use of the elimination and disposal services of the ecological system. Hence, they are use of natural resources and thus an input to production. The present paper discusses an approach to evaluate the returns of these kind of services as a production factor.First, four main types of industrial emission are chosen —SO ₂,CO ₂,NO _xandparticulate matter — and integrated in a Cobb-Douglas production function. With this approach, the production elasticities and the marginal product of these types of emission can be estimated.Based on these results and assuming that marginal product equals price, the demand curve for emission is estimated. With this demand curve the consequences of different kinds of environmental policy are considered. Under further assumptions of optimal behaviour it can be shown that the demand curve for emission is equal to the curve of marginal costs of avoidance (MCA). Thus, the estimates of the demand curves can be considered as estimates of the MCA-curves. Furthermore the price elasticities of these four types of emission are estimated with this approach. The method used in the paper is suggested for calibration of CGE models.     

The Chamberlin and Stackelberg Duopoly Relation*

The paper investigates and identifies an important relationship between the Chamberlin and Stackelberg duopoly models. Under conditions of symmetry, linear demand and constant costs, the two iso-profit curves identifying the Stackelberg leadership points are shown to be tangent at the Chamberlin point. Under these conditions profit-maximising duopolists are indifferent to being Stackelberg output leaders and coalescing in an equal-shares-joint-monopoly solution. This result is shown to be sensitive to the constant cost and linear assumptions. Under increasing linear marginal costs, the joint monopoly solution is preferred by both sellers to a leader-follower solution.     

Min, Max, and Sum

This paper provides characterization theorems for preferences that can be represented by U(x₁, …, x_n)=min{x_k}, U(x₁, …, x_n)=max{x_k}, U(x₁, …, x_n)=∑ u(x_k), or combinations of these functionals. The main assumption is partial separability, where changing a common component of two vectors does not reverse strict preferences, but may turn strict preferences into indifference. We discuss applications of our results to social choice. Journal of Economic Literature Classification Numbers: C0, D1, D6.     

Convergence and approximation results for non-cooperative Bayesian games: Learning theorems

Summary LetT denote a continuous time horizon and {G ^t :tT} be a net (generalized sequence) of Bayesian games. We show that: (i) if {x ^t : tT} is a net of Bayesian Nash Equilibrium (BNE) strategies for G^t we can extract a subsequence which converges to a limit full information BNE strategy for a one shot limit full information Bayesian game, (ii) If {x ^t : tT} is a net of approximate or _t-BNE strategies for the game G^t we can still extract a subsequence which converges to the one shot limit full information equilibrium BNE strategy, (iii) Given a limit full information BNE strategy of a one shot limit full information Bayesian game, we can find a net of _t-BNE strategies {x ^t : tT} in {G ^t :tT} which converges to the limit full information BNE strategy of the one shot game.We wish to thank Larry Blume, Mark Feldman, Jim Jordan, Charlie Kahn, Stefan Krasa, Gregory Michalopoulos, Wayne Shafer, Bart Taub, and Anne Villamil for several useful discussions. The financial support of the University of Illinois at Urbana-Champaign Campus Research Board is gratefully acknowledged.     

Forecasting the Forecasts of Others in the Frequency Domain

This paper studies a class of models developed by R. M. Townsend (1983, J. Polit. Econ.91, 546–588) and T. J. Sargent (1991, J. Econom. Dynam. Control15, 245–273). These models feature dynamic signal extraction problems and an infinite regress in expectations. This paper uses frequency domain methods to compute an analytical solution to the fixed point problem posed by the infinite regress in expectations. The advantage of a frequency domain approach vis-à-vis a time domain approach derives from the fact that these models produce equilibria with non-fundamental moving average representations, in which market observations do not reveal the underlying shocks to agents' information sets. As a result, decision rules contain moving average components that are more easily handled in the frequency domain than in the time domain.     

Market equilibrium with heterogeneous recursive-utility-maximizing agents

Summary The paper by C. Ma [1] contains several errors. First, statement and proof of Theorem 2.1 on the existence of intertemporal recursive utility function as a unique solution to the Koopmans equation must be amended. Several additional technical conditions concerning the consumption domain, measurability of certainty equivalent and utility process need to be assumed for the validity of the theorem. Second, the assumptions for Theorem 3.1 need to be amended to include the Feller's condition that, for any bounded continuous functionf C(S × ⁿ ₊), (f(S_t+1, )¦s_t =s) is bounded and continuous in (s, ). In addition, for Theorem 3.1, the pricep, the endowmente and the dividend rate as functions of the state variables S are assumed to be continuous.The Feller's condition for Theorem 3.1 is to ensure the value function to be well-defined. This condition needs to be assumed even for the expected additive utility functions (See Lucas [2]). It is noticed that, under this condition, the right hand side of equation (3.5) in [1] defines a bounded continuous function ins and. The proof of Theorem 3.1 remains valid with this remark in place.A correct version of Theorem 2.1 in [1] is stated and proved in this corrigendum. Ozaki and Streufert [3] is the first to cast doubt on the validity of this theorem. They point out correctly that additional conditions to ensure the measurability of the utility process need to be assumed. This condition is identified as conditionCE ₄ below. In addition, I notice that, the consumption space is not suitably defined in [1], especially when a unbounded consumption set is assumed. In contrast to what claimed in [3], I show that the uniformly bounded consumption setX and stationary information structure are not necessary for the validity of Theorem 2.1.I would like to thank Hiroyuki Ozaki and Peter Streufert for pointing out correctly some mistakes made in the original article. Comments and suggestions from an anonymous referee are gratefully appreciated. Financially support from SSHRC of Canada is acknowledged.     

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 .      

An Empirical Examination of the Pollution Haven Hypothesis for India: Towards a Green Leontief Paradox?

Using input–output analysis, we examine whether India can be regarded as a pollution haven. We calculate the extra CO₂, SO₂ and NO _x emissions induced by 1 billion rupees of additional exports. This is compared with the reduction of Indian pollution caused by an import increase of equal size. In contrast to what the pollution haven hypothesis states for developing countries, we find that India considerably gains from extra trade. Comparing 1996/1997 with 1991/1992, the gains have only increased, indicating that India has moved␣further away from being a pollution haven. The outcome is robust to changes in the underlying assumptions.      

Impact of FDI and trade on environmental quality in the CAFTA-DR region

This study investigates the relationship between foreign direct investment (FDI), trade and industrial emissions in member countries of the Central American Free Trade Agreement–Dominican Republic (CAFTA-DR) between 1979 and 2010. Our model is based on extant literature about the Environmental Kuznets’ Curve framework. In this study, we consider sulphur dioxide (SO₂), nitrogen oxides (NO_x) and carbon dioxide (CO₂) as our dependent variables. Our key independent variables are FDI and trade. Our study finds evidence that foreign investment and trade have had a negative impact on our selected emissions. However, our models also estimate turning points which are below the current GDP per capita values for all CAFTA-DR member countries. This is an encouraging trend in terms of the potential reduction in emissions in the region.     

ON THE INTERPRETATION OF COVARIATE ESTIMATES IN INDEPENDENT COMPETING-RISKS MODELS*

Competing-risks models are becoming increasingly pervasive in applied research to explain the factors determining both the time in a state (i.e. unemployment) and the exit route from the state (is. leaving unemployment for a job or non-participation). However, as in many limited dependent variable models, the interpretation of the covariate estimates requires care. Despite assertions to the contrary in many published papers, it is shown that the estimated qualitative effect of a covariate on the hazard for risk j typically conveys no information on its qualitative effect on either the likelihood of, or expected time until, exit via j. This is because such magnitudes depend on the qualitative and quantitative effects of the covariate on other risks which cannot be ignored. The point is demonstrated by using UK data on the unemployment to re-employment transitions of a sample of male job losers.     

Judging quality by price,snob appeal,and the new consumer theory

Conclusion The analysis contained in this paper has served two purposes. First, it has demonstrated the richness of the new consumer theory by showing how this new approach can incorporate the questions of judging quality by price and price-snob appeal. And second, the paper has derived analytically the conditions under which these phenomena will yield a positively sloping demand curve in a two-commodity, two-attribute world.In traditional theory the consumer's response to a change in the price of a good is conceptually divided into an income effect and a substitution effect. The new approach to consumer theory partitions the consumer's response differently, namely, into an efficiency substitution and a utility substitution. When a general price attribute is introduced each of these divisions retains its individual validity. The conclusion that the efficiency substitution is always non-positive also remains valid. But, the traditional substitution effect may now be positive and of sufficient magnitude to make theentire response to an own-price changepositive,x _i /p _i >0. We have shown analytically, then, as the verbal discussions of traditional consumer theory lead us to believe, that judgment of quality by price and price-snob appeal can result in positively sloped demand curves.The research described in this paper was supported in part by the Econometric Research Program at Princeton University. The authors would like to thank Professors W. J. Baumol, O. Morgenstern, and R. E. Quandt, Messrs. F. D. Gately and R. J. Sweeney, and other members of the Seminar on Research in Progress, Department of Economics, Princeton University, for their helpful comments and suggestions. Of course, any errors that may remain are solely our responsibility.     

Axiomatizations of two types of Shapley values for games on union closed systems

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson value for games with limited communication.     

A New Matrix Theorem: Interpretation in Terms of Internal Trade Structure and Implications for Dynamic Systems

Economic systems often are described in matrix form as x = Mx. We present a new theorem for systems of this type where M is square, nonnegative and indecomposable. The theorem discloses the existence of additional economic relations that have not been discussed in the literature up to now, and gives further insight in the economic processes described by these systems. As examples of the relevance of the theorem we focus on static and dynamic closed Input-Output (I-O) models. We show that the theorem is directly relevant for I-O models formulated in terms of difference or differential equations. In the special case of the dynamic Leontief model the systems behavior is shown to depend on the properties of matrix M = A + C where A and C are the matrices of intermediate and capital coefficients, respectively. In this case, C is small relative to A and a perturbation result can be employed which leads directly to a statement on the systems eigenvalues. This immediately suggests a solution to the well-known problem of the instability of the dynamic Leontief model.     

Health care utilization and self-assessed health: specification of bivariate models using copulas

The discernment of relevant factors driving health care utilization constitutes one important research topic in health economics. This issue is frequently addressed through specification of regression models for health care use (y—often measured by number of doctor visits) including, among other covariates, a measure of self-assessed health (sah). However, the exogeneity of sah within those models has been questioned, due to the possible presence of unobservables influencing both y and sah, and because individuals’ health assessments may depend on the quantity of medical care received. This article addresses the possible simultaneity of (sah, y) by adopting a full information approach, through specification of the bivariate probability function (p.f.) of these discrete variables, conditional on a set of exogenous covariates (x). The approach is implemented with copula functions, which afford separate consideration of each variable margin and their dependence structure. The specification of the joint p.f. of (sah, y) enables estimation of several quantities of potential economic interest, namely features of the conditional p.f. of y given sah and x. The adopted models are estimated through maximum likelihood, with cross-sectional data from the Portuguese National Health Survey of 1998–1999. Estimates of the margins’ parameters do not vary much among different copula models, while, in accordance with theoretical expectations, the dependence parameter is estimated to be negative across the various joint models.     

Remarks on the application of statistical games to technological development forecasting

This work presents the probability of determining a quantitative forecast of technological development S(t) defined by a set m of parameters S⁽¹⁾(t),S⁽²⁾(t),…,S^(m)(t), based on statistical game theory. Assuming that the coordinates S⁽ⁱ⁾(t) (i = 1, 2,…,m) of a forecasted vector S(t) are stochastic processes with given probabilistic characteristics, a formula of a function forecasting the value of a coordinate S⁽ⁱ⁾(t) of this vector can be obtained. This formula permits to determine a vector of forecasts _τT(x) of technological development S(t) at a given moment t = τ+T.     

On a probabilistic model of forecasting

One of the methods of studying complex objects is the construction of a mathematical model, containing such information about the object that is necessary to solve a definite problem connected with it.Mathematical modeling, based on the construction of models of various kinds can be used in forecasting. Let a forecasting object A(X) be described by vector X = (X₁, X₂,…,X_n) whose coordinates are parameters characterizing this object. The work presents a probabilistic model of forecasting and gives the example of a forecast of the object described by a set two parameters.     

BOOTSTRAPPING COVARIATE UNIT ROOT TESTS: AN APPLICATION TO INFLATION RATES

This paper proposes a bootstrap procedure for the covariate point optimal tests (CP_T) of Elliott and Jansson. Although the covariate tests enjoy large power gains over the traditional univariate unit root tests, our simulations show that they still suffer from severe size distortions at finite samples. Through simulations, we demonstrate the superiority of the bootstrap procedure in the sense that it can yield desirable size and power properties for the CP_T tests when the Akaike's information criterion is used. Moreover, we show the empirical relevance of the bootstrap tests by applying them to inflation in the G‐10 countries, and then obtain strong evidence against the unit root hypothesis for most countries at the 5% significance level.     

Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.