Yet another look at temporal aggregation in diffusion models of first-time purchase

This paper gives yet another look at the impact of temporal aggregation on the parameter estimates for the familiar Bass diffusion model. It is shown that aggregation leads to larger values of the innovation parameter p and that it is leads to smaller values of the imitation parameter q, at least in theory. The last finding is in contrast with the results in Technological Forecasting and Social Change [51 (1996) 265]. We use simulation experiments to substantiate our results.     

On the Relative Equitability of a Family of Taxation Rules

A taxation problem consists of collecting a given amount of taxes out of a population whose gross income vector is given. A tax rule R is more equitable than a rule R′ when the after‐tax income vector generated by R Lorenz dominates that generated by R′. In this paper, we present a one‐parameter family of tax rules whose members are fully ranked in terms of relative equitability, for any (finite) income distribution.     

The Envelope Theorem and Comparative Statics of Nash Equilibria

The Envelope Theorem for Nash equilibria shows that the strategic reaction of the other players in the game is important for determining how parameter perturbations affect a given player's indirect objective function. The fundamental comparative statics matrix of Nash equilibria for theithplayer in anN-player static game includes the equilibrium response of the otherN−1players in the game to the parameter perturbation and is symmetric positive semidefinite subject to constraint. This result is fundamental in that it holds for all sufficiently smooth Nash equilibria and is independent of any curvature or stability assumptions imposed on the game.Journal of Economic LiteratureClassification Numbers: C72, C61.     

Fictitious play in games: The transition between periodic and chaotic behaviour

In the 1960s Shapley provided an example of a two-player fictitious game with periodic behaviour. In this game, player A aims to copy B's behaviour and player B aims to play one ahead of player A. In this paper we generalise Shapley's example by introducing an external parameter. We show that the periodic behaviour in Shapley's example at some critical parameter value disintegrates into unpredictable (chaotic) behaviour, with players dithering a huge number of times between different strategies. At a further critical parameter the dynamics becomes periodic again, but now both players aim to play one ahead of the other. In this paper we adopt a geometric (dynamical systems) approach. Here we prove rigorous results on continuity of the dynamics and on the periodic behaviour, while in the sequel to this paper we shall describe the chaotic behaviour.     

On the (non-)lattice structure of the equilibrium set in games with strategic substitutes

This paper studies models where the optimal response functions under consideration are not increasing in endogenous variables, and weakly increasing in exogenous parameters. Such models include games with strategic substitutes, and include cases where additionally, some variables may be strategic complements. The main result here is that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Indeed, for a given parameter value, a pair of distinct equilibria are never comparable. Therefore, with multiple equilibria, some of the established techniques for exhibiting increasing equilibria or computing equilibria that use the largest or smallest equilibrium, or that use the lattice structure of the equilibrium set do not apply to such models. Moreover, there are no ranked equilibria in such models. Additionally, the analysis here implies a new proof and a slight generalization of some existing results. It is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games of strategic substitutes with real-valued action spaces, symmetric equilibria increase with the parameter.)      

Knife-edge conditions in the modeling of long-run growth regularities

Balanced (exponential) growth cannot be generalized to a concept which would not require knife-edge conditions to be imposed on dynamic models. Already the assumption that a solution to a dynamical system (i.e. time path of an economy) satisfies a given functional regularity (e.g. quasi-arithmetic, logistic, etc.) imposes at least one knife-edge assumption on the considered model. Furthermore, it is always possible to find divergent and qualitative changes in dynamic behavior of the model – strong enough to invalidate its long-run predictions – if a certain parameter is infinitesimally manipulated.     

Uncertainty,Learning and Heterogeneity in International Environmental Agreements

This paper concerns the formation of International Environmental Agreements under uncertainty about environmental damage with different models of learning (complete learning, partial learning or no learning). The results of the existing literature are generally pessimistic: the possibility of either complete or partial learning generally reduces the level of global welfare that can be achieved from forming an IEA relative to no learning. That literature regards uncertainty as a parameter common to all countries, so that countries are identical ex ante as well as ex post. In this paper we extend the literature to the case where there is no correlation between damage costs across countries; each country is uncertain about a particular parameter (in our case the benefit-cost ratio) drawn from a common distribution but, ex post, each country’s realized parameter value is independently drawn. Consequently, while countries remain identical ex ante, they may be heterogeneous ex post. We show that this change reinforces the negative conclusions about the effects of partial learning on international environmental agreements, but, under certain conditions, moderates the negative conclusions about the effects of complete learning.     

Growth and equilibrium indeterminacy: the role of capital mobility

Summary. The paper presents a human capital driven endogenous growth model which, in general, permits a multiplicity of equilibrium balanced growth paths. It is shown that allowing for perfect capital mobility across countries increases the range of parameter values for which the model permits equilibrium indeterminacy. As opposed to the closed capital markets case, simple restrictions on preferences are no longer sufficient to eliminate the indeterminacy. Intuitively, under perfect capital mobility agents are able to smooth consumption completely. This induces an economy with open capital markets to behave like a closed economy with linear preferences thereby increasing the possibility of equilibrium indeterminacy. Received: 18 November 1998; revised version: 10 August 1999     

When does Learning by Doing generate current losses?

We study under which conditions a learning by doing effect in the industry causes a monopolist to operate at a loss for some initial periods. Those conditions involve a parameter of the learning process, the slope of inverse demand function and the discount parameter. In order to get results, we explore the analytical solution to a T-period learning by doing model, which is also a novelty. Numerical examples are presented.     

Climate Policy,Uncertainty, and the Role of Technological Innovation

We study how uncertainty about climate change severity affects the relative benefits of early abatement and a portfolio of research and development (R&D) in lowering future abatement costs. Optimal early abatement depends on the curvature of the marginal benefit and marginal abatement cost (MAC) functions and how the uncertain parameter affects marginal benefits. R&D in a particular technology depends on whether uncertainty increases early abatement; whether investment lowers marginal costs for that technology; whether R&D lowers the slope of that technology's MAC function; and the shape of that technology's MAC function. We illustrate, focusing on the role of backstop technologies.     

Adherence to guidelines for sensitivity analysis: cost-effectiveness analyses of dual oral antiplatelet therapy

Abstract

Objective: Cost-effectiveness analyses of new treatments for cardiovascular disease frequently require input parameters whose values are known with uncertainty due to limited data. The objective of this paper is to examine the extent to which published sensitivity analyses addressing this uncertainty adhere to Health Technology Assessment (HTA) guidelines.

Research design and methods: A systematic review of published cost-effectiveness analyses was performed for an example drug treatment scenario, dual oral antiplatelet therapy compared with aspirin alone following acute coronary syndromes and/or percutaneous coronary intervention. The following medical literature databases were searched for articles published from January 1997 to June 2007: PubMed, Cochrane Collaboration, EMBASE and the Health Economic Evaluation Database (HEED). Evidence tables were created to show the sensitivity of the cost-effectiveness estimates to changes in the input parameter values, as well as the data sources used for the reference-case and sensitivity analysis input parameter values. The extent to which the sensitivity analyses adhered to HTA guidelines were also examined.

Results: Cost-effectiveness ratios were most sensitive to changes in the efficacy of dual antiplatelet therapy and reference-case model assumptions about costs beyond the trial period. Although alternative values tested in the sensitivity analysis for some input parameters were based on observed ranges or distributions, alternative values tested for many other input parameters were assumed without justification.

Conclusions: Sensitivity analyses in the cost-effectiveness studies of dual oral antiplatelet therapy were not fully adherent with HTA guidelines. In particular, long-term costs and benefits were not always included in the sensitivity estimates, the impact of differential effects on death and myocardial infarction was not explored, and justification for the alternative parameter values tested was not always provided.     

The importance of considering optimal government policy when social norms matter for the private provision of public goods

We study optimal government policy in a reference model (Rege, 2004, Journal of Public Economic Theory, 6, 65–77) of public good provision and social approval in a dynamic setting. We show that even if complete adherence to the social norm maximizes social welfare it is by no means necessarily optimal to push society toward it. We stress the different roles of social externality and the public good problem. We discuss the problem with the standard crowding in and out argument and analyze the relationship with Pigouvian taxes. We discuss the role of the cost of public funds and show how it can create path dependency, the multiplicity of both optimal equilibria and optimal paths, and discuss the role of parameter instability.     

Testing theories of behavior for extensive-form two-player two-stage games

We examine choices in two-player extensive-form games that give subjects opportunities for individualistic as well as other-regarding behavior, and where each subject makes choices in a variety of games. Following an extensive search over models, where we estimate a single parameter vector for all the games rather than different parameter vectors for each game, we find that (1) the level-n model organizes the data well, (2) other-regarding behaviors in these games appear to consist primarily of egalitarian and utilitarian behaviors, and (3) there is no significant evidence for reciprocal behavior. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

BREAKING THE GLASS CEILING: SLOW PROGRESS AHEAD

Studies show that the percentage of female senior managers in large corporations continues to grow slowly. I consider a firm that initially has an entirely male management structure. If this firm suddenly shifts its behavior and begins to hire male and female managers in equal numbers and treats them equally, then the gender composition of the firm's managers will change over time. Using well‐established mathematical methods, I derive equations that show how rapidly this change will occur. Using data from previously published studies to establish parameter bounds, I draw random samples for parameter values and use these to investigate how quickly the gender composition of a firm's management structure can change. I find that the gender composition at lower management levels changes quickly, compared to the upper management levels. (JEL J71)     

Some empirics of the bivariate relationship between average subjective well-being and the sustainable wealth of nations

The World Bank's Millennium Capital Assessment (MCA) has provided per capita estimates of total wealth and its major subcategories for a large number of countries. In this article, these macro-level estimates are used to explore bivariate cross-country ‘wealth–happiness’ relationships, focussing on issues of appropriate functional form, parameter stability and outliers. For comparative purposes, ‘income–happiness’ relationships are also explored. Total wealth turns out to be strongly related to Gross National Income (GNI) per capita, due to the importance of produced and intangible capital, but not to natural capital. In contrast, when the most natural capital intensive countries are excluded as outliers, a strong relationship emerges between Subjective Well-Being (SWB) and natural capital, especially amongst high income countries. In these countries, natural capital seems to be an important wealth correlate of SWB, despite accounting for only a very small proportion of total wealth.     

Coalitional Colonel Blotto Games with Application to the Economics of Alliances

In Borel’s Colonel Blotto game two players simultaneously allocate their respective endowments of a resource across n battlefields, the higher allocation wins each battlefield, and players maximize the number of battlefields won. Here we examine two players who may form an alliance before separately competing in two disjoint Colonel Blotto games against a common adversary. Despite a lack of common interests, unilateral transfers—in a direction consistent with the exploitation hypothesis—arise for a range of parameter configurations. Such transfers alter the adversary’s strategy and the combination of the direct and strategic effects benefits both allies.     

Group assessment of multivariate prior distributions

This paper addresses the problem of how to generate subjective prior distributions for p-dimensional unobservables. The context assumed is one in which you would like your multivariate prior distribution to reflect the combined views of some respected group. The recommended procedure is to administer a battery of p questions to each of N subjects in a homogeneous panel of randomly selected experts. Each subject answers questions each of which is about only one-dimensional (marginal) parameters. A multistage qualitative controlled feedback interrogation procedure is suggested. The N p-vectors of responses from the panel are combined to form the multivariate subjective prior density of the p-dimensional parameter.     

The Box-Cox transformation-of-variables in regression

The application of the Box-Cox transformation to the dependent and independent variables is discussed. Maximum likelihood and iterative GLS estimators are used and bootstrapping is carried out to compare the bootstrap sample variability with the finite sample variability (RMSE) and improve RMSE estimation. The biases of parameter estimators were shown to be substantial in small samples. The standard errors obtained from the Hessian matrix were a poor measure of the finite sample variability. Thet-ratios of the linear parameter estimators may not be normally distributed in small samples.The authors acknowledge the helpful comments of two referees.     

试析人民币对外升值与对内贬值并存

Since 2002, RMB has shown a phenomenon which is the co-existence of the external appreciation and the domestic inflation. This new monetary phenomenon has been strengthened in the context that US dollar depreciates internationally and that domestic economy is overwhelmed with excessive liquidities. The new monetary phenomenon is the reflection of the real economy that continuing trade surplus, triggered robustly by the export-driven economy, which brings a huge amount of foreign exchange reserve and accelerates sequentially the expansion of domestic money supply. Furthermore, a refrained appreciation of RMB tends to deteriorate the domestic inflation, which is not simply a traditional concept of CPI but a broad inflation parameter including a variety of asset prices. It is sure that the new phenomenon is becoming a new challenge to the macroeconomic equilibrium as well as the decision maker of monetary policy. __________ Translated from Jingji yanjiu 经济研究 (Economic Research Journal), 2007, (9): 32–48