Anonymous sequential games: Existence and characterization of equilibria

Summary In this paper we consider Anonymous Sequential Games with Aggregate Uncertainty. We prove existence of equilibrium when there is a general state space representing aggregate uncertainty. When the economy is stationary and the underlying process governing aggregate uncertainty Markov, we provide Markov representations of the equilibria.Table of notation Agents' characteristics space ( ) - A Action space of each agent (aA) - Y Y = x A - Aggregate distribution on agents' characteristics - (X) Space of probability measures onX - C(X) Space of continuous functions onX - _X Family of Borel sets ofX - State space of aggregate uncertainty ( ) - x _t=1 aggregate uncertainty for the infinite game - = (₁,₂,...,_t,...) - ^{t t} (₁, ₂,..., _t) - L₁(^t,C ×A),v _t Normed space of measurable functions from ^t toC( x A) - 8o(^t,( x A)) Space of measurable functions from ^tto( x A) - X^t X^t= x _s=1 ^t X - _X ^t Borel field onX ^t - v Distribution on - v_t Marginal distribution of v on ^t - v(^t)((¦^t)) Conditional distribution on given ^t - v^t(^s)(v_t(¦^s)) Conditional distribution on ^t given ^s (wheres) - _t Periodt distributional strategy - Distributional strategy for all periods =(₁,₂,...,_t,...) - _t Transition process for agents' types - ( _t,^t,y)(P _t+1(, _t , ^t ,y)) Transition function associated with _t - u _t Utility function - V _t (, a, , ^t) Value function for each collection (, a, , ^t ) - W _t (, , ^t ) Value function given optimal action a - C() Consistency correspondence. Distributions consistent with and characteristics transition functions - B() Best response correspondence (which also satisfy consistency) - E Set of equilibrium distributional strategies - x _t=1 ( ^t , (x A)) - S Expanded state space for Markov construction - (, a, ) Value function for Markov construction - P( _t ^* , _t y)(P(, _t ^* , _t , _y )) Invariant characteristics transition function for Markov game We wish to acknowledge very helpful conversations with C. d'Aspremont, B. Lipman, A. McLennan and J-F. Mertens. The financial support of the SSHRCC and the ARC at Queen's University is gratefully acknowledged. This paper was begun while the first author visited CORE. The financial support of CORE and the excellent research environment is gratefully acknowledged. The usual disclaimer applies.     

The dynamic effects of a currency union on trade

The response of trade to a monetary union is a dynamic process. An empirical study of the European monetary union finds that the extensive margin of trade in new goods responded several years ahead of EMU implementation and ahead of overall trade volume. A dynamic rational expectations trade model shows that early entry of new firms in anticipation is explainable as a rational forward-looking response to news. The model helps identify which types of trading frictions are reduced by a currency union, and shows how new entry can be affected by uncertainty about EMU.     

Volatility due to offshoring: Theory and evidence

Existing models of offshoring are not equipped to explain how global production sharing affects the volatility of economic activity. This paper develops a trade model that can account for why offshoring industries in low wage countries such as Mexico experience fluctuations in employment that are twice as large as in high wage countries such as the United States. We argue that a key to explaining this outcome is that the extensive margin of offshoring responds endogenously to shocks in demand and transmits those shocks across borders in an amplified manner. Empirical evidence supports the claim that the extensive margin of offshoring is an active margin of adjustment, and quantitative simulation experiments show that the degree of movement of this margin in the data is sufficient to explain relative employment volatility in Mexico and the U.S.     

On the continuity of correspondences on sets of measures with restricted marginals

Summary. Consider the set of probability measures on a product space with the property that all have the same marginal distributions on the coordinate spaces. This set may be viewed as a correspondence, when the marginal distributions are varied. Here, it is shown that this correspondence is continuous. Numerous problems in economics involve optimization over a space of measures where one or more marginal distributions is given. Thus, for this class of problem, Berge's theorem of the maximum is applicable: the set of optimizers is upper-hemicontinuous and the value of the optimal solution varies with the parameters (marginals) continuously. Received: April 23, 1997; revised version: January 16, 1998     

Introduction to: the euro at twenty

Review of World Economics -     

Does exchange rate variability matter for welfare? A quantitative investigation of stabilization policies

This paper studies what degree of exchange rate stabilization is optimal for several types of open economies. This is accomplished through a quantitative evaluation of optimal monetary policy rules in a two-country sticky-price model. First, a calibrated benchmark model with incomplete asset markets supports past conclusions from simpler models, emphasizing inflation stabilization rather than exchange rate stabilization. It also highlights that the utility gains from optimal stabilization policy are small. Second, while an economy extended to include consumer habits implies greater sensitivity by households to consumption variability, it has only minor effects on the benchmark conclusions and benefits. Finally, these conclusions are altered under an alternative environment where international asset markets exhibit asymmetry in the form of “original sin.” Such countries can benefit from policies that aggressively stabilize the exchange rate, with utility gains larger than the previous cases.     

Industry dynamics with stochastic demand

We study the dynamics of an industry subject to aggregate demand shocks where the productivity of a firm's technology evolves stochastically over time. To characterize the intertemporal evolution of the distribution of firms, we discuss in particular how exit decisions, aggregate output, profits, and distributions of firm productivities vary (a) across different demand realization paths; (b) along a demand history path, detailing the effects of continued good or bad market conditions; and (c) for different anticipated future market conditions. We show how poor demand conditions can lead to increased exit of low‐productivity firms at all future dates and states and raise welfare due to the impact on exit decisions.     

Productivity, tradability, and the long-run price puzzle

Long-run cross-country price data exhibit a puzzle. Today, richer countries exhibit higher price levels than poorer countries, a stylized fact usually attributed to the Balassa-Samuelson (BS) effect. But looking back 50 years, this effect virtually disappears from the data. What is often assumed to be a universal property is actually quite specific to recent times, emerging a half century ago and growing steadily over time. What might potentially explain this historical pattern? We develop an updated BS model inspired by recent developments in trade theory, where a continuum of goods are differentiated by productivity, and where tradability is endogenously determined. Firms experiencing productivity gains are more likely to become tradable and crowd out firms not experiencing productivity gains. As a result the usual BS assumption—that productivity gains be concentrated in the traded goods sector—emerges endogenously, and the BS effect on relative price levels likewise evolves gradually over time.     

Knowledge Work Through Social Media Applications: Team Performance Implications of Immersive Virtual Worlds

Knowledge is key to competitive advantage, and the social reach of knowledge can amplify its power in terms of organizational performance. Leveraging such amplification, social media applications are expected broadly to improve the performance of organizational work, which highlights teams, groups, and organizations as particularly appropriate units of analysis. The technological intermediation of knowledge work within and among such social aggregations of people remains a complex endeavor, however. This pertains in particular to immersive, 3D environments supporting virtual social and game worlds. As with other social media applications, such virtual worlds can amplify knowledge broadly, but they also offer potential to approach the sensations of face-to-face (F2F) interaction in terms of presence, copresence, psychological engrossment, and affective experience. In this exploratory study, we employ both quantitative and qualitative research techniques to investigate how teamwork performed through virtual worlds can approach that accomplished via F2F interactions. This leads to important findings, insights, guidelines, and suggestions for expanded research as well as enhanced practice.     

The extensive margin and monetary policy

The creation of new firms, referred to as the extensive margin, is a significant but overlooked dimension of monetary policy. A monetary VAR documents that monetary policy has significant effects on firm creation. An analytically tractable model combining sticky prices and firm entry shows that entry alters the transmission of monetary policy innovations, acting much like a type of investment in more standard models. Monetary policy rules that offset the uncertainty of productivity shocks can raise the mean level of entry and thereby welfare, suggesting a new motivation for stabilization policy.