Proportional Dynamics in Exchange Economies

We study the Proportional Response dynamic in exchange economies, where each player starts with some amount of money and a good. Every day, the players bring one unit of their good and submit bids on goods they like, each good gets allocated in proportion to the bid amounts, and each seller collects the bids received. Then every player updates the bids proportionally to the contribution of each good in their utility. This dynamic models a process of learning how to bid and has been studied in a series of papers on Fisher and production markets, but not in exchange economies. Our main results are as follows: - For linear utilities, the dynamic converges to market equilibrium utilities and allocations, while the bids and prices may cycle. We give a combinatorial characterization of limit cycles for prices and bids. - We introduce a lazy version of the dynamic, where players may save money for later, and show this converges in everything: utilities, allocations, and prices. - For CES utilities in the substitute range $[0,1)$, the dynamic converges for all parameters. This answers an open question about exchange economies with linear utilities, where tatonnement does not converge to market equilibria, and no natural process leading to equilibria was known. We also note that proportional response is a process where the players exchange goods throughout time (in out-of-equilibrium states), while tatonnement only explains how exchange happens in the limit.Comment: 25 pages, 6 figure

A Dynamic Equilibrium Model of Real Exchange Rates with General Transaction Costs

We study the behavior of real exchange rates in a two­country dynamic equilibrium model. In this model, consumers can only consume domestic goods but can invest costlessly in capital stocks of both countries. Nevertheless, transporting goods between the two countries is costly and, hence, the rebalancing of the capital stock can only happen finitely often. We propose a realistic cost structure for goods transportation, wherein the total cost increases with the amount of shipment but the unit cost decreases with it due to economies of scale. Given such a cost structure, the optimal decisions on when and how much to transfer need to be determined jointly. The dual decision depends upon the magnitude of economies of scale, the production technology specifications, and the consumer preferences. The model can reconcile the observed large short­term volatility of the real exchange rate with its slow convergence to parity. Further, the drift and diffusion of the real exchange rate are not uniquely determined by the real exchange rate level. The dynamics of the real exchange rate can only be determined by a joint analysis of the real exchange rate and the underlying economic fundamentals such as the capital stock imbalance between the two countries.costs of goods transportation; economies of scale; real exchange rate; purchasing power parity; nonlinearity.

Financial Distress in Chinese Industry:Microeconomic, Macroeconomic and Institutional Infuences

We study the impact of both microeconomic factors and the macroeconomy on the financial distress of Chinese listed companies over a period of massive economic transition, 1995 to 2006. Based on an economic model of financial distress under the institutional setting of state protection against exit, and using our own firm-level measure of distress, we find important impacts of firm characteristics, macroeconomic instability and institutional factors on the hazard rate of financial distress. The results are robust to unobserved heterogeneity at the firm level, as well as those shared by firms in similar macroeconomic founding conditions. Comparison with related studies for other economies highlights important policy implications

Financial Distress in Chinese Industry:Microeconomic, Macroeconomic and Institutional Influences

We study the impact of both microeconomic factors and the macroeconomy on the financial distress of Chinese listed companies over a period of massive economic transition, 1995 to 2006. Based on an economic model of financial distress under the institutional setting of state protection against exit, and using our own firm-level measure of distress, we find important impacts of firm characteristics, macroeconomic instability and institutional factors on the hazard rate of financial distress. The results are robust to unobserved heterogeneity at the firm level, as well as those shared by firms in similar macroeconomic founding conditions. Comparison with related studies for other economies highlights important policy implications

The Limit-Price Dynamics — Uniqueness, Computability and Comparative Dynamics in Competitiive Markets

In this paper, a continuous-time price-quantity trading process is defined for exchange economies with differentiable characteristics. The dynamics is based on boundedly rational agents exchanging limit-price orders to a central clearing house, which rations infinitesimal trades according to Mertens (2003) double auction. Existence of continuous trade and price curves holds under weak conditions and in particular even if there is no long-run competitive equilibrium. Every such curve converges towards a Pareto point, and every Paretian allocation is a locally stable rest-point. Generically, given initial conditions, the trade and price curve is piecewise unique, smooth and computable, hence enables to effectively perform comparative dynamics. Finally, in the 2 x 2 case, the vector field induced by the limit-price dynamics is real-analytic.Non-tatonnement, price-quantity dynamics, limit-price mechanism, myopia, computable general equilibrium.

Black market and official exchange rates: Long-run equilibrium and short-run dynamics

This paper provides further empirical results on the relationship between black market and official exchange rates in six emerging economies (Iran, India, Indonesia, Korea, Pakistan, and Thailand). First, it applies both time series techniques and heterogeneous panel methods to test for the existence of a long-run relation between these two types of exchange rates. Second, it tests formally the validity of the proportionality restriction implying a constant black-market premium. Third, in addition to the long-run equilibrium, it also analyses the short-run dynamic responses of both markets to shocks. Evidence of market inefficiency and incomplete (or long-lived) reversion to long-run equilibrium is found. This implies that financial managers can only partially reduce the exchange rate risk, whilst monetary authorities can effectively pursue their policy objectives by imposing foreign exchange or direct controls

The Diffusion of Humans and Cultures in the Course of the Spread of Farming

The most profound change in the relationship between humans and their environment was the introduction of agriculture and pastoralism. [....] For an understanding of the expansion process, it appears appropriate to apply a diffusive model. Broadly, these numerical modeling approaches can be catego- rized in correlative, continuous and discrete. Common to all approaches is the comparison to collections of radiocarbon data that show the apparent wave of advance of the transition to farming. However, these data sets differ in entry density and data quality. Often they disregard local and regional specifics and research gaps, or dating uncertainties. Thus, most of these data bases may only be used on a very general, broad scale. One of the pitfalls of using irregularly spaced or irregularly documented radiocarbon data becomes evident from the map generated by Fort (this volume, Chapter 16): while the general east-west and south-north trends become evident, some areas appear as having undergone anomalously early transitions to farming. This may be due to faulty entries into the data base or regional problems with radiocarbon dating, if not unnoticed or undocumented laboratory mistakes.Comment: 20 pages, 5 figures, submitted to Diffusive Spreading in Nature, Technology and Society, edited by Armin Bunde, J\"urgen Caro, J\"org K\"arger, Gero Vogl, Chapter 1

Optimal Budget Deficit Rules

This paper discusses the problem of the optimal determination of budget deficit limits in cases where the fiscal authority wishes to keep the budget deficit close to a reference value. It is assumed that the fiscal authority minimizes the expected discounted value of squared deviations from the reference value. Lump-sum and proportional intervention costs are considered. This paper is also an example of integration between stochastic process optimal control methods and the continuous time stochastic models. In fact, the characteristics of the stochastic process that rules the path of the budget deficit are taken from a previously developed continuous time stochastic model (Amador, 1999). Finally, simulation methods are used in order to conduct a comparative dynamics analysis. The paper concludes that, in the case of proportional intervention costs, the optimal ceiling depends positively on the cost parameter and on the variance of the budget deficit. On the contrary, the optimal ceiling depends negatively on the average budget deficit. These results remain valid in the case where there are both lump-sum and proportional intervention costs. Finally, in a stationary equilibrium context, we conclude that economies with higher tax rates and lower public expenditure should set higher budget deficit ceilings. The same is true for economies with a higher variance in technology and public expenditure shocks.