From Planning Models to Descriptive General Equilibrium

I had known Manohar Rao for a long time. For many years I tried to lure him to join the Indira Gandhi Institute of Development Research. He always gave me his disarming smile but his loyalty to Bombay University and to his students was unshakable. He was deeply interested in improving tools for better policy analysis. Hence in this paper I raise some related issues.

     

Possible economic impacts of a shutdown of the thermohaline circulation: an application of <Emphasis Type="Italic">FUND</Emphasis>

Climate change can lead to a substantial reduction of the strength of the thermohaline circulation in the world oceans. This is often thought to have severe consequences particularly on the North Atlantic region and Northern and Western Europe. The integrated assessment model FUND is used to estimate the extent of these impacts. The results indicate that, owing to a slower warming (rather than cooling) of the regions most affected by a thermohaline circulation collapse, climate change induced damages in these regions would be smaller in case of a shutdown of the thermohaline circulation. However, even with a thermohaline circulation collapse, the total and marginal impacts of climate change are negative.JEL Classification: Q510, Q540We are grateful to Till Kuhlbrodt for providing the CLIMBER data and to Andre Krebber for processing them. The German Federal Ministry for Education and Research through the INTEGRATION project, the US National Science Foundation through the Center for Integrated Study of the Human Dimensions of Global Change (SBR-9521914) and the Michael Otto Foundation provided welcome financial support.     

Does Increased Extraction of Natural Gas Reduce Carbon Emissions?

Without an international climate agreement, extraction of more natural gas could reduce emissions of CO₂ as more clean natural gas may drive out dirty coal and oil. Using a computable equilibrium model for the Western European electricity and natural gas markets, we examine whether increased extraction of natural gas in Norway reduces global emissions of CO₂. We find that both in the short run and in the long run total emissions are reduced if the additional quantity of natural gas is used in gas power production in Norway. If instead the additional quantity is exported directly, total emissions increase both in the short run and in the long run. However, if modest CO₂-taxes are imposed, increased extraction of natural gas will reduce CO₂ emissions also when the additional natural gas is exported directed.earlier version of this paper was presented at the 25th Annual IAEE International Conference in Aberdeen June 2002.     

A two-stage core with applications to asset market and differential information economies

Summary. We introduce a new core concept, called the two-stage core, which is appropriate for economies with sequential trade. We prove a general existence theorem and present two applications of the two-stage core: (i) In asset markets economies where we extend our existence proof to the case of consumption sets with no lower bound, in order to capture the case of arbitrary short sales of assets. Further, we show that the two-stage core is non empty in the Hart (1975) example where a rational expectations equilibrium fails to exist. (ii) In differential information economies where we provide sufficient conditions for the incentive compatibility of trades. Namely, that no coalition of agents can misreport the true state and provide improvements to all its members, even by redistributing the benefits from misreporting. Received: December 20, 1995; revised version: December 6, 1996     

An Approach to a Visual Language for Convective Fluid Flows: Visualization of Geophysical Simulations

It was known that deep within numbers and binary data from simulations of geophysical convective flows resided various patterns. Two models of convective fluid flows were being considered. One was a model of two-dimensional (768 × 256) air convection with finite Prandtl number of one and Rayleigh number of 10⁸?10¹⁰, and another was a model of three-dimensional (up to 120 × 120 × 90) mantle convection with infinite Prandtl number and Rayleigh number of 10⁶?10⁸. Clearly, phenomena existed which superceded each individual dimensionless computer model to provide a piece of information regarding actual fluid flows. The problem was how to find, prove, and communicate these patterns and phenomena for convection simulations with gigabytes of data. In a search for such an analytical and communicative tool, the alternative of visualization was considered. The need for visualization was recognized and discussed. Then, utilizing both two- and three-dimensional models of high Rayleigh number convection, basic techniques of style and content were developed. Applications of the visualization techniques were designed utilizing IBM’s Data Explorer in order to create communicative images and movies, and after the applications, the problems of data storage and transfer became apparent. Throughout the process though, it became clear how important the language of vision actually could be in the geophysics community. In a field in which words such as plumes and internal waves have in ways replaced mathematics as the basic language for science, there is a need for another resource, another language-the visualization of convective fluid flows.     

Robust Volatility Estimation with and Without the Drift Parameter

We find the closed form solution for the joint probability of the running maximum and the drawdown of the Brownian motion with a non-zero drift parameter at a random time that is exponentially distributed and independent of the Brownian motion. This characterization leads us to come up with a robust method of estimating volatility using open, high, low and closing prices. We rigorously show the independence of robust volatility estimators based on extreme values of asset prices relative to the standard robust volatility estimator based on closing price alone. We further prove that the proposed robust volatility ratio is unbiased with no drift parameter. Moreover, we find that the robust volatility ratio with a non-zero drift parameter has only a second order effect. We have shown that our proposed extreme value robust volatility estimator is 2–3 times relatively more efficient when compared to the classical robust volatility estimator based on Monte Carlo simulation experiment. On the empirical side, we test the proposed robust volatility ratio based on high and low prices on different asset classes like stock indices, exchange rate and precious metals.

     

How many voters are needed for paradoxes?

Summary. This paper presents a general procedure for finding profiles with the minimum number of voters required for many important paradoxes. Borda's and Condorcet's classic examples are revisited as well as generalizations. Using Saari's procedure line, we obtain an upper bound for the minimum number of voters needed for a profile for which the Condorcet winner is not strictly top ranked for all weighted positional procedures. Also we give a simple upper bound on the minimum number of voters needed for a set of prescribed voting outcomes. In contrast to situations wherein small numbers of voters are needed, we consider paradoxes requiring arbitrarily large numbers of voters as well as large numbers of alternatives. Finally we indicate connections with statistical rank based tests. Received: April 18, 2001; revised version: May 25, 2001     

Stock return, risk, and legal environment around the world

This paper investigates how the legal environment in a country influences performance and risk of stock across countries at different developmental stages and of various rules of jurisdiction. Using data of 4916 stocks from 37 countries, our empirical findings confirm that equities in countries with English common law origin have higher risk premiums than those in civil law countries, particularly for countries of the French/Spanish code. The indicators representing high efficiency in law system, low corruption, strong legal protection of investors' rights, and reliable political environment are associated with low risk and high performance. The various elements of legal procedural formalism, however, have differing effects on volatility and return.