Arbitrage and equilibrium in economies with infinitely many commodities

An ‘arbitrage opportunity’ for a class of agents is a commodity bundle that will increase the utility of any of the agents and that has non-positive price. The non-existence of ‘arbitrage opportunities’ is necessary and sufficient for the existence of an economic equilibrium. A bundle is ‘priced by arbitrage’ if there is a unique price that it can command without causing an ‘arbitrage opportunity’ to exist. For economies that have infinitely many commodities, appropriate notions of ‘arbitrage opportunities’ and ‘bundles priced by arbitrage’ depend on the continuity of agents’ preferences. This paper develops these notions, thereby providing a foundation for recent work in financial theory concerning arbitrage in continuous-time models of securities markets.     

Pareto optima,non-convexities and regulated market equilibria

In a differentiable setting without convexity assumptions, a typical local Pareto optimum can be sustained by a combination of a price system and a system of market regulations. Some consumers are required to consume fixed amounts of some basic commodity bundles, and some producers are required to produce fixed amounts of other basic commodity bundles. The agents are otherwise free to maximize utility and profit (locally). No more than l–1 agents are subject to regulation, where l is the number of commodities.     

Economies with a mean demand function

The present paper shows one way to look at G. Debreu and W. Hildenbrand's conjecture that certain atomless economies have mean demand functions. We conclude within the continuity framework that an economy gives rise ‘in general’ to a continuous mean demand function, and that the class of all atomless economies is ‘big’ in the space of all economies with a continuous mean demand function. The same problems are reconsidered within the framework of a space of differentiable preferences at the end.     

Modelling market fundamentals: A model of the aluminium market

The standard approach to modelling primary commodity markets under rational expectations is to relate the commodity price to the production and consumption ‘surprises’ (i.e. the innovations on the equations). Using the world aluminium market, we show how this approach can be modified so that both the price and stock can be written in terms of one or more market ‘fundamentals’ which reflect the supply—demand balance on the market. This approach allows joint estimation of production, consumption, stock demand and price equations subject to cross-equation restrictions. It may be seen as a formalization of the approach adopted by metals industry analysts.     

Equilibria with coordination failures

This paper extends the literature on equilibria with coordination failures to arbitrary convex sets of admissible prices. This makes it possible to address coordination failures for cases with price indexation or more general price linkages between commodities. We introduce a new equilibrium concept, called quantity constrained equilibrium (QCE), giving a unified treatment to all cases considered in the literature so far. At a QCE the expected trade opportunities on supply and demand are completely determined by a rationing vector satisfying that the prevailing price system maximizes the value of the rationing vector within the set of admissible prices. When the set of admissible prices is compact, we show the existence of a connected set of QCEs. This set connects two trivial no-trade equilibria, one with completely pessimistic expectations concerning supply opportunities and one with completely pessimistic expectations concerning demand opportunities. Moreover, the set contains for every commodity a generalized Drèze equilibrium, being a QCE at which for that commodity no binding trade opportunities on both supply and demand are expected, and also a generalized supply-constrained equilibrium at which no binding constraints on demand opportunities are expected and for at least one commodity also not on supply. We apply this main result to several special cases, and also discuss the case of an unbounded set of admissible prices.     

On the behavior of commodity prices when speculative storage is bounded

This paper investigates the implications of bounded speculative storage, storage bounded from below at zero and above at a capacity, on commodity prices. Binding capacity mirrors the non-negativity constraint on storage and leads to negative price spiking and higher volatility when the market is in deep contango, i.e. low current prices at high stock levels. With bounded storage there is no need to restrict storage to be costly to ensure a rational expectations equilibrium. This allows the model to cover a wide range of storage technologies, including free and productive storage. We also provide an alternative expression for speculative prices that highlights the key role of the storage boundaries. The competitive equilibrium price is the sum of discounted future probability weighted boundary prices. The boundary prices can be viewed as dividends on commodities in storage reflecting the realization of economic profits from storage.     

Speculation in the Oil Market

The run‐up in oil prices since 2004 coincided with growing investment in commodity markets and increased price co‐movement among different commodities. We assess whether speculation in the oil market played a role in driving this salient empirical pattern. We identify oil shocks from a large dataset using a dynamic factor model. This method is motivated by the fact that a small‐scale vector autoregression is not informationally sufficient to identify the shocks. The main results are as follows. (i) While global demand shocks account for the largest share of oil price fluctuations, speculative shocks are the second most important driver. (ii) The increase in oil prices over the last decade is mainly driven by the strength of global demand. However, speculation played a significant role in the oil price increase between 2004 and 2008 and its subsequent collapse. (iii) The co‐movement between oil prices and the prices of other commodities is mainly explained by global demand shocks. Our results support the view that the recent oil price increase is mainly driven by the strength of global demand but that the financialization process of commodity markets also played a role. Copyright © 2014 John Wiley & Sons, Ltd.     

Price uncertainty, saving, and welfare

We analyze how commodity price uncertainty affects saving behavior and welfare in a dynamic model with multiple commodities, portfolio hedging, and a preference structure that disentangles ordinal preferences, attitudes towards risk, and attitudes towards intertemporal substitution. We show that the effect of price uncertainty on savings boils down to knowing (1) hf degree of resistance to intertemporal substitution and (2) the effect that uncertainty has on the certainty-equivalent real interest rate. We also show that, if the certainty-equivalent real interest rate is lower with uncertainty, consumers' welfare is also lower.     

The empirical relevance of the competitive storage model

The empirical relevance of models of competitive storage arbitrage in explaining commodity price behavior has been seriously challenged in a series of pathbreaking papers by [Deaton and Laroque, 1992], [Deaton and Laroque, 1995] and [Deaton and Laroque, 1996]. Here we address their major criticism, that the model is in general unable to explain the degree of serial correlation observed in the prices of twelve major commodities. First, we present a simple numerical version of their model which, contrary to Deaton and Laroque (1992), can generate the high levels of serial correlation observed in commodity prices, if it is parameterized to generate realistic levels of price variation. Then, after estimating the [Deaton and Laroque, 1995] and [Deaton and Laroque, 1996] model using their data set, model specification and econometric approach, we show that the use of a much finer grid to approximate the equilibrium price function yields quite different estimates for most commodities. Results are obtained for coffee, copper, jute, maize, palm oil, sugar and tin that support the specifications of the storage model with positive constant marginal storage cost and no deterioration as in Gustafson (1958a). Consumption demand has a low response to price and, except for sugar, stockouts are infrequent. The observed magnitudes of serial correlation of price match those implied by the estimated model.     

Price effects of steel commodities on worldwide stock market returns

We analyze the price effects of steel commodities on stock market returns in emerging and developed economies. These commodities have recently attained increased media exposure due to the rise in the U.S. steel import tariffs, which pose the threat of reducing global demand for steel products and, consequently, lowering prices abroad. However, little has been investigated on the impact of steel commodity prices on worldwide stock market returns. By performing structural VAR and GARCH techniques on a weekly-frequency time series from 2002 to 2015, we find positive and statistically significant effects of linear and non-linear steel commodity price shocks on real stock returns in the commodity markets. In the highly diversified financial markets such as U.S. and Germany, real stock returns do not significantly respond to steel commodity price shocks, although we find highly significant positive responses from developed economies such as Australia, Japan and South Korea. Results are robust to different model specifications. Our evidence suggests that higher tariffs on steel imports represent a larger disadvantage to commodity markets which are more largely impacted by steel commodity prices. We provide economic policy implications based on recent literature.     

Core and competitive equilibria: An approach from discrete convex analysis

We extend the assignment market (Shapley and Shubik, 1972; Kaneko, 1976, 1982) by utilizing discrete convex analysis. We consider the market in which buyers and sellers trade indivisible commodities for money. Each buyer demands at most one unit of commodity. Each seller produces multiple units of several types of commodities. We make the quasi-linearity assumption on the sellers, but not on the buyers. We assume that the cost function of each seller is M^♮-convex, which is a concept in discrete convex analysis. We prove that the core and the competitive equilibria exist and coincide in our market model.     

Investigating properties of commodity price responses to real and nominal shocks

This paper studies dynamic adjustments of 49 world commodity prices in response to innovations in the nominal exchange rate and the world real GDP. After we estimate the dynamic elasticity of the prices with respect to these shocks, we obtain the kernel density of our estimates to establish stylized facts on the adjustment process of the commodity price toward a new equilibrium path. Our empirical findings imply, on average, that the law of one price holds in the long-run, whereas the substantial degree of short-run price rigidity was observed in response to the nominal exchange rate shock. The real GDP shock tends to generate substantial price fluctuations in the short-run because adjustments of the supply can be limited, but have much weaker effects in the long-run as the supply eventually counterbalances the increase in the demand. Overall, we report persistent long-lasting effects of the nominal exchange rate shock on commodity prices relative to those of the real GDP shock.     

Indivisible commodities and the nonemptiness of the weak core

We consider a sufficient condition for the nonemptiness of the weak core in a finite exchange economy where every commodity is available only in integer quantities. We show that if the aggregate upper contour set is discretely convex, then the weak core is nonempty. In addition, we give two sufficient conditions for the aggregate upper contour set to be discretely convex. One is that every upper contour set of every agent is M^?${\text{M}}^{?}$-convex. The other is that the number of commodities is two and every agent’s preference relation is weakly monotone and discretely convex.     

Equal risk pricing under convex trading constraints

In an incomplete market model where convex trading constraints are imposed upon the underlying assets, it is no longer possible to obtain unique arbitrage-free prices for derivatives using standard replication arguments. Most existing derivative pricing approaches involve the selection of a suitable martingale measure or the optimisation of utility functions as well as risk measures from the perspective of a single trader.We propose a new and effective derivative pricing method, referred to as the equal risk pricing approach, for markets with convex trading constraints. The approach analyses the risk exposure of both the buyer and seller of the derivative, and seeks an equal risk price which evenly distributes the expected loss for both parties under optimal hedging. The existence and uniqueness of the equal risk price are established for both European and American options. Furthermore, if the trading constraints are removed, the equal risk price agrees with the standard arbitrage-free price.Finally, the equal risk pricing approach is applied to a constrained Black–Scholes market model where short-selling is banned. In particular, simple pricing formulas are derived for European calls, European puts and American puts.     

A Disaggregated Econometric Model Based on Flexible Functional Forms

This paper introduces an econometric input—output model for Western Germany in a disaggregation of 12 commodities and sectors. The ‘Jorgenson’-type equilibrium model is based on flexible functional forms on the supply and on the demand side of the commodity markets. For intermediate demand, the relationship between the translog function and its special cases—the Cobb-Douglas function— is exploited. Prices and production are endogenized by market-clearing conditions. The fully integrated model also endogenizes capital accumulation, a rudimental govern-ment budget and income distribution, as well as wages and labour demand on rationed labour markets. The results of a dynamic ex post simulation show that the model is able to depict the sectoral economic development in Germany in the sample period from 1970 to 1986.     

Price volatility and the political economy of resource-rich nations

This paper attempts to understand how price volatility affects the political transition of a resource-rich nation. Two states reflect price volatility: ‘high prices’ and ‘low prices’. We argue that whether or not political transition (i.e., a switch from one regime to another) will take place in a particular state depends critically on the kind of goods a country produces. If the main economic activity in a country is the extraction of “point-source” resources such as oil that demands capital-intensive production, the opportunity cost of switching the existing regime does not alter if the price of the resource changes but the benefit becomes more lucrative. Therefore, the incumbent group is most vulnerable during ‘high prices’. If the main economic activity of the nations is the production of “diffused resources” such as coffee that requires labor, prices do affect the opportunity cost. Nations concentrating in these commodities face acute political crisis during downturns.     

Supply-constrained fixed price equilibria in monetary economies

In this paper we consider an economy with restrictions on the relative prices of non-money commodities. The non-money commodities are partitioned into two groups, index makers and price following commodities. Then two cases are considered, namely that the relative prices of the index makers are fixed, respectively free. In both cases the money prices are flexible, whereas the relative prices of the price following commodities are tied to the prices of the index makers. The existence of a supply-constrained equilibrium is proved with (i) no rationing on the money commodities (stores of value), and (ii) at least one non-money commodity is not rationed. If prices of the index makers are fixed the result strengthens a theorem of Dehez and Drèze, if the prices are free a theorem of Kurz is strengthened. This paper is not only concerned with these existence results, but also with the question whether supply-constrained equilibria should appear more frequently than demand-constrained equilibria.     

A theoretical relationship between the rank-size rule and Clark's law of urban population distribution: Duality in the rank-size rule

This paper theoretically shows the necessary and sufficient conditions for the robust rank-size rule: the rank-size rule that robustly holds for any choice of threshold urban population density by which populations of cities are determined. First, it is shown that when urban population distribution follows Clark's law, the robust rank-size rule holds if and only if the gradient parameter of the negative exponential distribution of the ith ranked city as √i times as large as that of the first ranked city and the population density at the center is the same for all cities. Second, when urban population distribution follows a certain general class of urban population distribution functions, the robust rank-size rule (of population) holds if and only if the boundary condition is satisfied and the rank-size rule holds with respect to urban areas. These two rank-size rules, the rank-size rule of population and the rank-size rule of urban areas, form the primal-dual relation. Third, if the robust rank-size rule holds, then the constant density rule holds, that is, the average population density of a city over its urban area is the same for all cities.     

Interindustry Linkages: Virtuous and Vicious?

Although overall linkages are steadily increasing in growth processes, em-pirical data supply strong evidence of large intercountry and intertemporal fluctuations of the domestic-to-overall linkages ratio. This paper tries to explain this phenomenon by modelling a producers' behaviour which appears more realistic than that usually assumed in interindustry or computable general equilibrium models. The main novelty of the results is that the same causes that generate interindustry multipliers can also ‘trap’ domestic linkages into reinforcing (‘virtuous’) or weakening (‘vicious’) circles, depending on whether the price competitiveness of domestic activities is above or below a threshold related to the non-price competitiveness of those activities. These results can help to explain the fluctuations of domestic linkages with respect to overall linkages by spatial and temporal shifts of the threshold between the vicious and the virtuous ‘areas’. Moreover, they emphasize the importance of supply policies-mainly R&D policies—because of their ‘pushing down’ effect on this threshold.