The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging

In this article we compare three models of the stochastic behavior of commodity prices that take into account mean reversion, in terms of their ability to price existing futures contracts, and their implication with respect to the valuation of other financial and real assets. The first model is a simple one-factor model in which the logarithm of the spot price of the commodity is assumed to follow a mean reverting process. The second model takes into account a second stochastic factor, the convenience yield of the commodity, which is assumed to follow a mean reverting process. Finally, the third model also includes stochastic interest rates. The Kalman filter methodology is used to estimate the parameters of the three models for two commercial commodities, copper and oil, and one precious metal, gold. The analysis reveals strong mean reversion in the commercial commodity prices. Using the estimated parameters, we analyze the implications of the models for the term structure of futures prices and volatilities beyond the observed contracts, and for hedging contracts for future delivery. Finally, we analyze the implications of the models for capital budgeting decisions.     

Training and Promotion: Allocation of Skills or Incentives?

This paper analyzes the impact of training on the probability of promotion. Results from the British Household Panel Survey indicate that training increases the probability of promotion of female workers, but not that of male workers. In terms of wages, men obtain significant returns from (general and specific) training acquired with their current employer, while women profit from general training. Overall, results suggest that career moves of women are importantly affected by the market value of their skills, while those of men fit better a model of promotions as providers of incentives.     

VERTICAL INTEGRATION AND SHARED FACILITIES IN UNREGULATED INDUSTRIES

In this paper we analyze the equilibrium market structure, following liberalization, of an industry involving an essential facility. Two alternative modes of market entry are considered, in conjunction with vertical integration, namely: (i) full entry, which means building a new and more efficient facility at a positive fixed cost; and (ii) partial entry, which means purchasing existing capacity from the incumbent, at a fixed price per unit that is freely negotiated between the incumbent and the entrant. We show that vertical integration is a dominant strategy for each firm under either entry mode, and that upstream firms choose to share the incumbent's facility when the entrant's fixed cost exceeds a positive threshold. In addition, welfare analysis shows that in many situations the market can efficiently solve the trade-off between fixed-cost savings and softened downstream competition, thus providing a rationale for the liberalization of such industries. Several competition policy implications are discussed.     

Audits or Distortions: The Optimal Scheme to Enforce Self‐Employment Income Taxes

I investigate the optimal auditing scheme for a revenue‐maximizing tax collection agency that observes not only reported profits, but also a single factor of production at each firm. Each firm is owned by a single entrepreneur whose managerial ability is random. The optimal auditing scheme is discontinuous and nonmonotone in ability. In intermediate audit costs, less productive entrepreneurs face auditing probabilities that increase in ability, whereas the ablest ones are not audited. Finally, the effective tax rate is higher in the middle of the managerial ability distribution; thus, the overall regressive (or progressive) bias that arises from evasion is unknown.     

Millian Efficiency with Endogenous Fertility

Should governments implement policies that affect fertility decisions on efficiency grounds? What is the correct notion of efficiency to use? To address these issues, this paper develops an extension of the notion of Pareto efficiency, referred to as Millian efficiency , to evaluate symmetric allocations in an overlapping generations setting with endogenous fertility. This extension is based on preferences of those agents who are actually alive, and exclusively allows for welfare comparisons of symmetric allocations. First, we provide necessary and sufficient conditions to determine whether an allocation is Millian efficient or not, and we show that the sufficient conditions for dynamic efficiency offered by Cass (1972) and Balasko and Shell (1980) cannot be directly applied when fertility decisions are endogenous. Second, we characterize Millian efficient allocations as the equilibria of a decentralized price mechanism, and we present a sufficient condition for dynamic efficiency that uses the sequence of prices associated to such decentralized equilibria. Finally, we analyse how intergenerational policies should be designed to restore efficiency and achieve net welfare gains in two different settings in which markets yield inefficient allocations: dynamic inefficiencies and financial market incompleteness regarding human capital. In the former, a pay-as-you-go social security system eliminates dynamic inefficiencies, provided pensions are explicitly linked with fertility decisions. In the latter, a specific link between social security and public education becomes a necessary condition for Millian efficiency.     

LYON Taming

A Liquid Yield Option Note (LYON) is a zero coupon, convertible, callable, puttable bond. This paper presents a simple contingent claims pricing model for valuing LYONS and uses the model to analyze a specific LYON issue.