Duane W. Rockerbie

Revenue Sharing, Conjectures, and Scarce Talent in a Sports League Model

This article develops a model of a representative professional sports club operating in a league that has the option of adopting one of two different forms of revenue sharing: traditional revenue sharing or central-pool-type revenue sharing. To adopt either form of revenue sharing, the league requires tehat a majority of clubs increase their profit with adoption of the plan. We derive necessary conditions for either plan to garner enough support for a majority vote. The likelihood of forming a majority depends on the distribution of team revenues and the conjectures on acquiring talent that clubs possess. Competitive conjectures make the adoption of revenue sharing more likely, whereas cartel conjectures make its adoption less likely. This may partly explain why salary caps and revenue sharing tend to be used together in some leagues.

Overtime! Rules and Incentives in the National Hockey League

We construct a simple 2-period game model to determine the effects of recent National Hockey League rule changes on team incentives to win. The effects differ depending on the relative quality of the contestants and whether the contestants compete in the same conference. The model predicts that the average number of points during a season will rise, yet the average point differential among clubs within the same conference will fall. The model also predicts that the expected value of points per contest will be higher when playing nonconference opponents but lower when playing conference opponents. Because only a small percentage of contests are nonconference, we predict that more effort will be devoted to conference contests, particularly by lesser-talented clubs. The result is more competitive and exciting conference games requiring fewer overtime periods and potential ties. Empirical data support these hypotheses.

What's in a Default? Lending to LDCs in the Face of Default Risk

This paper develops an expected profit maximizing framework for characterizing the default risk associated with international lending during the early and mid-1980s. We identify the risk of default as associated with arrears in payments rather than rescheduling of principal or interest.

Gold prices and gold production: Evidence for South Africa

Abstract This paper develops a model of gold production which makes use of the relationship between the price of gold and the average mill pay limit, which allows for the possibility of an inverse gold supply curve. Increases in the price of gold, with constant production costs, reduce the average mill pay limit which gives an incentive for producers to step up production and move into deeper shafts of lower quality ore. If the decrease in the average grade of ore outweighs the increase in the quantity of ore milled, the actual amount of gold produced will fall. An econometric specification of the model using South African production data suggests that the necessary conditions for a perversely downward sloping supply curve of gold are unlikely to exist.

Explaining interest spreads on sovereign Eurodollar loans: LDCs versus DCs, 1978–84

The purpose of this paper was to estimate equations relating spreads above the London Interbank Offer Rate (LIBOR) charged on sovereign-guaranteed private Eurodollar loans to various indicators of default risk for both lesser developed countries (LDCs) and developed countries (DCs). The Study focused on the period 1978–84 using sample loan data of 27. LDCs and 14 developed countries. The results suggest that spreads charged to LDCs are functions of indicators reflecting default risk, while spreads charged to DCs are to a lesser extent. Holding defult risk constant across both LDCs and DCs, a statistically significant gap in the average interest spreads favours DCs. This gap was subsequently explained by variables reflecting investment return from borrowed capital. Significant differences in risk coefficients between LDCs and DCs still persisted for the terms of trade, the debt-service–exports ratio, the investment–GNP ratio and the debt–GNP ratio.

The Passing Premium Puzzle Revisited

The passing premium puzzle states that NFL teams do not call enough passing plays, despite rule changes since the late 1970s that have increased the expected return to passing. This paper develops a simple portfolio model to determine how a coach could determine an optimal share of running and passing plays to maximize the expected yardage return from the portfolio. Coaches are assumed to be risk-averse so that they perceive a tradeoff between a higher expected return to passing and running, and a higher variance of yardage to each. The model is tested by computing the optimal share of running plays and comparing to the actual share of running plays for the 2006 NFL season. It is also demonstrated that a tradeoff does exist between expected yardage return and risk which is the basis for the portfolio model. Finally, portfolio selection is shown to, at least partly, determine winning percentage.

Does IMF Conditionality Benefit Lenders

The purpose of this paper has been to assess whether official and private lenders benefit from IMF participation in rescheduling sovereign LDC debt via the Paris Club. If IMF participation increases the expected value of any existing or newly rescheduled official or private debt contracts, then lenders benefit. The transmission process can be via the immediate liquidity the IMF provides through various loan facilities, which allows for debt service payments to be met in a timely fashion, and/or through the increased ability of the sovereign to meet future debt service payments due to the conditions attached to IMF liquidity. The results from this paper suggest that the provision of immediate IMF liquidity provides a benefit to lenders but that the attached conditions do not. These results were obtained for a large sample of 84 LDCs over the sample period 1978-1987 and may differ when specific cases are considered. IMF participation reduced the average spread over LIBOR by 155 to 179 basis points, based on a simple model relating interest spreads to default probabilities. Heavily indebted sovereign borrowers may have experienced larger reductions. The design and implementation of IMF conditions has been criticized in the literature because they confer little benefit on the sovereign borrower. Our results support the consensus view that the conditions themselves have little effect. However, our contribution results from seeing the issue from the perspective of rational lenders who expend resources to evaluate IMF conditionality programs.

Fighting as a profit maximizing strategy in the National Hockey League: more evidence

ABSTRACT This article estimates the effect of fighting in hockey games on attendance in the National Hockey League (NHL) over the 1997–1998 through 2009–2010 seasons. After estimating a system of equations developed from a model of a profit-maximizing club owner, it was found that fighting had a small negative effect on attendance implying that encouraging fighting on the ice is not a profit-maximizing strategy. The results are quite robust when incorporating capacity constraints on attendance and exogenous ticket pricing. Other factors that determine club performance and market size were found to significantly affect attendance. The empirical results also suggest that NHL club owners are maximizing profit.

Optimal Government Subsidies to Universities in the Face of Tuition and Enrollment Constraints

This paper develops a simple static model of an imperfectly competitive university operating under government‐imposed constraints on the ability to raise tuition fees and increase enrollments. The model has particular applicability to Canadian universities. Assuming an average cost pricing rule, rules for adequate government subsidies (operating grants) are derived under conditions of a forced reduction in tuition fees and limiting the increase in tuition fees in the face of increasing demand. These rules are simple to operationalize and interpret.

Exploring Interleague Parity in North America The NBA Anomaly

The relative standard deviation measure of league parity is persistently higher for the National Basketball Association (NBA) than for the other three major sports leagues in North America. This anomaly spans the last three decades and is not explained by differences in demographic and market characteristics. With a much greater number of scoring attempts in each game, basketball reduces the influence of random outcomes in the number of points scored per game and also season winning percentage. Our simulations demonstrate that lesser parity in the NBA is inherent in the rules of the game so that interleague comparisons must be interpreted carefully.