Competition, Entry, and the Duration of Contracts: Bundling Over Time (PRELIMINARY: NOT FOR DISTRIBUTION)

What determines the length of a contract? A contract that is too short bears the burden of excessive transaction costs. On the other hand, contracts that are too long eliminate the option of switching among the lowest-cost providers. Equilibrium contracts balance these two forces. Fundamentally, the tradeoff of transaction costs and supply costs is a question of bundling. The optimal bundle size (contract duration) generates the lowest expected cost per unit (period) while accounting for the additional costs of separate transactions. In this paper, I focus on the application to bundling across time. Within this theoretical framework, I estimate a model of procurement auctions where 1) contract length is determined endogenously, 2) the distribution of private costs depends on the length of the contract, and 3) there is unobserved auction-specific heterogeneity. I demonstrate nonparametric identification when only the winning bids are observed and entry is exogenous. The nonparametric identification of private values and auction-level heterogeneity holds for models without endogenous cost-shifters (contract length). In markets with imperfect competition, the efficient contract is generally not equal to the equilibrium (procurer-optimal) contract. Buyers or sellers may use the duration of a contract to exercise ex ante market power. In a dataset on U.S. federal labor contracts for janitors, I find that about three-quarters of the contracts are too short and one-quarter are too long. Counter-intuitively, I find that the efficiency loss is increasing in the number of bidders. The nature of buyer-seller relationships varies across markets. In some markets, such as the market for computer processors, a single seller (Intel) supplies the needs of the buyer ∗Department of Economics, University of Chicago ([email protected]). 1 (Apple) over a long period. In others, such as commodity spot markets, the buyer-seller relationships are transient and perhaps anonymous. Across many markets, these relationships are governed by fixed-term contracts.1 In a classic survey of industrial prices, Stigler and Kindahl (1970) found that over a quarter of business-to-business supply transactions were under fixed-term contracts. In electricity markets, fixed-term contracts are common between purchasers and producers, as well as between producers and suppliers of raw inputs like coal (Joskow (1985)) and natural gas (Crocker and Masten (1985)). In labor markets, the prevalence of such contracts varies from country to country; on average, 14 percent of labor contracts in the European Union are of limited duration.2 This paper provides a theory of buyer-seller relationships governed by fixed-term contracts: why these contracts vary in length, and how market-determined contracts may differ from efficient contracts. Contracts that are determined by market participants (buyers and sellers) may be too long or too short, resulting in wasteful social costs. Counterintuitively, these extra costs may increase as a market become more competitive. Therefore, from a policy standpoint, highly competitive markets may be of more concern for regulators than those that are more concentrated. This result occurs because market participants care about price rather than cost, and the price responds more quickly to a change in contract length than the cost when the number of bidders is large.3 What determines the equilibrium duration of a contract? For concreteness, suppose a seller (the government) is issuing contracts of a set duration. With no transaction costs and a moderate degree of competition, the seller would like the contracts to be as short as possible, to ensure that the bidder with the lower cost over each time increment is the winning bidder. When the contracts are long, averaging across many periods increases the expected costs for the winning bidders. With transaction costs, the procurer increases the duration of the contract to reduce the frequency of these costs. In equilibrium, the marginal cost of the transaction is balanced against the cost-reducing benefit of switching more frequently. This tradeoff is mediated by the degree of competition; for many cost distributions, the optimal contract length that is U-shaped in the number of suppliers. For moderate levels of competition, having more bidders increases the return to shorter contracts. When competition is sufficiently intense, 1Why do continued relationships arise in some markets and not in others? Relationships arise naturally when there is variation in supply costs across sellers. The variation may be exogenous (e.g., due to seller-specific private costs) or endogenous (e.g., due to relationship-specific learning). When the costs of suppliers are observable, these relationships are efficiently governed by evergreen contracts when ex post inefficiencies are not present, where either party can terminate at any time. In many cases, however, costs are known imperfectly. In these settings, fixed-term contracts present an efficient solution to the problem of balancing the transaction costs of finding the lowest-cost supplier against the benefit of a better price. 2Source: Eurostat 2014. 3If we think of expected price as the expected second-order statistic, and the cost as the first-order statistic, then we have some intuition for why this could be true. The second-order statistic responds more strongly to a change in variance (or mean) than the first-order statistic when the number of draws is large and the cost distribution is bounded from below. The buyer (or seller) internalizes the contract length’s effect on the second-order statistic rather than its effect on the first-order statistic.