Multi-period Contracts Research Articles

Measuring the Impact of Financial Intermediation: Linking Contract Theory to Econometric Policy Evaluation.

We study the impact that financial intermediation can have on productivity through the alleviation of credit constraints in occupation choice and/or an improved allocation of risk, using both static and dynamic structural models as well as reduced form OLS and IV regressions. Our goal in this paper is to bring these two strands of the literature together. Even though, under certain assumptions, IV regressions can recover accurately the true model-generated local average treatment effect, these are quantitatively different, in order of magnitude and even sign, from other policy impact parameters (e.g., ATE and TT). We also show that laying out clearly alternative models can guide the search for instruments. On the other hand adding more margins of decision, i.e., occupation choice and intermediation jointly, or adding more periods with promised utilities as key state variables, as in optimal multi-period contracts, can cause the misinterpretation of IV as the causal effect of interest.

Competition and the Ratchet Effect

The 'ratchet effect' refers to a situation where a principal uses private information that is revealed by an agent's early actions to the agent's later disadvantage, in a context where binding multi-period contracts are not enforceable. In a simple, context-rich environment, we experimentally study the robustness of the ratchet effect to the introduction of ex post competition for principals or agents. While we do observe substantial and significant ratchet effects in the baseline (no competition) case of our model, we find that ratchet behavior is nearly eliminated by labor-market competition; interestingly this is true regardless of whether market conditions favor principals or agents.

Promised Lead-Time Contracts Under Asymmetric Information

We study the important problem of how a supplier should optimally share the consequences of demand uncertainty (i.e., the cost of inventory excesses and shortages) with a retailer in a two-level supply chain facing a finite planning horizon. In particular, we characterize a multiperiod contract form, the promised lead-time contract, that reduces the supplier's risk from demand uncertainty and the retailer's risk from uncertain inventory availability. Under the contract terms, the supplier guarantees on-time delivery of complete orders of any size after the promised lead time. We characterize the optimal promised lead time and the corresponding payments that the supplier should offer to minimize her expected inventory cost, while ensuring the retailer's participation. In such a supply chain, the retailer often holds private information about his shortage cost (or his service level to end customers). Hence, to understand the impact of the promised lead-time contract on the supplier's and the retailer's performance, we study the system under local control with full information and local control with asymmetric information. By comparing the results under these information scenarios to those under a centrally controlled system, we provide insights into stock positioning and inventory risk sharing. We quantify, for example, how much and when the supplier and the retailer overinvest in inventory as compared to the centrally controlled supply chain. We show that the supplier faces more inventory risk when the retailer has private service-level information. We also show that a supplier located closer to the retailer is affected less by information asymmetry. Next, we characterize when the supplier should optimally choose not to sign a promised lead-time contract and consider doing business under other settings. In particular, we establish the optimality of a cutoff level policy. Finally, under both full and asymmetric service-level information, we characterize conditions when optimal promised lead times take extreme values of the feasible set, yielding the supplier to assume all or none of the inventory risk—hence the name all-or-nothing solution. We conclude with numerical examples demonstrating our results.

Bank Lending Policy, Credit Scoring, and the Survival of Loans

To evaluate loan applicants, banks increasingly use credit scoring models. The objective of such models typically is to minimize default rates or the number of incorrectly classified loans. Thereby they fail to take into account that loans are multiperiod contracts, for which reason it is important for banks not only to know if but also when a loan will default. In this paper a bivariate tobit model with a variable censoring threshold and sample selection effects is estimated for (1) the decision to provide a loan or not and (2) the survival time of granted loans. The model proves to be an effective tool to separate applicants with short and with long survival times. The bank's loan provision process is shown to be inefficient: loans are granted in a way that conflicts with both default risk minimization and survival time maximization. There is thus no trade-off between higher default risk and higher return in the lending policy.

Bank Lending Policy, Credit Scoring and the Survival of Loans

To evaluate loan applicants, banks increasingly use credit scoring models. The objective of such models typically is to minimize default rates or the number of incorrectly classified loans. Thereby they fail to take into account that loans are multiperiod contracts for which reason it is important for banks not only to know if but also when a loan will default. In this paper a bivariate Tobit model with a variable censoring threshold and sample selection effects is estimated for (1) the decision to provide a loan or not and (2) the survival of granted loans. The model proves to be an effective tool to separate applicants with short survival times from those with long survivals. The bank's loan provision process is shown to be inefficient: loans are granted in a way that conflicts with both default risk minimization and survival time maximization. There is thus no trade-off between higher default risk and higher return in the lending policy.

Equilibrium Contracts In a Bilateral Monopoly with Unequal Bargaining Powers

Real-world bilateral monopolies often indicate that one party exercises slightly Superior bargaining power than the other party. We analyze long-term, cooperative Contracts in bilateral monopolies with unequal bargaining powers. We assume that the Two parties bargain for a determinate price and quantity of the intermediate product by Optimizing a joint objective which takes into account the profits and bargaining power of Each party. We use a Bowley price leadership model to develop the multi-period Contracts and derive conditions that induce a Nash equilibrium at the jointly determined Points of operation. [C71,C78]

Financial intermediaries and the design of loan contracts within the Australasian pastoral sector before the Second World War

Simon Ville and Grant Fleming, Financial intermediaries and the design of loan contracts within the Australasian pastoral sector before the Second World WarThis paper examines the pooling and separating contracts designed by Australasian financial intermediaries in the late nineteenth and early twentieth centuries. We show that, after an initial screening process, these agents altered interest rates and collateral requirements to separate out risk types to reveal additional information on borrowers. In multi-period contracts, agents opted for flexible contract structures which permitted changes in individual or community-wide circumstances.

Dynamic incentives and responsibility accounting

In dynamic principal–agent relationships, unless a principal can commit to a multiperiod contract, incentives are affected by a problem known as the ratchet effect. We present a two-period agency model to show that the use of more aggregate performance measures and greater consolidation of responsibility helps mitigate the ratchet effect. For example, an aggregate measure may be preferred to a set of disaggregate measures to avoid aggravating the ratchet effect. Similarly, it may be preferable to consolidate responsibility for two activities in the hands of one agent despite the potential loss of performance evaluation information implied by consolidation.

Price and interest rate dynamics induced by multiperiod contracts

This paper suggests a mechanism by which nominal price rigidities can create a transmission mechanism for monetary shocks through relative price distortions in an economy with both spot and contract markets. The globally unique equilibrium time path of interest rates and prices following an impulse shock to the money supply is characterized. The model predicts that prices and interest rates cycle around the new steady state, with real interest rates initially falling and prices overshooting in the case of a positive shock. The volatility of spot prices and interest rates exceeds that of contract prices.

Why Do Labor Contracts Offer Guaranteed Annual Wage Increments?

An interesting feature of wage contracts for tenured academic staff in United Kingdom universities is that they formally embody the principal that wages should increase with seniority. Individuals are hired at, or near, the bottom of a wage scale that has seventeen different wage levels each separated by approximately 5%. Once hired, lecturers are guaranteed the right to move at least one step up this pay ladder each year.' Of course this whole scale is renegotiated annually, resulting in additional wage increases, superimposed on the automatic increments. Many other U.K. public sector labor contracts employ a similar wage ladder, for example those of civil servants, local government employees, school teachers and health service workers. Although employment of these groups is very secure, contracts of university lecturers are particularly interesting because tenure guarantees to the individual, over some range, both increasing wages and future employment. Thus, although the evidence for seniority wages from econometric studies has been mixed [1; 2], we have in these contracts a clear cut case to explain, and one with the additional wrinkle of guaranteed future employment. In this paper we adopt an explicitly multi-period framework in order to investigate guaranteed wage increments over time. A critical feature of the model is the assumption that consumption is allocated across periods according to the life-cycle hypothesis. Multi-period contracts are therefore evaluated by the lifetime utility which they yield. It should be emphasized that even for contracts where wage increments are guaranteed, there still remains residual uncertainty about future earnings since the possibility exists that a worker may receive a better outside offer. In section II this uncertainty is motivated by incomplete search and in section III by the fact that ability only becomes known after the first period of employment. These essentially represent different interpretations of the same model. The analysis of section II assumes that all workers are offered a tenure contract and it is shown that seniority wages arise naturally in such a framework. This in followed in section III by a joint analysis of seniority wages and the firm's decision whether to offer a tenure contract. In this case, seniority wages can again arise and, importantly, tenure contracts can actually be more profitable for the firm than contracts with no tenure. Two

Tie-in arrangements of life insurance and savings: an economic rationale

Cash-value life insurance contracts can be viewed as tying life insurance with savings. The main purpose of this article is to provide an economic rationale for this widespread practice. It is assumed that there is an asymmetry of information between the insurers and insureds, where the latter know better their probability of death, and hence adverse selection may cause a market failure. To overcome this problem, a multiperiod (for exposition purposes a three-period model is used) contract and a single-period contract are offered. The multiperiod contract specifies a savings element which may be received by the insured at his or her discretion if the insured lives at the end of the second period. lt is shown that by the right choice of the savings element and the return on this element, the insurers can induce insureds to self select. Insureds with lower probabilities of death will choose the multiperiod conitract whereas insureds with higher mortality rates will choose successive single-period contracts. It is therefore shown that tie-in arrangements of savings and insurance may help solve the problem of adverse selection and hence an economic rationale is provided for their existence. Cash-value life insurance contracts tie savings and risk of death insurance. Many researchers tried to explain the popularity of such tie-in arrangements, and whether they can dominate a strategy of buying risk insurance (i.e., term insurance) and savings separately (see, e.g., Ferrari, 1968; Fortune, 1973;

Dissolution of marital property : Tie-in arrangements of life insurance and savings: An economic rationale, by Itzhak Venezia (University of California, Los Angeles and Hebrew University, Jerusalem)

Cash-value insurance contracts can be viewed as tying life insurance with savings. The main purpose of this article is to provide an economic rationale for this widespread practice. It is assumed that there is an asymmetry of information between the insurers and insureds, where the latter know better their probability of death, and hence adverse selectin may cause a market failure. To overcome this problem, a multiperiod (for exposition purposes a three-period model is used) contract and a single-period contract are offered. The multiperiod contract specifies a savings element which may be received by the insured at his or her discretion. If the insured lives at the end of the second period. It is shown that by the right choice of the savings element and the return on this element, the insurers can induce insureds to self-select. Insureds with lower probabilities of death will choose the multiperiod contract whereas insureds with higher mortality will choose successive single-period contracts. It is therefore shown that tie-in arrangements of savings and insurance may help the problem of adverse selection and hence an economic rationale is provided for their existence. (reprinted with permission).

Long-Term Financial Contracts can Mitigate the Adverse Selection Problem in Project Financing

This paper shows that long-term contracts can be used in competitive financial markets to separate entrepreneurs of different abilities. In equilibrium poor entrepreneurs are financed with a sequence of standard-debt contracts. Good entrepreneurs are financed with a modified contract, in which the terms of the second part of the contract are contingent upon whether default is observed at the first date. Sorting is achieved through the contingent term in the contract. In equilibrium good entrepreneurs will typically pay high interest rates to start with, followed by relatively lower rates later if they are successful. The solution in the paper is contrasted with the use of collateral. Incomplete information plays an important role in explaining the existence and form of enduring relationships. When agents have private information and cannot precommit to future actions and announcements there may be a role for multiperiod contracts (see Townsend 1982 and Hart and Holmstrom 1986). Such contracts tie future contractual terms to current behaviour. Moreover, these contracts can be self-enforcing, simply relying upon the self interest of agents to see them through. This paper shows that long-term relationships may help overcome adverse selection problems. The basic idea is very simple. Entrepreneurs have different probabilities of completing successive projects successfully. Observation of the returns cannot reveal the type of project. However, repeated observation of returns does give information about the type of project, by the law of large numbers. Even if there are only two observations at successive dates it may be possible to separate types by making the terms of the contract at the second date conditional upon whether default is observed at the first. We consider an entrepreneur who is risk neutral and who has a project at each of two successive dates. The projects may require outside finance from banks. Risk neutral banks offer two-period credit contracts to the entrepreneur. We assume that there are two types of entrepreneur, one with a high probability of completing projects successfully and a second with a low probability. The probability of success is private information to the entrepreneur, it is not known by the bank. The problem of generalising the analysis to more entrepreneur types is discussed in the conclusion. In Section 2 of the paper it is shown that in this setting an adverse selection problem may arise. We consider a sequence of standard-debt contracts which specify a fixed payment at each date. The important point to note here is that with

Inflation and wage indexation with multiperiod contracts: A comment

In a recent paper, Spivak, Weinblatt and Zilberfarb claim that, when contracts are overlapping and uniformly distributed over time, indexation always increases the absolute value of inflation and its variability. However, it can be shown that this result depends on a peculiar and implausible assumption on the indexation scheme in this framework, i.e., that the wage in a sector is indexed on the price of the good produced in that sector. When wages are indexed on the general price level, it is found that the absolute value of inflation and its variability do not necessarily increase with the indexation degree.

Tying life insurance and savings decisions: A multiperiod expected utility approach

Many whole-life insurance contracts provide, in addition to protection in case of death of the insured, also a savings element. The main purpose of this article is to provide an economic rationale for this practice. Two alternative models are offered. In both models it is assumed that there is an asymmetry of information between the insurers and insureds, where the know better their probability of death, and hence adverse selection may cause a market failure. It is shown that by offering several deliberately designed contracts tying savings and insurance the insurers can induce the insureds to self select. That is, insureds with higher probability of death will voluntarily choose different contracts than those with a lower probability of death, and hence will reveal their probability of death to the insurers. The problem of adverse selection is thus overcome. In the first model contracts differ in the amount of insurance they specify and the amount of savings tied with insurance. In the second model a multiperiod (actually two period) contract and a single period contract are offered. The multiperiod contract specifies a savings element which will be received by the insured if he or she lives at the end of the second period. It is shown that by the right choice of the return on the savings part, insureds with lower probabilities of death will choose the multiperiod contract whereas insureds with higher probability of death will prefer two successive single period contracts. Again self selection is achieved. These two models show that tie-in arrangements of savings and insurance may help overcome the adverse selection problem, and hence an economic rationale is provided for their existence. The paper also examines the demand for life insurance and savings. The sensitivity of the demand for these products to variations in key parameters is analyzed. The differences between the sensitivity analyses results obtained when insurance and savings decisions are made separately and those obtained when these decisions are simultaneosly made are highlighted and explained.

Long-term contracts, consumption smoothing and wage-profit dynamics

Implicit contract theory stresses that stockholders' access to capital markets is superior to that of workers. This paper analyzes the implications of this assumption in an intertemporal context with uninsurable, macroeconomic risk. The optimal multiperiod contract between risk-averse stockholders and workers uses the firm as a financial intermediary and its retained earnings are their joint savings. A specific example is worked out that yields closed-form solutions for wages, profits and investment that are broadly consistent with their observed behavior over the business cycle.

Inflation and wage indexation with multiperiod contracts

This paper deals with the impact of wage indexation on the rate of inflation in two alternative institutional settings: simultaneous and overlapping multiperiod contracts. The results show that in the case of simultaneous contracts, the degree of indexation determines the timing of price changes but not its intercontract magnitude. When contracts are overlapping and uniformly distributed over time, indexation always increases the absolute rate of inflation and its variability.

On the Duration of Agreements

A model of optimal contracts between two infinitely-lived parties, a borrower and lender, is presented and analyzed. The objective is to explain the phenomenon of finite-length, multi-period contracts. It is shown how costly information acquisition can account for multi- period contracts which are of bounded length. Comparative-statics results on how contract length responds to exogenous parameters, such as the cost of information acquisition, are also derived. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

The large-small bank dichotomy in the federal funds market

Despite the central importance of the federal fund market, little research has been undertaken on the micro-decision making of individual market participants and their interactions. This paper demonstrates that there are asymmetries of information between federal funds' lenders and borrowers that can only be resolved through frequent and continuous trading. Smaller banks are constrained in their ability to borrow federal funds due to their size and location. It is shown that information asymmetries and resulting adverse selection problems may be resolved through the use of implicit multi-period contracts.

Contracts without memory in multiperiod agency models

Settings are considered in which optimal multiperiod contracts can have no memory, i.e., where second period payments do not need to depend on first period outcomes. If contracts have no memory, a repeated agency game can be played myopically; there are no gains to long-term relationships. Conditions on preferences for a no memory contract are presented. In an agency game with moral hazard on the act selection, preference separability and domain additivity imply the existence of a no memory contract. In a setting without moral hazard but with asymmetric information on the outcome, domain additivity implies no memory.