Multi-period Contracts Research Articles

Valuation of a financial claim contingent on the outcome of a quantum measurement

We consider a rational agent who at time 0 enters into a financial contract for which the payout is determined by a quantum measurement at some time T > 0. The state of the quantum system is given in the Heisenberg representation by a known density matrix p^ . How much will the agent be willing to pay at time 0 to enter into such a contract? In the case of a finite dimensional Hilbert space H , each such claim is represented by an observable X^T where the eigenvalues of X^T determine the amount paid if the corresponding outcome is obtained in the measurement. We prove, under reasonable axioms, that there exists a pricing state q^ which is equivalent to the physical state p^ such that the pricing function Π0T takes the linear form Π0T(X^T)=P0Ttr(q^X^T) for any claim X^T , where P0T is the one-period discount factor. By ‘equivalent’ we mean that p^ and q^ share the same null space: that is, for any |ξ⟩∈H one has p^|ξ⟩=0 if and only if q^|ξ⟩=0 . We introduce a class of optimization problems and solve for the optimal contract payout structure for a claim based on a given measurement. Then we consider the implications of the Kochen–Specker theorem in this setting and we look at the problem of forming portfolios of such contracts. Finally, we consider multi-period contracts.

A sharing rule for multi-period interest-sensitive insurance contracts

As sales of interest-sensitive products grow in insurance markets, determining a sharing rule for allocating investment returns between a policyholder and an insurer is crucial. This paper discusses a theoretical sharing rule for a multi-period contract, reflecting that the insurer’s investment efforts are unobservable and that a stream of information inferring the quality of the efforts exists. Our sharing rule is developed by selecting multi-period excess returns as available information and maximizing the expected utility of the policyholder. The empirical analysis shows that the effect of multi-period excess returns on insurers’ sharing patterns is consistent with the theoretical findings.

Equilibrium foreign currency mortgages

This paper proposes a novel explanation for why foreign currency denominated loans to households have become so popular in some emerging economies. Our argument is based on what we call the debt limit channel, which arises when multi-period contracts are offered against collateral that is established on newly acquired assets. Whenever the difference between domestic and foreign interest rates is positive, this effect allows financially constrained agents to backload the real payments on their loans if they choose to borrow in foreign currency. We demonstrate in a structural macroeconomic framework that the debt limit channel is quantitatively important and can result in dollarization of debt despite realistic and correctly perceived exchange rate risk. Comparing this outcome to allocations under constrained-optimal policy reveals that much of the identified bias towards foreign currency is due to a pecuniary externality, i.e. borrowers' failure to internalize how their currency choice affects house prices.

Multiperiod Contracting and Salesperson Effort Profiles: The Optimality of “Hockey Stick,” “Giving Up,” and “Resting on Laurels”

The authors study multiperiod sales force incentive contracting in which salespeople can engage in effort gaming, a phenomenon that has extensive empirical support. Focusing on a repeated moral hazard scenario with two independent periods and a risk-neutral agent with limited liability, the authors conduct a theoretical investigation to understand which effort profiles the firm can expect under the optimal contract. The authors show that various effort profiles that may give the appearance of being suboptimal, such as postponing effort exertion (“hockey stick”) and not exerting effort after a bad or a good initial demand outcome (“giving up” and “resting on laurels,” respectively) may indeed be induced optimally by the firm. This is because, under certain conditions that depend on how severe the contracting frictions are and how effective effort exertion is in increasing demand, the firm wants to concentrate rewards on extreme demand outcomes. Doing this induces gaming and reduces expected demand but also makes motivating effort cheaper, thus saving on incentive payments. On introducing dependence between time periods, such as when the agent can transfer demands between periods, this insight continues to hold and, furthermore, “hockey stick,” “giving up,” and “resting on laurels” can be optimal for the firm even under repeated short time horizon contracting. The results imply that one must carefully consider the setting and environmental factors when making inferences about contract effectiveness from dynamic effort profiles of agents.

Multi-Period Contracting and Salesperson Effort Profiles: The Optimality of 'Hockey Stick,' 'Giving Up' and 'Resting on Laurels'

We study multi-period sales-force incentive contracting where salespeople can engage in effort gaming, a phenomenon that has extensive empirical support. Focusing on a repeated moral hazard scenario with two independent periods and a risk-neutral agent with limited liability, we conduct a theoretical investigation to understand which effort profiles the firm can expect under the optimal contract. We show that various effort profiles that may give the appearance of being sub-optimal, such as postponing effort exertion (“hockey stick”) and not exerting effort after a bad or a good initial demand outcome (“giving up” and “resting on laurels,” respectively) may indeed be induced optimally by the firm. The reason is that, under certain conditions that depend on how severe the contracting frictions are and how effective effort exertion is in increasing demand, the firm wants to concentrate rewards on extreme demand outcomes; this induces gaming and reduces expected demand, but also makes motivating effort cheaper thus saving on incentive payments. On introducing dependence between time periods, such as when the agent can transfer demands between periods, this insight continues to hold and, furthermore, “hockey stick,” “giving up” and “resting on laurels” can be optimal for the firm even under repeated short time horizon contracting. Our results imply that one must carefully consider the setting and environmental factors when making inferences about contract effectiveness from dynamic effort profiles of agents.

Effectiveness of Macroprudential Policies under Maturity Mismatch

ABSTRACT This paper studies the role of reserve requirements as a macroprudential policy tool in China. In a factor-augmented vector autoregression of China, we find that banking system works as a shock absorber. To explain this “financial attenuator” effect, we extend an otherwise standard New-Keynesian model including (i) a banking sector with financial frictions with households, (ii) a credit in multi-period contracts, (iii) a central bank that conducts monetary policy by adjusting the nominal interest rate in response to the money-growth rate, and (iv) the reserve requirement (RR) as a macroprudential policy instrument. The quantitative analysis of the estimated model shows that the presence of a maturity mismatch makes a bank’s leverage less procyclical, which offsets the effects of financial frictions and makes the bank’s balance sheet function as a shock absorber. Our analysis also suggests that countercyclical RR adjustment can enhance welfare compared to fixed an RR ratio in the presence of a maturity mismatch but faces important implementation challenges. In particular, an RR policy countercyclically responding to bank lending can effectively stabilize the economy but increase financial fragility, as the “credit attenuator” effect stemming from the maturity mismatch will be offset by this policy.

Repeated Moral Hazard with Costly Self Control

We consider a repeated principal-agent model, where a single agent exhibits problems of self control modelled using Gul and Pesendorfer (2001) type temptation preferences. In such a setting, for a parameterized strength of self-control, we solve for the optimal multi-period contract. Our analysis identifies a new channel of principal and agent interactions, that can be used to provide incentives, this being the reduction of agent's self control costs. In fact, the principal computes (and uses) agent's most tempting item but never finds it optimal to reduce the agent's self-control cost to zero. Presence of this new channel challenges typical results obtained in models with no-temptation on the agent's side. For example, the intrinsic motivation (resulting from costly self-control) can substitute for standard (external) incentives, and hence the moral hazard problem can be mitigated (for suficiently high temptation parameter). Moreover, the optimal contract calls for a lower deferred part of the bonus (or consumption smoothing) than in the model with no temptations. Under limited commitment, presence of self-control also reduces agent's willingness to break or renegotiate the contract after output realization within some period, and make the optimal contract spot implementable (again for suficiently high temptation). Impact of self-control on the cost of implementation as well as willingness to safe/borrow is ambiguous, however.

Relative incentive rate in a multi-period and multi-task agency

This study explicitly calculates the relative incentive rate in an N-period contract with multiple tasks. The inter-temporal covariance risk, as well as the within-period risk premium, prevents the first best allocation of effort from being endogenously achieved even if the first best allocation is feasible. The inter-temporal covariance risk reduces the effective sensitivity of a performance measure, and thus the performance measure with a bigger inter-temporal covariance risk is assigned a weaker relative incentive rate. From these results, an empirical prediction is derived that a performance measure with larger positive (negative) inter-temporal covariances is assigned a weaker (stronger) relative incentive rate in multi-period contracts.

Strongly Loss Averse CEO Compensation: Long Calls or Short Puts?

This paper studies how compensation and incentives are provided to a loss averse agent with reference-dependent preferences, first in a single-period and then in a multiperiod setting. In the single-period contract, when the agent's actions are not observable by the principal (moral hazard), the paper shows how the presence of loss aversion can lead to simple contracts in contrast with the more complex contracts of classical principal-agent theory. Further, under these circumstances, the principal should offer the agent a base plus malus contract rather than base plus bonus as is current practice. Regarding multiperiod contracts, the two-period contract is different contingent on whether or not the agent has committed to remain both periods or not. Whether or not the agent has committed to remain, the two-period moral hazard contract compensates the agent in the second period based on his performance in the first period, providing incentives both immediate and intertemporal. The analysis of the general T-period contract shows that the single-period results hold in every period and the two-period results hold in all but the last period.

New and Revised Results for 'Building Reputation for Contract Renewal: Implications for Performance Dynamics and Contract Duration'

In this paper we present some new results for the dynamic agent model by Iossa and Rey (2014, Building Reputation for Contract Renewal: Implications for Performance Dynamics and Contract Duration,'' Journal of the European Economic Association, 12, 549−574) while also correcting some errors in that article. Iossa and Rey study the performance of an agent who repeatedly receives multi-period contracts and determine the optimal duration of such contracts in the context of an infinitely repeated multi-period agent model. We amend the characterization of the unique Markov perfect equilibrium for this model. In addition, we review the original welfare analysis of the model and either provide corrected proofs when possible or provide counterexamples. Our counterexamples overturn the main comparative statics results of the original analysis. We demonstrate that both the agent's optimal investment decision and the optimal contract duration depend non-monotonically on the information persistence and the agent's discount factor. In the final part of the analysis, we establish new results on the agent's optimal investment decision.

Developing a temporary workforce transaction mechanism from risk sharing perspectives

In a low-profit environment, numerous firms no longer use traditional hiring practices and are forced to use a temporary workforce; these practices result in a more flexible workforce. Although outsourcing provides several benefits, it has a high level of risk. Therefore, implementing an enterprise risk management programme is crucial for using temporary labour. This study investigated the condition under which the multiperiod contract of a temporary work agency prohibits labour shortages. This investigation was performed to improve the effectiveness of dispatch contract designs. This study incorporated the concepts of labour demand forecasting and risk sharing and proposes two types of quantity flexibility contracts, period quantity adjustment and total quantity adjustment, to develop an optimal manpower dispatch contract model. An optimal manpower dispatch contract model must coordinate the interests of a temporary work agency and user firms to increase profits for both firms and must be flexible enough to allow for numerous order adjustments. To achieve this objective, this study used sensitivity analysis and an experimental design methodology to analyse the benefits of period quantity adjustment and total quantity adjustment and, accordingly, determine the factors that influence the total expected profit.

Target Ratcheting and Achievability of Earnings Targets

A fundamental problem of incentive contracting, often referred to as the ratchet effect, is that good performance in one period may be penalized by next-period targets that are more difficult to achieve. Several studies provide evidence that favorable performance relative to target is associated with target increases in the next period. The maintained assumption in much of this literature is that target revisions upward render targets more difficult to achieve. In contrast, our study uses data from a unique survey panel to directly examine whether favorable performance relative to target leads to next-period targets that are more difficult to achieve. First, we replicate prior results that favorable performance relative to target is associated with next-period target increases. Second, and contrary to the maintained assumption in prior work, we show that favorable performance relative to target is also associated with increases in the likelihood that next-period targets will be achieved. Thus, our results suggest that firms revise performance targets in a way that allows well-performing managers to repeatedly meet their targets. This is consistent with the theory that commitment facilitates multi-period contracting and allows firms to overcome the adverse incentive consequences of the ratchet effect.

Monetary and Macroprudential Policy with Multi-Period Loans

We study the implications of multi-period loans for monetary and macroprudential policy, considering several realistic modifications – variable vs. fixed loan rates, non-negativity constraint on newly granted loans, and possibility for the collateral constraint to become slack – to an otherwise standard DSGE model with housing and financial intermediaries. Our general finding is that multiperiodicity affects the working of both policies, though in substantially different ways. We show that multi-period contracts make the monetary policy less effective, but only under fixed rate mortgages, and do not generate significant asymmetry to its transmission. In contrast, the effects of macroprudential policy do not depend much on the type of interest payments, but exhibit strong asymmetries, with tightening having stronger effects than easening, especially for short and medium maturities.

Multiperiod Coordination Models of Coal-Electricity Supply Chain with Double Price Regulations

Using game models, we study multiperiod coordination contract and model of coal-electricity supply chain under the condition of double price regulations to alleviate the price conflicts of coal and electricity enterprises. The study reveals that, in boom seasons of coal demand, the multiperiod coordination mechanism may not only reduce the price of thermal coal but also increase the fulfillment rate of thermal coal. Meanwhile, the ordering quantity of thermal coal is increased and the shortage probability of electricity supply is decreased. Thereby, the conflicts between coal and electricity are also alleviated effectively.

BUILDING REPUTATION FOR CONTRACT RENEWAL: IMPLICATIONS FOR PERFORMANCE DYNAMICS AND CONTRACT DURATION

We study how career concerns affect the dynamics of incentives in a multi-period contract, when the agent’s productivity is a stochastic function of his past productivity and investment. We show that incentives are stronger and performance is higher when the contract approaches its expiry date. Contrary to common wisdom, long-term contracts may strengthen reputational effects whereas short-term contracting may be optimal when investment has persistent, long-term effects.

Monetary and Macroprudential Policy with Multiperiod Loans

We study the implications of multi-period loans for monetary and macroprudential policy, considering several realistic modifications – variable vs. fixed loan rates, non-negativity constraint on newly granted loans, and possibility for the collateral constraint to become slack – to an otherwise standard DSGE model with housing and financial intermediaries. Our general finding is that multiperiodicity affects the working of both policies, though in substantially different ways. We show that multi-period contracts make the monetary policy less effective, but only under fixed rate mortgages, and do not generate significant asymmetry to its transmission. In contrast, the effects of macroprudential policy do not depend much on the type of interest payments, but exhibit strong asymmetries, with tightening having stronger effects than easening, especially for short and medium maturities.

A COMPARATIVE ANALYSIS OF INTEREST RATES: FORMAL SECTOR BANKS, LOCAL MONEYLENDERS AND MICROFINANCE INSTITUTIONS

This study examines the interest rate differences paid to a bank, a Micro Finance Institution (MFI) and a local moneylender. In a multi-period lending contract, a borrower discounting the future income stream at a constant rate is willing to pay the highest interest rate to the local moneylender, comparatively lower rate to a MFI and the lowest to a formal sector bank. In other words, if the interest rate charged by each of the three lenders is the same, the repayment rate will be highest for a moneylender followed by a MFI and the lowest for a formal sector bank.

Adverse Selection in Insurance Contracting

In this survey we present some of the more significant results in the literature on adverse selection in insurance markets. Sections 1 and 2 introduce the subject and Section 3 discusses the monopoly model developed by Stiglitz (1977) for the case of single-period contracts extended by many authors to the multi-period case. The introduction of multi-period contracts raises many issues that are discussed in detail; time horizon, discounting, commitment of the parties, contract renegotiation and accidents underreporting. Section 4 covers the literature on competitive contracts. The analysis is more complicated because insurance companies must take into account competitive pressures when they set incentive contracts. As pointed out by Rothschild and Stiglitz (1976), there is not necessarily a Cournot-Nash equilibrium in the presence of adverse selection. However, market equilibrium can be sustained when principals anticipate competitive reactions to their behavior or when they adopt strategies that differ from the pure Nash strategy. Multi-period contracting is discussed. We show that different predictions on the evolution of insurer profits over time can be obtained from different assumptions concerning the sharing of information between insurers about individual's choice of contracts and accident experience. The roles of commitment and renegotiation between the parties to the contract are important. Section 5 introduces models that consider moral hazard and adverse selection simultaneously and Section 6 covers adverse selection when people can choose their risk status. Section 7 discusses many extensions to the basic models such as risk categorization, multidimensional adverse selection, symmetric imperfect information, reversed or double-sided adverse selection, principals more informed than agents, uberrima fides and participating contracts.

The role of information and financial reporting in corporate governance and debt contracting

We review recent literature on the role of financial reporting transparency in reducing governance-related agency conflicts among managers, directors, and shareholders, as well as in reducing agency conflicts between shareholders and creditors, and offer researchers some suggested avenues for future research. Key themes include the endogenous nature of debt contracts and governance mechanisms with respect to information asymmetry between contracting parties, the heterogeneous nature of the informational demands of contracting parties, and the heterogeneous nature of the resulting governance and debt contracts. We also emphasize the role of a commitment to financial reporting transparency in facilitating informal multiperiod contracts among managers, directors, shareholders, and creditors.

The Role of Information and Financial Reporting in Corporate Governance and Debt Contracting

We review recent literature on the role of financial reporting transparency in reducing governance-related agency conflicts among managers, directors, and shareholders, as well as in reducing agency conflicts between shareholders and creditors, and offer researchers some suggested avenues for future research. Key themes include the endogenous nature of debt contracts and governance mechanisms with respect to information asymmetry between contracting parties, the heterogeneous nature of the informational demands of contracting parties, and the heterogeneous nature of the resulting governance and debt contracts. We also emphasize the role of a commitment to financial reporting transparency in facilitating informal multi-period contracts among managers, directors, shareholders, and creditors.