Experimentation, Private Observability of Success, and the Timing of Monitoring

Similar documents
Economics 2202 (Section 05) Macroeconomic Theory Practice Problem Set 3 Suggested Solutions Professor Sanjay Chugh Fall 2014

Sequential Procurement Auctions and Their Effect on Investment Decisions

FOREST CITY INDUSTRIAL PARK FIN AN CIAL RETURNS EXECUTIVE SUMMARY

TOTAL PART 1 / 50 TOTAL PART 2 / 50

Associate Professor Jiancai PI, PhD Department of Economics School of Business, Nanjing University

AUDITING COST OVERRUN CLAIMS *

0NDERZOEKSRAPPORT NR TAXES, DEBT AND FINANCIAL INTERMEDIARIES C. VAN HULLE. Wettelijk Depot : D/1986/2376/4

Managerial Legacies, Entrenchment and Strategic Inertia

Managerial Legacies, Entrenchment and Strategic Inertia

Problem Set 8 Topic BI: Externalities. a) What is the profit-maximizing level of output?

Economics 602 Macroeconomic Theory and Policy Problem Set 4 Suggested Solutions Professor Sanjay Chugh Summer 2010

Explanatory Memorandum

Asymmetric Integration *

Strategic Dynamic Sourcing from Competing Suppliers: The Value of Commitment

Are Hard Budget Constraints for Sub-National GovernmentsAlwaysEfficient?

i e AT 16 of 2008 INSURANCE ACT 2008

Consumption smoothing and the welfare consequences of social insurance in developing economies

Output and Expenditure

Risk Sharing and Adverse Selection with Asymmetric Information on Risk Preference

The Economics of Setting Auditing Standards

Decision-making Method for Low-rent Housing Construction Investment. Wei Zhang*, Liwen You

Dynamic Pricing of Di erentiated Products

Transport tax reforms, two-part tariffs, and revenue recycling. - A theoretical result

i e SD No.2015/0206 PAYMENT SERVICES REGULATIONS 2015

The Impact of Capacity Costs on Bidding Strategies in Procurement Auctions

The Simple Economics of White Elephants

The Simple Economics of White Elephants

Retirement Benefits Schemes (Miscellaneous Amendments) RETIREMENT BENEFITS SCHEMES (MISCELLANEOUS AMENDMENTS) REGULATIONS 2014

Contending with Risk Selection in Competitive Health Insurance Markets

Limiting Limited Liability

CHAPTER 9 BUDGETARY PLANNING SUMMARY OF QUESTIONS BY STUDY OBJECTIVES AND BLOOM S TAXONOMY. True-False Statements. Multiple Choice Questions

Exogenous Information, Endogenous Information and Optimal Monetary Policy

PROSPECTUS May 1, Agency Shares

Licensing and Patent Protection

Page 80. where C) refers to estimation cell (defined by industry and, for selected industries, region)

NBER WORKING PAPER SERIES MYOPIA AND THE EFFECTS OF SOCIAL SECURITY AND CAPITAL TAXATION ON LABOR SUPPLY. Louis Kaplow

Multi-Firm Mergers with Leaders and Followers

Optimal Disclosure Decisions When There are Penalties for Nondisclosure

The Simple Economics of White Elephants

Kyle Bagwell and Robert W. Staiger. Revised: November 1993

Economics 325 Intermediate Macroeconomic Analysis Practice Problem Set 1 Suggested Solutions Professor Sanjay Chugh Spring 2011

Study on Rural Microfinance System s Defects and Risk Control Based on Operational Mode

Optimal Contracting with Unknown Risk Preference

Source versus Residence Based Taxation with International Mergers and Acquisitions

ON TRANSACTION COSTS IN STOCK TRADING

Libertarian Paternalism, Information Sharing, and Financial Decision-Making

Giacomo Calzolari and Giancarlo Spagnolo*

Clipping Coupons: Redemption of Offers with Forward-Looking Consumers

Valuation of Bermudan-DB-Underpin Option

A Truthful Budget Feasible Multi-Armed Bandit Mechanism for Crowdsourcing Time Critical Tasks

Optimal Auditing Standards

Globalization, Jobs, and Welfare: The Roles of Social Protection and Redistribution 1

CONSUMPTION-LABOR FRAMEWORK SEPTEMBER 19, (aka CONSUMPTION-LEISURE FRAMEWORK) THE THREE MACRO (AGGREGATE) MARKETS. The Three Macro Markets

Myopia and the Effects of Social Security and Capital Taxation on Labor Supply

THE STUDY OF RELATIONSHIP BETWEEN CAPITAL STRUCTURE, FIRM GROWTH WITH FINANCIAL LEVERAGE OF THE COMPANY LISTED IN TEHRAN STOCK EXCHANGE

Policy Consideration on Privatization in a Mixed Market

Intermediating Auctioneers

Importantly, note that prices are not functions of the expenditure on advertising that firm 1 makes during the first period.

CONSUMPTION-LEISURE FRAMEWORK SEPTEMBER 20, 2010 THE THREE MACRO (AGGREGATE) MARKETS. The Three Macro Markets. Goods Markets.

i e SD No.2017/0343 PAYMENT SERVICES (AMENDMENT) REGULATIONS 2017

Important information about our Unforeseeable Emergency Application

Ranking dynamics and volatility. Ronald Rousseau KU Leuven & Antwerp University, Belgium

Class Notes: Week 6. Multinomial Outcomes

Should platforms be allowed to charge ad valorem fees?

Analysing the Distributional Impacts of Stablisation Policy with a CGE Model: Illustrations and Critique for Zimbabwe

This article attempts to narrow the gap between

Centre de Referència en Economia Analítica

Transfer of Functions (Isle of Man Financial Services Authority) TRANSFER OF FUNCTIONS (ISLE OF MAN FINANCIAL SERVICES AUTHORITY) ORDER 2015

First-price equilibrium and revenue equivalence in a sequential procurement auction model

Lecture 7: The Theory of Demand. Where does demand come from? What factors influence choice? A simple model of choice

COLLECTIVE INVESTMENT SCHEMES (DEFINITION) ORDER 2017

The Impact of Personal and Institutional Investor Sentiment on Stock. Returns under the Chinese Stock Market Crash. Kexuan Wang

Exogenous Information, Endogenous Information and Optimal Monetary Policy

Monetary Policy, Leverage, and Bank Risk-Taking

Investment and capital structure of partially private regulated rms

Optimal Monetary Policy in a Model of the Credit Channel

Nash Bargaining Part I - The Continuous Case

AUTHOR COPY. The co-production approach to service: a theoretical background

Hillgrove Resources Ltd

DISCUSSION PAPER SERIES. No MARKET SIZE, ENTREPRENEURSHIP, AND INCOME INEQUALITY. Kristian Behrens, Dmitry Pokrovsky and Evgeny Zhelobodko

Bidding for network size

Merger Review for Markets with Buyer Power

Bonus-Malus System with the Claim Frequency Distribution is Geometric and the Severity Distribution is Truncated Weibull

At a cost-minimizing input mix, the MRTS (ratio of marginal products) must equal the ratio of factor prices, or. f r

T R A D E A N D I N D U S T R I A L P O L I C Y S T R A T E G I E S

PwC International Business Reorganisations Network Monthly Legal Update

The Government of the State of Israel and the Government of the Republi of Argentina, hereinafter referred to as the "Contrating Parties," DESIRING to

Carbon leakage: a mechanism design approach

Damage, Death and Downtime Risk Attenuation in the 2011 Christchurch Earthquake

Implementing the 2018/19 GP contract

ARTICLE IN PRESS. Journal of Health Economics xxx (2011) xxx xxx. Contents lists available at SciVerse ScienceDirect. Journal of Health Economics

CERGE-EI GOVERNMENT S (IN)ABILITY TO PRECOMMIT, AND STRATEGIC TRADE POLICY: THE THIRD MARKET VERSUS THE HOME MARKET SETUP.

GOVERNMENT GAZETTE REPUBLIC OF NAMIBIA

Trade Scopes across Destinations: Evidence from Chinese Firm

Tax-loss Selling and the Turn-of-the-Year Effect: New Evidence from Norway 1

Availability Analysis with Opportunistic Maintenance of a Two Component Deteriorating System

Managing Future Oil Revenues in Ghana

GENERAL DESCRIPTION OF THE DB GLOBAL SOVEREIGN INDICES

Decision, Risk & Operations Working Papers Series

Econ 455 Answers - Problem Set Consider a small country (Belgium) with the following demand and supply curves for cloth:

Transcription:

Experimentation, Private Observability of Suess, and the Timing of Monitoring Alexander Rodivilov Otober 21, 2016 For the latest version, please lik here. Abstrat This paper examines the role of monitoring in experimentation when agents may observe suess privately and therefore delay announing suess. In the benhmark model without monitoring, private observability of suess is inonsequential as we show that the agent never wants to delay announing suess. However, with monitoring of the agent s effort, private observability of suess plays a role in hoosing the optimal time for monitoring. When suess is observed publily, the optimal time for a prinipal to hire a monitor is at the start of the relationship. On the ontrary, if the agent observes suess privately, and the disount fator is high enough, monitoring is performed during the final period. Keywords: Experimentation; Monitoring; Private observability of suess. JEL lassifiation: D83; D86. I am grateful to Fahad Khalil and Jaques Lawarrée for their invaluable suggestions and insightful onversations. I also am thankful for the helpful omments of Philip Bond, Renato Gomes, Quan Wen, partiipants at Midwest Eonomi Theory Meetings 2016 and Stony Brook International Conferene on Game Theory 2016. Department of Eonomis, University of Washington, Seattle, WA, USA. Email: arodivil@uw.edu. 1

1 Introdution Consider a venture apitalist (prinipal) who provides funds to an entrepreneur (agent) hoping to sueed in a risky but lurative projet. Both parties are initially unsure whether the projet is "good", i.e., if it is possible to implement it suessfully at all. The entrepreneur is asked to experiment with the projet a ertain period of time. The prinipal needs to determine how long the experimentation will last. She faes two problems: the effort of the agent may not be observable (moral hazard) and the result of eah experiment may not be publily observed. The prinipal may therefore not have the orret information about the viability of the projet as experimentation proeeds. Consider first the ase when suess is observed publily. Suppose the agent seretly shirks and suess is not ahieved. The prinipal uses the observed failure to update his beliefs on projet quality and beomes more pessimisti from that period on. The agent, in ontrast, knowing that the experiment was not suessful beause he was shirking, will not update his beliefs regarding the projet quality. Furthermore, if suess is privately observed then the agent might postpone announing suess when the projet is suessfully implemented. This report makes the prinipal more pessimisti while the agent knows the projet is ertainly good. Another example is a pharmaeutial ompany that employs a researh organization to arry out linial trials on a group of volunteers to demonstrate the effetiveness of a new drug. If the ompany does not to observe the agent testing the drug diretly, it may doubt whether the agent is exerting effort. If the agent hooses to shirk, he simply an report that the drug was tested unsuessfully. If the ompany remains unaware of this falsehood, it will adjust its beliefs about the drug s quality aordingly, beoming more pessimisti. Even if the agent disovers the drug is performing well, he may delay announing suess in favor of personal gain. In this paper, we ask whether the prinipal an benefit from hiring a monitor in this environment. In a dynami relationship, olleting information during every period is prohibitively ostly, raising the question of when monitoring is most effetive. First, we derive the optimal ontrat without monitoring that determines the length of the prinipal-agent relationship and solves the agent s moral hazard, ensuring that he works properly during every period of the relationship and announes ahieved suess promptly. Seond, we study the benefits of monitoring of the agent s effort. The optimal ontrat then beomes ontingent on the monitor s reports. Finally, we examine how private observability of suess influenes the struture of the optimal ontrat and the optimal timing of monitoring. 2

To answer these questions, we use a simple two-armed bandit model 1 : The agent an "pull the risky arm" by exerting effort toward implementing the projet (ahieve suess), or he an "pull the safe arm" and shirk. While pulling the risky arm is ostly, it allows the projet to be implemented suessfully if it is good. Pulling the safe arm, however, yields zero return, regardless of projet quality. Our results show that, in the benhmark ase without monitoring, the prinipal ommits to terminating the relationship if the agent does not sueed by a ertain period. The agent is rewarded only if the projet is implemented suessfully and reeives nothing otherwise. The nominal value of the reward inreases to aount for rising pessimism as the projet does not sueed over time. In partiular, the agent is rewarded for earlier suess, as the disounted payments are dereasing over time. So even if the agent observes suess privately, he will never delay announing suess and the optimal ontrat is unhanged. Surprisingly, with monitoring of the agent s effort, private observability of suess plays a role in hoosing the optimal time for monitoring. We show that in the ase in whih suess is observed publily, the prinipal should monitor the agent at the beginning of their relationship. If the agent observes suess privately, the optimal time for monitoring is affeted by patiene. For high enough disount fator, monitoring should be performed during the final period. Consider the first-best senario, in whih effort and all the information the agent learned are observed publily. Sine eah attempt to implement the projet is ostly, and the prinipal beomes more pessimisti with every period in whih suess is not announed, the first-best solution is haraterized by a stopping rule. The agent is allowed to attempt to implement the projet for several periods only. In the seond-best ase, the prinipal faes two problems: the agent hooses effort level privately (moral hazard), and, in addition, suess may not be publily observed. Suppose suess is observed publily. In the ase the agent seretly shirks and suess is not ahieved, the prinipal beomes relatively more pessimisti from that period on. She then would adjust the agent s reward to indue him to exert effort aordingly: After every period the agent does not sueed, the prinipal supplies him with larger payments to enourage him to ontinue working in the next period. The agent, in ontrast, understands that the observed failures are uninformative, and at the beginning of the next period would hold the same beliefs as in the previous one. Besides, private observability of suess may exaerbate the problem. In some settings, the prinipal an observe suess easily. In the example of the pharmaeutial ompany, the linial researh organization may have diffiulty hiding a revolutionary drug s suess. However, suess might be muh more diffiult to asertain when information gathering does 1 See Keller et al. (2005) for more details. 3

not involve extreme outomes. Consider the agent s inentive to announe privately observed suess at a ertain period of the relationship. This deision is affeted not only by the payment tied to suess or failure in this partiular period, as determined by the optimal ontrat, but also by payments in all subsequent periods of the relationship. For example, if the disounted value of the promised future reward exeeds the urrent value, then the agent will postpone an announement. We show that under the optimal ontrat, if the agent postpones an announement of suess, the disounted value of his reward will only derease. Thus, private observability does not worsen the problem, as the agent annot benefit from hiding suess; however, it beomes a ruial fator in defining the optimal time for monitoring. Given the optimal ontrat, the agent reeives a stritly positive rent, and, as a result, the projet is terminated ineffiiently early. One way the prinipal an alleviate this ineffiieny is by hiring a monitor who an observe the effort level hosen by the agent. The prinipal an avoid paying the promised reward sine the moral hazard problem vanishes when the monitor is hired. The prinipal values monitoring as it mitigates the rent paid to the agent and, onsequently, allows the relationship to be extended. The prinipal benefits from monitoring as she pays the agent a smaller reward in ase he sueeds during the monitoring period - we refer to this as the stati effet. Moreover, reall that the agent an shirk and attempt to implement the projet during later periods. As a result, his inentives to work during eah period, exept for the final one, depend not only on the payment determined by the ontrat and suess of that partiular period, but also on the payments for all subsequent periods. 2 The effets of future monitoring reflet in the earlier periods, as monitoring ats as a threat that auses the agent to pereive shirking as less attrative. Thus the dynami effet emerges: The prinipal an diminish all of the agent s rewards in all periods before he is monitored. We demonstrate that the dominating effet depends on whether the agent observes suess privately or not. The optimal timing of monitoring is governed by the sum of the two effets. Sine without monitoring, the agent is rewarded for earlier suess, the expeted reward is stritly dereasing. This implies that the benefit from the stati effet is stritly dereasing in monitoring timing as well. With the dynami effet, the prinipal benefits even if the agent does not sueed at the period of monitoring: For earlier periods of monitoring, the benefit from the dynami effet is stritly inreasing, as it allows paying less in several periods. However, as time passes without suess, both parties beome suffiiently pessimisti, and the benefit from the dynami effet dereases eventually. 2 Hala et al. (2016) disuss this dynami ageny effet in their model with moral hazard and adverse seletion. 4

Consider first the ase in whih suess is observed publily. Beause monitoring eradiates the moral hazard problem during the monitoring period, the prinipal benefits from it only if the agent sueeds in this speifi period, whih in turn is possible only if the projet is good. In earlier periods, the benefit from the stati effet inreases while the benefit from the dynami effet goes up, whereas benefits from both effets deline toward the end of the relationship. The benefit from the stati effet dereases faster than the benefit from the dynami effet inreases - this result is at the heart of our analysis. Reall that the benefit from the dynami effet inreases only in earlier periods: Beause the prinipal is promising to pay less with eah period, the hane that the agent will shirk grows smaller. The prinipal saves more in these early periods by opting to monitor later due to the dynami effet. The optimal ontrat, in ontrast, mitigates the moral hazard problem for every period, not only for those in whih the benefit from the dynami effet is inreasing, as it indues the agent to exert effort as long as the relationship lasts. Thus, when suess is observed publily, the stati effet dominates, and monitoring is optimal during the first period. When the agent observes suess privately, the benefit from the stati effet beomes smaller beause the prinipal now still pays some rent to the agent during the monitoring period. Reall that when the agent announes suess, he takes into aount not only the payment tied to suess in this preise period but also payments for suess in all subsequent periods of the relationship: If the disounted value of the promised reward in the next period exeeds the urrent reward, then the agent will postpone an announement. Given that the optimal ontrat without monitoring inludes a dereasing disounted reward value, the prinipal an derease the reward in one period up to the disounted value of the reward in the following period at most. As the disount fator inreases, the benefit from the stati effet dereases for all periods exept the final one. 1.1 Related Literature Our paper ontributes to the literature on inentives for experimentation. Most studies model experimentation based on Keller et al. s (2005) study, whih used a two-armed bandit model with a risky arm that might yield exponentially distributed payoffs and a safe arm that offers a safe payoff. The literature on inentives for experimentation ould be divided into two parts, depending on who is initially the owner of the projet. A group of papers onsidered an entrepreneur who owns a projet and is raising the funds neessary to implement a projet in a ompetitive market. In settings with private learning and moral hazard, Bergemann and Hege (1998) onsidered the provision of venture apital in a dynami ageny model. The optimal share ontrat operates on the provision that if 5

the entrepreneur sueeds, he onveys a part of the projet to the investor. In Bergemann and Hege s study, the share in the earlier periods an rise or fall, but the agent reeives the expeted value of the projet. In our paper, on the other hand, a nominal reward for suess is always (weakly) inreasing, and the agent reeives a positive rent. Bergemann and Hege s (2005) study built on their 1998 study, with one ruially distint feature - the time horizon is infinite, and the funding deision is renegotiated eah period. Another group of papers onsidered a prinipal who owns a researh idea but laks the deisive skills neessary to implement it and must hire an agent in order to do so. Hala et al. (2016) onsidered the hallenges of reating a ontrat for a projet of unertain feasibility with adverse seletion and moral hazard. The optimal ontrat involves paying the agent initially and penalizing him progressively if suess has not been observed. Our researh differs from Hala et al. s (2016) in that we assume the probability of suess is known, but the agent is proteted by limited liability. The agent thus annot be penalized for failure; instead, we show how bonus ontrats and optimal monitoring disourage the agent from hiding suess. Bonatti and Horner (2016) studied a model in whih the quality of the projet depends on a worker s skill that is revealed through output, and wage is based on the expeted output, or assessed ability. However, the authors do not assume limited liability and allow punishment for ahieving ertain deadlines. Manso (2011) applied a similar model to study a manager who must be inentivized to perform an innovative task. The optimal inentive sheme exhibits signifiant tolerane and even reward for both early failure and long-term suess. Gerardi and Maestri (2012) analyzed how an agent an be inentivized to obtain and announe information over time. The authors assumed that the prinipal observes the state of nature with some time lag, and, with the optimal ontrat, he an reward or punish the agent after omparing the agent s report with the revealed state. In this study, the agent is rewarded only if his report mathes the true state, whereas in our study, the true state is learned only if the projet is suessfully implemented. Mason and Valimaki (2015) onsidered an infinitely lasting relationship in a model without learning and with moral hazard and ontinuous effort. They demonstrated that the agent s wage delines over time; however, they did not study monitoring. When studying monitoring, Bonatti and Horner (2011) onsidered a team of agents who work together on a projet of unertain feasibility. In their model, agents observe only their own effort levels and form beliefs regarding the effort of other teammates only. An intriguing result is that monitoring (whih allows the effort level of all other agents to be known) does not neessarily improve the outome. A trade-off arises: Though observing other teammates effort hoies prevents unreasonable pessimism, this also may lead to early high-level effort 6

and faster learning, and later low-level effort. However, in a setting with one agent only, we show that the prinipal benefits from observing the agent s effort hoies. The only researhers who have studied optimal monitoring time sets in optimal ontrats for experimentation are Bergemann and Hege (1998). In this study, when suess is publily observed, monitoring is optimal toward the end of the projet, whereas in our model, the monitor is hired optimally at the beginning of the relationship. Our paper omplements Bergemann and Hege s (1998) result in that it highlights the pivotal role of market struture on the optimal timing of monitoring. In addition, our paper extends Bergemann and Hege s (1998) result, as we show that when the agent observes suess privately, patiene influenes the optimal timing of monitoring, whih was not explored in their paper. As the disount fator inreases, the prinipal must promise idential rewards for suess at every period exept the final one, making monitoring more valuable at the end of the relationship and supporting Bergemann and Hege s (1998) result. Most of these papers assumed projet suess would be publily observed. 3 We, in ontrast, assume that the agent ould observe suess privately. We also assume that information is hard - that is, the agent an either postpone announing a suessful implementation or hide it ompletely by destroying evidene. 4 We argue that our findings are not only theoretial, but also empirially signifiant. Following our example of the pharmaeutial ompany, it is widely aknowledged that onsite linial trial monitoring is a soure of signifiant ineffiieny in the ondut of linial trials, and that urrent monitoring ativities do not always lead to inreased quality in linial trials. 5 The business literature 6 on venture apital for innovation emphasizes the importane of relationship finaning and monitoring. For example, Gorman and Sahlman (1989) found in their survey that venture apitalists visit their ompanies frequently and devote signifiant amount of time to partiipating in deision-making. With respet to optimal monitoring time, Lerner (1995) demonstrated that venture apitalists representation on the board of diretors inreases over ertain periods, espeially during hief exeutive offier turnover. While a venture apitalist may have reasons to partiipate in the firm s reruitment of a management team and strategi planning, this paper, does not examine suh motives and onsiders monitoring that serves the purpose of eliminating the moral hazard problem only. 3 Hala et al. (2016) disuss the robustness of an optimal ontrat to projet suess being privately observed by the agent. 4 Henry (2009) makes a similar assumption. Gerardi and Maestri (2012) onsider a ase of soft information, i.e., when the agent an make up the evidene of suess. 5 Eisenstein et al. (2005) estimated the ost of on-site monitoring to onstitute between 25 and 30 perent of linial trial osts. 6 See Gorman and Sahlman (1989), Sahlman (1990) and referenes therein. 7

The rest of the paper is organized as follows: Setion 2 explains the model and the ontrat spae with payoffs, and provides a solution for the first-best benhmark; Setion 3 provides a desription of the optimal ontrat with moral hazard and private observability of suess; Setion 4 extends results for the ase in whih the prinipal an hire a monitor with private as well as publi observability of suess; and Setion 5 onludes the paper. 2 Model 2.1 The projet A prinipal owns a valuable idea that ould result in a lurative projet, but he laks the deisive skills needed to implement it. He hires an agent proteted by limited liability to perform the projet. Both parties initially are unertain about the projet s quality; that is, the ommon prior on the projet being "good" is β 0 (0, 1). 7 If the projet is good, then it an be implemented suessfully with a known positive probability, in whih ase it will yield a fixed return of V > 0, whih is ommonly known at the beginning of the relationship. To implement the good projet, the agent must exert effort that is assumed to be subjet to a binary hoie: e {0, 1}. If the projet is bad, then it will yield zero, regardless of effort. 8 Exerting effort osts > 0 per period. The agent s ability, λ, whih is the probability of ahieving suess given that the projet is good, onditional on exerting effort, is ommon knowledge during ontrating. Finally, we assume that the effort hoie is not observable and that the agent an postpone announement of or hide a suessful implementation. 2.2 Learning the quality of the projet An important feature of this model is learning projet quality. When the agent does not sueed, despite exerting effort, he updates 9 his beliefs regarding the quality of the projet using Bayes rule and beomes more pessimisti. Denoting by β t, the updated belief of the agent that the projet is good at the beginning of period t after t 1 failures, we present: β t = β t 1 (1 λ) β t 1 (1 λ) + 1 β t 1, whih simplifies to β t = β 0 (1 λ) t 1 β 0 (1 λ) t 1 + 1 β 0. 7 It is important that β 0 is stritly positive and stritly less than one. Otherwise, no additional information arrives as the relationship proeeds; in this ase, there is no learning regarding the quality of the projet, and the problem simplifies to standard dynami moral hazard. 8 We refer to an implementation of the projet as "suess" and to lak of suess as "failure." 9 A failure is more informative if beliefs are lose to 1 2, while beliefs hange slowly when parties are relatively ertain about the quality of the projet. See Bergemann and Hege (1998) for more details. 8

Sine the agent hooses effort level privately, both parties do not share the same beliefs neessarily as their relationship evolves. The prinipal beomes more pessimisti every period the agent does not announe suess. However, if the agent seretly shirks he beomes relatively more optimisti from that period on. Consider a hypothetial senario in Figure 1 below: Figure 1. Learning the quality of the projet with λ = 0.15 and β 0 = 0.7. Given the parameters, the bold line reflets the evolution of beliefs if the agent ontinues exerting effort for 10 periods. Suppose the agent seretly shirks at t = 5, but reports that suess has not been ahieved, despite exerting effort. The prinipal would use this report to update his beliefs and beome relatively more pessimisti from period t = 6 on. The agent, in ontrast, would understand that the reported failure was uninformative, and at the beginning of period t = 6 would have the same beliefs as in the previous period. Importantly, this differene in beliefs following one deviation at t = 6 would arry into all future periods until the relationship ends. 2.3 Contrats and payoffs The optimal ontrat has to take into aount four ruial features of the relationship between the prinipal and the agent: First, the results of eah period affets the relationship; with eah failure the agent reports, the prinipal beomes more pessimisti. Seond, during eah period, the agent hooses privately whether to exert the effort neessary for the projet to sueed. Third, the agent is proteted by limited liability, so the prinipal annot sell the projet to the agent. Finally, the agent observes suessful projet implementation privately. As a result, the payment struture must ensure that the agent neither postpones nor hides the announement of a suessful implementation. 9

Both parties are risk neutral and share a ommon disount fator δ (0, 1]. An optimal ontrat must speify how many failures the prinipal will tolerate and a sequene of transfers as a funtion of the agent s reports, 10 whih in this ase is whether or not the agent sueeded. All transfers are from the prinipal to the agent. The ontrat is given by ϖ = (T, {b t } T t=1, {w t } T t=1), where T N is the duration of the relationship, b t is the payment to the agent in ase he reports suess at period 1 t T and w t is the payment to the agent onditional on reporting failures from the beginning of the relationships up to period 1 t T. Under ertain irumstanes, the agent an postpone or even hide suess. To understand how this fat matters and if it affets the struture of the optimal ontrat, onsider the agent s inentive to announe that he suessfully ompleted the projet at t < T. This deision is affeted not only by the payment tied to suess or failure in this partiular period, as determined by the optimal ontrat, but, in addition, by payments in all subsequent periods of the planning stage. For example, if the disounted value of the promised reward for suess in the future exeeds the urrent value, then the agent will postpone an announement; if the agent is rewarded for onseutive failures, 11 he would benefit from hiding suess ompletely. To prevent the agent from hiding suess, the optimal ontrat will have to satisfy the following inentive ompatibility onstraint for every period 1 t T : (IC) b t δb t+1 for t = 1,..., T 1, b t w t for t = 1,..., T. Given the optimal ontrat and effort levels the agent hooses, we an speify the agent s expeted utility and the prinipal s expeted profit. The agent s expeted utility from aepting ontrat ϖ at time zero while exerting an effort profile e and reporting eah projet truthfully as a failure or suess is: U(ϖ, e) = (1 β 0 ) T t=1 δt (w t e t ) +β 0 T t=1 δt ( t 1 s=1 (1 λe s))(e t (λb t ) + (1 λe t )w t ), where e = (e 1,..., e T ) is an effort profile with e t {0, 1} 12 for 1 t T. First, the agent has a hane to sueed during the relationship; this ours only if both the projet is good, whih is true with probability β 0, and if the agent is exerting effort. 10 Beause suess is observed privately, both parties do not neessarily share the same history as the relationship evolves. 11 For example, Manso (2011) and Chade and Kovrijnykh (2016) explored models where the agent is rewarded for delivering bad news in a different setting. 12 We refer to e t = 1 as "work" and to e t = 0 as "shirk". 10

Conditional on the projet being good, the relationship lasts for an arbitrary period, t T, with probability t 1 s=1 (1 λe s). If the agent exerts effort at period t, his expeted payoff at this period is: λb t + (1 λ)w t, whereas in ase he shirks, the agent reeives only w t, as defined by the ontrat. Seond, if the projet is bad, whih happens with probability 1 β 0, the agent never sueeds, regardless of effort profile. The prinipal s expeted profit from offering ontrat ϖ at time zero if the agent exerts an effort profile e and reports failures and projet suess truthfully is: π(ϖ, e) = (1 β 0 ) T t=1 δt w t +β 0 T t=1 δt ( t 1 s=1 (1 λe s))(e t λ(v b t ) (1 λe t )w t ). The optimal ontrat will have to satisfy the following moral hazard onstraint at eah period for all possible histories and all possible effort paths in the future: (MH) 1 arg max e U(ϖ, e). Given that the MH onstraint is satisfied, the prinipal s expeted profit from offering ontrat ϖ at time zero beomes: π(ϖ, 1) = (1 β 0 ) T t=1 δt w t + β 0 T t=1 δt (1 λ) t 1 (λ(v b t ) (1 λ)w t ). 2.4 The first-best benhmark Consider the first-best ase: The prinipal observes the effort hoie and projet outome. As the relationship proeeds, if suess is not being ahieved, then every period the marginal benefit, λ β t V, is the expeted value of the projet and takes into aount both probability of suess and urrent beliefs. Sine beliefs are delining as time goes on without suess, the marginal benefit dereases stritly. The marginal ost-of-effort,, is onstant. As a result, the first-best solution is haraterized by stopping time T N, suh that the agent is allowed to exert effort up until that date only, as follows: T F B = arg max t {λ β t V } 13. Consider the example in Figure 2 below, where λ = 0.15, β 0 = 0.7, V = 20 and = 1, and where the agent starts with MB 1 = 2.1 and ontinues experimenting with the projet for ten periods at most. 13 Reall that β t are beliefs evolved as a result of the agent exerting effort in all periods until t. 11

Figure 2. The first-best benhmark with λ = 0.15, β 0 = 0.7, V = 20 and = 1. 3 The Seond-Best Contrat When the agent hooses effort level privately, the optimal ontrat must ensure the agent works in every period, whih is guaranteed by the MH onstraint. Sine the agent is proteted by limited liability, he annot pay the prinipal, as the LL onstraint reflets. In addition, the IC onstraint ensures the agent neither postpones suess nor hides it. The prinipal s optimization problem in this ase beomes the following 14 : [P SB ] max ϖ π(ϖ, 1) subjet to (MH) 1 arg max e U(ϖ, e), (IC) b t δb t+1 for t = 1,..., T 1, b t w t for t = 1,..., T, (LL) b t, w t 0 for t = 1,..., T. In this model, the moral hazard problem in eah period translates into asymmetri information regarding beliefs about the projet s quality in all onseutive periods. Before we present a detailed solution to the prinipal s optimization problem, onsider the agent s inentives to deviate at period t T, assuming that the agent was behaving 1 s < t without suess in all prior periods and will work t < s T in all subsequent periods. In ase the agent deides to shirk at the beginning of period t T, his ontinuation value from the relationship is: 14 We assume that V is high enough, and it is optimal for the prinipal when the agent exerts effort in every period. 12

U t (ϖ, (0, 1,..., 1)) = w t + (1 β t ) T s=t+1 δs t (w s ) + β t T s=t+1 δs t (1 λ) s t 1 (λb s + (1 λ)w s ). Note that if the agent follows this one-period deviation, he gets only w t at period t, sine he fails for sure. If the projet is good, whih, based on history, is true with urrent beliefs β t, then the agent has a hane to sueed in all future periods s > t until the relationship is terminated. If the projet is bad, whih is true with probability 1 β t, the agent will reeive w s in all future periods s > t despite exerting effort. In ontrast, if the agent deides to work at period t, his ontinuation value from the relationship is: U t (ϖ, (1, 1,..., 1)) = + λ β t b t + (1 λ β t )w t + (1 β t ) T s=t+1 δs t (w s ) + β t T s=t+1 δs t (1 λ) s t (λb s + (1 λ)w s ). Notie that at period t, the agent has a hane to sueed and reeive b t. This ours either if the projet is good or with probability λ β t. In ase the agent is unluky, with probability 1 λ β t, he gets w t, despite exerting high effort. As in the ase where the agent deviates, if the projet is bad, the agent will reeive w s for all future periods. When the agent deviates at period t, he knows that failure at this period should not hange beliefs and make parties more pessimisti regarding the projet s quality. However, if this deviation is not observed by the prinipal, she will onsider a failure reported at period t as a signal that the projet is more likely to be bad. Importantly, this differene in beliefs reverberates into all future periods. Thus, in this model, the moral hazard problem in eah period translates into asymmetrial information regarding beliefs about the projet s quality in all onseutive periods. Combining the two ontinuation values, the moral hazard onstraint at period t (assuming that the agent was behaving in all prior periods s < t and will work in all subsequent periods s > t) beomes the following: (MH t ) b t w t λ β + T s=t+1 δs t (1 λ) s t 1 (λb s + (1 λ)w s ). t When the agent hooses his effort level privately, he reeives a stritly positive rent. The agent ould shirk and report that the projet failed. The prinipal an motivate the agent to exert effort by paying a higher reward for suess and a lower one for failure. The gap between these payments must be wide enough for the agent to believe it is in his best interest to exert all his efforts after taking into aount urrent beliefs of the projet s quality and probability of suess. If the agent and prinipal share the same beliefs about the projet s quality, a standard moral hazard problem takes plae within eah period 15. Instead, the 15 To minimize risk, the prinipal ideally would sell the projet to the agent; however, this is not feasible beause the agent is proteted by limited liability. 13

agent reeives a positive moral hazard rent. Sine the prinipal benefits only if the projet is released to market, it gains advantage by awarding little to the agent if failure, and, given the limited liability onstraint, the agent is paid nothing if he fails overall. Moreover, if the agent and the prinipal do not hold ommon beliefs, the former reeives additional reward (the learning rent). If the agent deviates from projet goals at one period, his hane to sueed in all future periods remains. Although the agent will not reeive anything if he deviates from his duties during a partiular period, he beomes relatively more optimisti than the prinipal for all future periods. That means a deviation at one period arries into all future periods by reating asymmetri beliefs among parties. In some sense, the agent is relatively more patient 16 than the prinipal in all periods exept the last. During this final period, the agent annot benefit from shirking, sine he will not gain from this, and his rent is ontingent on the ombination of moral hazard and limited liability only. Beause of the positive rent the agent reeives, the projet ould be terminated ineffiiently early. Proposition 1. The agent reeives a positive reward if the projet is implemented suessfully and nothing otherwise. In partiular, w t = 0 and b t = if δ = 1 b t is onstant 17, λ β t + T t s=1 δs 1 β 0 β 0 (1 λ) t+s 1 for 1 t T SB with the following properties: if 0 < δ < 1 b t is stritly inreasing whereas δb t is stritly dereasing. Moreover, the projet is terminated ineffiiently early; that is, T SB T F B. Proof: See Appendix A. Our results show that the agent s nominal reward is weakly inreasing while the disounted value of the reward is weakly dereasing in time. For δ = 1, similar reward struture holds in Hala et al. (2016) who argue that in the ase of no disounting, the prinipal an be restrited to use onstant bonus ontrats 18. When the disount fator is less than one, the agent s reward is stritly inreasing while the expeted reward is stritly dereasing. This resembles the payment sheme in Gerardi and Maestri (2012) when the agent s report mathes the true state observed by the prinipal. In ontrast, in Bergemann and Hege (1998), the agent s reward for earlier suess an rise or fall and even beomes stritly dereasing for high enough disount fator. 16 In Bonatti and Horner (2016) the agent fails to take into aount the value of suess, whih is inreasing in the effort; this makes the agent more patient then the prinipal. 17 Note that when δ = 1 the optimal ontrat is unique up to payoff-irrelevant alteration. 18 Bonatti and Horner (2011) have a similar result in their model with one agent only. 14

An immediate and perhaps fasinating onlusion from Proposition 1 is that the agent s private observability of suess does not exaerbate the problem; that is, the agent will never postpone an announement of suess even if the IC onstraint was not taken into aount diretly when solving the prinipal s optimization problem. The reason is that the optimal ontrat makes the value of the disounted reward stritly dereasing. This result plays a key role in our analysis, as we will demonstrate that private observability of suess beomes ritial when it omes to optimal monitoring timing. To demonstrate the intuition behind Proposition 1, we larify the dynamis of the moral hazard and learning rents. The first omponent is always inreasing, sine the agent beomes more pessimisti as time proeeds without suess, and his motivation to exert himself beomes ostlier. The seond omponent, however, is non-monotoni and depends on the disount fator. Consider a ase in whih both the agent and the prinipal are patient (the disount fator equals one). Under these irumstanes, the prinipal an wait for suess indefinitely. Without loss of generality, the prinipal an offer a ontrat with onstant nominal reward and a deterministi deadline that will ensure the agent will exert effort in every period. Sine the moral hazard rent is inreasing stritly and the nominal reward is onstant, the learning rent dereases stritly. If the prinipal is patient, the agent benefits less from deviating from projet goals sine the fixed deadline gives him a smaller horizon to benefit from asymmetri beliefs. However, if parties to a ontrat are impatient (the disount fator is less than one), the learning rent beomes non-monotoni. Sine T t s=1 δs 1 β 0 β 0 = δ(1 β 0) (1 λ) T t δ T t (1 λ) t+s 1 β 0, (1 λ δ) (1 λ) T 1 the learning rent is inreasing at period 1 t T if and only if either δ < 1 λ and ( 1 λ δ )T t ln δ > ln(1 λ) or δ > 1 λ and ( 1 λ δ )T t ln δ < ln(1 λ). This means that exept for the final period, if the agent shirks and does not inur the ost-of-effort, he will have an additional attempt to suessfully implement the projet and reeive a reward. This weakens the agent s inentives to work during eah period. The prinipal, however, benefits if the projet is suessfully implemented only, and it annot wait indefinitely, as later suess are disounted. This allows the agent to be relatively more patient than the prinipal. By this logi, the learning rent is inreasing. However, the later the agent deviates, the fewer periods remain to exploit the differene in beliefs and, as a result, the learning rent eventually dereases before vanishing ompletely during the final period. Sine the agent has more inentives to deviate at the beginning of the relationship, the optimal ontrat makes the disounted reward stritly dereasing. The agent s inentive to announe suess at a ertain period of the relationship is affeted by the payment tied to suess or failure in this partiular period and, in addition, by 15

payments in all subsequent periods of the relationship. For instane, if the urrent value of the reward is smaller than the disounted value of the promised future reward, the agent will postpone an announement of suess. We show that the optimal ontrat makes the disounted reward stritly dereasing; this feature prevents private observability of suess from exaerbating the ontrating environment. We present a partiular example to better demonstrate the deomposition of the two rents in Figure 3 below. Suppose λ = 0.15, β 0 = 0.7, δ = 1 and = 1. Note that when there is no disounting, the nominal value of b t is onstant, whereas the disounted value of the reward is dereasing, as suggested by Proposition 1. In this ase, ( 1 λ δ )T t ln(δ) > ln(1 λ) and δ > 1 λ, and the learning rent is dereasing for all periods. Figure 3. The optimal ontrat with λ = 0.15, β 0 = 0.7, δ = 1 and = 1. Figure 4. The optimal ontrat with λ = 0.15, β 0 = 0.7, δ = 0.9 and = 1. Now onsider an example with disounting, as depited in Figure 4 above. Suppose that λ = 0.15, β 0 = 0.7, δ = 0.9 and = 1. In this ase, δ > 1 λ and ( 1 λ δ )T t ln(δ) < ln(1 λ) 16

for t 12, and the learning rent is inreasing for these periods and dereasing thereafter. As in the previous ase, the moral hazard rent is inreasing stritly to aount for the agent s inreasing pessimism. 4 Monitoring Given the optimal ontrat desribed in the previous setion, the agent reeives a stritly positive rent, and the projet onsequently is terminated ineffiiently early. One way the prinipal an alleviate this ineffiieny is by hiring a monitor who assumedly an observe the effort level the agent hooses perfetly. In reality, monitoring is widely used in ontrating for experimentation. For example, when running linial trials, the pharmaeutial ompany hires an independent data safety monitoring board (DSMB) onsisting of experts in the relevant linial disipline. The DSMB members shedule several meetings as the trials proeed and advise on the ondut of the trial and the integrity of the data. They also evaluate interim analyses and judge effiay and net linial effets. The prinipal values monitoring beause it mitigates the rent paid to the agent and allows the relationship to be extended. For simpliity we assume that monitoring allows a perfet assessment of the agent s effort; however, our results ould be extended easily to aount for noisy monitoring. In addition, we assume that monitoring osts γ > 0 per period, the salary of the monitor. The benefit of hiring a monitor is that for the period the monitor is hired, the prinipal an promise to pay less sine the moral hazard problem is alleviated, induing the stati effet. Reall that without monitoring, the agent is rewarded more for earlier suess and, onsequently, the expeted reward stritly dereases in the optimal ontrat. This influenes the stati effet, whih stritly dereases in time. In addition, the dynami effet from monitoring emerges, whih redues the learning rent the agent reeives in all periods prior to monitoring. The prospet of future monitoring ats as a threat and makes the agent less likely to shirk in the earlier periods sine the benefit of doing so is smaller. As demonstrated previously, the learning rent is non-monotoni, whih makes the dynami effet non-monotoni, as well. Thus, the optimal time for monitoring is governed by the sum of the two aforementioned effets. We demonstrate that the dominating effet depends on whether the agent observes suess privately or not. This is an important result, sine without monitoring, private observability does not play any role in the optimal ontrat. However, it is ruial in determining the optimal monitoring timing. 17

4.1 Suess is publily observed We begin the analysis of the optimal timing of monitoring with an example, where the relationship lasts exogenously for two periods (T = 2), and the prinipal an perfetly observe the effort level during one period only when suess is publily observed. The prinipal s optimization problem (assuming it is optimal when the agent exerts effort in every period) is: max ϖ π(ϖ, 1) subjet to (MH) 1 arg max e U(ϖ, e), (LL) b 1, b 2, w 1, w 2 0. First, suppose the prinipal hooses to monitor the agent at the beginning of the relationship. In this ase, the MH onstraint ould be replaed by: (MH 2 ) λ βb 2 + (1 λ β)w 2 w 2, whih ensures that the agent behaves at t = 2, given that suess has not been ahieved at period t = 1. Then, a solution to the optimization problem with monitoring involves b 2 = λ β and w 2 = 0, where β β 0 (1 λ) =. The prinipal s expeted profit in this ase is β 0 (1 λ) + 1 β 0 the following: π m=1 = β 0 2 t=1 δt (1 λ) t 1 λv δ 2 β 0 (1 λ)λb 2 γ = β 0 2 t=1 δt (1 λ) t 1 λv δ 2 (1 λβ 0 ) γ. Seond, suppose the prinipal hires the monitor at t = 2. In this ase, the MH onstraint ould be replaed by: (MH 1 ) λβ 0 b 1 + (1 λβ 0 )w 1 w 1, whih ensures that the agent behaves at t = 1, given that he will exert effort at t = 2. Then, the solution to the optimization problem involves w 1 = b 2 = w 2 = 0 and b 1 = prinipal s expeted profit is the following: π m=2 = β 0 2 t=1 δt (1 λ) t 1 λv δβ 0 λb 1 γ = β 0 2 t=1 δt (1 λ) t 1 λv δ γ. λβ 0. The Sine δ 2 (1 λβ 0 ) > δ, it is optimal to monitor at t = 1. The intuition is that if monitoring ours at t = 1, the prinipal expets to pay a reward at t = 2, onditional on the agent failing at t = 1, despite exerting effort as refleted by (1 λβ 0 ) in the prinipal s 18

expeted profit π m=1. The example above is straightforward but does not apture the main intuition fully, as when the relationship lasts for two periods and the monitor is hired, the agent does not reeive any learning rent. We will demonstrate, however, that the result of this example extends to a general setting where the duration of the ontrat is long enough that the agent is granted a stritly positive learning rent. Suppose now the prinipal an monitor the agent perfetly at any period m T M P ubli, where TP M ubli is the duration of the ontrat with monitoring when suess is publily observed. We would like to understand all the benefits from monitoring in this ase. First, the prinipal an avoid paying b m sine the moral hazard problem at period m vanishes. This stati effet is at the heart of our analysis, as it will be playing an important role when suess is observed privately. Sine the stati effet alleviates the moral hazard problem at the period of monitoring, the prinipal benefits from it only if the agent sueeds at period m, whih in turn is possible only if the projet is good. Thus, the stati effet is: SE m = δ m P rob(suess at m)b m = δ m β 0 (1 λ) m 1 λb m. Seond, reall from the MH m onstraint that if the prinipal dereases a reward for suess, b m, he an sale down all the rewards in all the preeding periods, 1 s < m. This effet, whih we all the dynami effet, will be shown to play an auxiliary role in the environment we onsider. Importantly, unlike with the stati effet, the prinipal benefits from the dynami effet even if the agent does not sueed at some period m. Sine the agent always, exept for the final period, has a hane to sueed in the later periods, the future rewards make it ostlier to ensure the agent behaves at the beginning of the relationship. Intuitively, the promise of future monitoring ehoes into the earlier periods, as it ats as a threat and it hanges the agent s options if he deides to shirk in the earlier periods. The dynami effet is defined as: DE m = m 1 t=1 δt P rob(suess at t < m)[nominal derease in b t ]. What is a nominal derease in b t for t < m that is possible beause of monitoring that will our at period m? Under the optimal ontrat all the MH t onstraints are binding: (MH t ) b t w t = λ β t + T s=t+1 δs t (1 λ) s t 1 (λb s + (1 λ)w s ), and, given that the agent reeives nothing if the projet does not sueed, we have b t = λ β t + T s=t+1 δs t (1 λ) s t 1 (λb s ). Consequently, a nominal derease in b t for t < m due to monitoring at period 1 m T is: 19

δ m t (1 λ) m t 1 λb m. Finally, the dynami effet beomes: DE m = δ m β 0 λ 2 (1 λ) m 2 (m 1)b m. Thus, the total effet of monitoring at period m, T E m = DE m + SE m, ombines the benefit of paying less at period m, whih is dereasing in time, and the benefit of saling down all the rewards in previous periods, whih is non-monotoni. It turns out that the former effet is dominant, as stated in Proposition 2. To understand how monitoring hanges rewards onsider a numerial example. Suppose λ = 0.15, β 0 = 0.7, δ = 0.9 and = 1. Assume monitoring ours at period m = 10. Sine a nominal derease in b t for t < m due to monitoring is δ m t (1 λ) m t 1 λb m, the prinipal now makes rewards for suess smaller for periods t = 1,..., 9, as refleted in Figure 5 below. Figure 5. Rewards with monitoring at t = 10 when suess is publily observed with λ = 0.15, β 0 = 0.7, δ = 0.9 and = 1. Proposition 2. When suess annot be hidden, monitoring is optimal at the beginning of the relationship. Moreover, the projet is terminated ineffiiently early: T SB T M P ubli T F B. Proof: See Appendix B. Why does the stati effet dominate when suess is publily observed? First, the stati effet eradiates the moral hazard problem at the period of monitoring, and this mitigates the moral hazard rent, 19 whih was shown to be stritly inreasing. What does the dynami effet aomplish? It mitigates the learning rent, as it makes shirking a less attrative option for 19 The prinipal benefits from the stati effet only if the agent sueeds at the period when he is monitored, whih in turn is possible only if the projet is good. 20

the agent. The dynami effet inreases only during earlier periods: Monitoring influenes these periods, but as parties to a ontrat beome inreasingly pessimisti, the dynami effet dereases. Under the optimal ontrat, however, the payment struture optimally mitigates the learning problem for every period of the relationship, not just those in whih the dynami effet is inreasing, as this indues the agent to exert effort throughout the length of the relationship. That is why when suess is publily observed, the stati effet dominates. We illustrate this setion with a numerial example. Suppose λ = 0.15, β 0 = 0.7, δ = 0.9 and = 1. The stati effet, SE t = δ t β 0 (1 λ) t 1 λb t, is stritly dereasing, as refleted in Figure 6 below. The dynami effet, DE t = δ t β 0 λ 2 (1 λ) t 2 (t 1)b t, is non-monotoni. For early periods t 6, the agent has to be paid more to behave, sine if he deviates one, he an leverage the fat that he is relatively more optimisti until the deadline. However, as time goes by without suess, both parties beome more pessimisti, and sine the expeted value of b t goes down, the dynami effet diminishes, as well. Figure 6. Effet from monitoring when suess is publily observed with λ = 0.15, β 0 = 0.7, δ = 0.9 and = 1. 4.2 Suess is privately observed Suppose the agent an postpone an announement of a suessful implementation. We will denote TP M rivate as the duration of the ontrat with monitoring when suess is observed privately. The prinipal an still benefit from hiring a monitor; however, now the modified reward struture must ensure the agent does not have inentives to postpone or hide suess. This is where the additional IC onstraints: (IC) b t δb t+1 for t = 1,..., T 1, b t w t for t = 1,..., T, 21

beome relevant and, as we will demonstrate, will be binding for the period when monitoring is implemented. How an the prinipal benefit from monitoring when the agent observes suess privately? First, as with publi observability, the prinipal an pay less during the monitoring period beause the moral hazard problem at period m vanishes. The stati effet, however, is different. The reason is that when the agent announes suess he takes into aount not only the payment tied to suess in this preise period but also payments tied to suess in all future periods: in ase the disounted value of the promised reward in the very next period exeeds the urrent reward, then the agent will postpone an announement. For example, if the prinipal sets b m = 0, then in the ase the agent sueeds at this exat period, he will postpone an announement until the later period as then he gets a positive reward. Given that the optimal ontrat without monitoring exhibits a dereasing disounted reward value, the prinipal an derease the reward in one period at most up to the disounted value of the reward in the following period only. As the disount fator inreases, the stati effet beomes smaller for all periods exept the very last one. Thus, the stati effet now has to be modified and beomes: SE m = δ m β 0 (1 λ) m 1 λ(b m δb m+1 ), where b T M P rivate +1 = 0. In addition, the dynami effet, has to be modified to take into aount the IC onstraint, as well. As in the previous ase, we will first onsider an example where the relationship lasts for two periods (T = 2), and the prinipal an perfetly observe the effort level during one period only when the agent privately observes suess. The prinipal s optimization problem is: max ϖ π(ϖ, 1) subjet to (MH) 1 arg max e U(ϖ, e), (IC) b 1 δb 2, b 1 w 1, b 2 w 2, (LL) b 1, b 2, w 1, w 2 0. First, suppose the prinipal monitors the agent at t = 1. In this ase, the MH onstraint ould be replaed by: (MH 2 ) λ βb 2 + (1 λ β)w 2 w 2, (IC) b 1 δb 2, 22