Dynamic financial contracting with persistent private information

• Published date: 01 June 2019
• Date: 01 June 2019
• Author: Shiming Fu,R. Vijay Krishna
• DOI: http://doi.org/10.1111/1756-2171.12275

RAND Journal of Economics

Vol.50, No. 2, Summer 2019

pp. 418–452

Dynamic financial contracting with

persistent private information

Shiming Fu∗

and

R. Vijay Krishna∗∗

We study a dynamic agency model where the agent privately observes the firm’s cash flows that

are subject to persistent shocks. We characterize the policy dynamics and implement the optimal

contract by financial securities. Because bad performance distorts investors’ beliefs downward,

the agent has less incentive to misrepresent information. The agent’s compensation is less than

what he can divert and is convex in performance.As private information becomes more persistent,

(i) the agent is compensated more by stock options; (ii) firm credit limits vary more with history,

dropping after bad performance; (iii) the firm is financially constrained for longer time.

1. Introduction

There is considerable evidence that funding for firms, especially young firms, is far from

efficient, and that firms must grow over time into their optimal size. In particular, financing

constraints greatly affect firm size, growth, and a young firm’s prospects.1Jensen and Meckling

(1976) initiated a large literature that has focused on the conflicting interests of investors and

agents—that is, agency problems—as a key friction that constrains firm financing and investment.

Agency problems arise because agents have more information about their own actions, and

consequently, about firm behavior, than do outside investors. The owners of the firm therefore

design securities and firm policies to mitigate such agency conflicts.

∗Shanghai University of Finance and Economics; fushiming@gmail.com.

∗∗Florida State University; rvk3570@gmail.com.

We thank Hengjie Ai, Marina Halac, David Martimort (the Editor), Adriano Rampini, Philipp Sadowski, Lukas

Schmid, S. Viswanathan, Neil Wallace, Yuzhe Zhang, an anonymous referee, and seminar/conference participants at

Duke University, New York University, University of Rochester, Johns Hopkins University, Georgia State University,

Columbia/Duke/MIT/Northwestern IO Theory Conference (2015), Midwest Economic Theory Conference (2016), PSU-

Cornell Macro Conference (Penn State, 2016), Econometric Society North America Summer Meeting (2016), Finance

Theory Group Summer Conference (2016), and SED Annual Meeting (2016), for helpful comments. Krishna is grateful

to the National Science Foundation for financial support through grant no. SES-1132193. This work began whileKrishna

was visiting Duke University. He is most grateful to that institution for its hospitality.

1Gertler and Gilchrist (1994) find that manufacturing significantly declines in small firms when monetary policy

tightens. Similarly,Beck, Demirg ¨

uc¸-Kunt, and Maksimovic (2005) demonstrate that financial constraints create obstacles

to the growth of small firms.

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An influential recent literature analyzes agency problems in dynamic contexts.2Forinstance,

Clementi and Hopenhayn (2006) and DeMarzo and Fishman (2007b) characterize the optimal

long-term contract when agency frictions are involved. These models provide joint predictions

about how firm policies are designed and evolve in dynamic environments. Moreover, these

models typically assume that the agent’s private information about firm behavior is independent

and identically distributed (i.i.d.) over time, in part because considering persistence has proved

challenging in this class of models. However, in practice, firms’ profitability and other economic

behavior exhibit high autocorrelation. For instance, Gomes (2001) calibrated that autocorrelation

of firm productivity shocks is 0.62 at the annual frequency. Many other studies show even higher

numbers, which suggests that private information about firm behavior may well be persistent.

This article studies the implications of persistent private information for firm compensation,

capital structure, investment, and growth dynamics. The firm in our model consists of a risk-

neutral agent and a risk-neutral principal (representing investors of the firm). The agent has the

operating expertise, whereas the principal provides funds to launch the firm and finance risky

investments over time. The agency problem is that the cash flows from investment projects are

privately observed by the agent, and the agent can divert cash flows for consumption. Persistence

in this setting means that firm cash flows are subject to positively correlated shocks which follow

a two-state Markov process.

One might expect that persistence of productivity shocks would exacerbate the agency

problem. On the contrary, we find that it alleviates the agency problem via an additional channel

that is not present in the i.i.d. case. The agent can always misreport firm performance and divert

any cash flow. In the i.i.d. case, the misreport will not affect any party’s belief about future shocks.

However, in the persistent case, it distorts downward the principal’s belief about the firm’sfuture

prospects, so that it is optimal for the principal to scale down future investment,leading to smaller

future information rents for the agent. Accordingly, the agent has less incentive to misrepresent

firm performance today, and is paid less than what he can divert.

Our model shows that the qualitative and quantitative features of the optimal contract are

sensitive to the level of persistence. As noted above, this is because persistent private informa-

tion forces the agent to weigh the trade-offs between truth-telling versus diverting cash today

and receiving smaller information rents in the future, rents that become smaller as persistence

increases. Indeed, if persistence becomes sufficiently high, then the principal can ignore the in-

centive constraint completely—private information is no longer relevant! However, distortions

from the efficient levelwill still persist until the agent ear ns enough equity to abnegate the limited-

liability constraints. That is, because the principal will still want to punish the agent after poor

performance (especially if the preceding period had good performance), his only impediment is

the agent’s limited-liability constraint.

In terms of qualitative features, as private information becomes persistent, the agent’s com-

pensation becomes strictly convex (instead of linear) in performance. The pay-performance

sensitivity increases to incorporate a dynamic information rent in addition to the current cash

flow. Moreover, the payout boundary, and the investment of the unconstrained (mature) firm both

vary with performance. If persistence is sufficiently high, the constrained (young) firm needs to

experience consecutive good shocks to become financially unconstrained, and therefore can stay

in small size for longer time than in the i.i.d. case. Also, if persistence is sufficiently high, the

agent gets paid only when consecutive good performances are observed. In Section 1 below, we

elaborate on these and other features of our contract, their relation to stylized facts, and how some

of these features cannot be reconciled by a model with i.i.d. private information.

The article also provides an implementation of the optimal contract in terms of financial

securities. In the implementation, the agent holds equity and stock options. The firm is financed

by a credit line with limit contingent on the firm’s performance history. Both the current and the

2A related literature of dynamic firm financing considers limited enforcement issues, for instance, Albuquerque

and Hopenhayn (2004) and Rampini and Viswanathan(2013).

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420 / THE RAND JOURNAL OF ECONOMICS

expected future credit limits drop immediately after bad performance. As persistence increases,

the agent is compensated more by option payoff, and the principal holds more equity. The firm’s

credit line limit varies more with performance history as persistence goes up. On the contrary,

the agent is compensated purely by equity, and the credit line limit is a constant in the i.i.d. case.

To showthe above results, a tractable recursive formulation is needed because the approach

used in i.i.d. settings is no longer sufficient. The contract in our model promises the agent utilities

contingent on performance today and tomorrow.In par ticular,the contract promises two different

pairs of continuation utilities from tomorrow onward according to good or bad performance

today. This approach is shown to be convenient in finding the proper domain of the problem and

in characterizing the contract properties.

We now proceed as follows. Section 1 summarizes some stylized facts about firm financ-

ing and our model implications. Section 1 reviews the relevant theoretical literature. Section 2

introduces the model, whereas Section 3 discusses our recursive formulation. Whereas Section 4

descries the full information benchmark, Section 5 shows the properties of the financially con-

strained and unconstrained firm. Section 6 describes our implementation of the optimal contract.

Section 7 concludes.

Stylized facts and model implications. Wenow discuss some stylized facts about financial

contracts, their uses in firms, and what theoretical models have to say about them. Throughout,

we first describe the relevant stylized facts, and then discuss how our model with persistence

is able to explain these facts, whereas the i.i.d. model makes predictions inconsistent with the

empirical observations.

Compensation and stock options. Empirically, stock options are a popular way of compen-

sating executives and employees. 71% of the 250 largest US companies in the Standard & Poor’s

500 Index use stock options as incentive grant.3According to Larcker and Tayan (2017), option

payment accounts for 15% of Chief Executive Officer (CEO) compensation of companies listed

in the S&P 500 Index. Bergman and Jenter (2007) also show that stock options plans are the most

common method for employee compensation below the executive rank.

In dynamic settings, the variation of future information rents provides incentives for the

agent to report cash flow truthfully. In the i.i.d. case, the expected information rent becomes

constant in the long run. The only way to provide incentives is to pay the agent the amount of

cash he can divert. Thus, compensation is linear in firm performance.4

With persistent information, the principal’s belief about future prospects is always down-

graded after a bad performance, leading to smaller expected information rents. Hence, the agent

has less incentive to misreport and the principal can carve out some cash flow. Because total firm

revenues vary with historical shocks due to persistence but the amount retained by the principal

is constant, a larger fraction is paid to the agent as revenue increases, resulting in a strictly

convex compensation structure. If information is highly persistent, the principal can carve out all

the firm revenue when it is low. The agent gets paid only when consecutive good performances

are observed. So, a report of a bad shock today in our model has a longer-lasting impact on

compensation (affecting both today and tomorrow) than in the i.i.d. setting (only affecting to-

day). The convex compensation scheme is implemented by granting the agent equity and stock

options. As information becomes more persistent, the option payoff accounts for a larger portion

of total compensation.

Credit line with contingent limit. Credit lines are an important tool for firm financing and

liquidity management. According to Demiroglu and James (2011), draw-downs of credit lines

3See the Frederic W. Cook survey of long-term incentive grant, http://www.fwcook.com/alert_letters/

The_2014_Top_250_Report_Long-Term_Incentive_Grant_Practices_for_Executives.pdf www.fwcook.com/.

4Both DeMarzo and Sannikov (2006) and DeMarzo and Fishman (2007b) assume that the agent can divert a

fraction λ≤1 of the firm’s cash flow. Following Clementi and Hopenhayn (2006), our model corresponds to the case

where λ=1, although it can readily be extended to the case of λ<1.

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