Too Much, Too Soon, for Too Long: Chemla, Rivera & Shi (2025)

What this is. The paper’s core results, the model it builds on (dynamic principal-agent contracting embedded in a general equilibrium with endogenous outside options), and its main propositions: enough to know what it found and how, without reading all 50 pages. To replicate or extend it, read the full source at the original.

TL;DR

The paper embeds a continuous-time dynamic moral hazard problem (in the spirit of DeMarzo and Sannikov (2006)) into a general equilibrium economy where outside options for managers and liquidation values for firms are endogenously determined by equilibrium compensation. Firms compete for managers by promising deferred pay (“carrots”) backed by termination threats (“sticks”). The framework builds on the two-period binary setup of Bolton and Scharfstein (1990) and the continuous-time limit of Biais et al. (2007). The welfare criterion follows Dicks (2012) (maximize shareholder value). In contrast to static governance externality models such as Acharya and Volpin (2010) and frictionless assortment theories of executive compensation such as Gabaix and Landier (2008), the central finding here is that competitive markets generate overcompensation even without rent extraction. Evidence that executive pay rises sharply when CEOs move to a new firm (Falato, Li, and Milbourn (2015)) motivates the focus on endogenous outside options. The resulting competitive equilibrium is inefficient: firms fail to internalize the effect of their compensation packages on the outside options of managers at other firms. This “compensation externality” leads to executives being paid too much (overcompensation), too soon (insufficient deferral), and keeping their jobs for too long (excessively low turnover), while the associated capital structure features excessively low credit line limits and long-term debt.

Core results

Magnitudes and significance are as reported. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	Equilibrium compensation exceeds the social optimum (overcompensation): firms fail to internalize that raising pay increases the manager’s outside option, reducing the effectiveness of termination for all other firms	Corollary 2, p. 2940; Figure 4 Panel B, p. 2946	In the baseline calibration, equilibrium initial compensation W0* is approximately 15.4 vs the planner’s W0^p = kA = 5.3; equilibrium compensation roughly 3x the planner level
R2	Insufficient deferral: overcompensation is front-loaded; managers receive their first payment sooner in equilibrium than under the social optimum	Proposition 4, eq. (19)-(20), p. 2941; p. 2946	Front-loading proxy S*(W0*) = 0.78 > 0.65 = S^p(W0^p); manager paid roughly 20% sooner in equilibrium than optimal
R3	Excessively long tenure: overcompensation causes the manager’s continuation value to drift upward faster, reducing the likelihood of hitting the termination threshold	Proposition 4, eq. (20), p. 2941; p. 2946	T*(W0*) = 0.17 < 0.21 = T^p(W0^p); equilibrium forced-turnover rate 2.2% per year vs the planner’s higher rate
R4	Capital structure distortion: the equilibrium compensation contract is implemented with excessively low credit line limits and long-term debt relative to the social optimum	Proposition 5, p. 2942	CL* < CL^p and D* < D^p; debt and credit lines are lower in equilibrium because high, front-loaded compensation requires low debt instruments to remain incentive-compatible
R5	Managerial bargaining power amplifies overcompensation: as managers capture a larger share of the surplus, equilibrium compensation more than doubles and shareholder value falls disproportionately	Lemma 6, eq. (23), p. 2955; Figure 9, p. 2955	Raising manager bargaining power beta from 0 to 0.25 more than doubles W0*; shareholder value decreases disproportionately because higher pay raises manager outside options, further undermining termination threats
R6	Moral hazard severity and cash-flow volatility amplify the distortions: industries with higher lambda or sigma see a larger gap between equilibrium and optimal compensation, more front-loading, and less turnover	Section IV.C, Figures 5-7, pp. 2947-2950	The shareholder value gap F(W0^p; R^p, L^p) - F(W0*; R*, L*) is increasing in lambda and sigma; compensation W0* rises steeply in lambda while the planner’s W0^p stays near kA

Overall (paper’s conclusion). The compensation externality arises because firms are price-takers with respect to the equilibrium outside option: when an individual firm raises pay to maximize its own shareholders’ value, it inadvertently increases the outside option for all managers, making termination less effective as an incentive device across the economy. The resulting equilibrium is inefficient even when firms hold all bargaining power and are well-intentioned. A benevolent planner can achieve Pareto improvements by coordinating future compensation down, restoring termination effectiveness without harming managers.

Theory / model

The model has two parts: an illustrative two-period binary setup (Section I, pp. 2926-2930) and the full continuous-time infinite-horizon model (Section II, pp. 2931-2937).

Two-period setup (Section I). The economy has a continuum of risk-neutral firms and managers. Each period, a project generates a binary cash flow: high ($y > 0$) with probability $p$ or zero with probability $1-p$. The manager privately observes realized cash flows and can divert them, receiving a fraction $\lambda \in (0, 1]$ of diverted funds. Limited liability requires all compensation payments to be nonneg.

The one-period (static) optimal contract is $\Gamma^S = \{\tilde{x}, c_H, c_L\}$ where the firm pays $c_H = \lambda y$ if reported cash flow is high and $c_L = 0$ otherwise. Outside values satisfy (p. 2927, eq. (1)):

$$R = \tilde{x}\delta\lambda\mu - \kappa_A \quad \text{and} \quad L = \tilde{x}(1-\lambda)\mu - \kappa_P. \tag{1}$$

For the two-period dynamic contract $\Gamma^D = \{x, c\}$ (continuation probability in the low state $x$, period-1 high-state compensation $c$), the principal maximizes shareholder value subject to the incentive-compatibility constraint (p. 2929, eq. (2)):

$$\text{IC-1}: \quad c + \delta\lambda\mu \geq x\delta\lambda\mu + (1 - x)R + \lambda y. \tag{2}$$

This IC shows that termination threats (setting $x < 1$) reduce the cost of incentive provision in the high state by an amount $\delta\lambda\mu - R$ that depends critically on the manager’s outside option $R$. When $R$ is high (outside options are lucrative), termination becomes less effective, so firms must compensate more.

Lemma 1 (p. 2929): When agent termination cost $\kappa_A > \tfrac{1-p}{p}\kappa_P$, agents are terminated after poor performance and expected compensation is $(\delta + \delta^2)\lambda\mu - \delta\kappa_A$; shareholder value is $2(1-\lambda)\mu + p\kappa_A - (1-p)\kappa_P$.

Lemma 2 (p. 2930): If moral hazard is sufficiently severe ($p\delta\lambda > (1-p)(1-\lambda)$), the equilibrium features overcompensation. The planner sets outside options to zero by shutting down new matches; shareholders gain up to $\Delta\mu$ where $\Delta \equiv p\delta\lambda - (1-p)(1-\lambda)$.

Full continuous-time model (Section II). Time is continuous and infinite, $t \in [0, \infty)$. Cash flows follow

$$dY_t = \mu\, dt + \sigma\, dB_t,$$

where $B_t$ is a standard Brownian motion. The manager privately observes cumulative cash flows $Y = \{Y_t\}_{t \geq 0}$ while the firm relies on reported cash flows $\hat{Y}$. The manager can divert $dY_t - d\hat{Y}_t$ and receive a fraction $\lambda$ of diverted funds. Firms discount at rate $r$; managers discount at $\gamma > r$ (managers are impatient).

The firm’s initial value under contract $\Gamma = (C, \tau)$ (cumulative compensation process and termination time) is (p. 2932):

$$F_0(\hat{Y}; \Gamma) \equiv \mathbb{E}\!\left[\int_0^\tau e^{-rt}(d\hat{Y}_t - dC_t) + e^{-r\tau}L\right].$$

The manager’s initial value is:

$$W_0(\hat{Y}; \Gamma) \equiv \mathbb{E}\!\left[\int_0^\tau e^{-\gamma t}\!\left(dC_t + \lambda(dY_t - d\hat{Y}_t)\right) + e^{-\gamma\tau}R\right].$$

The optimal contract solves (p. 2933, eqs. (3)-(5)):

$$\max_{W_0, \Gamma} F_0(Y; \Gamma) \tag{3}$$

subject to the promise-keeping constraint $W_0(Y; \Gamma) = W_0$ and the incentive-compatibility constraint $W_t(Y; \Gamma) \geq W_t(\hat{Y}; \Gamma)$ for all $t \in [0, \tau]$.

The equilibrium conditions pin down the endogenous outside option $R^*$ and liquidation value $L^*$ (p. 2934, eqs. (6)-(7)):

$$R^* = W_0^* - \kappa_A, \tag{6}$$ $$L^* = F_0^* - \kappa_P. \tag{7}$$

Proposition 1 (p. 2937, eq. (16)): Under Assumption 1, the unique equilibrium compensation level $W_0^*$ satisfies

$$F'(W_0^*; R^*, L^*) = 0. \tag{16}$$

The firm maximizes its value function at the interior point where the marginal value of promised compensation is zero, taking outside options as given.

Proposition 3 (Social Optimum, p. 2939, eq. (18)): The socially optimal compensation $W_0^p$ satisfies

$$F'(W_0^p; R^p, L^p) + \frac{\partial}{\partial R}F(W_0^p; R^p, L^p) \leq 0. \tag{18}$$

The second term, $\frac{\partial}{\partial R}F < 0$, is the general equilibrium effect: a $1 increase in compensation raises managers’ outside options by $1, reducing firm value. Firms in equilibrium set $F'(W_0^*) = 0$, ignoring this negative externality, so $W_0^* > W_0^p$ (Corollary 2).

Method

This is a theory paper. The solution method combines:

1. Optimal contract characterization via the HJB/ODE. Following DeMarzo and Sannikov (2006), the firm’s value function $F(W; R, L)$ is characterized by an ODE (Corollary 1, p. 2936, eqs. (11)-(13)):

$$rF(W; R, L) = \mu + \gamma W F'(W; R, L) + \tfrac{1}{2}\lambda^2\sigma^2 F''(W; R, L), \quad R \leq W < \bar{W}, \tag{11}$$ $$F'(W; R, L) = -1, \quad W \geq \bar{W}, \tag{12}$$

with boundary conditions $F(R; R, L) = L$ and $rF(\bar{W}; R, L) = \mu - \gamma\bar{W}$. The optimal contract (Lemma 3, p. 2935) specifies:

• (i) Pay-for-performance: $dW_t = \gamma W_t\, dt - dC_t + \lambda(dY_t - \mu\, dt)$.
• (ii) Deferral: payments only when $W_t \geq \bar{W}$.
• (iii) Termination: $\tau = \min\{t \mid W_t = R\}$.

The ODE is solved numerically; existence and uniqueness of the equilibrium are established analytically (Propositions 1, Appendix D-E, pp. 2961-2965).

2. Equilibrium fixed-point. The equilibrium $(R^*, L^*)$ is found as a fixed point of eqs. (6) and (7) given the solution to the firm’s contracting problem. Proposition 1 shows that the FOC $F'(W_0^*) = 0$ pins down the unique interior equilibrium.

3. Calibration. Parameters are calibrated to data moments (Table I, p. 2943): $r = 0.04$ (annual interest rate), $\gamma = 0.09$ (manager discount rate), $\mu = 10$ (normalization), $\sigma = 9$ (matching 10-15% fraction with operating losses), $\lambda = 0.29$ (moral hazard; Ward (2023)), $\kappa_P = 15$ (6% CEO replacement cost; Taylor (2010)), $\kappa_A = 5.3$ (2.2% forced turnover rate; Taylor (2010)).

The model is extended in Section V to incorporate: (i) noncompete clauses (Lemma 4), (ii) endogenous termination costs via a search framework (Lemma 5), (iii) Nash bargaining (Lemma 6, eq. (22)-(23)), and (iv) forward-looking firm liquidation values (Lemma 7).

Empirical specifications

This is a pure theory and calibration paper with no regression analysis. There are no panel regressions, no instrumental variable designs, and no event studies. The “empirical” content consists of:

• Calibration targets matched to observed moments: fraction of firms with operating losses, annual interest rates, manager discount rate (Ward (2023), Chen et al. (2023)), forcing-turnover rate (Taylor (2010), Eisfeldt and Kuhnen (2013), Jenter and Kanaan (2015)), and CEO replacement costs (Taylor (2010)).
• Quantitative comparative statics (Figures 5-9, pp. 2947-2955): the model computes equilibrium versus planner outcomes as each parameter ($\lambda$, $\kappa_A$, $\kappa_P$, $\beta$) varies, holding others at calibrated values from Table I.
• Welfare comparisons: the gap $F(W_0^p; R^p, L^p) - F(W_0^*; R^*, L^*)$ is computed numerically (Figures 3-4) and reported as the gain from planner intervention.

The paper generates the following testable empirical predictions (Section IV.C, pp. 2947-2950): (1) CEO overcompensation is more severe in industries with more mobile managers (lower $\kappa_A$) or higher CEO replacement costs for firms (higher $\kappa_P$); (2) overcompensation, insufficient deferral, and excessive tenure are most pronounced in industries with high cash-flow volatility or severe moral hazard; (3) the credit line limits and long-term debt of firms are excessively low in equilibrium.

Datasets used

This is a pure theory paper. It does not use empirical datasets directly. Calibration relies on parameter estimates reported in the literature:

Source	Role in paper	Wiki page
Ward (2023) estimates of CEO discount rate and moral hazard parameter	Calibrate $\gamma = 0.09$ and $\lambda = 0.29$ (Table I)	No page yet
Taylor (2010) structural estimates of CEO replacement costs and turnover	Calibrate $\kappa_P = 15$ (6% replacement cost) and $\kappa_A = 5.3$ (2.2% forced turnover)	No page yet
Chen et al. (2023) manager discount rate estimates	Cross-check for $\gamma$ (11% estimate; paper uses 9%)	No page yet
Eisfeldt and Kuhnen (2013); Jenter and Kanaan (2015)	Cross-check for forced turnover rate lower bound (1.6-2.8%)	No page yet

When to read the full paper

Use the original if you are: (a) building or extending a dynamic contracting model in a general equilibrium setting; (b) analyzing the policy implications of executive compensation externalities (noncompete clauses, pay transparency mandates); (c) studying the connection between optimal incentive contracts and capital structure in the spirit of DeMarzo and Sannikov (2006); or (d) replicating the quantitative calibration and comparative statics (Figures 2-9). The Internet Appendix contains proofs of renegotiation-proofness and the tax-implementation of the social optimum as an equilibrium.

Attribution and rights

Source: peer-reviewed, The Journal of Finance 80(5). This distillation was extracted by an LLM on 2026-06-05 and is not human-verified or independently reproduced. The CC BY 4.0 licence permits mirroring; the verbatim PDF is not hosted in this batch.

Attribution (CC BY 4.0). Chemla, Gilles, Alejandro Rivera, and Liyan Shi. “Too Much, Too Soon, for Too Long: The Dynamics of Competitive Executive Compensation.” The Journal of Finance 80, no. 5 (October 2025): 2921-2970. DOI: 10.1111/jofi.13470. © 2025 The Author(s). Licensed under CC BY 4.0. This page is an adaptation by the Institute for Automated Research: core results extracted and re-expressed; changes were made.