برخی از پیامدهای ناخوشایند تعادل عمومی قراردادهای جبران انگیزه اجرایی

We consider a simple real business cycle model in which shareholders hire self-interested executives to manage their firm. A generic family of compensation contracts similar to those employed in practice is studied. When compensation is convex in the firmʼs dividend, an increase in the firmʼs output results in a more than proportional increase in the managersʼ income. Incentive contracts of sufficient yet modest convexity are shown to result in an indeterminate general equilibrium, one in which business cycles are driven by self-fulfilling fluctuations in managersʼ expectations. The proposed family of contracts may yield first-best outcomes for specific parameter choices.

Executive compensation in public companies typically is provided in the form of three components, a cash salary (the wage and pension contributions), a bonus related to the firmʼs short term operating profit, and stock options (or other related forms of compensation based on the firmʼs share price). In seeking to create stronger links between pay and performance, the use of stock options, in particular, has emerged as the single largest ingredient of U.S. executive compensation. According to Hall and Murphy [15], “in fiscal 1999, 94% of S&P 500 companies granted options to their top executives. Moreover, the grant-date value of stock options accounted for 47% of total pay for S&P 500 CEOs in 1999.” CEOs of the largest U.S. companies frequently receive annual stock option awards that are on average larger than their salaries and bonuses combined.34 Frydman and Jenter [12] report that for the period 2000–2005, options and other long term incentive pay averaged 60% of total executive compensation; in 2008 the salary component had fallen to only 17% of average total pay. Executive options contracts represent a particular instance of a highly non-linear convex style contract.5 In this paper we demonstrate that convex executive pay practices, within the context of the separation of ownership and control in the modern corporation, may have dramatic, adverse business cycle consequences. In particular, we show that convex compensation contracts may give rise to generic sunspot equilibria in otherwise standard dynamic stochastic general equilibrium models. Sunspot equilibria (indeterminacy) formalize the notion that expectations not grounded in fundamentals may lead to behavior by which they are fulfilled. These equilibria may involve arbitrarily large fluctuations in macroeconomic variables even though production is characterized by constant returns to scale at the social as well as private level. As such, convex managerial compensation contracts provide an entirely new mechanism by which indeterminacy may arise in real (non-monetary) economies. An even more disturbing observation is that convex contracts may lead, under certain parameter configurations, to non-stationary behavior. Practically speaking this means that convex contracts may induce the self-interested manager to adopt investment policies that drive his firmʼs equilibrium capital stock to zero.6 Our focus on convex contracts derives from the fact that these contracts will also be shown to arise endogenously in our model context: the optimal contract, optimal in the sense of generating the first best allocation, is convex in the firmsʼ aggregate free cash flow (dividends). This feature is necessary to align the incentives of managers and shareholders who are assumed to have different elasticities of intertemporal substitution and thus different preferences for intertemporal consumption allocations.7 The optimal contract in this model does not, per se, generate equilibrium indeterminacy. We show, however, that the equilibrium indeterminacy discussed above can easily arise in the face of small deviations from the optimal contract. By small deviations we mean that the contract involves a slightly higher degree of convexity than is required to perfectly align incentives, or involves a fixed salary component that is added to the managerʼs incentive compensation, features that characterize actual compensation contracts. Nevertheless, while we derive the optimal contract in the model ultimately to justify our interest in convex compensation contracts in general, the focus of the analysis remains on the equilibrium consequences of a general class of convex compensation contracts which resemble contracts actually observed in practice. To keep the analysis as simple as possible and to isolate the key source of equilibrium indeterminacy in the model, we assume that both consumer-worker-shareholders and managers have the same information. This assumption stands in contrast with standard principal-agent theory that focuses either on the effects of hidden information as to the managerʼs type or on the managerʼs hidden actions (effort). Our results apply more broadly, however, to contexts where consumer-shareholder-workers and managers have differing information regarding the economyʼs state variables.8 We eschew this added generality for two reasons: First, it allows us to focus exclusively on the indeterminacy generating mechanism which is the same in either context. Second, for the model presented here, the presence or absence of indeterminacy is related only to the managerʼs elasticity of intertemporal substitution, and the terms of the contract given to him. Nothing else is relevant. Further augmenting the model to allow for hidden information regarding the managerʼs “type” or actions, while likely providing additional justifications for offering a convex contract, would not, per se, affect the presence or absence of indeterminacy.9 The earlier literature on equilibrium indeterminacy in dynamic models relies on a variety of other mechanisms; e.g., aggregate increasing returns, a difference between social and private returns to scale, a variable degree of competition, or monetary phenomena to generate multiple equilibria.10 In our economy with delegated management and a convex executive compensation contract, the wedge between the actual return on capital and the return on capital as experienced by the manager is at the heart of the indeterminacy result. The power (degree of convexity) of the performance portion of the executive compensation contract tends to magnify the effective rate of return on capital from the managerʼs perspective. As a result, the expectation of a high return on capital may increase the income of the manager next period to such an extent that consumption smoothing considerations dictate a diminished level of investment today, thereby fulfilling the high return expectation. Nevertheless, our analytical and numerical results reveal that the degree of contract convexity required for indeterminacy is very low, especially so relative to a standard call options style incentive contract. An outline of the paper is as follows: Section 2 describes the model and presents the family of compensation contracts we propose to study. It also details the precise circumstances under which equilibrium indeterminacy and instability arise. Section 3 provides an overview of the methodology by which an indeterminate equilibrium may be computed numerically and applies it to the study of the economyʼs business cycle characteristics. Section 4 provides a theoretical justification for the analysis of the proposed family of contracts by demonstrating that they yield first best outcomes for specific parameter choices. Section 5 concludes. 2. Convex contracting in a general equilibrium model of delegated management We focus on the context of a self-interested manager and the consumer-shareholder-workers on whose behalf he undertakes the firmʼs investment and hiring decisions in light of his compensation contract. We assume that there exists a continuum of measure 1 of identical consumer-worker-shareholders who consume a single good and supply homogeneous labor services to a continuum of measure 1 of identical firms.11 The consumer-shareholder-workers delegate the firmʼs management to a measure μ∈[0,1]μ∈[0,1] of managers who receive sufficient compensation to be willing to oversee the firm. We assume that once the manager agrees to operate the firm, he commits to it for the indefinite future. We further assume full information in the sense that both the consumer-worker-shareholder (principal) and the manager (agent) know the realization of all present and past variables.12 Since there is no distortion in this economy, the first best can potentially be achieved. In the benchmark model, we suppose that the managers have no access to financial markets. With no opportunity to borrow or lend, they consume all of their income in each period. Guided by their compensation contract, they seek to smooth their consumption over time by undertaking the firmʼs investment and hiring decisions. In Appendix F, we extend the model to allow managers to buy or sell riskless bonds. This is done to show that the results to be presented here are not sensitive to the assumption that managers are excluded from financial markets. We start by describing the environment surrounding the consumer-shareholder-worker, the firm and the manager and introduce the family of compensation contracts we propose to consider.13 We then characterize the economyʼs equilibrium allocation and characterize the nature of equilibrium indeterminacy and instability. In Section 4, we then demonstrate that the same equilibrium is Pareto optimal when the contract parameters assume specific values.

The message of this paper is clear and direct: when confronted with compensation contracts which are mildly convex to the firmʼs stock price or free cash flow, CEOs may well find it in their self-interest to adopt investment policies that lead to equilibrium indeterminacy or instability. As a result, the time path of the economyʼs macroeconomic aggregates, as well as the executivesʼ compensation, at least with respect to volatility, may bear little association to fundamentals. In this sense, highly convex CEO compensation contracts may substitute for technological increasing returns, a typical requirement of the earlier indeterminacy literature. Within a standard dynamic macroeconomic setup, these results appear to hold for a wide class of model parameters, at least for the compensation contracts studied here. These results suggest that the early twenty-first century explosion in the incentive compensation among financial firms may have unforeseen consequences. We are only now beginning to see what these consequences are.