## Abstract

We develop a model of a cooperative power game between a chief executive officer (CEO) and labor over a proposed corporate outsourcing, and test the model’s predictions concerning the decision to outsource, division of profits, and post-outsourcing firm performance using a sample of outsourcing deals by US firms. In accord with the model, we find that a firm is more likely to outsource when CEO power is greater, production costs are higher, and the industry is more homogeneous. Notably, we find that the outsourcing decision does not affect the CEO’s share of profits, and that CEO power is positively related to post-outsourcing performance. Additionally, poor prior firm performance moderates the power dynamics between the CEO and labor. These findings imply that labor can supplement traditional governance mechanisms and act as an effective managerial monitor when the firm undergoes a major restructuring.

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## Data availability

The datasets generated and analyzed during the current study are obtained from the Factiva database and the WRDS database.

## Notes

For a criticism of the shareholder model, see, for instance, Donaldson and Preston (1995), who state, “The plain truth is that the most prominent alternative to the stakeholder theory (i.e., the ‘management serving the shareholders’ theory) is morally untenable. The theory of property rights, which is commonly supposed to support the conventional view, in fact – in its modern and pluralistic form – supports the stakeholder theory instead.” Jensen (2001) also states, “As a statement of corporate purpose or vision value maximization is not likely to tap into the energy and enthusiasm of employees or managers to create value. Since a firm cannot maximize value if it ignores the interest of its stakeholders, enlightened value maximization can utilize much of the structure of stakeholder theory by accepting long run maximization of the value of the firm as the criterion for making the requisite tradeoffs among its stakeholders”.

Various authors (DeAngelo and DeAngelo, 1991; Hallock, 1998; Banning and Chiles, 2007) show that CEO pay decreases with labor negotiation or union activism. Agrawal (2012), however, shows that union pension funds pursue worker interests rather than firm value in their investment decisions. Freeman and Kleiner (1999) argue that unions push CEOs to increase wages to the point where union firms may expand less rapidly than nonunion firms. Addison and Hirsch (1989) find that the pressure of wage increase from labor forces the CEO to cut research and development expenses, which slows firm growth.

See, for instance, Statement of the International Union, United Automobile, Aerospace and Agricultural Implement Workers of America (UAW) on the Subject of Protecting Employees and Retires in Business Bankruptcies Act of 2010 (H.R. 4677), submitted to the Subcommittee on Commercial and Administrative Law, Committee on the Judiciary, United States House of Representative, May 25, 2010.

United Airlines used deteriorating cash balance and bankruptcy prospects in securing labor agreement for significant wage concessions in exchange for equity and board participation. http://en.wikipedia.org/wiki/United_Airlines#Bankruptcy_and_reorganization.

See the cases of GM (

*Wall Street Journal*October 18, 1999), FedEx (*Wall Street Journal*November 23, 1998), and the Boston Globe (Outsourcing: “Boston Globe, not Bangalore Globe”—new union ad campaign,*The Earth Times*, 15 March 2007). When the Boston Globe outsourced the firm’s publishing jobs in 2007, the firm’s union ferociously protested, calling it an “egregious mistake,” although officials said that “the outsourcing decision is difficult, but necessary for the paper's long-term health”.This formulation is in the spirit of Raith (2003) and Aggarwal and Samwick (1999), both of which model in a principal–agent framework the interaction between product market competition and incentives by having the agent exert unobservable effort that lowers the marginal cost of production of the firm.

Because the firm has a monopoly, we are unable to formally examine the role of the extent of competition on the outsourcing decision. However, we proxy for this via the price elasticity of demand, which determines how price-sensitive are consumers and thereby the availability of substitutes.

This demand function arises if the representative consumer has CES preferences over a bundle of goods, such that the price elasticity of demand equals the elasticity of substitution across any pair of goods.

Three assumptions, respectively, mean \(\varepsilon > 1\) (revenue function is increasing in output), \(\theta \le 1\) (concave cost function), and \(m < 1\) (decreasing returns to TFP). m is the returns to TFP. \(\mathrm{m}=\frac{\upvarepsilon -1}{\upvarepsilon \left(1-\uptheta \right)+\uptheta }\). For details, see “Appendix 1”, subsection 2.

Choi et al. (2021) also finds that the likelihood of outsourcing will be higher, the greater the degree of ex ante financial constraints.

Labor monitoring means the capacity of labor bargaining with the management, achieving a full steady-state equilibrium concerning labor payoffs with and without outsourcing outcomes—where outsourcing probability itself is determined as a result of relative labor-management power as well as the division of firm’s profits between labor and management.

In addition, we use CEO pay slice as an alternative measure of CEO power. It is calculated as the fraction of the aggregate compensation of the top-five executive team in a firm’s upper echelon. The results are insignificant; hence we do not report them separately.

The information was obtained from The Union Membership and Coverage Database, available at www.unionstats.com. Constructed by Hirsch and MacPherson (2003), the database provides labor union membership, coverage, and density estimates compiled from the Current Population Survey (CPS), a monthly household survey. The database reports those estimates by state, industry (four-digit SIC codes), occupation, and metropolitan area, while the firm-level estimates are not publicly available. Matsa’s (2010) firm-level estimates of union coverage are provided by Richard Freeman and Barry Hirsch.

The

*G-index*is a comprehensive measure of corporate governance based on 24 firm-specific provisions. A large value of*G-index*implies poor corporate governance and potentially severe agency conflicts.We define R

_{jt}as the continuously compounded rate of return for firm*j*on day*t*; R_{mt}as the market rate of return on day*t;*and_{j}and_{j}as estimates of regression parameters for firm*j*, estimated over the 150-day period beginning at 250 trading days and ending at 101 trading dates prior to announcement. We then have: \(AR_{jt} = R_{jt} - (\alpha_{j} + \beta_{j} R_{mt} )\;{\text{and}}\;CAR_{j} = \sum\nolimits_{t \in wiondow} {AR_{jt} }\)We also obtained Total Similarity Data from the 10-K Text-based Network Industry Concentration (TNIC) data from the Hoberg–Phillips Data Library. The results are insignificant, so they are not reported in the tables.

Note that our framework exhibits the same properties as a neoclassical growth model in the macroeconomics literature. As in such models, we can also show that the steady state is unique and stable because there are decreasing returns to TFP under assumption (A1). TFP does not grow along the balanced growth path (BGP) because there is no source of exogenous growth, nor is there an engine of endogenous growth. This is derived in Lemma 1 in “Appendix 2”.

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## Appendices

### Appendix 1: Derivation of the SSMPE

This Appendix provides detailed derivation of the model outlined in the text, in backwards induction, from Step 3 on cost minimization in subsection 1 to Step 2 on production problem in subsection 2, and Step 1 on the TFP problem in subsection 3 and solution of the SSMPE in subsection 4. Step 0 determines equilibrium split of profits between the CEO and labor and solves for outsourcing decision in subsection 5.

### 1.1 1 The cost minimization problem of the stage game (Step 3)

Let *T* denote the equilibrium level of TFP determined in Step 1. Given the firm desires to produce *q* units of output, its cost-minimization problem in Step 3 is

Applying Theorem 3.4 in Jehle and Reny (2011, p. 140), we can show that the cost function associated with (1) satisfies

where \(c(z)\) is an increasing and concave function of the vector of input prices *w* and *z* is an index that equals 1 if the firm is outsourcing and 0 otherwise. From Shephard’s lemma, factor demand is given by \(X_{k} (z) = c_{k} (z)(q/T)^{1/\theta }\), where \(c_{k} (z) = \partial c(z)/\partial w_{k}\). If the firm outsources, then it faces the cost function \(c(1)\); otherwise, it faces the cost function \(c(0)\), where \(c(0) > c(1)\). For simplicity, we assume the outsourcing decision does not affect the product’s quality. This reflects the fact that, when outsourcing, a firm has access to cheaper factors of production and an enlarged set of factors of production, which potentially affects its entire mix of inputs. Since outsourcing may involve a complex mix of domestic and foreign inputs, we abstract away from such details by modeling instead the impact of outsourcing as reducing the cost function faced by the firm. Hereafter, we suppress the index *z* until subsections 4 and 5 wherein we derive the equilibrium and solve the outsourcing decision.

### 1.2 2 The production problem of the stage game (Step 2)

The CEO and labor anticipate that the cost function in Step 3 is \(c(z)(q/T)^{1/\theta }\). The firm’s output problem in Step 2 is to maximize monopoly profits:

The first-order condition (FOC) yields the output policy \(q(z) = [(1 - 1/\varepsilon )s\theta T^{1/\theta } /c(z)]^{\varepsilon \theta /(\varepsilon (1 - \theta ) + \theta )}\). It follows that the firm profits \(\Pi (z) = sq(z)^{1 - 1/\varepsilon } - c(z)(q/T)^{1/\theta }\) as a function of TFP are

where \(\pi (z) \equiv [1 - (1 - 1/\varepsilon )\theta ]\{ s^{\varepsilon } [(1 - 1/\varepsilon )\theta /c(z)]^{(\varepsilon - 1)\theta } \}^{1/(\varepsilon (1 - \theta ) + \theta )}\) measures the profitability of the firm as a function of its outsourcing decision and \(m \equiv \frac{\varepsilon - 1}{{\varepsilon (1 - \theta ) + \theta }}\) determines the responsiveness of firm profits to TFP, thus we refer to *m* as the *returns to TFP*.

To satisfy the second-order condition (SOC) of the output problem, we assume demand is elastic (such that the revenue function is increasing in output), \(\varepsilon > 1\), and that there are constant or decreasing returns to scale in production (such that the cost function is convex), \(\theta \le 1\); and to satisfy the SOC associated with the TFP problem in Step 1 (to be solved below), we assume there are decreasing returns to TFP, \(m < 1\):

*Assumption 1*: \(\varepsilon > 1\), \(\theta \le 1\), \(m < 1\).

The assumptions \(\varepsilon > 1\) and \(\theta \le 1\) have two further implications. First, they ensure firm profits \(\Pi (z) = \pi (z)T^{m}\) are positive. Second, they imply the returns to TFP, *m* is increasing in the price elasticity of demand \(\varepsilon\) and the homogeneity \(\theta\) of the firm’s production function. Hence, the more elastic is demand and the greater are the returns to scale, the more responsive are firm profits to increases in TFP; that is, the more the firm has to gain from effort being exerted by the CEO and labor.

### 1.3 3 The TFP problem of the stage game (Step 1)

Let \(\alpha_{i}\) denote the equilibrium equity stake of player *i*, for \(i = C,\;L\), as determined in Period 0. The CEO and labor anticipate that the firm profits to be split in Step 2 are \(\Pi (z) = \pi (z)T^{m}\). For ease of exposition, in this sub-section, we suppress the outsourcing indicator *z*. Taking as given the effort of player *j*, the value function of player *i* satisfies the Bellman equation

subject to the law of motion

The FOC with respect to effort is

The SOC with respect to effort is

The envelope condition (EC) with respect to TFP is

Applying the FOC (7), the EC (9) becomes \(V^{\prime}_{i} (T) = \alpha_{i} \pi mT^{m - 1} + \frac{{d_{i} (1 - \delta )}}{{\lambda \beta_{i} e_{i}^{{\beta_{i} - 1}} e_{j}^{{\beta_{j} }} }}\). Shifting this forward in time, we obtain \(V^{\prime}_{i} (T^{\prime}) = \alpha_{i} \pi m(T^{\prime})^{m - 1} + \frac{{d_{i} (1 - \delta )}}{{\lambda \beta_{i} (e^{\prime}_{i} )^{{\beta_{i} - 1}} (e^{\prime}_{j} )^{{\beta_{j} }} }}\). Applying this to the FOC (7) yields

Equations (6) and (10) jointly define a non-linear dynamical system with three state variables consisting of the two effort policies and the TFP of the firm. The evolution of this system describes the Markov perfect equilibrium.

### 1.4 4 The steady state Markov perfect equilibrium (SSMPE)

To render the problem tractable, we restrict the analysis to the SSMPE. We show in Lemma 1, which is stated and proved in the “Appendix 2”, that the SSMPE arises under the restriction that TFP and the effort levels of the CEO and labor grow at the same constant rate over time.^{Footnote 17} Let an upper bar denote the steady state value of a variable. The steady state effort policy of player *i* is

and the steady state level of TFP is

The outsourcing decision *z* affects the profitability of the firm via the cost function: \(\pi (z) = [1 - (1 - 1/\varepsilon )\theta ]\{ s^{\varepsilon } [(1 - 1/\varepsilon )\theta /c(z)]^{(\varepsilon - 1)\theta } \}^{1/(\varepsilon (1 - \theta ) + \theta )}\). Furthermore, the outsourcing decision may affect the profit shares of the CEO \(\alpha_{C} (z)\) and labor \(\alpha_{L} (z)\). If the firm outsources, then it faces lower costs of production, which enhance firm profitability. The implications are that, holding constant the split of profits between the CEO and labor, the CEO and labor exert greater effort if the firm outsources, and the steady state TFP of the firm is greater if the firm outsources.

The ratio of steady state effort policies is

Suppose the CEO and labor incur the same marginal cost of exerting effort (i.e., \(d_{C} = d_{L}\)) and have the same relative importance in the accumulation of TFP (i.e., \(\beta_{C} = \beta_{L}\)); then the CEO exerts more effort than labor if it has a greater share of profits [i.e., \(\alpha_{C} (z) > \alpha_{L} (z)\)].

To further simplify the framework, we assume the CEO and labor seek to maximize their steady state value function. From the Bellman Eq. (5), the steady state value function of player *i* satisfies \(\overline{V}_{i} (z) = \alpha_{i} (z)\pi (z)\overline{T}(z)^{m} - d_{i} \overline{e}_{i} (z) + (1 + r)^{ - 1} \overline{V}_{i} (z)\). Combining the steady state effort policy and TFP equations (11) and (12), respectively, we obtain the relation \(\overline{e}_{i} (z) = \left( {\frac{{\alpha_{i} (z)\beta_{i} }}{{d_{i} }}} \right)\left( {\frac{m\pi (z)\delta }{{r + \delta }}} \right)\overline{T}(z)^{m}\), which, when applied to the Bellman equation, yields the steady state value function of player *i* in terms of TFP:

Under Assumption 1 that there are decreasing returns to TFP (i.e., \(m < 1\)), the steady state value functions are non-negative, such that the CEO and labor obtain positive returns. We show in Lemma 2, which is stated and proved in the “Appendix 2”, that the SOC with respect to effort Eq. (8) is satisfied in the steady state.

### 1.5 5 Equilibrium split of profits and outsourcing decision (Step 0)

In Step 0, the split of profits between the CEO and labor and the outsourcing decision of the firm are implemented via Nash bargaining in Period 0. The players bargain so as to maximize their steady state value function. To capture the fact that labor receives benefits when the firm does not outsource, let \(\overline{V}_{LO} (z)\) denote the steady state present value that accrues to labor stemming directly from the outsourcing decision *z*, independently of the profits it earns. All other things being equal, labor is more content if the firm does not outsource, \(\overline{V}_{LO} (1) < \overline{V}_{LO} (0)\), reflecting all implicit and explicit benefits it earns (such as higher employment in the absence of outsourcing). Let \(\psi \in (0,1)\) denote the weight that labor assigns to the steady state present value of profits \(\overline{V}_{L} (z)\) and \(1 - \psi\) the weight it assigns to \(\overline{V}_{LO} (z)\). For tractability, the CEO and labor have a payoff of zero if they do not participate in the relationship, such that the Nash product is \(\overline{V}_{C} (z)^{{\gamma_{C} }} (\overline{V}_{L} (z)^{\psi } \overline{V}_{LO} (z)^{1 - \psi } )^{{\gamma_{L} }}\).

Define \(\hat{\pi } \equiv [1 - (1 - 1/\varepsilon )\theta ]\{ s^{\varepsilon } [(1 - 1/\varepsilon )\theta ]^{(\varepsilon - 1)\theta } \}^{1/(\varepsilon (1 - \theta ) + \theta )}\), which is independent of the outsourcing decision *z*, such that \(\ln \pi (z) = \ln \hat{\pi } - \theta m\ln c(z)\). Applying the steady state TFP equation (12) to the steady state value function of the CEO and labor (14), and taking the log, the Nash bargaining problem is

which is maximized subject to the conditions \(\alpha_{C} + \alpha_{L} = 1\) and \(\gamma_{C} + \gamma_{L} = 1\).

The FOC with respect to \(\alpha_{C}\) yields the equilibrium share of the CEO:

while that of labor is

The firm outsources (i.e., \(z = 1\)) if and only if

### Appendix 2: Derivation of Lemmas 1 and 2

### Lemma 1

Maintain Assumption 1. Along a balanced growth path (BGP), wherein TFP and the effort levels of the CEO and Labor are restricted to grow at the same constant rate over time (steady state).

### Proof of Lemma 1

Let *g* denote the common growth rate, such that \(T^{\prime} = (1 + g)T\) and \(e^{\prime}_{i} = (1 + g)e_{i}\) for \(i = C,\;L\). From the law of motion (6), we obtain the following relationship between contemporaneous TFP and the effort policies:

Applying Assumption 1 to the law of motion (6), we obtain the effort policy of player *i* in terms of TFP the next period:

Applying the effort policy (20) to (19), we obtain the following expression for TFP the next period:

We infer that along the BGP, TFP is constant over time, i.e., \(g = 0\), which arises if the effort policies are constant over time.

### Lemma 2

Assume Assumption 1 holds. In the SSMPE, the SOC with respect to effort (8) is satisfied.

### Proof of Lemma 2

From the EC with respect to TFP (9), in the steady state, we have \(\overline{V}^{\prime}_{i} = \alpha_{i} \pi m\overline{T}^{m - 1} + (1 - \delta )(1 + r)^{ - 1} \overline{V}^{\prime}_{i}\), which yields the steady state marginal return on TFP:

Take the derivative of the EC with respect to TFP and evaluate it at the steady state, to obtain

In the steady state, the SOC (8) is \(- (1 - \beta_{i} )\overline{V}^{\prime}_{i} + \lambda \beta_{i} \overline{e}_{i}^{{\beta_{i} }} \overline{e}_{j}^{{\beta_{j} }} \overline{V}^{\prime\prime}_{i} \le 0\). Applying (22) and (23), and using the fact that \(\overline{T} = \lambda \overline{e}_{C}^{{\beta_{C} }} \overline{e}_{L}^{{\beta_{L} }} /\delta\), the steady state SOC is given by

which is satisfied given \(m < 1\) under Assumption 1.

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Choi, J.J., Ju, M., Plehn-Dujowich, J.M. *et al.* Outsourcing as a cooperative game between the CEO and labor: theory and evidence.
*Rev Quant Finan Acc* **59**, 1095–1131 (2022). https://doi.org/10.1007/s11156-022-01071-x

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DOI: https://doi.org/10.1007/s11156-022-01071-x