Organizational Change and Reference-Dependent Preferences

Schmidt and von Wangenheim develop a dynamic model of organizational change in which workers have reference-dependent preferences — specifically loss aversion and social comparisons — to explain several empirically observed patterns that standard models cannot easily account for: organizational inertia in normal times, sudden productivity jumps during crises, persistent total factor productivity (TFP) differences across firms in the same industry, and effort and wage compression within firms.

The motivating empirical puzzle is the early-1980s collapse of the Great Lakes iron ore and steel industry, which had been geographically shielded from foreign competition for over 100 years. When Brazilian competitors undercut prices, the industry responded by roughly doubling labor productivity within a few years — not through new technology or capital investment, but through organizational improvements and more efficient use of existing capital (Schmitz 2007). The broader puzzle is Syverson’s (2004) finding that at the four-digit industry level, the 90th-percentile firm has TFP 1.9 times that of the 10th-percentile firm, a gap that cannot be explained by observable input differences.

The model features a principal (firm owner) bargaining with loss-averse workers (represented by a union) over organizational change — represented as a worker effort level x that adapts the firm to the state of technology θ. Workers’ reference point is a convex combination of the status quo contract and their rational expectations of the agreed contract, with weight α on the status quo. Loss aversion parameter λ > 0 means that losses relative to the reference point are weighted more heavily than gains.

The core static result (Proposition 1) is that loss aversion drives a wedge of 1 + αλ between the workers’ marginal cost and the firm’s marginal benefit of organizational change. Below a threshold θ defined by ∂v(x₀,θ)/∂x = 1 + αλ, there is complete inertia: the firm does not change the effort level at all. Above θ, the firm adjusts effort, but to x(θ) < x^ME(θ), undershooting the materially efficient level. Higher λ or higher α both widen the inertia range and reduce the amount of implemented change (Proposition 2).

A crisis — modeled as a cost shock that makes the status quo contract generate negative profits, threatening firm closure — changes workers’ outside option from their current utility U₀ to the unemployment utility of zero. Workers are now willing to accept either wage cuts or effort increases to keep their jobs. Crucially, because both concessions are perceived as losses of equal size by workers, the firm prefers to increase effort rather than cut wages, since increasing effort is more productive when x < x^ME. The model thus provides a microfoundation for downward nominal wage rigidity: in a recession, workers make concessions through harder work rather than wage cuts.

In the infinite-horizon dynamic model, workers accumulate a quasi-rent over time equal to αλ(x_{t-1} − x₀), which represents compensation paid for past effort increases. This quasi-rent is what the firm expropriates during a crisis, allowing a discontinuous jump in effort toward the materially efficient level. Firms founded at different times or hitting different idiosyncratic shocks will therefore have different effort histories and different productivity levels, generating persistent TFP differences even among firms with identical technologies. When forward-looking players anticipate the possibility of crisis, inertia in normal times actually widens further (x̃(θ) ≤ x(θ)), because firms rationally delay effort adaptation knowing it will be cheaper to implement change during a crisis.

The expectations-management extension (Section 4) introduces a moral-hazard problem with a manager who chooses the probability of successful change. Because a higher probability of change raises the workers’ expectation-based reference point and reduces their perceived adaptation cost, the firm’s optimization problem becomes convex when the cost of effort for management is sufficiently low relative to (1−α)λΔx. This delivers a bang-bang result: the principal induces either full implementation (p = 1) or no change (p = 0), never an interior probability. This formalizes the management-consulting advice that commitment and urgency are essential to organizational change.

The social-comparisons extension (Section 5) shows that when workers compare their wages and effort to colleagues, the firm optimally compresses effort differences across workers — inducing the less productive worker to work more than efficiency requires and the more productive worker to work less. If productivity differences between workers are sufficiently small, the firm sets identical effort levels. Wage compression follows from effort compression. To avoid the cost of social comparisons entirely, it may be optimal for the firm to split into separate legal entities whose workers no longer form a common reference group — a new explanation for organizational unbundling.

Q: What is the core mechanism by which loss aversion generates organizational inertia in normal times? A: Workers have a reference point that is a convex combination (weight α on status quo, weight 1−α on rational expectations) of their current contract and the expected new contract. Because workers perceive an effort increase above their reference effort as a loss, the firm must pay a wage premium of αλ per unit of additional effort on top of the material effort cost of 1. This raises the effective marginal cost of implementing change from 1 to 1 + αλ, so the firm only implements change when the marginal revenue of effort strictly exceeds 1 + αλ. Below the threshold technology level θ (defined by ∂v(x₀,θ)/∂x = 1 + αλ), there is complete inertia and the firm keeps x* = x₀.

Q: How does a crisis break the inertia? A: A crisis is a cost shock large enough to make the firm’s profits negative under the status quo contract, so the firm would close unless workers make concessions. Workers’ outside option shifts from their accumulated utility U₀ to the unemployment utility of zero. Because wage cuts and effort increases are both perceived as losses of equal magnitude, the firm prefers to demand effort increases (which raise revenue) over wage cuts (which do not). At the margin, when workers are at zero utility, the loss-aversion terms cancel from the marginal rate of substitution, and the firm can push effort up to the materially efficient level x^ME — a discontinuous jump.

Q: Why do wages not fall during a recession in this model? A: Workers perceive both wage cuts and effort increases as losses of equal per-unit utility cost. Since increasing effort by one unit and cutting wages by one unit impose the same utility cost on workers but effort increases raise firm revenue while wage cuts do not, it is always more efficient for the firm to extract concessions through higher effort rather than lower wages. The firm therefore first drives effort to x^ME before cutting wages, and cuts wages only if the zero-utility constraint still is not binding at x^ME. This provides a microfoundation for Bewley’s (1999) observation that wages do not fall during recessions.

Q: Where does the quasi-rent exploited during a crisis come from? A: Every time the firm implements an effort increase in normal times it must compensate workers with a permanent wage increase to cover both the permanent higher effort cost (x_{t}−x_{t-1}) and the one-time behavioral adaptation cost αλ(x_{t}−x_{t-1}). Because the compensation for the adaptation cost must be spread over all future periods as a permanent payment, workers accumulate a quasi-rent that by period t equals αλ(x_{t-1}−x₀) above their initial utility U₀ = w₀−x₀. This is the rent the firm expropriates in a crisis to fund the discontinuous effort increase.

Q: How does the dynamic model generate persistent TFP differences across firms in the same industry? A: Firms founded at different times start with different initial status-quo effort levels relative to the current technology θ. Because each firm’s path of organizational adaptation is history-dependent — inertia regions, timing of crises, and accumulated quasi-rents all depend on when the firm was founded and what idiosyncratic shocks it experienced — firms that start later (or hit crises earlier) can remain more productive than older firms for extended periods. The numerical example with v(x,θ) = θ ln(x), α = 0.5, λ = 1, δ implied parameters shows that a firm founded when θ = 7 at the materially efficient point can maintain a substantial productivity advantage over a firm founded when θ = 4 that has accumulated inertia, even though both firms have access to the same technology.

Q: Does rational anticipation of a future crisis increase or decrease inertia in normal times? A: It strictly increases inertia. When players assign probability µ > 0 to a crisis each period, forward-looking workers demand higher compensation for effort increases in normal times — specifically, the per-period compensation for behavioral adaptation cost rises from (1−δ)αλ to γ = (1−δ(1−µ))αλ, which is increasing in µ. Simultaneously, the firm anticipates that effort adaptation will be cheaper to achieve in a crisis and therefore delays effort increases. The result is that the inertia threshold shifts from x(θ) to x̃(θ) ≤ x(θ), a strictly wider inertia region (Proposition 6).

Q: What is the expectations-management result and what drives it? A: When a manager chooses the probability of successful change p at cost c(p) = (c/2)p², the wage the firm must pay workers is concave in p (equation 22): w = x₀ + p(1+λ)Δx − p²(1−α)λΔx + U₀. The concavity arises because a higher p raises the expectation-based component of the reference point, lowering workers’ perceived adaptation cost. When c < (1−α)λΔx, this makes the principal’s profit function convex in p, so the optimum is at a corner: the principal induces either p = 1 (full implementation) or p = 0 (no change). Even when an interior solution obtains, a decrease in α (more weight on expectations) increases p. This formalizes the practitioner prescription that organizational change requires convincing everyone that change is certain and unavoidable.

Q: What is the effort and wage compression result under social comparisons? A: When each worker compares his situation to his colleague’s, with weight β on the peer’s wage and effort in forming the reference point, the firm must pay both workers a social-comparison premium of λβ(x₂−x₁) per unit of effort difference (Lemma 5). The firm therefore optimally compresses effort differences: it induces the less productive worker to exert effort above his efficient level and the more productive worker below his efficient level, at first-order conditions ∂v₁/∂x = 1 − 2λβ and ∂v₂/∂x = 1 + 2λβ respectively. If the productivity difference is small enough (specifically if ∂v₂(x*,θ)/∂x < 1 + 2λβ at the equal-effort point), the firm sets x₁* = x₂* = x*, eliminating wage inequality entirely (Proposition 8).

Q: Why might it be optimal for a firm to split into separate entities? A: Social comparisons impose costs on the firm by requiring higher wages for both workers (each receives a premium of λβ(x₂−x₁) regardless of their relative rank) and by distorting effort levels away from their efficient values. If workers employed by legally separate firms no longer treat each other as part of their reference group — because β falls to zero across firm boundaries — the firm can eliminate these comparison costs by spinning off activities into independent entities. This provides an efficiency rationale for organizational unbundling that does not rely on asset specificity or transaction costs, addressing what the authors call the “Williamson puzzle.”

Q: What are the implications for older workers and for social insurance policy? A: Older workers have two compounding reasons to be more resistant to organizational change: shorter remaining time horizons reduce the present value of permanent wage compensation for adaptation costs, and Gächter, Johnson, and Herrmann (2022) report that loss aversion λ increases with age, income, and wealth. Both factors raise the cost of implementing change with older workers. For social insurance, generous unemployment benefits or policies preventing layoffs (such as short-time work schemes) reduce workers’ concession costs in a crisis, weakening the mechanism by which crises trigger change. The model suggests this may contribute to slower technology adoption in countries with stronger labor market protections.

Q: What empirical facts from the existing literature does the model account for? A: The model accounts for: (1) Syverson’s (2004) finding of a 90th/10th percentile TFP ratio of 1.9 in four-digit US industries; (2) the iron ore and steel case study (Schmitz 2007) in which labor productivity doubled within a few years of a competitive shock with no new technology; (3) Bloom et al.’s (2014) correlation between more intense competition and higher TFP; (4) Holmes and Schmitz’s (2010) survey finding that competitive shocks raise industry productivity mainly through survival and improvement of existing firms; (5) Bewley’s (1999) downward nominal wage rigidity; and (6) Hjort, Li, and Sarsons (2022) on multinational firms using headquarters wages as reference points for wages in low-wage locations.

Loss aversion (λ): The parameter measuring the degree to which workers weight losses relative to their reference point more heavily than gains. A meta-analysis (Brown et al. 2023) across 607 empirical estimates finds an average loss aversion parameter of 1 + λ = 1.955. In this paper, λ > 0 means workers perceive a wage cut and an effort increase as losses, raising the effective marginal cost of organizational change by a factor of 1 + αλ.

Reference point (w^r, x^r): The benchmark wage and effort level against which workers evaluate outcomes. Defined as a convex combination of the status quo contract (w₀, x₀) with weight α and the rational expectation of the agreed contract (w^e, x^e) with weight 1−α. Losses occur when the realized wage falls below w^r or the realized effort exceeds x^r.

Organizational inertia: The firm’s failure to implement materially efficient organizational change even when doing so would increase total surplus. In the model, inertia arises because the effective marginal cost of effort to the firm is 1 + αλ rather than 1, so the firm only implements change above a threshold technology level θ. The range of inertia widens with higher λ, higher α, and higher initial effort x₀.

Quasi-rent: The utility accumulated by workers above their initial utility U₀ = w₀−x₀ as compensation for past effort increases. By period t it equals αλ(x_{t-1}−x₀). This quasi-rent is the source of concessions the firm can extract in a crisis: workers accept higher effort (or lower wages) in exchange for keeping their jobs rather than losing this accumulated utility through unemployment.

Behaviorally efficient effort x(θ): The effort level that maximizes joint surplus taking behavioral adaptation costs into account, defined by ∂v(x,θ)/∂x = 1 + (1−δ)αλ in the dynamic model. This is strictly below the materially efficient effort x^ME(θ) (defined by ∂v/∂x = 1) and strictly above the firm’s privately optimal effort in normal times.

Effort compression: The result under social comparisons that the principal optimally reduces the effort difference between workers relative to the efficient allocation — inducing the less productive worker to work more and the more productive worker to work less than efficiency requires. Driven by social-comparison costs λβ(x₂−x₁) that both workers receive as premiums regardless of relative rank.

Expectations management: The strategic use of commitment to high probability of change in order to shift workers’ expectation-based reference point and reduce the perceived adaptation cost. When α is small (rational expectations dominate the reference point), making change more certain lowers the wage cost of implementation, creating a complementarity between commitment and cost reduction that produces the bang-bang result: implement with certainty or not at all.