Week 4. Pay, Incentives, Multitasking, and Relational Contracts

Learning Objectives¶

By the end of this week, students should be able to distinguish the level, slope, timing, and credibility of compensation; use a compact principal–agent model to explain incentive and insurance tradeoffs; separate changes in worker behavior from changes in who enters or remains; and design an evaluation that measures both the rewarded activity and an independently meaningful outcome. They should also distinguish formal enforcement, repeated-relationship incentives, reciprocity, and self-commitment, and explain what evidence would discriminate between them.

The research deliverable is an incentive-reform design that separates at least two competing mechanisms, with a contract dictionary, an assignment/observation timeline, a credible comparison, an independent quality outcome, a worker-welfare measure, and a result that would contradict the preferred mechanism. Students are not expected to identify every preference parameter or write an optimal contract from one reform.

Opening Orientation¶

Central question: How do formal pay rules and informal commitments change effort, risk, selection, and cooperation?

A firm introduces a bonus. Measured output rises, some workers earn more, and quits change. Did the bonus increase effort per hour, extend working time, attract different workers, redirect attention from quality to quantity, change customer allocation, or make a previously unreliable promise credible? These are different mechanisms with different implications for the next policy the firm might adopt.

This week moves from measuring performance to attaching consequences to it. The contract is not just the column called “bonus” in a payroll file. It is the complete rule workers understand before acting: eligibility, thresholds, rates, measurement windows, peer comparisons, payout dates, exceptions, and what happens when the employer does not honor a promise. The same average payment can be generated by very different marginal incentives.

Gibbons and Prendergast provide complementary guides to the economic logic of compensation; Hoffman and Stanton connect that logic to the contemporary personnel-economics evidence Gibbons, 1998Prendergast, 1999Hoffman & Stanton, 2025. We use three required research readings to organize the week: Leaver and coauthors on separating recruitment and post-entry incentives, Friebel and coauthors on a team-bonus intervention, and Brown–Falk–Fehr on relational enforcement in a laboratory market. Other readings supply mechanisms, counterexamples, and feasible designs for student projects rather than a compulsory reading marathon.

The compact models and numerical examples below are original teaching constructions, not exact reproductions or calibrations of any cited author’s full model. Each comparative static depends on the stated assumptions.

Core Points¶

Bridge¶

Imagine two shops whose staff receive the same average weekly pay. In one, that amount was guaranteed before work began. In the other, staff knew they would receive a bonus only if sales crossed a target. Equal payroll does not imply equal incentives: the second contract changes the reward to an additional sale near the target, exposes earnings to customer demand, and may redirect effort from service quality. To evaluate a reform, first reconstruct what staff knew and could influence; then follow sales, hours, independent quality, and who enters or leaves.

Week 3 separated production from recording and employer beliefs. We now ask how workers respond to rewards based on those records. Treat information quality as a starting point, not a solved nuisance: a newly rewarded metric can become a less faithful signal after people adapt to it.

Week 2’s selection problem reappears because contracts help determine who applies and who stays. We recap it only to design incentive evaluations. Detailed managerial allocation belongs in Week 5, training and promotion paths in Week 6, team formation and communication in Week 7, bargaining and outside-option incidence in Week 8, and comprehensive organizational change in Week 9. Full mechanism-design derivations from the labor-design course are background; this week’s distinctive contribution is to connect contracts to actual work, data, and competing empirical explanations.

Field Core¶

1. Read the contract before reading the regression¶

Write down the promised pay schedule before analyzing realized compensation. A useful generic representation is

where $i$ indexes workers, $g$ their group, and $t$ the work period; $T$ is the group target; $a$ is guaranteed pay, $b$ a piece rate on individual measured performance $m$, $B$ a threshold bonus based on a group-period measure $M$, and $r$ a discretionary component depending on the history $\mathcal H_t$. This is an organizing template, not a claim that every employer uses all four terms. Caps, floors, delayed commissions, returns, clawbacks, and eligibility restrictions can change its shape substantially.

The researcher needs the rule that was available when work occurred. A payout file tells us who received money after outcomes were realized. It does not establish which reward was expected, when it became known, or which alternatives a worker faced. A zero bonus may mean that the worker was ineligible, missed the target, left before payout, or was denied an earned award. Preserve those categories.

For each contract version, request the announcement date, effective work dates, measurement window, target-setting date, eligible roster, actual payout date, and amendment history. Link those records to tasks, hours, quality, and exits. Reconcile the contractual payment against the realized payment, retaining a reason code for discrepancies. Do not silently overwrite promises with payroll outcomes.

A signing bonus changes the value of entry or staying until a vesting date. A piece-rate increase changes the return to another unit. An unexpected gift arrives after an earlier work decision. A promised discretionary bonus depends on beliefs about payment. Calling all four “higher incentives” erases the economic treatment.

Read the announced rule at the time of action, not only the realized payment. The entries below are a research-design map; they are not interchangeable treatments.

Interpretive discipline. Effort, gross output, quality-adjusted output, revenue, contribution margin, total profit, and worker welfare are separate objects. An accounting measure can improve while a welfare measure deteriorates. A contract’s risk and hours implications should be measured rather than presumed.

Hypothetical threshold example. Pay is $20+0.10m+5\mathbf1\{m\geq100\}$. Moving from 98 to 99 measured units adds 0.10; moving from 99 to 100 adds 5.10; moving from 100 to 101 adds 0.10. The discontinuity creates a potentially large return near the threshold but not a universally high marginal reward. With uncertainty, the incentive to act earlier depends on the chance of crossing the target, not the eventual payout category. These are invented amounts for teaching, not a firm’s contract.

2. A compact principal–agent benchmark: incentive intensity versus insurance¶

Use a one-task model to clarify the mechanism before adding organizational complications. Output is $q=e+\epsilon$, effort costs $c(e)=e^2/(2k)$ with $k>0$, and the contract is $w=a+bq$. Noise is normal with mean zero and variance $\sigma^2$. A risk-neutral firm values output at $p>0$ per unit; noise is independent of chosen effort. The worker has constant absolute risk aversion $\rho>0$, and the normal-linear environment gives the certainty equivalent

The worker chooses $e^*=kb$. The first part is familiar: a larger marginal return increases effort under the specified technology. The second is equally important: stronger performance pay exposes the worker to more income risk. If the firm can adjust guaranteed pay freely and the participation constraint binds at $\bar U$, then

With $p=k=\rho=1$, noise variance one gives $b^*=0.5$ and effort 0.5. Noise variance four gives $b^*=0.2$ and effort 0.2. This is a teaching derivation conditional on operating the employment relationship, under unrestricted fixed transfers, an interior optimum, known parameters, and no selection, limited liability, minimum pay, or multitasking. It is not a calibration of a real compensation system. Maximized profit is $p^2k^2/[2(k+\rho\sigma^2)]-\bar U$. If this is below the firm’s outside profit (zero in the simplest shutdown comparison), the conditional optimum does not imply that the firm hires the worker. Binding worker participation is not the same as firm viability.

Three lessons translate into research. First, lower-powered pay need not reveal managerial incompetence: it may insure workers against noise. Second, an observed correlation between job risk and pay sensitivity does not identify the formula above; firms also choose measurement, task allocation, supervision, and whom they employ. Third, an intervention that raises $b$ while holding $a$ fixed is not the same intervention as the model’s optimal contract adjustment. Distinguish an exogenous change in one contract term from movement along an equilibrium menu Gibbons, 1998Prendergast, 1999.

Research use. Record the full distribution of payments, downside exposure, guarantees, hours, and worker choices. A willingness to choose variable pay can reflect ability, risk tolerance, liquidity, beliefs, or outside options. Do not read one latent preference directly from that choice. A higher wage is also not itself a welfare estimate when work intensity and risk change.

3. Incentives versus selection: three empirical designs, three claims¶

Lazear studies the switch to performance pay at Safelite using personnel data. The paper links the compensation change to productivity and workforce composition; it is not a randomized assignment of workers to pay regimes Lazear, 2000. The teaching value is the distinction between changes among observed workers and changes in the workforce itself. Worker fixed effects do not automatically remove time-varying assignment, learning, or selective retention.

Shearer’s tree-planting field experiment observes individual workers under piece rates and fixed wages, making the within-worker incentive comparison especially tangible. The paper separately uses structural assumptions to extrapolate beyond experimental planting conditions Shearer, 2004. The contrast is a template for distinguishing evidence inside an experiment from a model-based external-validity exercise; it does not establish a universal piece-rate effect across occupations.

Leaver and coauthors use two stages of experimental variation: recruitment markets (district × subject-family cells) receive different advertised contracts, and schools receive an unexpectedly re-randomized realized contract after teachers have been placed. That design separates recruitment and post-entry incentive margins more directly than a single before/after reform Leaver et al., 2021. Keep the two assignment units and their timing visible. Do not label a pupil-learning contrast as direct observation of teachers’ latent effort, or mechanically reproduce a selection decomposition from a survivor-only sample.

A simple accounting identity makes the composition issue explicit. Let $s_h^r$ be the share of worker type $h$ in regime $r$ and $q_h^r$ its mean output. Then

The identity is exact for the stated weighting convention. Neither term becomes causal merely because it has a label. Types may be latent, output may be measured only among stayers, and alternative decomposition weights reallocate interaction terms.

Worked illustration. Initially, 30% are high-output workers producing 12 units and 70% produce 8, giving 9.2. Under the new regime, the share is 60% and outputs are 14 and 9, giving 12. The increase of 2.8 equals 1.3 from within-type changes at old shares plus 1.5 from composition at new outputs. In real data, those counterfactual type means require evidence; in the lab they are known only because the instructor generated them.

A student’s design should choose its target population before estimating: baseline incumbents, entrants, all eligible positions, or the firm’s current workforce. Output per current worker, total firm contribution from baseline workers, and earnings of former workers are different objects. Preserve people who leave in a baseline-cohort outcome when that outcome remains well defined and observed; do not set unknown post-exit well-being to zero.

4. Multitasking: increasing the target can lower the value of work¶

Holmström–Milgrom show why imperfectly balanced incentives across tasks can matter for compensation and job design Holmström & Milgrom, 1991. The empirical problem is not simply noisy output. It is that workers can redirect effort toward the dimension receiving the reward.

Use an original, risk-neutral, two-task teaching model. Both tasks are observed perfectly here, deliberately isolating task reallocation from Week 3’s measurement noise. Let marginal rewards be $b_1,b_2$, and

At an interior solution, $\partial e_2^*/\partial b_1=-\kappa/(1-\kappa^2)$. Positive $\kappa$ makes the tasks compete through effort costs. Negative $\kappa$ produces the opposite comparative static. Check nonnegativity constraints before using the interior formula.

For $\kappa=0.6$, rewards $(0.8,0.8)$ produce effort $(0.5,0.5)$. Raising only the quantity reward to $(1.2,0.8)$ produces $(1.125,0.125)$. If the firm values work at $v=e_1+2e_2$, value falls from 1.5 to 1.375 despite a large increase in the first task. Balanced rewards $(1,1)$ instead produce $(0.625,0.625)$ and value 1.875. These are gross-value examples, not profit comparisons: payroll, effort disutility, and the cost of measuring the second task still matter.

Design implication. Pair the incentivized metric with outcomes outside its definition: product returns, rework, independently audited quality, safety, customer retention, or help to coworkers. Use prespecified definitions and follow-up windows so that a short-run gain cannot hide a later loss. If task assignments change after the reform, the total policy effect includes that reallocation. Controlling for the new task mix changes the estimand rather than “cleaning” it automatically.

Larkin studies nonlinear sales incentives and the timing and prices of enterprise-software transactions. The paper is useful because it follows economic consequences beyond recorded sales: the timing of deals and discounts can move with incentives Larkin, 2014. Oyer supplies broader evidence on fiscal-year patterns consistent with nonlinear incentives Oyer, 1998. Neither paper should be described as an RD merely because a compensation schedule has a threshold. Sales near a threshold are chosen, and fiscal timing can share confounders with inventory, customer demand, and accounting rules.

5. Thresholds, tournaments, and the incentives to move someone else’s outcome¶

A tournament pays for rank rather than absolute output. In a simple two-person teaching case, assume a risk-neutral worker, effort costs measured in money, and a prize spread $\Delta W$. An interior best response satisfies

The slope depends on the opponent and on noise. Common shocks may cancel in rank comparisons, but unequal territories, handicaps, field conditions, or prior ability can make the contest very uneven. Lazear–Rosen provide the classic analytical starting point Lazear & Rosen, 1981. Ordinal ranking is a contract component, not a complete welfare criterion.

A worker can sometimes improve relative standing by withholding help or making someone else’s job harder. The same prize that rewards production may therefore discourage cooperation. Conversely, a team bonus may reward helping a colleague even when individual output falls. To study this, record coworker outcomes, transfers of tasks, customer assignment, and time spent supporting others—not only the focal worker’s score.

Bandiera–Barankay–Rasul’s 2005 comparison changes relative incentives to piece rates and links responses to social relationships and observability Bandiera et al., 2005. Their 2013 study adds rankings and then monetary tournament prizes to an existing team-piece-rate environment, allowing team composition to change Bandiera et al., 2013. Crucially, the latter uses sequential within-subject regimes, not simultaneous random assignment of different teams to regimes. Its interpretation requires addressing seasonal change. It is also not a comparison of individual versus team pay.

Research template. A rank intervention can change information, status, money, and competition at once. A better design separates a rankings-only arm from a rankings-plus-prize arm where feasible, while acknowledging any shared information or spillovers. Measure who competes against whom and whether that set changes. A stable average effect can mask redistribution across workers or teams. Keep full team-production and endogenous team-formation analysis for Week 7; here the object is the externality introduced by the pay rule.

6. Team bonuses: the treatment is the opportunity to earn, not the bonus received¶

Friebel and coauthors randomize team-bonus eligibility in a retail chain. The study reports effects on shop outcomes and compensation and investigates mechanisms including effort complementarities; it does not establish peer pressure as the dominant explanation Friebel et al., 2017. This is the week’s main lab anchor because it makes the assignment unit, group production, and realized-payout problem concrete.

Suppose $Z_g$ indicates an offered shop bonus and $P_{gt}=Z_g\mathbf1\{M_{gt}\geq T_{gt}\}$ indicates receiving it. Regressing sales on $P$ compares successful treated shops with a mixture of other shops. A positive association can be created by the payment rule even when $Z$ has no effect on production. The first causal estimand should therefore be assignment-based:

A participation or receipt effect requires an additional identification argument. Using eligibility as an instrument for payout can fail exclusion because an offer may change effort even among shops that narrowly miss payment. “Did not receive a bonus” is not synonymous with “untreated.”

A team-level treatment need not produce an equal gain for all workers. Compare total sales, customer counts, unit prices, payroll, hours, complaints, and staff turnover. Follow the allocation of the bonus among members and document whether non-recipients share workload or help meet targets. To infer complementarities rather than pressure, seek separate variation or mechanism measures; a team-level treatment effect alone cannot identify the production function.

For a matched-pair shop experiment, let $\Delta Y_{pj}$ be shop $j$’s mean post-period outcome minus its mean pre-period outcome in pair $p$. Label the offered and control shops $T$ and $C$. The equal-pair-weighted teaching estimator is

Its reference SE is the sample standard deviation of the pair contrasts divided by $\sqrt{12}$. Inference reflects the number and assignment of shops or pairs, not the number of cash-register transactions. With 12 independent randomized pairs, there are $2^{12}=4096$ assignments to enumerate for an appropriate sharp-null test. This is the synthetic lab’s design, not a claim about the published study’s exact randomization algorithm. The exact test conditions on that paired assignment and no cross-shop interference, and tests zero assignment effect for every shop. It does not test every heterogeneous zero-average-effect null. The primary outcome is gross sales; secondary p-values are unadjusted.

7. Reciprocity and commitment: beyond the contemporaneous piece-rate slope¶

An unexpected wage increase can change how workers feel toward their employer without changing the return to the next unit. DellaVigna and coauthors vary private incentives, the employer’s return, and gifts in field experiments. Their findings distinguish productivity from extra work, illustrating why the response margin must be measured rather than assumed DellaVigna et al., 2022. This is not equivalent to a repeated self-enforcing contract: one-shot reciprocity can operate without a future relationship.

Davies–Fafchamps provide a recent online experiment framed as employment. The experiment varies the feasible contract sets; employers then choose offers, and workers accept and choose effort across samples recruited in different locations Davies & Fafchamps, 2025. Its role here is to ask which predictions and behavioral motives travel. It is not a representative comparison of national workplaces, and randomizing the feasible contract set is different from randomizing employers’ realized offers or participants’ national culture.

Kaur–Kremer–Mullainathan study self-control using a field experiment with data-entry workers, including voluntary commitment contracts and payday variation Kaur et al., 2015. The teaching distinction is between the causal effect of an offered opportunity and the selected group choosing a restrictive contract. Payoff-dominated at a fixed output is not necessarily utility-dominated when the worker values changed future behavior. Payday responses can also motivate questions about liquidity and payment timing; they are not a universal diagnostic for present bias. The associated correction concerns an anecdotal quotation rather than the empirical estimates; do not repeat the corrected anecdote Kaur et al., 2022.

Design implication. Separate: promised from surprise pay; amount from marginal incentive; delayed from immediate payment; freely chosen from imposed restrictions. Document what participants knew when they chose and when outcomes were produced. A commitment device that helps a voluntary chooser does not justify imposing it on everyone. A worker may value discipline, dislike coercion, and face liquidity constraints simultaneously.

8. Relational contracts: credible promises have an enforcement constraint¶

Some valuable actions cannot be specified or verified cheaply by an external enforcer. A firm may promise to reward judgment, protect time for learning, credit help to coworkers, or avoid revising targets opportunistically. The promise matters only if the worker expects it to be honored.

Levin supplies a formal account of self-enforced incentive contracts Levin, 2003. Baker–Gibbons–Murphy explain why explicit and subjective incentives can be substitutes or complements: an improved formal contract changes not only performance measurement but the parties’ fallback positions Baker et al., 1994. Gibbons–Henderson add a useful organizational distinction between credibility and clarity—keeping a promise and sharing an understanding of what the promise entails are not the same problem Gibbons & Henderson, 2012.

A deliberately simplified enforcement calculation is enough for the opening intuition. At the payment node, the firm can save a promised bonus $B$ by reneging. Cooperation provides per-period profit above the punishment outcome of $\Delta\Pi>0$. Let $d=\delta s$, with $0\leq d<1$, where $\delta$ discounts time and $s$ is an assumed exogenous probability that the relationship continues. Honoring the promise requires

With $B=3$ and $\Delta\Pi=1$, the minimum effective continuation factor is 0.75. At $d=0.8$ the future surplus available is 4; at 0.6 it is 1.5. The calculation illustrates the firm’s payment incentive under a particular punishment and stationary continuation value. It is not sufficient to establish a full equilibrium: worker participation, effort incentives, off-path behavior, and the credibility of punishments also need to hold. If separation is an endogenous response, multiplying by an exogenous survival probability is no longer an adequate model.

A practical identification problem follows. Long tenure and high effort can reflect good matches, worker selection, learning, or credible promises. They do not uniquely reveal relational enforcement. Stronger evidence distinguishes what was promised, which action was noncontractible, who could verify fulfillment, how future opportunities changed, and what happened after a perceived breach.

Brown–Falk–Fehr compare enforcement environments in a laboratory market and study the relationships that emerge Brown et al., 2004. Use it as controlled evidence about market interactions under those environments, not as a field estimate of the effect of tenure. The repeated setting can support several motives; do not identify every cooperative action with a single textbook mechanism.

A researchable contrast. Consider a change in the person authorized to approve discretionary awards while formal rates stay fixed. A panel could track promised and paid awards, prior relationships, complaints, and independently measured output. But supervisor reassignment may also change skill, tasks, and customer allocation. A credible design needs an assignment argument or more targeted variation in enforcement, not merely a dummy for “new manager.” Week 5 will develop that manager-assignment problem.

9. Recent evidence: separate channels rather than declaring contracts good or bad¶

Cai–Luo–Wang’s 2025 working paper experimentally varies signing bonuses and monitoring for new hires at a Chinese automobile manufacturer. Its primary-source summary distinguishes hours, manager-evaluated performance, and quits rather than treating both interventions as the same output mechanism Cai et al., 2025. This is an especially useful bridge from Week 3: a signing bonus is not a piece-rate increase, and a manager assessment is not direct latent effort. Keep the working-paper status explicit; the pack does not claim to have executed the original data.

Cai–Prat–Yu’s 2026 working paper combines merger events with employee reviews to study noncontractible benefits. The authors interpret patterns in satisfaction and review text as consistent with breaches of implicit commitments Cai et al., 2026. Review participation, workforce turnover, organizational disruption, and correlated firm changes remain important competing explanations for a new project. A text label for a perceived breach is evidence about reported experience, not a directly observed enforcement parameter.

Herkenhoff and coauthors’ 2025 working paper contrasts implicit-contract, market-power, and reallocation predictions in US private-equity buyouts using linked worker records, finding patterns they interpret as consistent with reallocation Herkenhoff et al., 2025. This is not a direct refutation of the review-based merger study: populations, events, and outcome domains differ. The pair teaches students to specify a mechanism’s observable implications and resist fitting every ownership change into the same story. Full ownership-change and reorganization analysis remains Week 9 material.

10. From compensation records to an incentive-reform design¶

Begin with an eligible roster defined before the intervention. Link the assignment rule to the contract workers knew, not just what they received. Define outcomes over enough time to observe returns, corrections, effort shifts, and exits. Maintain distinct work-date and pay-date records. Match the inference unit to the randomization or shock; a larger personnel panel does not create more independent interventions Cameron & Miller, 2015.

Selection requires its own strategy. A stayer-only comparison conditions on a possible response to the pay reform. Follow baseline cohorts, compare entry and exit explicitly, and use bounds only under defensible restrictions. Lee-style trimming requires monotone selection, which an incentive reform can violate if some workers stay while others leave in response to risk or competition Lee, 2009. Equal retention rates across arms are not proof that the same people would remain in both regimes.

For nonlinear contracts, reconstruct every rate, reset, eligibility window, and cap. Check alternative explanations for threshold bunching, such as rounding, reporting rules, or customer timing. For rankings, define the comparison pool. For team pay, state the interference structure and distinguish unit-level ITT from within-unit mechanisms. For promises, record fulfillment histories and alternatives after breakdown. Those tasks precede a sophisticated estimator.

Each row links a research question to the variation used and a claim students should not infer automatically. Published status is distinguished from working-paper status in the bibliography and source-verification file.

Use the theory readings to state predictions, not to treat empirical assumptions as proved: Gibbons, 1998Prendergast, 1999Holmström & Milgrom, 1991Baker et al., 1994Levin, 2003.

11. Open questions that follow from the evidence¶

Rewarding quality when technology makes quantity cheaper. A proposed study could vary quantity-only versus balanced rewards after a common technology change, with independent quality audits and stable prices. The contribution would be evidence on reward alignment, not another adoption-versus-nonadoption comparison. The main threats are post-treatment auditing, differential task assignment, and quality outcomes observed too late.

Promise credibility versus contract generosity. Hold the announced schedule fixed and exploit credible variation in guarantee or adjudication mechanisms. Measure beliefs before performance, fulfillment afterward, and independent outcomes. A higher expected payment can be generated by a more generous schedule or a more believable promise; separating them is the research opportunity. Any employer intervention must respect participants’ actual commitments and avoid manufacturing harmful breaches.

The value of incentives when opportunities differ. Some workers have little discretion over customer traffic, machine uptime, or assigned cases. A project can study whether an incentive is effective only when workers can change an outcome, using predetermined opportunity measures rather than realized success. A high baseline score need not identify high responsiveness.

Dynamic target resetting. Workers may anticipate that strong current output raises next period’s quota. A credible study would document both the explicit bonus and the target-update process, with unexpected or randomized update rules if institutionally feasible. The key data are forecasts, target versions, and behavior across several reset cycles, not one period’s bunching.

Pay reform and welfare beyond the wage. Pair payroll and retention with uncertainty, hours, schedule control, effort burden, and independently collected well-being measures. Measure those outcomes for an interpretable population, not only enthusiastic survivors. This supplies the incidence ledger that Week 8 will develop rather than assuming firm profit and worker welfare move together.

Research Lab¶

Reproduce¶

Primary anchor: Friebel et al. (2017). The official AEA-linked repository is identified in the resource bibliography Friebel et al., 2017. Repository listings were verified; original microdata were not downloaded or executed for this pack. An original-data replication is optional and must begin with access, file, assignment, and dependency checks.

The guaranteed route is a synthetic design reconstruction, not a reproduction of published estimates. The supplied standard-library starter constructs a shop panel with an offered bonus, a frozen target, realized payout, sales, returns, payroll, and a margin-accounting outcome. It generates 24 shops in 12 randomized pairs over 12 weeks. All units, schedules, parameter values, and outcomes are invented. Students reconstruct payout mechanically, estimate a pair-weighted ITT, and perform assignment-aligned sharp-null inference.

Diagnose¶

First compare assignment to realized payout. A separate zero-effect simulation shows why bonus recipients can have higher observed sales even when the offer has no causal effect on sales. Next examine an invented two-task response in which measured quantity rises while gross quality-adjusted value falls. Finally use a two-type accounting exercise to separate a known synthetic within-type change from a known composition change. In observational personnel data those latent components are not handed to the researcher.

The lab also computes the principal–agent examples and a relational-enforcement grid. Students must state that the latter is an employer-side necessary condition under the specified model, not an empirical estimate of trust or a proof that all equilibrium constraints are satisfied.

Transfer¶

Use Leaver et al. as the design comparison for distinguishing recruitment and post-entry incentives; its separate archive is provided Leaver et al., 2021. Propose a reform with two observable competing mechanisms, a prespecified randomization or comparison unit, an independent quality measure, and a worker-welfare measure. The submission is a two-page memo plus a contract/data dictionary—not a claim to have designed a universally optimal compensation system.

Methods Box¶

Required memo ledger: intervention → information available before action → behavioral margin → competing mechanism → comparison → outcome population → inference unit → welfare limitation. The student must name a result that would contradict their preferred mechanism.

A useful empirical contract contains four linked but distinct records: offered terms, worker awareness/eligibility, performance and production, and realized payments. A fifth record tracks participation, exits, and missing outcomes. Merging them into a single “treatment” indicator discards the very variation needed to distinguish mechanisms.

The data map separates reading links and repository listings from genuine microdata access. The IAB Linked Personnel Panel offers a relevant employer–employee perspective, but research versions and the teaching-oriented Campus File are different products; neither should be inferred from a paper’s appendix Institute for Employment Research, Research Data Centre, n.d.. The DellaVigna et al. archive is a separate candidate for students interested in the distinction between productivity and extra work DellaVigna et al., 2022.

No access application, data-provider contact, login workaround, or download of restricted data is authorized by the editing prompt. Link to original papers instead of bundling copyrighted PDFs. Store confidential payroll/personnel records outside public teaching assets.

Minimum reporting standard. Report the assignment/contract timeline, eligibility denominator, announced and realized reward schedule, primary ITT, independent outcome family, wage and hours distribution, participation/attrition, inference unit, and explicit limits on mechanism claims. Report transformations and aggregation weights. Any conditional estimate must explain what post-treatment selection it conditions on. A difference in statistical significance across outcomes is not a statistically significant difference between effects.

Reading Ladder And References¶

Three required research readings¶

Leaver et al. (2021): draw both stages of randomization and identify the population relevant to each contrast. Friebel et al. (2017): distinguish an offered team contract from a payout and separate shop performance from individual incentives. Brown–Falk–Fehr (2004): identify the enforcement environment and explain which findings are experimental and which interpretations invoke a model.

Foundations and optional derivation route¶

Gibbons and Prendergast orient the field. Holmström–Milgrom motivates multitasking; Lazear–Rosen motivates relative rewards; Baker–Gibbons–Murphy, Levin, and Gibbons–Henderson organize subjective and relational incentives. Lazear and Shearer provide contrasting empirical incentive designs. These readings support selective preparation, not seven additional compulsory full papers.

Rotating empirical and frontier presentations¶

Choose among nonlinear incentives (Oyer; Larkin), social and team pay (the two Bandiera papers), reciprocity and self-commitment (DellaVigna et al.; Kaur et al., with correction), and contemporary mechanisms (Cai–Luo–Wang; Davies–Fafchamps; the two ownership-change working papers). Every presentation must state a comparison, an outcome, a mechanism not identified, and a feasible extension. Working-paper status is part of the citation.

Foundations and rotating presentations

Intuitive theory: Gibbons and Prendergast, followed by selected sections of Holmström–Milgrom, Baker–Gibbons–Murphy, Levin, and Lazear–Rosen Gibbons, 1998Prendergast, 1999Holmström & Milgrom, 1991Baker et al., 1994Levin, 2003Lazear & Rosen, 1981. The local teaching models summarize a mechanism; they are not exact replicas of every cited model.

Effort and sorting: Lazear and Shearer Lazear, 2000Shearer, 2004. Contrast quasi-experimental personnel data, within-worker experimental variation, and structural extrapolation.

Externalities and nonlinear rewards: the two Bandiera papers, Oyer, and Larkin Bandiera et al., 2005Bandiera et al., 2013Oyer, 1998Larkin, 2014. A team or tournament regime changes who benefits from another worker’s action.

Reciprocity, self-commitment and portability: DellaVigna et al., Kaur et al. with the erratum, and Davies–Fafchamps DellaVigna et al., 2022Kaur et al., 2015Kaur et al., 2022Davies & Fafchamps, 2025. Separate the work margin, experimental population, and mechanism.

Relational capability and current applications: Gibbons–Henderson plus three clearly labeled working papers Gibbons & Henderson, 2012Cai et al., 2025Cai et al., 2026Herkenhoff et al., 2025. Compare observable implications, rather than presenting every organization as evidence for the same theory.

Methods and data follow-up: cluster inference, selection bounds, personnel-economics synthesis and IAB documentation Cameron & Miller, 2015Lee, 2009Hoffman & Stanton, 2025Institute for Employment Research, Research Data Centre, n.d..

A suggested extended meeting uses roughly 25 minutes for contract/model foundations, 35 for experimental and quasi-experimental comparisons, 25 for multitasking/team/relational mechanisms, and 20 for a design clinic. The offline lab is separate. Select rotating readings rather than compressing every paper into an unreadable deck.

Exercises And Discussion Prompts¶

1. Two contracts have the same expected payment. One pays a fixed amount; another pays for each measured unit. State which assumptions make effort differ and which data would reveal the risk borne by workers.

2. Derive the one-task optimal slope and identify the assumptions needed to treat the fixed payment as freely adjustable. Explain why a fixed-pay laboratory comparison need not trace the optimal-contract formula.

3. Recompute the two-task example with $\kappa=-0.2$. Does raising the first reward still crowd out the second task? Check whether effort remains feasible.

4. Explain why regressions on bonus receipt can be misleading even in a randomized bonus-offer experiment. Propose a valid assignment-based comparison.

5. In the workforce decomposition, change the order of weights used for composition and behavior. Why does the accounting allocation change, and what would identify causal components?

6. Construct a timeline for a sales quota that resets each month. Name three ways to reach the target other than increasing total annual value, and specify an outcome that distinguishes each.

7. A firm reneges on a discretionary payment after a demand collapse. Which observations distinguish a credibility channel from the direct consequences of the demand shock?

8. Explain the difference between a reciprocal response to an unexpected gift, a voluntary commitment device, and a relational contract. Design one test that separates two of them.

9. A team bonus increases sales and retention. Give two explanations other than peer pressure and identify the additional data required to test them.

10. Write an incentive-reform memo with a worker-welfare outcome. State what evidence would cause you to reject your preferred mechanism even if the headline performance effect is positive.

Reproducibility And Code Lab Note¶

Download the teaching repository (ZIP), or clone the repository. Keep its folder structure and open books/special-topic8-organizational/labs/04-pay-incentives-multitasking-and-relational-contracts/; the lab README supplies the run instructions. Weeks 1–3 use the shared plotting module supplied with the repository.

The Week 4 lab handout and lab README distinguish three routes: optional authorized original-data replication, mandatory synthetic design reconstruction, and analytical teaching calculations. The executed route combines the latter two; empirical_replication is false. The optional original-data route is omitted because actual archive files, permissions, dependencies, and the original assignment protocol have not been inspected. Original data must never be silently replaced while retaining a replication label.

From the course root, run the lab and then regenerate the chapter figure:

ENV_NAME=research bash labs/04-pay-incentives-multitasking-and-relational-contracts/smoke.sh
conda run -n research python assets/scripts/build-week4-multitask.py

The core reconstruction and smoke use the Python standard library; figure generation uses the installed Matplotlib environment. The smoke executes the actual code, checks shop/period keys, contract timing and frozen targets, paired assignment, bonus and accounting formulas, and 4096-assignment inference. It compares two fresh same-seed runs and executes an additional seed. It requires no credentials, API, proprietary data, network, or GPU. Synthetic estimates are teaching results rather than evidence about actual retail workers. The transfer memo template requires competing predictions, an independent quality outcome, and a worker-welfare measure.

Slide Companion Note¶

The Week 4 slide deck (PDF) and Beamer source provide a substantial lecture plus lab or a two-meeting route. They cover the contract ledger, risk–incentive model, recruitment and post-entry designs, multitasking, nonlinear and group rewards, gifts and commitment, relational enforcement, contemporary evidence, and the paired-assignment lab. Model assumptions accompany the main comparative statics; long evidence maps remain in the chapter.

Compile from the course root:

conda run -n research latexmk -cd -pdf -interaction=nonstopmode slides/week4/04-pay-incentives-multitasking-and-relational-contracts.tex

The deck uses the finished course’s Beamer style and the generated teaching figure. Numerical constructions are hypothetical; no article figure or unpublished instructor result is reused.

Bridge Forward¶

Contracts delegate part of the organization’s response to workers, but managers still choose assignments, targets, discretion, coaching, and exceptions. Week 5 turns to those managerial contributions and the allocation of authority. Carry forward this week’s question: when a measured outcome changes, which organizational decision and which behavioral margin actually produced it?