A software engineer finishes their formal workday of documentation and bug fixes, then stays late to tinker with a side tool they’ve been building. That extra time never shows up on a timesheet, but it’s not exactly a gift to the employer either. The engineer is doing it because they want to.
This ordinary scene sits at the center of a new NBER working paper by Joshua S. Gans of the University of Toronto’s Rotman School of Management. Gans builds a model to answer a specific question: when some productive tasks are intrinsically enjoyable, and workers voluntarily add unpaid hours to them, how does that change the way firms design jobs, decide what to automate, and how payroll data should be read?
The puzzle behind AI’s murky footprint
Recent studies of generative AI at work have turned up patterns that don’t quite line up. Adoption can save users large amounts of time, yet recorded earnings and hours barely move. AI exposure sometimes stretches the working day rather than shrinking it. And within a single job, the mix of tasks can shift toward what workers describe as the “core” or higher-value parts, while auxiliary work fades.
Gans wants to know whether a single contracting mechanism can produce all three patterns. His answer builds on a specific asymmetry between what an employer can require and what a worker can voluntarily supply.
Two ways to write an hourly contract
The model considers one firm, one worker, and many complementary tasks arranged in what economists call an O-ring production technology, meaning every task is essential and each depends on the others being done well. The worker values leisure and may find any given task pleasant, neutral, or unpleasant at the margin.
Gans compares two versions of an hourly contract. In a “controlled-bundle” contract, the firm dictates the complete mix of tasks the worker performs during paid hours and posts an hourly wage. In a “paid-floor” contract, the firm specifies a minimum required composition of paid work but cannot stop the worker from tacking on additional unpaid time to any task they find attractive enough.
The paid-floor setup fits situations Gans describes as natural for the model: research, software development, creative work, and professional problem-solving, where deliverables can be verified but capping self-directed effort is difficult. It fits less well for tightly scheduled shift work.
The first result: unpaid work isn’t a bargain
Gans’s first finding runs against a common intuition. Suppose a worker voluntarily contributes free hours to a task they enjoy. It’s tempting to conclude the firm is getting a discount. The model says otherwise.
For any final allocation of tasks that both contract types can support, the total wage bill is identical. The reason is that under either regime, a task that’s enjoyable at the margin lowers the compensating wage the firm must pay to get the worker to do it. Voluntary top-up doesn’t add a further discount on top of that; it simply shifts where the accounting line between paid and unpaid work falls.
Where the two regimes genuinely differ is in the set of allocations they can achieve. A paid-floor contract cannot force a worker to spend fewer hours on a task the worker finds rewarding enough to pursue on their own time. That’s an implementability constraint, and it turns out to matter a great deal for automation.
A new reason to automate
Standard task-based models of automation identify two forces. Replacement removes compensated tasks. Scale raises the marginal productivity of the human tasks that remain. Both apply here too, with a twist: intrinsic enjoyment re-weights replacement, because a task the worker finds pleasant costs less to retain.
Gans identifies a third force he calls containment. Under paid floors, a firm may automate a task precisely because it cannot cap the worker’s voluntary expansion of it. Keeping the task in the human bundle would let the worker push it beyond the level that maximizes the firm’s paid-floor value. Automating it is a way to sidestep that problem.
Enjoyment therefore pulls in two directions on the same task. Rewarding tasks save money on the wage bill, which favors keeping them human. But rewarding tasks also risk voluntary overexpansion, which favors automating them. Gans is explicit that the model does not imply a clean rule where less enjoyable tasks get automated first. That ordering follows only under additional restrictions.
Why payroll numbers can mislead
The model’s empirical payoff is a warning about interpreting standard labor data. Gans constructs a numerical example with two configurations that share the same automated task, the same AI technology, the same hourly wage, the same wage bill, and the same paid hours. In one configuration, the worker puts in two hours total, all paid. In the other, the worker puts in six hours total, only two of which are paid. Total output differs by roughly 70 percent between the two.
A researcher looking only at wage rates, wage bills, and paid hours would see identical jobs. Time-use data, output measures, or AI-input use would separate them, but payroll alone cannot.
Gans is careful about the scope of this claim. It is not that a specific worker with fixed preferences can slide between the two allocations without any payroll response. It is that cross-sectional payroll observables, when task-level preferences are unobserved, do not pin down what’s actually happening inside the job.
Three empirical fingerprints that do separate the mechanisms
Even if payroll can’t distinguish replacement from voluntary expansion, other data can. Gans points to three margins.
The first is the gap between worked time and paid time. Replacement tends to shrink both together, while voluntary expansion opens a wedge where unpaid hours rise even as paid hours stay flat. Detecting this requires time-use surveys or self-reports.
The second is the within-worker task mix. If a worker shifts toward more enjoyable tasks because compensated auxiliary tasks were subtracted, that looks different from a worker who pushed into a rewarding task voluntarily, even though the observed mix might be similar.
The third is worker-reported intensity and well-being. Two configurations with the same payroll footprint can differ in total hours and in the utility value of retained tasks, which shows up in surveys of meaning at work and willingness-to-pay estimates for job conditions.
The salaried alternative
Gans closes with a benchmark: what happens if the firm can price a complete job bundle with a fixed salary rather than paying by the hour? Under rich salaried bundle pricing, the hourly distortion disappears. The firm can implement what an efficient planner would want, and voluntary unpaid top-up vanishes at the efficient allocation because every task hour is already priced into the salary.
The catch is that this requires effective control over the task bundle and the ability to price it completely. Statutory rules, collective agreements, monitoring limits, and professional norms may prevent that even for salaried workers. Gans’s takeaway is that persistent unpaid productive time points not to a failure of worker optimization but to restricted contracts, incomplete measurement, or institutional rules governing what counts as paid work.
One important limit the paper flags: intrinsic enjoyment is just one reason workers put in unrecorded time. Promotion incentives, deadlines, professional norms, fear of displacement, and managerial pressure can all produce similar behavior. Distinguishing among these mechanisms is not something the model itself can do.
