A model of indirect crowding

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The introduction of material rewards has often been proposed to improve the participation of disadvantaged people in areas such as education, politics, and sustainability. But people differ in their intrinsic motivation to exert effort on a given task. And, as the literature on "crowding" effects emphasizes, introducing incentives can sometimes alter intrinsic motivation, or its association with effort. We introduce a distinction between "direct" crowding, which directly affects intrinsic motivation, and "indirect" crowding, which affects the relationship between intrinsic motivation and effort. The former is intriguing, but likely of limited generalizability. The latter, we argue, is of greater prevalence. We present a simple model of indirect crowding, building on extant cognitive and social scientific approaches. The model shows that if the marginal costs increase quickly (relative to the marginal benefits), then increasing material incentives leads to "indirect crowding out": individuals with low intrinsic motivation increase effort at a greater rate than highly motivated individuals. Conversely, if marginal costs increase slowly relative to marginal benefits, "indirect crowding in" occurs, with highly motivated individuals pulling away from lesser motivated ones. However, this result only holds if total benefit is the sum of intrinsic and extrinsic benefit. If intrinsic and extrinsic benefit are multiplicative, only crowding in can occur. The model demonstrates that introducing or increasing extrinsic rewards may inadvertently increase inequality, with implications for policy makers.
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