Testing capacity-constrained learning

We introduce a general test of capacity-constrained learning models. Learning has capacity constraints when the set of possible ways to learn is exogenously fixed, as in the widely used fixed-capacity versions of rational inattention (Sims, 2003) and efficient coding (Woodford, 2012). With such models, changes in incentives do not alter the extent of attention, only how individuals decide to allocate their scarce attention. We show that choice data are consistent with capacity-constrained learning if and only if they satisfy a No Improving (Action or Attention) Switches (NIS) condition. Based on existing experiments in which the incentives for being correct are varied, we find strong evidence that participants fail NIS for a wide range of standard perceptual tasks: identifying the proportion of ball colors, recognizing shapes, and counting the number of balls. We further show that violations of NIS occur systematically in response to higher incentives, suggesting that incentives often expand attention beyond what capacity-constrained models allow. However, we find that this is not true for all existing perceptual tasks in the literature, which offers insights into settings where we do or do not expect incentives to impact the extent of attention.