Bounded Rationality as Limited Optimization: Stochastic Gradient Descent Agents in Macroeconomic Models

This paper proposes a novel equilibrium concept in which agents are fully rational in preferences and constraints but computationally bounded, with decision rules parameterized and improved via stochastic gradient methods applied to simulated expected utility. In a standard RBC model with GHH preferences, we define a Stochastic Gradient Descent equilibrium as a fixed point (in expectation) of the stochastic-gradient update rule together with market clearing and firm optimality. The fixed-point condition requires that the expected gradient of the household’s truncated utility function vanishes at the equilibrium decision rules, so that the agent has no incentive, on average, to revise her policy further. We establish conditions under which the SGD equilibrium converges to the rational expectations solution in the sequential limit as the planning horizon and training intensity increase without bound. Away from this limit, tighter computational budgets generate systematic, state-dependent deviations summarized by an intratemporal labor wedge and an intertemporal capital wedge, whereas large horizon planning and extensive training deliver policies close to the rational expectations benchmark. These wedges are endogenous and time-varying, providing a structural bridge to the business-cycle accounting framework of Chari et al. (2007) without introducing non-productivity shocks or real frictions.