Abstract

Cognitive discounting has become a workhorse device for bounded rationality in monetary economics. It is specified on perceived states or on selected expected terms and used mostly in linearized models, while the questions it is asked to answer — the effective lower bound, large shocks, risk, regime change — are intrinsically nonlinear. This paper introduces a variable-specific behavioral-expectations operator, defined directly on the nonlinear equilibrium conditions of DSGE models, including nonstationary and regime-switching ones. Before the rational expectation is taken, the operator contracts selected forward-looking variables toward reference points, in stated coordinates. The reference points may move over time or depend on the regime. At first order the operator reproduces Gabaix’s (2020) one-step discounting of expectations, except that each selected variable is discounted in every equation in which it appears. At second order and above it discounts risk : each variable’s k-th conditional cumulant of one-step deviations from its reference point, in the chosen coordinates (logs or levels), is scaled by the k-th power of its attention. This can turn divergent conditional expectations into convergent ones, a candidate structural complement to pruning. We illustrate the methodology by estimating a nonstationary nonlinear New Keynesian model with an occasionally binding lower bound on pre-2020 US data. With attention estimated variable by variable, the data decisively prefer cognitive discounting to rational expectations, by about 14 log points of marginal likelihood. Posterior mean attention is uneven across variables. Which restrictions the data accept depends on the model and the observables.