Equilibrium Selection and Closure in DSGE Solution Methods

Standard DSGE solution practice closes forward-looking equilibrium problems by combining model specification with criteria that select one operational equilibrium from multiple candidate paths, yet this closure step typically remains implicit. This paper formalizes that closure step as a substantive operation in standard DSGE solution practice. By separating the economic specification ($S$), the self-referential operator ($T$), and the equilibrium selection rule ($Π$), the $(S, T, Π)$ triad provides a descriptive semantic grammar for comparing closure choices across familiar solution environments. The framework clarifies what standard solver diagnostics actually report, captures the regime-iteration logic of piecewise-linear methods like OccBin, explains why independent linear solvers often reproduce the same selected equilibrium, and distinguishes within-model refinements from specification-augmenting closure changes under indeterminacy.