eprintid: 4980 rev_number: 21 eprint_status: archive userid: 351 dir: disk0/00/00/49/80 datestamp: 2016-01-15 02:08:03 lastmod: 2021-08-27 17:15:48 status_changed: 2016-01-15 02:08:03 type: monograph metadata_visibility: show item_issues_count: 2 creators_name: Barucci, E. creators_name: Posch, M. creators_id: 1643 title: The Rise of Complex Beliefs Dynamics ispublished: pub internal_subjects: iis_ecn internal_subjects: iis_met divisions: prog_dyn abstract: We prove that complex beliefs dynamics may emerge in linear stochastic models as the outcome of bounded rationality learning. If agents believe in a misspecified law of motion (which is correctly specified at the Rational Expectations Equilibria of the model) and update their beliefs observing the evolving economy, their beliefs can follow in the limit a beliefs cycle which is not a self-fulfilling solution of the model. The stochastic process induced by the learning rule is analyzed by means of an associated ordinary differential equation (ODE). The existence of a uniformly asymptotically stable attractor for the ODE implies the existence of a beliefs attractor, to which the learning process converges. We prove almost sure convergence by assuming that agents employ a projection facility and convergence with positive probability dropping this assumption. The rise of a limit cycle and of even more complex attractors is established in some monetary economics models assuming that agents update their beliefs with the Recursive Ordinary Least Squares and the Least Mean Squares algorithm. date: 1996-05 date_type: published publisher: WP-96-046 iiasapubid: WP-96-046 price: 10 creators_browse_id: 1515 full_text_status: public monograph_type: working_paper place_of_pub: IIASA, Laxenburg, Austria pages: 29 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/book citation: Barucci, E. & Posch, M. (1996). The Rise of Complex Beliefs Dynamics. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-96-046 document_url: https://pure.iiasa.ac.at/id/eprint/4980/1/WP-96-046.pdf