Economic Geometry and Crisis Dynamics: A Riemannian DSGE Framework for Iran’s Economy

This paper develops a dynamic stochastic general equilibrium (DSGE) framework in which the macroeconomy is modeled as a Riemannian manifold with endogenously time-varying curvature. Unlike standard linearized DSGE models, the proposed framework captures nonlinear shock amplification through a metric tensor derived from welfare-based adjustment costs, providing rigorous microfoundations for the geometric structure. We term this the Najkar framework to distinguish it from conventional linearized approaches. Scalar curvature κserves as an operational measure of amplification potential: higher curvature indicates greater sensitivity of the economy to structural shocks, analogous to how a curved surface distorts distances relative to flat space. The model is estimated via Bayesian methods on quarterly Iranian data spanning ۱۹۹۱Q۱–۲۰۲۱Q۴ — an economy defined by dual exchange rate regimes, recurring sanctions episodes, a large informal sector (۳۰–۴۰% of GDP), and volatile oil revenues. Estimation reveals that κrises from ۰.۰۴–۰.۰۶ during normal periods to ۰.۱۵–۰.۱۸ during sanctions crises, a three- to fourfold increase. High-curvature states (κ>۰.۱۰) characterize approximately ۲۳% of the sample. Relative to standard first-order linearized DSGE models, this framework improves four-quarter-ahead forecasts by ۱۸–۲۳% during these high-curvature episodes. Counterfactual policy experiments yield two main findings. First, a curvature-contingent monetary policy rule — augmenting the standard Taylor rule with a term ϕ_κ κ_t, where the optimal response coefficient is ϕ_κ≈+۰.۲— delivers welfare gains equivalent to ۲.۶% of steady-state consumption, with the rule prescribing systematically tighter policy as curvature rises. Second, structural reforms that reduce nominal rigidities lower equilibrium curvature by ۳۵%, generating additional welfare benefits worth ۳.۲% of consumption. Together, these results demonstrate that the Najkar framework provides actionable guidance for macroeconomic management in emerging markets exposed to sanctions, financial fragmentation, and deep structural nonlinearities.

کلیدواژه ها:

Riemannian geometry ، DSGE models ، scalar curvature ، nonlinear dynamics ، Iranian economy ، sanctions ، informal sector ، Bayesian estimation ، forecast accuracy ، welfare analysis