Open Access

Gregor Böhl

• Occasionally binding constraints have become an important part of economic modelling, especially since western central banks see themselves (again) constraint by the so-called zero lower bound (ZLB) of the nominal interest rate. A binding ZLB constraint poses a major problem for a quantitative-structural analysis: Linear solution methods do no work in the presence of a non-linearity such as the ZLB and existing alternatives tend to be computationally demanding. The urge to study macroeconomic questions related to the Great Recession and the Covid-19 crisis in a quantitative-structural framework requires algorithms that are not only accurate, but that are also robust, fast, and computationally efficient. A particularly important application where efficient and fast methods for occasionally binding constraints (OBCs) are needed is the Bayesian estimation of macroeconomic models. This paper shows that a linear dynamic rational expectations system with OBCs, depending on the expected duration of the constraint, can be represented in closed form. Combined with a set of simple equilibrium conditions, this can be exploited to avoid matrix inversions and simulations at runtime for signifcant gains in computational speed.