Existence and Uniqueness of Solutions to Dynamic Models with Occasionally Binding Constraints

Abstract

Occasionally binding constraints (OBCs) like the zero lower bound (ZLB) can lead to multiple equilibria, and so to belief-driven recessions. To aid in finding policies that avoid this, we derive existence and uniqueness conditions for otherwise linear models with OBCs. Our main result gives necessary and sufficient conditions for such models to have a unique (“determinate”) perfect foresight solution returning to a given steady state, for any initial condition. While standard New Keynesian models have multiple perfect-foresight paths eventually escaping the ZLB, price level targeting restores uniqueness. We also derive equilibrium existence conditions under rational expectations for arbitrary non-linear models.

Approximately Right?: Global v. Local Methods for Open-Economy Models with Incomplete Markets

“…Under these assumptions, we show in Appendix C.3 that h b in all the local methods is given by the following expression: 13 Figure 1 yields a key finding: The value of ρ b is nearly identical across 2OA and RSS for any 0 ≤ ψ ≤ 0.1, which is an interval that includes the baseline and targeted calibration values and also all the values of η r implied by the ψ values used in the papers listed in Table 1. 15 Hence, for 13 This result applies for both full and partial RSS. 14 Schmitt-Grohé and Uribe (2003) obtained similar results by deriving the analytic solution of the decision rule of NFA for an endowment economy with log utility and using the stationarity-inducing assumption by which the rate of time preference depends on aggregate consumption.…”

“…Moreover, since in the baseline and targeted calibrations it is also the case that the terms related to the quadratic and interaction terms of the 2OA decision rule of b are nearly zero, it follows that we can expect the 2OA and RSS solutions to produce similar second and higher-order moments for all endogenous variables, as the results reported below will confirm. 16 Figure 1 also shows that ρ b switches from decreasing to increasing in ψ at a sufficiently high value of ψ (i.e., ψ ≥ 0.5). However, ψ ≥ 0.5 would imply much larger values of η r than those used in the literature, including estimated models.…”

“…14 Schmitt-Grohé and Uribe (2003) obtained similar results by deriving the analytic solution of the decision rule of NFA for an endowment economy with log utility and using the stationarity-inducing assumption by which the rate of time preference depends on aggregate consumption. 15 The highest ψ in the literature is ψ = 2.8 in Garcia-Cicco et al ( 2010), and with their value of b dss = −0.007 yields η r = −0.0196. For the interval 0 ≤ ψ ≤ 0.1 with our b dss = −0.51 we obtain an interval of elasticities 0 ≥ η r ≥ −0.051.…”

“…DynareOBC is equivalent to the Guerrieri-Iacoviello OccBin method when using a first-order approximation, with the difference that it is guaranteed to converge in finite time Holden (2016b). showed that a second-order approximation integrating over future uncertainty can be used to approximate precautionary savings in models with simple constraints, but this method is significantly slower and for the SS model produced results that deviate sharply from the GLB and firstorder DynareOBC solutions.…”

Diplomatic relations and cross-border investments in the European Union

“…different possible regime sequences, can also arise for the simpler standard OccBin simulations with given initial states and the shocks. SeeHolden (2019).…”