Indeterminacy and endogenous fluctuations with arbitrarily small liquidity constraint

Indeterminacy with constant money growth rules and income-based liquidity constraints

“…For constraint (1) to be locally binding, the Lagrange multiplier ν, evaluated at the steady state, must be strictly positive, which means, in the light of the first order condition (3), that u 0 (c) − λ must be positive. Straightforward computations show that this is actually true if and only if Assumption 3 does hold.…”

“…In order to reconcile the Cooley and Hansen view with the Abel's one, we draw on a recent contribution by Bosi and Magris (2003).…”

“…3 Inde-terminacy is shown to prevail for any value of the intertemporal elasticity of substitution, provided that the share of consumption purchases requiring cash in advance is below a certain threshold. When the share is above that threshold, indeterminacy arises only when the relative risk aversion of households is high enough (greater than 2, for example, in the standard Cooley and Hansen (1989) model with full liquidity constraint on consumption).…”

“…However, our paper addresses also a question of empirical plausibility and whishes to investigate the robustness of the indeterminacy findings. We study whether the inclusion of investment in the liquidity constraint strongly modifies the range of parameters values giving rise to indeterminacy, by comparison to the reference economy studied in Bosi and Magris (2003) in which this constraint applies only to consumption. As seen above, our results show that it does, but in a way which is contrasted for the indeterminacy region: the inclusion of investment strongly increases a lower bound on the share of good purchases requiring cash below which the steady state is always indeterminate, but it creates a higher bound on this share above which the steady-state is always determinate.…”

Government Expenditure Financing in a Two‐Sector Cash‐In‐Advance Model of Endogenous Growth

“…Bosi and Magris () and Bosi, Magris and Venditti () assume that the share of the purchases of the consumption good that needs to be financed using cash can take a value that is smaller than 1. In this case, the CIA constraint that we would need would be of the form where denotes the fraction of consumption purchases that are subject to the liquidity constraint.…”