Stationarity-Inducing Techniques in Small Open Economy Models with Collateral Constraints
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Stationarity-Inducing Techniques in Small Open Economy Models with Collateral Constraints Vasiliki Dimakopoulou1 Accepted: 30 October 2020 © The Author(s) 2020
Abstract I show that the alternative stationarity-inducing techniques that have been used to “close” the standard small open economy model (like an endogenous discount factor and a debt-elastic interest rate premium) have different implications for the equilibrium dynamics once I add a commonly-used collateral-type financial constraint. Given this non-equivalence, my results further show that a small open economy model with a credit constraint that embodies an endogenous discount factor is superior to the debt-elastic interest rate model when one tries to match this kind of models to the data. Keywords Small open economy · Stationarity · Borrowing constraints JEL Classification E44 · F41
1 Introduction As is well known, one has to add a “friction” to make the equilibrium dynamics of a standard small open economy (SOE) model stationary and so get a well-defined solution. Two particularly popular frictions have been an endogenous discount factor (EDF) in agents’ optimization problem and a debt-elastic interest rate (DEIR) at which domestic agents borrow from abroad.1 But, then, as is also well known, if one uses an appropriate parameterization, the choice of the friction, and hence of the model, is trivial because they predict identical steady states and transition dynamics
1 See Schmitt-Groh´ e and Uribe (2003) and Uribe and Schmitt-Groh´e (2017). See also e.g. Uribe and Yue (2006), Mendoza (1991, 2002, 2010), Korinek and Mendoza (2014) and many others. Vasiliki Dimakopoulou [email protected]
1
Department of Economics, University of Warwick, Coventry, CV4 7AL, England
V. Dimakopoulou
at business-cycle frequencies.2 What I show in this short paper is that, once I add a collateral constraint, this equivalence does not hold any more and so the choice between an EDF model and a DEIR model ceases to be a trivial issue. I build upon the baseline small open economy model. I first add an EDF and a DEIR mechanism as in the above literature and, in turn, I also add a simple financial constraint, as in e.g. Mendoza (2002), which is also used by the literature on sudden stops.3 The latter means that domestic agents cannot borrow more than a fraction of their assets from the world capital market so that, when it binds, it is like having a sudden stop. To demonstrate the different implications of the two mechanisms, I first solve and evaluate the two models (i.e. the EDF and the DEIR) by comparing their steady state solutions both when the collateral constraint is binding and when it is not binding. Then, I solve and evaluate their dynamics. In particular, I assume that both models happen to be at the financially unconstrained steady state equilibrium (which is the same across models) and are then hit by a temporary adverse shock to TFP. Again, I compare the two models with and without the collateral constraint, where, in the case with, I
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