The role of macroprudential policies in addressing pecuniary externalities that may lead to in-creased financial fragility has long been discussed in the literature. In an economy with financial frictions, overborrowing can arise and aggravate the economic conditions when a negative shock hits, andLorenzoni(2008) shows that policy interventions that preventively restrict borrowings can restore constrained efficient allocations, though the welfare improvements from reduced costs of a financial crisis come at the cost of reducing investment ex ante, as he warns. In a small open economy with occasionally binding credit constraint, Bianchi (2011) quantifies that the policy gains from correcting the systemic credit externality include a reduction of the probability to a financial crisis by more than tenfold and a significant mitigation of the severity of consumption drop and real exchange rate fall that characterize emerging market crises. Bianchi and Men-doza(2018) study optimal macroprudential policy design in an environment in which financial amplification and fire sale externality working through collateral asset prices produce financial crises. They find that the forward-looking nature of asset prices, which is not present in the two works cited above, leads to time-inconsistent optimal policy under commitment and point that due to its complexity macroprudential policies can be counterproductive if not designed care-fully. Dávila and Korinek(2018) identify two types of pecuniary externalities, distributive and collateral externalities, that arise in economies with financially constrained agents, and show that the externalities not only do not necessarily result in inefficiencies but the effects can in general
go in any direction.
Pecuniary externality is not the only theoretical motivation that justifies macroprudential in-terventions. Farhi and Werning (2016) identify a different source of inefficiency, the aggregate demand externality, focusing on economies with nominal rigidities. They develop a framework in which both pecuniary and aggregate demand externalities can be incorporated, and their joint characterization of optimal monetary and macroprudential policies point to a Pigouvian correc-tive role of government interventions in financial markets that can overcome the identified market failures. Schmitt-Grohé and Uribe(2016) show that when nominal wage adjustments are down-ward rigid, the combination of a fixed exchange rate and free capital mobility creates a negative externality that causes overborrowing during booms and high unemployments during busts. Liu and Spiegel(2015) incorporate imperfect asset substitutability in a New Keynesian setting with nominal rigidities and incomplete markets, and find that the optimal policy response to foreign shocks calls for the joint use of capital account restrictions and adjustments of the government’s portfolio of foreign reserves, domestic bond and money supply. Aoki, Benigno and Kiyotaki (2018) study monetary and financial policies explicitly modeling financial intermediaries that take deposits in domestic currency while also borrowing in foreign currency, and their results suggest significant welfare gains from cyclical macroprudential taxes on foreign borrowings.
Our modeling of household borrowing and saving and welfare evaluation are adapted from the closed economy model in Lambertini, Mendicino and Punzi (2013) that studies monetary and macroprudential policies that lean againts house-price and credit cycles. Korinek and San-dri (2016) also models an economy with domestic borrowers and savers that lend or borrow from foreign agents, but unlike our classification that distinguish between a currency-based and a residency-based policy, they differentiate between an intervention that segments domestic and
international financial markets and one that impose a segmentation between borrowers and all types of lenders. In one application Farhi and Werning (2016) analyzed an environment with non-contingent nominal debt denominated in local and foreign currency, similar to the setting studied in our current paper, and used a two-period model to show that optimal policy calls for a higher tax on foreign-currency debt than local-currency debt. We followLiu and Spiegel(2015) in the modeling of the central bank’s balance-sheet decisions as well as the portfolio adjustment costs that lead to imperfect substitutability between domestic and foreign assets. We then extend the capital inflow tax in their model to a set of linear policy rules that allows the quantification of the relative welfare performance of different policy proposals and evaluate the optimal magnitude and persistence of interventions.
It is worth pointing out that in this paper we do not assume ex ante net aggregate foreign borrowing nor differential domestic and foreign interest rates in the steady state. As Schmitt-Grohé and Uribe(2017) pointed out, the assumption that households are impatient are needed in, for example,Bianchi(2011) cited above that calibrated the discount factor of the representative agent so that the average net foreign asset position-to-GDP ratio matches its historical average of -29% in Argentina, to generate empirically plausible frequencies of financial crises, and they demonstrated that countercyclical interventions on capital flows may no longer be optimal in alternative settings. On the other hand,Aoki, Benigno and Kiyotaki(2018) calibrated their model so that the steady state domestic interest rate is 2% higher annually than its foreign counterpart to reflect the higher growth prospects enjoyed by the emerging market economies. In this paper the differences between the two interest rates are driven by shocks capturing unexpected changes in the international financial market. Consistently, we find that policy rules that imply a persistent intervention of private intertemporal decisions are stricly inferior to temporary policy responses
that are meant to mitigate the impact of external shocks.
2 The Model Economy
We start by constructing a model economy with international capital flows but imperfect substi-tutability between domestic and foreign assets. Domestic agents in this economy have access to both kinds of assets, but adjusting portfolio investments requires care and thus incurs transaction costs. In order to generate international borrowing and lending in both currencies, we model the economy as comprising of two types of households characterized by the heterogeneity in discounting future to the present.
2.1 Households
The small open economy is populated by a unit mass of domestic borrowers B and a unit mass of domestic savers S. The two types of agents differ in their subjective discount factors βB< βS, their asset and equity positions, and have preferences represented by
Ui= E0
∞ t=0
∑
βitu(cit, mit, lit) , (1)
where E(·) is the expectations operator, βi ∈ (0, 1) is the subjective discount factor of agent i∈ {B, S}, cit is a consumption index given by
cit ≡
Z 1
0
cit( j)1−θ1d j
θ −1θ ,
with cit( j) denoting the quantity of good j consumed by agent i in period t and θ > 1 denoting the elasticity of substitution between different goods, mit is real money holdings, and lit = 1 − nit denotes leisure, where nit represents hours worked.
The households face a convex cost of holding financial assets in quantities different from their long-run levels. We assume the portfolio adjustment costs to be of a quadratic form with weights Ψ1 and Ψ2 measuring the size of the friction. Hence the sequential budget constraint of agent i∈ {B, S} is
Ptcit+ Mit+ Bit+ StB?it = Wtnit+ Mi,t−1+ Rt−1Bi,t−1+ StRt−1? B?i,t−1
+ Ptdit+ Pttrt 2 −Ψ1
2
Bit Pt −Bi
P
2
−Ψ2
2
StB?it Pt −B?i
P
!2
,
and the optimal allocation of consumption expenditures among different goods implies that
cit( j) = pt( j) Pt
−θ
cit (2)
for all j ∈ [0, 1] representing the variety of goods, where pt( j) is the price of good j and Pt ≡
R1
0 Pt( j)1−θd j1−θ1
is an aggregate price index.
In this expression, Mit is the nominal money balance and MPit
t = mit; Bit and B?it are holdings of one-period non-state-contingent domestic and foreign bonds, respectively; R?t is the world-determined gross nominal interest rate, St is the nominal exchange rate quoted as the price of a unit of foreign currency in terms of the domestic currency, and both Rt?and St are taken as given by the small open economy; Wt denotes the nominal wage rate and WPt
t = wt, Rt the domestic gross nominal interest rate; dt is the profit income from the households’ ownership shares of firms, denoted in terms of the composite consumption good; trt is a lump-sum transfer from the government; Bi, B?i are scalars denoting the long-run levels of the respective asset holdings and Pis the steady state price level.
The world interest rate Rt?is stochastic, and captures the “global financial cycle” phenomenon documented inRey(2013). The nominal exchange rate St is modeled as an independent AR(1) process reflecting the observed persistent and volatile pattern found in empirical studies. We
define the real exchange rate to be the ratio
εt≡ StPt? Pt ,
where Pt?denotes the world price level and is normalized so that Pt?= P?= 1 for all t.
Rewriting the sequential budget constraint in real terms gives
cit+ mit+ bit+ εtb?it = wtnit+mi,t−1
where the lower-case letters are used to denote the real value of the corresponding variables.
From now on we follow the convention of using lower-case letters for individual variables and upper-case letters for aggregate variables.
The agents maximize (1) subject to (3) taking prices as given. The maximization problem yields the following optimality conditions for each period t:
u3(cit, mit, lit) = wtu1(cit, mit, lit), (4)
We assume that the foreign households are symmetrically described by the same utility rep-resentation as the domestic agents, with β?, Ψ?1, and Ψ?2 denoting the subjective discount factor and portfolio adjustment costs parameters, bf t is the real value of domesic bonds held by foreign
agents, and b?f t is the amount of foreign bonds held by foreign agents. Their intertemporal Euler equations are given by
u1(ct?, m?t, lt?)
1 + Ψ?1 bf t εt − bf
= β?Et
u1(c?t+1, mt+1? , lt+1? )Rt εt εt+1
1 πt+1
, (8)
and
u1(c?t, mt?, lt?)h
1 + Ψ?2
b?f t− b?fi
= β?Etu1(ct+1? , mt+1? , lt+1? )R?t . (9)