Letting the aggregate output be defined as Yt≡ R1
0yt( j)1−θ1d j
θ
θ −1 and denoting the total port-folio and price adjustment costs of the domestic economy by
Ψt≡Ψ1 market clearing in the goods market requires that the country’s trade balance (net exports) is given by
T Bt= Yt−Ct− Ψt, (22)
that is, output is either consumed domestically, paid for adjustment costs, or consumed abroad.
Aggregate employment is given by the sum of employment across firms
Nt = clear-ing requires that the real wage adjusts so that labor supply implied by equation (4) equals the firms labor demand.
In equilibrium, money supply equals money demand, domestic bonds issued by the govern-ment equal that held by the domestic and foreign households, and total foreign asset holdings equals an exogenously given foreign bond supply b?t. Thus
mst = mBt+ mSt (24)
bt= bBt+ bSt+ bf t (25)
and
bt?= b?Bt+ b?St+ b?gt+ b?f t. (26)
By definition the current account CAt is the sum of the trade balance and net investment income on the country’s net foreign asset positions
CAt≡ T Bt+
εtR?t−1− 1 b?t−1− [Rt−1(1 − τt−1) − 1]bf,t−1 πt
(27)
(the macroprudential tax revenues from foreign asset holdings are rebated to the households thus are part of domestic income, so τt? does not appear in the previous expression). We can also express the current account as changes in net foreign assets using the balance of payment identities
CAt= ∆NFAt ≡ εt bt?− b?t−1 − bf t− bf,t−1 . (28)
Before proceeding to the definition of competitive equilibrium, we first summarize in the next table the international transactions taking place in the model economy4. To determine the signs of the trade balance and the official reserves account is straightforward, but the conclusions for the investment income account and the capital account are much less obvious. It is clear that, for example, suppose that bf,t−1 and b?S,t−1 are both positive, indicating that the foreigners hold a positive amount of domestic-currency bonds and the domestic savers also hold a positive amount of foreign-currency bonds, then the former results in an interest payment by the country to foreigners, (Rt−1− 1)bf,t−1, while the latter results in a receipt by the country of interest from foreigners, εt(Rt−1? − 1)b?S,t−1. However, if these variables flip signs due to changes in economic conditions, then the directions of the income flows also changes. The same is true for the capital account as it is determined by the asset/debt positions of the domestic borrowers and savers as
4The illustrations in Table 1 is adapted from Exhibit 4.1 inBekaert and Hodrick(2017).
well as the foreign agents. For example, an increase in the country’s ownership of foreign assets, b?S,t− b?S,t−1 > 0, gives rise to a capital outflow while a decrease in the country’s ownership of foreign assests, b?S,t− b?S,t−1 < 0, indicates a capital inflow. A decrease of foreign ownership of the country’s assets, bf,t− bf,t−1< 0, gives rise to a capital outflow while an increase in foreign ownership of the country’s assets, b?S,t− b?S,t−1< 0, indicates a capital inflow.
Table 1: The Balance of Payments
Account Debits (−) Credits (+)
CURRENT ACCOUNT
(A) TRADE BALANCE Imports if T Bt< 0 Exports if T Bt> 0
(B) INVESTMENT INCOME ACCOUNT e.g., (Rt−1− 1)bf,t−1 e.g., εt(R?t−1− 1)b?S,t−1 CAPITAL ACCOUNT
Capital outflows if b?S,t− b?S,t−1> 0 Capital inflows if bf,t− bf,t−1> 0 Capital outflows if bf,t− bf,t−1< 0 Capital inflows if b?S,t− b?S,t−1< 0 OFFICIAL RESERVES ACCOUNT
Foreign reserves accumulation Foreign reserves decrease if b?g,t− b?g,t−1> 0 if b?g,t− b?g,t−1< 0
Given government policies (the interest rate rule and macroprudential policy rules τt and τt? specified below) and exogenous processes {At, St, R?t}, a competitive equilibrium of this economy is a sequence of prices {Pt, πt, wt, εt, Rt} and quantitiescBt, cSt, nBt, nSt, lBt, lSt, bt, bBt, bSt, bf t, b?Bt,
b?St, b?gt, b?f t, b?t, mBt, mSt, mst, dBt, dSt,trSt,trBt,tr?Bt,tr?St,Yt, Nt,Ct, Ψt, T Bt,CAt, NFAto
as well as the prices {Pt( j)} and quantities {yt( j), nt( j)} for each firm j ∈ [0, 1] such that
1. taking all prices but its own as given, the prices and allocations for each firm solves its profit-maximizing problem;
2. taking all prices as given, the households’ choices satisfy the optimality conditions as well as the budget constraints (we note that the assumption that only one of the two types of agents has access to equity holdings affects the inequality of consumption between the households);
3. markets for the final goods, labor, money balances, and bond holdings all clear.
3 Quantitative Analysis
In this section, we first calibrate the baseline economy in which there is perfect capital mobility, that is, τt= 0 and τt?= 0, and the home country’s monetary policy follows the Taylor rule previ-ously described. Then we turn our attention to evaluating the full toolkit available to the policy makers.
3.1 Calibration
We assume that a part of domestic agents are impatient relative to outsiders, thus they have incentives to borrow from foreign investors. We calibrate the economy to be such that in the non-stochastic steady state, domesic borrowers assume both foreign currency and domestic currency-denominated debts with levels matched by the positive amount of assets held by the domestic savers, that is, −bB= −b?B= bS= b?S> 0, thus net borrowing is zero in the non-stochastic steady state. We follow Lambertini, Mendicino and Punzi (2013) to calibrate the domestic agents’
subjective discount factors βB= 0.97 and βS= 0.9925 in a quarterly setting, and assume that the foreign agents have the same discount rate as that of the domestic savers.
The borrows and savers in this economy share the same utility representation, with the
func-tional form assumed to be given by
u(c, m, l) = ln (c) + φmln (m) − φl(1 − l)1+η
1 + η , φm, φl, and η > 0. (29) The utility weights for leisure φl= 34.01 is calibrated so that the borrowers spend about one third of their time endowment working (and the equity-owning savers work roughly 16% less) in the non-stochastic steady state. The parameters regarding the macroeconomic and financial aspects of the model closely follows that inLiu and Spiegel (2015), in which the curvature pa-rameter η = 2 so that the Frisch elasticity of labor supply is 0.5 (Keane and Rogerson,2015) and the money demand parameter φm= 0.06 (Chari, Kehoe and Mcgrattan,2000).
Given the functional form of the utility representation, we can express the solution to the firms’ profit maximization problem (12) in a symmetric equilibrium that pt( j) = Pt for all j as the following
wt
At =θ − 1 θ +Ψ3
θ Ct
Yt [(πt− 1) πt− βSEt(πt+1− 1) πt+1] . (30) The domestic level of techonology that is common to all firms follows the process
ln (At) = ρaln (At−1) + εat (31)
with ρa∈ [0, 1] and εat i.i.d.
∼ N(0, σa). The mean level of the technology shock is normalized to one. The AR(1) process for the logged gross nominal foreign interest rate is
ln (R?t) = (1 − ρr) ln (R?) + ρrln Rt−1? + εrt (32)
where ρr denotes the persistence of the shock, R? is the steady-state level of the foreign interst rate, and εrt is an innovation to the shock and εrt i.i.d.∼ N(0, σr). The nominal exchange rate of the small open economy is modeled as
St= (1 − ρs) SPPP+ ρsSt−1+ εst (33)
Table 2: Calibrated Parameters
Parameter Description Value
Preference
βB Borrower’s subjective discount factor 0.97
βS Saver’s subjective discount factor 0.9925
β? Foreigner’s subjective discount factor 0.9925
φl Utility weight on leisure 0.06
φm Utility weight on money balances 34.01
η Inverse of Frisch elasticity of labor supply 2
Production
ρa Persistence of technology shocks 0.9
σa Standard deviation of technology shocks 0.005
θ Elasticity of substitution between differentiated goods 10
Ψ3 Price adjustment costs 60
Monetary Policy
λR Monetary policy inertia 0.59
λπ Monetary policy inflation feedback 1.44
λy Monetary policy output feedback 0.52
Asset Holdings
ρr Persistence of foreign interest rate shocks 0.9
σr Standard deviation of foreign interest rate shocks 0.001
ρs Persistence of nominal exchangne rate shocks 0.99
σs Standard deviation of nominal exchangne rate shocks 0.005 Ψ1 Portfolio adjustment costs: domestic bonds, domestic households 0.01 Ψ2 Portfolio adjustment costs: foreign bonds, domestic households 0.01 Ψ?1 Portfolio adjustment costs: domestic bonds, foreign households 0.01 Ψ?2 Portfolio adjustment costs: foreign bonds, foreign households 0.01
where ρs ∈ [0, 1], εst i.i.d.
∼ N(0, σs), and SPPP denotes the exchange rate such that the internal purchasing power of the domestic currency equals its external purchasing power.
The Taylor rule governing the domestic policy interest rate follows the estimation by Ia-coviello and Neri(2010). The parameters are summarized in Table 1.