2.1 Households

A representative household is infinitely-lived and seeks to maximize:

where C_t is a composite consumption index, H_t is hours of work, E_t is the mathematical expectation conditional upon information available at t, β is the representative consumer’s subjective discount factor where 0 < β < 1, σ > 0 is the inverse of the intertemporal elasticity of substitution and φ > 0 is the inverse elasticity of labour supply.

The composite consumption index, C_t, is given by:

where C_{H, t} and C_{M, t} are CES indices of consumption of domestic and foreign goods, represented by:

where j ∈ [0, 1] indicates the goods varieties and λ > 1 is the elasticity of substitution among goods produced within a country. Equation (2) suggests that the expenditure share of the domestically produced goods in the consumption basket of households is given by α and 0 < α < 1.⁶

The real exchange rate REX_t is defined as ${\mathit{\text{REX}}}_t=\frac{S_t{P}_t^{*}}{P_t}$, where S_t is the nominal exchange rate, domestic currency price of foreign currency, and $P_t^{*}\equiv {\left[{\displaystyle {\int }_0^1{P}_t^{*}{(j)}^{1-\lambda }dj}\right]}^{1/(1-\lambda )}$ is the aggregate price index for foreign country’s consumption goods in foreign currency. In contrast to standard open economy models, our two-country framework enables us to determine $P_t^{*}$ endogenously in the ROW block.

Households participate in domestic and foreign financial markets: they deposit their savings in domestic currency, $D_t^D$, or they can borrow from international financial markets in foreign currency, $D_t^H$, with a nominal interest rate of i_t and $i_t^{*}{{\Psi }}_{D,t}$. Due to imperfect capital mobility, households need to pay a premium, Ψ_{D, t}, given by ${{\Psi }}_{D,t}=\frac{{{\Psi }}_D}{2}[{exp}{(\frac{S_t{D}_{t+1}^H}{P_t{\mathit{\text{GDP}}}_t}-\frac{{\mathit{\text{SD}}}^H}{\mathit{\text{PGDP}}}-1]}^2$ when they borrow from the rest of the world.⁷ Households own all home production and the importing firms and thus are recipients of profits, Π_t. Other sources of income for the representative household are wages W_t, and new borrowing net of interest payments on outstanding debts, both in domestic and foreign currency. Then, the representative household’s budget constraint in period t can be written as follows:

The representative household chooses the paths for ${\{C_t,H_t,B_{t+1},D_{t+1}^H\}}_{t=0}^{\infty }$ in order to maximize its expected lifetime utility in (1) subject to the budget constraint in (3). ⁸

2.2 Firms

2.3 Entrepreneurs

The key players of the model are entrepreneurs. They transform unfinished capital goods and sell them to the production firms. They finance their investment by borrowing from domestic lenders and foreign lenders, channeled through perfectly competitive financial intermediaries. We denote variables for entrepreneurs borrowing from domestic resources with superscript D, and entrepreneurs borrowing from foreign resources with superscript F. In the absence of cost differences, entrepreneurs would be indifferent between borrowing from domestic and foreign resources, and therefore the amount borrowed from domestic and foreign resources would be equal.

There is a continuum of entrepreneurs indexed by k in the interval [0, 1]. Each entrepreneur has access to a stochastic technology in transforming $K_{t+1}^{\upsilon }(k)$ units of unfinished capital into ${\omega }_{t+1}^{\upsilon }(k)K_{t+1}^{\upsilon }(k)$ units of finished capital goods, where v is either F or D. The idiosyncratic productivity ω_t(k) is assumed to be i.i.d. (across time and across firms), drawn from a distribution F (.), with p.d.f of f(.) and E(.) = 1.¹¹

At the end of period t, each entrepreneur k of type υ has net worth denominated in domestic currency, ${\mathit{\text{NW}}}_t^{\upsilon }(k)$. The budget constraints of the entrepreneurs for two different types are defined as follows:

where $D_{t+1}^F\text{and}{D}_{t+1}^D$ denote foreign currency denominated debt and domestic currency denominated debt respectively. Equations (12 and 13) simply state that capital financing is divided between net worth and debt.

Productivity is observed by the entrepreneur, but not by the lenders who have imperfect knowledge of the distribution of ${\omega }_{t+1}^{\upsilon }(k)$. Following Curdia (2007, 2008) we specify the lenders’ perception of ${\omega }_{t+1}^{\upsilon }(k)$ as given by ${\omega }_{t+1}^{\upsilon *}(k)={\omega }_{t+1}^{\upsilon }(k){\varrho }_t^{\upsilon }$ where ${\varrho }_t^{\upsilon }$ is the misperception factor over a given interval [0, 1]. Further, the misperception factor, ${\varrho }_t^{\upsilon }$, is assumed to follow ${ln}({\varrho }_t^{\upsilon })={\rho }_{\varrho }{ln}({\varrho }_{t-1}^{\upsilon })+{\epsilon }_{\varrho }^{\upsilon }$ where ρ_ϱ denotes the persistence parameter. We take the origin of the capital inflows as a change in lenders’ perception regarding idiosyncratic productivity $({\epsilon }_{\varrho }^{\upsilon })$.¹²

Entrepreneurs observe ${\omega }_{t+1}^{\upsilon }(k)$ ex-post, but the lenders can only observe it at a monitoring cost which is assumed to be a certain fraction (µ) of the return.¹³ As shown by Bernanke et al. (1999), the optimal contract between the lender and the entrepreneur is a standard debt contract characterized by a default threshold, ${\overline{\omega }}_{t+1}^{\upsilon }(k)$, such that if ${\omega }_{t+1}^v(k)\ge {\overline{\omega }}_{t+1}^v(k)$, the lender receives a fixed return in the form of a contracted interest on the debt. If ${\omega }_{t+1}^{\upsilon }(k)<{\overline{\omega }}_{t+1}^{\upsilon }(k)$, then the borrower defaults, the lender audits by paying the monitoring cost and keeps what it finds. Therefore, we can define the expected return to entrepreneurs lenders, respectively, for υ = F, D as follows:

where $R_t^K$ denotes the ex-post realization of return to capital, and is the same regardless of the source of the financing due to arbitrage. $z^{\upsilon }(\overline{\omega })$ is the borrowers’ share of the total return. We use the definition of the lender’s perception of productivity shock ${\omega }_{t+1}^{\upsilon *}(k)$ represents the lenders’ share of in Equation (15) where $g^{\upsilon }({\overline{\omega }}^{\upsilon }(k);{\varrho }^{\upsilon })$ represents the lenders’ share of the total return, itself a function of both the idiosyncratic shock and the perception factor.

Clearly, for domestic and foreign lenders, the opportunity cost of lending to the entrepreneur is the domestic interest rate interest rate (1+i_t) and $(1+i_t^{*})$. Thus the loan contract must satisfy the following for the lenders to be willing to participate in it:

The optimal contracting problem identifies the capital demand of entrepreneurs, $K_{t+1}^{\upsilon }(k)$ and a cut off value, $\overline{{\omega }^{\upsilon }}t+1^{(k)}$ such that the entrepreneurs will maximize (14) subject to (16) and (17). The first order conditions yield:

where $(1+{{\Phi }}_{t+1}^F)\text{and}(1+{{\Phi }}_{t+1}^D)$ are the external risk premium on foreign and domestic borrowing defined by:

A greater use of external financing generates an incentive for entrepreneurs to take on more risky projects, which raises the probability of default. This, in turn, will increase the external risk premium. Therefore, any shock that has a negative (positive) impact on the entrepreneurs’ net worth increases (decreases) their leverage, resulting in an upward (downward) adjustment in the external risk premium.

In order to guarantee that self financing never occurs and borrowing constraints on debt are always binding, we follow Kiyotaki and Moore (1997) and Carlstrom and Fuerst (1997), in assuming that a proportion of entrepreneurs die in each period to be replaced by new-comers. Given that ω^υ (k) is independent of all other shocks and identical across time and across entrepreneurs, all entrepreneurs are identical ex-ante. Then, each entrepreneur faces the same financial contract specified by the cut off value and the external finance premium. This allows us to specify the rest of the model in aggregate terms.

At the beginning of period t, the entrepreneurs collect revenues and repay their debt contracted at period t − 1. Denoting the fraction of entrepreneurs who survive each period by ϑ, the net worth can be expressed as follows:

Equation (22) indicates that the entrepreneur’s net worth is made up of the return on investment and the entrepreneurial wage income. Given that the borrower’s and the lender’s share of total return should add up to $z^{\upsilon }({\overline{\omega }}_t^{\upsilon })+g^{\upsilon }({\omega }_t^{\upsilon },{\varrho }_t^{\upsilon })=1-v_t^{\upsilon }$ (where $v_t^{\upsilon }$ is the cost of monitoring, a deadweight loss associated with financial frictions) and by using the participation constraint (16), we can rewrite the net worth of the entrepreneurs borrowing from foreign and domestic sources as:

The entrepreneurs leaving the scene at time t consume their return on capital. The consumption of the exiting entrepreneurs, $C_t^{\upsilon E}$, can then be written as:¹⁴

The total capital in the economy is $K_t=K_t^F+K_t^D$. Because of investment adjustment costs and incomplete capital depreciation, entrepreneurs’ return on capital on average is not identical to the rental rate of capital, R_t. The entrepreneurs’ return on capital is the sum of the rental rate on capital paid by the firms that produce final consumption goods, the rental rate on used capital from the firms that produce unfinished capital goods, and the value of the non-depreciated capital stock, after the adjustment for the fluctuations in the asset prices $(\frac{Q_{t+1})}{Q_t})$:

2.4 Financial Intermediaries and Macroprudential Policy

There exists a continuum of perfectly competitive financial intermediaries which collect deposits from households and loan the money out to entrepreneurs in each period. They also receive capital inflows from the ROW in the form of foreign loans to domestic entrepreneurs. The sum of deposits and capital inflows make up the total supply of loanable funds. The zero profit condition on financial intermediaries implies that the lending rates are just equal to $E_t[(1+i_t^{*})(1+{{\Phi }}_{t+1}^F)]$ and $E_t[(1+i_t)(1+{{\Phi }}_{t+1}^D)]$ in the absence of macroprudential measures.

Either in the form of capital requirements or loan-to-value ceiling, or some other type, macroprudential policy entails higher costs for financial intermediaries. Rather than driving the impact of a particular type of macroprudential measure on the borrowing cost, we follow Kannan et al. (2009) and focus on a generic case where macroprudential measures lead to additional cost to financial intermediaries. These costs are then reflected to borrowers in the form of higher interest rates.¹⁵ The increase in the lending rates brought by macroprudential measures are named as “regulation premium” and is linked to nominal credit growth, rising as credit growth increases.¹⁶ Macroprudential policy is therefore countercyclical by design: countervailing to the natural decline in perceived risk in good times and the subsequent rise in the perceived risk in bad times.

In the presence of macroprudential regulations, the spread between lending rate and policy rate is affected by both the risk premium and “the regulation premium”. Hence, the lending costs for foreign borrowing and domestic borrowing, equations (18) and (19), become:

where RP_t is the regulation premium, which is defined in the baseline case a function of the aggregate nominal credit growth:

where $D_t=S_t{D}_t^F+D_t^D$. In this definition of macroprudential policy, it is implicit that the policy objective is defined in terms of aggregate credit activity. However, it should be noted that in the case of macroprudential measures that discriminate against foreign liabilities, the regulation premium only applies to foreign borrowing (27) and macroprudential policy instrument (RP_t) is defined only in terms of growth of nominal credit from foreign credit.

2.5 Monetary Policy

In the baseline calibration, we adopt a standard formulation for the structure of monetary policy-making. We assume that the interest rate rule is of the following form:

where i and Y denote the steady-state level of nominal interest rate and output, and π_t is the CPI inflation.

The foreign variables $Y_t^{*},P_t^{*}\text{and}{i}_t^{*}$ are endogenously determined in the ROW block of the model. Although asymmetric in size, SOE and ROW share the same preferences, technology and market structure for consumption and capital goods. We also assume an identical characterization for monetary policy in the SOE and the ROW.

3.1 Consumption, Production and Monetary Policy

We set the discount factor, β at 0.99, implying a riskless annual return of approximately 4 per cent in the steady state (time is measured in quarters). The inverse of the elasticity of intertemporal substitution is taken as σ =1, which corresponds to log utility. The inverse of the elasticity of labour supply φ is set to 2, which implies that 1/2 of the time is spent on working. We set the degree of openness, 1 − α, to be 0.35 which is within the range of the values used in the literature.¹⁸ The share of capital in production, η, is taken to be 0.35 consistent with other studies.¹⁹ Following Devereux et al. (2006), the elasticity of substitution between differentiated goods of the same origin, γ, is taken to be 11, implying a flexible price equilibrium mark-up of 1.1, and price adjustment cost is assumed to be 120 for all sectors. The quarterly depreciation rate δ is 0.025, a conventional value used in the literature. Similar to Gertler et al. (2007), we set the share of entrepreneurs’ labour, Ω, at 0.01, implying that 1 per cent of the total wage bill goes to the entrepreneurs. With regard to the parameters of export demand, we follow Curdia (2007, 2008), and assume that exports constitute 10 per cent of the total foreign demand and thus set α^* at 0.1 with a price elasticity of unity, γ^* =1. In the baseline calibration, we use the original Taylor estimates and set ϵ_π =1.5 and ϵ_Y =0.5, and the degree of interest rate smoothing parameter (ς) is chosen as 0.5. ρ_ϱ is assumed to 0.5, so that it takes 9 quarters for the shock to die away. Table 1 summarizes the parametrization of the model for consumption, production, and monetary policy used in the baseline calibration.²⁰

Table 1:

Parameter Values for Consumption, Production Sectors and Monetary Policy

Table 1:

Parameter Values for Consumption, Production Sectors and Monetary Policy

β = 0.99	Discount factor
σ = 1	Inverse of the intertemporal elasticity of substitution
γ = 1	Elasticity of substitution between domestic and foreign goods
φ = 2	Frisch elasticity of labour supply
(1 −α) = 0.35	Degree of openness
η = 0.35	Share of capital in production
λ = 11	Elasticity of substitution between domestic goods
δ = 0.025	Quarterly rate of depreciation
Ω = 0.01	Share of entrepreneurial labor
α* = 0.1	Share of exports in foreign demand
γ* = 1	Foreign demand price elasticity
ΨI = 12	Investment adjustment cost
ΨD = 0.0075	Responsiveness of household risk premium to debt/GDP
Ψi, ΨM = 120	Price adjustment costs for i = H, X
ϵπ = 1.5	Coefficient of CPI inflation in the policy rule
ϵY = 0.5	Coefficient of output gap in the policy rule
ρ ϱ	Persistence of the domestic perception shock

View Table

Table 1:

Parameter Values for Consumption, Production Sectors and Monetary Policy

β = 0.99	Discount factor
σ = 1	Inverse of the intertemporal elasticity of substitution
γ = 1	Elasticity of substitution between domestic and foreign goods
φ = 2	Frisch elasticity of labour supply
(1 −α) = 0.35	Degree of openness
η = 0.35	Share of capital in production
λ = 11	Elasticity of substitution between domestic goods
δ = 0.025	Quarterly rate of depreciation
Ω = 0.01	Share of entrepreneurial labor
α* = 0.1	Share of exports in foreign demand
γ* = 1	Foreign demand price elasticity
ΨI = 12	Investment adjustment cost
ΨD = 0.0075	Responsiveness of household risk premium to debt/GDP
Ψi, ΨM = 120	Price adjustment costs for i = H, X
ϵπ = 1.5	Coefficient of CPI inflation in the policy rule
ϵY = 0.5	Coefficient of output gap in the policy rule
ρ ϱ	Persistence of the domestic perception shock