2.1 Overview

The banking network is illustrated in Figure 2. There are two countries, Home and Foreign. The periphery emerging (home) economy is a small open economy of size $m \rightarrow 0$ , and the center (foreign) economy is of size $(1-m)$ . Each arrow in the figure stands for a lending contract. In each economy, investors lend to banks and banks lend to entrepreneurs. A crucial assumption is that entrepreneurs in the emerging economy borrow from both local banks and banks in the center, and so the banks in the center are called global banks.

Figure 2.

Chained credit contract in a two-country model.

In the following, there are five types of loan contract labeled $i\in \{B, B*, E, E*, E\times \}$ . A “B” contract is one in which banks in the emerging economy borrow from local investors; a “E” contract is one in which entrepreneurs in the emerging economy borrow from local banks. “ $B*$ ” and “ $E*$ ” contracts are analogous for the center, which go through global banks. Lastly, an “ $E\times$ ” contract is a cross-border loan contract between global banks and entrepreneurs in the emerging economy. ^{Footnote 4}

In each of the five types of contract, we assume that a lender lends to an infinite number of borrowers. ^{Footnote 5} Each of the five types of loan contract is subject to financial frictions because lenders face a CSV problem identical to BGG (1999). Each borrower’s return on investment faces an idiosyncratic shock $\omega^{i}$ drawn from the distribution $\log(\omega^{i})\sim N(-0.5(s^{i})^{2},(s^{i})^{2})$ , where $E(\omega^{i})=1$ and the cumulative density function is $F^{i} (\omega^{i})$ . ^{Footnote 6} Only the borrower in a loan contract can observe his own idiosyncratic shock costlessly. To find out the realization of the idiosyncratic shock for a specific borrower, the lender needs to pay monitoring costs, assumed to be a constant fraction $\mu^{i}$ of the revenue of the borrower.

Townsend (Reference Townsend1979) shows that as a result of the CSV problem, the lender does not monitor when the borrower’s draw of the shock is above a cutoff value $\tilde{\omega}^{i}$ . The borrower repays the lender with an agreed state-contingent contractual interest rate $Z^{i}$ and retains what remains. When the borrower’s draw is below the cutoff value, the borrower is bankrupt, the lender monitors and takes whatever remains from the bankrupt borrower. A loan contract then decides how the revenue is split between the borrower and lender. To see this, suppose a borrower in contract i borrows an amount $b^{i}$ , and his return on investment before the idiosyncratic shock is realized is given by $roi^{i}$ , then the cutoff value of idiosyncratic shock $\tilde{\omega}^{i}$ is defined by:

(1) \begin{equation}Z^{i}b^{i} = \tilde{\omega}^{i} roi^{i}. \end{equation}

Then the lender receives the expected revenue (before monitoring) given by:

\begin{eqnarray*} \int_{0}^{\tilde{\omega}^{i}} \omega^{i} roi^{i} dF^{i} + \int_{\tilde{\omega}^{i}}^{\infty} Z^{i}b^{i} dF^{i}= \Gamma^{i}(\tilde{\omega}^{i}) roi^{i},\end{eqnarray*}

where $\Gamma^{i}(\tilde{\omega}^{i})$ is the share of the total revenue that goes to the lender (before monitoring), given by:

(2) \begin{equation}\Gamma^{i}(\tilde{\omega}^{i}) \equiv G^{i}(\tilde{\omega}^{i}) +[1-F^{i}(\tilde{\omega}^{i})]\tilde{\omega}^{i}, \end{equation}

where $G^{i}(\tilde{\omega}^{i}) \equiv \int_{0}^{\tilde{\omega}^{i}}\omega^{i} dF^{i}(\omega^{i})$ accounts for what the lender gets on average (before monitoring occurs) if the borrower defaults, and $[1-F^{i}(\tilde{\omega}^{i})]\tilde{\omega}^{i}$ accounts for the payment when $\omega^{i}\geq \tilde{\omega}^{i}$ and the borrower does not default. Note that $F^{i}, G^{i}, \Gamma^{i}$ depend also on $s^{i}$ which measures the cross-sectional dispersion of risk, but I suppress $s^{i}$ for simplicity.

In the following, I discuss the details of the cashflow among investors, banks, and entrepreneurs as well as the optimal contracting problems faced by the banks. Hirakata et al. (Reference Hirakata, Sudo and Ueda2017) show that the solution to this optimal contracting problem is one in which the capital to net worth ratio is equalized within banks and within entrepreneurs, so one only needs to keep track of the aggregate quantities. For this reason, in the discussion below, entrepreneurs and banks of the same type are treated as a single agent.

2.2 Entrepreneurs

Entrepreneurs in the emerging economy have total net worth $N_{t}^{E}$ at the beginning of a period. They borrow $B_{Ht}$ units of nominal debt from local banks and and $B_{Ht}^{*}$ units of nominal debt from global banks to finance their purchase of capital $K_{t}$ at a (real) price $Q_{t}$ , receiving an average return of $R_{t+1}^{E}Q_{t}K_{t}$ . The balance sheet is then given by:

(3) \begin{equation}Q_{t}K_{t} = N_{t}^{E} + \frac{B_{Ht}}{P_{t}} + \frac{B_{Ht}^{*} \mathscr{E}_{t}}{P_{t}},\end{equation}

where $\mathscr{E}_{t}$ is the nominal exchange rate, defined as the price of home currency in terms of foreign currency, and $P_{t}$ is the price level in the emerging economy.

I follow Ueda (Reference Ueda2012) to abstract from the portfolio choice decision by assuming that a fraction $(1-\eta)$ of debt comes from a local bank and the remaining fraction $\eta$ from a global bank, where $\eta$ is an exogenous parameter capturing the emerging economy’s openness to cross-border lending, or the degree of financial integration. ^{Footnote 7} This means that $\frac{B_{Ht}}{P_{t}} = (1-\eta) (Q_{t}K_{Ht} -N_{t}^{E})$ , and $\frac{B_{Ht}^{*} \mathscr{E}_{t}}{P_{t}} = \eta (Q_{t}K_{Ft} -N_{t}^{E})$ , where $K_{t} =(1-\eta) K_{Ht} + \eta K_{Ft}$ . In Section 5, I will study the effect of financial integration by adjusting the value of $\eta$ .

Entrepreneurs in the center have total net worth $N^{E*}_{t}$ at the beginning of a given period. They only borrow from global banks to purchase capital $K_{t}^{*}$ at a price $Q_{t}^{*}$ , which earns an average return $R_{t+1}^{E*}Q_{t}^{*}K_{t}^{*}$ .

2.3 Global Banks

Global banks are located in the center. They borrow from investors in the center and lend to entrepreneurs in both the center and the emerging economy. The (real) total lending by global banks $X_{t}^{*}$ is given by:

(4) \begin{equation}X_{t}^{*} \equiv \frac{m}{1-m}\eta \frac{\left(Q_{t}K_{Ft}- N_{t}^{E}\right)}{S_{t}} + \left(Q_{t}^{*}K_{t}^{*}- N_{t}^{E*}\right),\end{equation}

where $S_{t} \equiv \mathscr{E}_{t}P_{t}^{*}/P_{t}$ is the real exchange rate. The first term denotes aggregate lending by global banks to entrepreneurs in the emerging economy using $E\times$ contracts, and the second term denotes aggregate lending by global banks to entrepreneurs in the center using $E*$ contracts.

The average (real) revenue of global banks’ lending, denoted as $R^{B*}_{t}X^{*}_{t-1}$ , is given by:

(5) \begin{eqnarray}R^{B*}_{t} X^{*}_{t-1} &=& \frac{m}{1-m} \eta \frac{\left[\Gamma^{E\times}\left(\tilde{\omega}^{E\times}_{t}\right) - \mu^{E\times} G^{E\times}\left(\tilde{\omega}^{E\times}_{t}\right)\right] R^{E}_{t} Q_{t-1} K_{Ft-1}}{S_{t}} \nonumber \\&&+ \left[\Gamma^{E*}\left(\tilde{\omega}^{E*}_{t}\right) - \mu^{E*}G^{E*}\left(\tilde{\omega}^{E*}_{t}\right) \right] R^{E*}_{t}Q^{*}_{t-1}K^{*}_{t-1}. \end{eqnarray}

The first term on the right-hand side is the gross revenue made by entrepreneurs in the emerging economy, where the term $(\Gamma^{E\times} - \mu^{E\times} G^{E\times})$ accounts for the share of revenue going to global banks after monitoring costs are paid. In other words, this is the repayment by home entrepreneurs to global banks. Analogously, the second term refers to the repayment by the entrepreneurs from the center to global banks.

Global banks have aggregate net worth $N_{t}^{B*}$ and borrow $(X_{t}^{*}-N_{t}^{B*})$ from investors in the center. The return on banking activity is subject to an idiosyncratic shock, $\omega_{t+1}^{B*}$ . They are subject to the participation constraints of entrepreneurs in the center and the emerging economy in each $t+1$ state of nature:

(6) \begin{eqnarray}\eta R^{E}_{t+1}Q_{t}K_{Ft} \left[1-\Gamma^{E\times} \left(\tilde{\omega}^{E\times}_{t+1}\right)\right] &\geq& \eta R^{E}_{t+1}N^{E}_{t}, \end{eqnarray}

(7) \begin{eqnarray}R^{E*}_{t+1} Q^{*}_{t}K^{*}_{t} \left[1-\Gamma^{E*} \left(\tilde{\omega}^{E*}_{t+1}\right)\right] &\geq& R^{E*}_{t+1}N^{E*}_{t}. \end{eqnarray}

Equation (6) is the participation constraint of the entrepreneurs in the emerging economy. Note that the left-hand side is the share of revenue that goes to the entrepreneur (a share of $(1-\Gamma^{E\times} )$ ). One interpretation of this equation is that global banks have market power, so when an entrepreneur wants to increase his credit, the bank will raise the contractual interest rate accordingly (and so the cutoff threshold, due to (1)), so that the entrepreneur is as well off as self-financing. Equation (7) is an analogous participation constraint for the entrepreneurs in the center.

Moreover, global banks are subject to the participation constraint of investors in the center in each $t+1$ state of nature:

(8) \begin{eqnarray}\left[\Gamma^{B*}\left(\tilde{\omega}^{B*}_{t+1}\right)- \mu^{B*} G^{B*}\left(\tilde{\omega}^{B*}_{t+1}\right)\right] R^{B*}_{t+1} X^{*}_{t} &\geq& R^{*}_{t} \left(X^{*}_{t}- N^{B*}_{t}\right). \end{eqnarray}

Equation (8) ensures that the return received by investors, represented by the left-hand side of the equation, is as high as the risk-free return.

Global banks choose the amount of lending to entrepreneurs in the center and the emerging market (which is equivalent to choosing $\{K^{*}_{t}, K_{Ft}\}$ ), and the contractual interest rates of the three contracts (which, given the one-to-one correspondence between $Z^{i}$ and $\tilde{\omega}^{i}$ shown in (1), is equivalent to choosing $\{\tilde{\omega}^{B*}_{t+1},\tilde{\omega}^{E\times}_{t+1},\tilde{\omega}^{E*}_{t+1}\}$ ) to maximize their expected profit function:

\begin{eqnarray*} E_{t} \left[1-\Gamma^{B*}\left(\tilde{\omega}^{B*}_{t+1}\right) \right] R^{B*}_{t+1} X_{t}^{*},\end{eqnarray*}

subject to constraints (6), (7), and (8). ^{Footnote 8}

The following proposition states the solution to the optimal financial contracting problem of the global banks: ^{Footnote 9}

PROPOSITION 1 Up to the first-order approximation, the first-order conditions associated with the global bank’s optimization problem arepro1

(9) \begin{eqnarray} E_{t}\left( \frac{R_{t+1}^{E*}}{R_{t}^{*}} \right) &=& E_{t} \left[ \rho^{B*}\left(\tilde{\omega}_{t+1}^{B*}; s_{t}^{B*}\right) \times \rho^{E*}\left(\tilde{\omega}_{t+1}^{E*}; s_{t}^{E*}\right) \right], \end{eqnarray}

(10) \begin{eqnarray} E_{t}\left( \frac{R_{t+1}^{E}}{R_{t}} \right) &=& E_{t} \left[ \rho^{B*}\left(\tilde{\omega}_{t+1}^{B*}; s_{t}^{B*}\right) \times \rho^{E\times}\left(\tilde{\omega}_{t+1}^{E\times}; s_{t}^{E\times}\right) \right], \quad \text{for}\quad \eta >0, \end{eqnarray}

where the function $\rho^{i}(\tilde{\omega}^{i}; s^{i}) \geq 1$ is given in Appendix B. Furthermore,

\begin{equation*} \frac{\partial \rho^{i}(\tilde{\omega}^{i}; s^{i})}{\partial \tilde{\omega}^{i}}>0, \;\; \frac{\partial \rho^{i}(\tilde{\omega}^{i}; s^{i})}{\partial s^{i}}>0.\end{equation*}

Consider the demand for credit in the center (9) first. It states that an exogenous rise in the external finance premium, $E_{t}(R_{t+1}^{E*})/R_{t}^{*}$ , leads to an increase in the default threshold for global banks, $\tilde{\omega}_{t+1}^{B*}$ , or an increase in the default threshold for foreign entrepreneurs, $\tilde{\omega}_{t+1}^{E*}$ , or both. Borrowers subject to a CSV problem have a risk-shifting incentive: when a borrower receives an unfavorable idiosyncratic shock and defaults, she does not care about how much she owes the lender; on the other hand, if she can repay the prespecified amount, she pockets the upside profit. As a result, when the external finance premium rises exogenously, the expected return increases and entrepreneurs have an incentive to increase their capital investment. For given net worth, either banks or entrepreneurs have to increase their credit, but this leads to higher default probability in either the $E*$ contract or the $B*$ contract, so the cutoff thresholds rise because lenders need to break even. (Note that the right-hand side of the first-order condition can be factorized into two $\rho$ terms related to the two subcontracts. This derivation is new relative to Hirakata et al. (Reference Hirakata, Sudo and Ueda2017) and corresponds to the intuition above.)

In equilibrium, the external finance premium is weakly greater than unity because lenders expect resources to be lost through monitoring, which are compensated by an external finance premium. Other things equal, a rise in the cutoff value $\tilde{\omega}_{t+1}^{i}$ implies an increase in defaults, so the external finance premium is increasing in the cutoff value. Furthermore, $\rho^{i}_{s}>0$ because a more dispersed distribution of idiosyncratic shock means more expected defaults, so higher external finance premium is needed.

The optimal cross-border lending decision, (10)1, has a similar interpretation. When entrepreneurs in the emerging economy borrow from global banks ( $\eta > 0$ ), the external finance premium for entrepreneurs in the emerging economy, $E_{t}(R^{E}_{t+1})/R_{t}$ , can also be factored into two components, $\rho^{B*}$ and $\rho^{E\times}$ , which correspond to lending by investors in the center to global banks and cross-border lending from global banks to entrepreneurs in the emerging economy.

As global banks borrow from investors in the center and are lenders to both center and emerging market entrepreneurs, the factor $\rho^{B*}$ appears in both (9) and (10)1. Since $\rho^{B*}_{s}>0$ , a rise in cross-sectional risk to global banks $s^{B*}$ increases their default probability and the monitoring costs faced by investors in the center. To compensate for higher monitoring costs, investors in the center require a higher external finance premia in the center and emerging economy simultaneously. This common lender effect is identified by Ueda (Reference Ueda2012). In the subsequent simulation exercise I focus on the shock $s^{B*}_{t}$ , which follows an exogenous AR(1) process: (For simplicity, dispersions of other idiosyncratic shocks are constant.)

(11) \begin{equation}\ln s^{B*}_{t} = (1-\lambda^{B*}) \ln \bar{s}^{B*} + \lambda^{B*}\ln s^{B*}_{t-1} + \epsilon^{B*}_{t},\end{equation}

where $\bar{s}^{B*}$ is the steady-state value of $s^{B*}_{t}$ , and $\epsilon^{B*}_{t} \stackrel{i.i.d}{\sim} N (0,(\sigma^{B*}_{t-1})^{2} )$ . This shock is similar to Christiano et al. (2014) which refers to a shock to the cross-sectional dispersion of productivity as a risk shock. Here, the shock increases the cross-sectional dispersion of global bank productivity, so I refer it as a financial risk shock.

2.4 Local Banks

Banks in the emerging economy borrow locally and lend to local entrepreneurs. They are subject to the same CSV friction as global banks but do not engage in cross-border lending. This assumption allows me to focus on the effect of cross-border bank lending. They solve a profit maximization problem subject to the chained credit contract structure similar to the one faced by global banks. The first-order condition is given by: ^{Footnote 10}

(12) \begin{eqnarray} E_{t} \left(\frac{R^{E}_{t+1}}{R_{t}}\right) &=& E_{t} \left[ \rho^{B}\left(\tilde{\omega}^{B}_{t+1}; s^{B}_{t+1}\right) \times \rho^{E}\left(\tilde{\omega}^{E}_{t+1}; s^{E}_{t+1}\right) \right]. \end{eqnarray}

3.1 Aggregate Quantities

Final goods for consumption $C_{t}$ , investment $I_{t}$ , and wasted resources due to monitoring in the financial contracts are Cobb–Douglas composites of center and periphery goods. Define variables $M = \{ C, I, MonCost \}$ as:

(13) \begin{equation} M_{t} = \frac{ M_{Ht}^{\nu} M_{Ft}^{1-\nu} }{\nu^{\nu} (1-\nu)^{1-\nu}}.\end{equation}

where the subscript H(F) denote goods produced in the emerging economy (center). The weight of imported goods in the good baset is denoted as $(1-\nu)$ and $(1-\nu)$ is given by $(1-\nu) \equiv (1-m) \zeta$ , where $\zeta$ is the trade openness. Similarly, households in the center have the following aggregator:

(14) \begin{equation} M^{*}_{t} = \frac{(M_{Ht}^{*})^{1-\nu^{*}}(M_{Ft}^{*})^{\nu^{*}}}{(\nu^{*})^{\nu^{*}} (1-\nu^{*})^{1-\nu^{*}}},\end{equation}

where $(1-\nu^{*}) = m \zeta^{*}$ . I follow Faia and Monacelli (Reference Faia and Monacelli2008) to restrict my attention to preferences that show a symmetric degree of home bias across countries such that $\zeta = \zeta^{*}$ . The corresponding price indices are given by $P_{t} = P_{Ht}^{\nu} P_{Ft}^{1-\nu}, \;\; P^{*}_{t} =(P^{*}_{Ht})^{1-\nu^{*}}(P^{*}_{Ft})^{\nu^{*}}$ .

I use $T_{t}$ to denote the terms of trade so that $T_{t}\equiv P_{Ft}/ P_{Ht}$ . Assuming that the law of one price holds across each variety of goods, then $P_{Ft} = \mathscr{E}_{t} P_{Ft}^{*}$ . Note that the real exchange rate $S_{t} = T_{t}^{\nu + \nu^{*}-1}$ is increasing in the terms of trade.

3.2 Households

A representative household in the emerging economy consumes, supplies labor, and saves. The household maximizes the following utility:

(15) \begin{equation} U_{0} = E_{0} \sum_{t=0}^{\infty} \beta^{t} u(C_{t}, L_{Ct}), \end{equation}

where $C_{t}$ is the consumption aggregate and $L_{Ct}$ is the labor supplied by the representative household. Utility is assumed to be additively separable:

\begin{equation*} u(C_{t}, L_{Ct}) = \ln C_{t} - \chi \frac{L_{Ct}^{1+\varphi}}{1+\varphi}.\end{equation*}

Households are subject to the following budget constraint:

(16) \begin{equation} P_{t}C_{t} + D_{t+1} = w_{Ct}P_{t}L_{Ct} + R_{t}^{N} D_{t} + tr_{t},\end{equation}

where $D_{t+1}$ is the payoff in period $t+1$ of the portfolio held at the end of period t, $w_{Ct}$ is the real wage for the household, and $tr_{t}$ denotes transfers. $R_{t}^{N}$ is the nominal interest rate. The usual transversality condition applies. The intratemporal labor supply condition and the consumption Euler equation are given by the following:

(17) \begin{eqnarray} -\frac{u_{Lt}}{u_{Ct}} &=& w_{Ct}, \end{eqnarray}

(18) \begin{eqnarray} 1 &=& \beta R_{t}^{N} E_{t} \left[\left( \frac{u_{Ct+1}}{u_{Ct}} \right) \frac{P_{t}}{P_{t+1}}\right],\end{eqnarray}

where $u_{C}$ and $u_{L}$ denote marginal utility of consumption and marginal disutiltiy of labor, respectively. Household savings are channeled to risk-neutral investors who lend to the banks.

3.3 Goods Producers

A final goods producer in each economy aggregates a continuum of intermediate goods $j\in[0,1]$ using a Dixit–Stiglitz aggregator, $Y_{t} = (\int_{0}^{1} Y_{t}(j)^{\frac{\epsilon-1}{\epsilon}} dj )^{\frac{\epsilon}{\epsilon-1}}$ , and the demand for each type of good is $Y_{t}(j) = [ \frac{P_{Ht}(j)}{P_{Ht}}]^{-\epsilon} Y_{t}$ , where $P_{Ht} \equiv [ \int^{1}_{0} P_{Ht}(j)^{1-\epsilon}dj ]^{\frac{1}{1-\epsilon}}$ .

Intermediate goods producers $j\in[0,1]$ are monopolistically competitive. Each produces a good variety with capital and aggregate labor as inputs:

(19) \begin{equation} Y_{t}(j) = [K_{t-1}(j)]^{\alpha} [L_{t}(j)]^{1-\alpha}, \end{equation}

where aggregate labor is supplied by households, entrepreneurs, and bankers, given by $L_{t}(j) = [L_{Ct}(j)]^{1-\Omega_{B}-\Omega_{E}}[L_{Bt}(j)]^{\Omega_{B}}[L_{Et}(j)]^{\Omega_{E}}$ . Intermediate goods producers choose capital and labor inputs taking wages and the rental rate $r_{t}^{K}$ as given. Moreover, they set prices subject to nominal rigidities a la Calvo (Reference Calvo1983). Specifically, with probability $(1-\kappa)$ a firm resets its price optimally in a given period; otherwise, the firm’s price is fixed. Intermediate goods producers maximize their discounted stream of profits, given by:

\begin{equation*} E_{t}\sum_{v=0}^{\infty} (\beta\kappa)^{v} \frac{u_{Ct+v}}{u_{Ct}}\frac{P_{t}}{P_{t+v}} \left\{ [P_{Ht}(j) - (1-\varrho) P_{t+v}MC_{t+v}(j)]Y_{t+v}(j) \right\},\end{equation*}

subject to the production function (19)1 and the demand function for each goods variety, where

\begin{equation*}MC_{t}(j) = T_{t}^{1-\nu} \frac{\left(r_{t}^{K}\right)^{\alpha} \left[ (w_{Ct})^{(1-\Omega_{B}- \Omega_{E})}(w_{Bt})^{\Omega_{B}}(w_{Et})^{\Omega_{E}} \right]^{1-\alpha}}{\alpha^{\alpha}\left[(1-\Omega_{B}- \Omega_{E})^{(1-\Omega_{B}- \Omega_{E})}\Omega_{B}^{\Omega_{B}}\Omega_{E}^{\Omega_{E}}(1-\alpha)\right]^{1-\alpha}} \equiv MC_{t}\end{equation*}

is the real marginal cost, and $ \varrho = \epsilon^{-1}$ is a government subsidy which ensures that the steady state of the system with nominal rigidities is efficient.

All intermediate goods producers who reset their prices choose the same optimal price, denoted as $P^{opt}_{Ht}$ . Define $p^{opt}_{Ht} \equiv P^{opt}_{Ht}/P_{Ht}$ , then it follows that:

(20) \begin{equation} p^{opt}_{Ht} = \frac{E_{t}\sum_{v=0}^{\infty} (\beta\kappa)^{v} u_{Ct+v} \left( \frac{P_{Ht}}{P_{Ht+v}}\right)^{-\epsilon} MC_{t+v} Y_{t+v} T_{t+v}^{-(1-\nu)}}{E_{t}\sum_{v=0}^{\infty} (\beta\kappa)^{v} u_{Ct+v} \left( \frac{P_{Ht}}{P_{Ht+v}}\right)^{1-\epsilon} Y_{t+v} T_{t+v}^{-(1-\nu)}}.\end{equation}

The evolution of the price level is given by:

(21) \begin{equation} 1 = (1-\kappa) \left(p^{opt}_{Ht}\right)^{1-\epsilon} + \kappa \left( \frac{P_{Ht}}{P_{Ht-1}}\right)^{-(1-\epsilon)}. \end{equation}

3.4 Capital Goods Producers

A representative capital goods producer buys previously installed capital and combines with investments good $I_{t}$ from final goods producers to produce new capital. ^{Footnote 11} Newly produced capital is sold back to the entrepreneurs within the same period. Production of new capital is subject to convex investment adjustment costs. The evolution of capital is given by:

(22) \begin{equation} K_{t} = (1-\delta) K_{t-1} + ( 1- Adj_{t})I_{t},\end{equation}

where $Adj_{t} \equiv 0.5\psi^{I} \left( I_{t}/I_{t-1} - 1 \right)^{2}$ . Capital goods producers maximize their discounted future profit $E_{t} \!\sum_{v=0}^{\infty} \beta^{v} \frac{u_{Ct+v}}{u_{Ct}} \Pi_{t+v}^{K}$ where $\Pi_{t}^{K}{=}\, Q_{t} [K_{t} - (1-\delta) K_{t-1}]\,{-}\,I_{t}$ . The first-order condition for the optimal investment choice is

(23) \begin{eqnarray} 1 &=& Q_{t} \left[ 1- Adj_{t} - \psi^{I} \frac{I_{t}}{I_{t-1}} \left( \frac{I_{t}}{I_{t-1}}-1\right) \right]\nonumber\\&& + \beta E_{t} \left[ \frac{u_{Ct+1}}{u_{Ct}} Q_{t+1} \psi^{I} \left(\frac{I_{t+1}}{I_{t}}\right)^{2} \left( \frac{I_{t+1}}{I_{t}}-1\right) \right].\end{eqnarray}

3.5 Evolution of Net Worth

Banks and entrepreneurs accumulate their net worth each period. To prevent them from growing indefinitely, I follow BGG (1999) and assume that in each period an exogenous fraction $\gamma^{B}$ of banks and $\gamma^{E}$ of entrepreneurs survive and these fractions are the same across the two economies. New banks and entrepreneurs enter in each period to keep the number of banks and entrepreneurs unchanged over time. Assume that bankers and entrepreneurs supply inelastically one unit of labor $(L_{Bt}=L_{Et} = 1$ ) to the goods producing firms and receive labor income, so newly joined bankers and entrepreneurs have positive net worth to start their business.

Entrepreneurial net worth evolves according to the following laws of motion:

(24) \begin{equation} N_{t}^{E} = \gamma^{E} R^{E}_{t} N_{t-1}^{E} + w_{Et}, \qquad N_{t}^{E*} = \gamma^{E} R^{E*}_{t} N_{t-1}^{E*} + w^{*}_{Et}.\end{equation}

The first term is the revenue retained by surviving entrepreneurs, and the second term is the wage income. Similarly, the net worth of banks in the emerging economy evolves as follows:

(25) \begin{align} N_{t}^{B} &= \gamma^{B} \left[ 1-\Gamma^{B}\left(\tilde{\omega}^{B}_{t}\right) \right] R_{t}^{B}X_{t-1} + w_{Bt},\nonumber\\[3pt] N_{t}^{B*} &= \gamma^{B} \left[ 1-\Gamma^{B*}\left(\tilde{\omega}^{B*}_{t}\right)\right] R_{t}^{B*}X^{*}_{t-1} + w^{*}_{Bt}.\end{align}

Finally, goods are wasted in the process of monitoring in the chained credit contracts. The monitoring costs are given by:

(26) \begin{eqnarray} {\textit{Moncost}}_{t} &=& (1-\eta)\mu^{E} G^{E}\left(\tilde{\omega}_{t}^{E}\right) R_{Ht}^{E} Q_{t-1}K_{Ht-1} + \mu^{B} G^{B}\left(\tilde{\omega}^{B}_{t}\right) R_{t}^{B} X_{t-1}, \end{eqnarray}

(27) \begin{eqnarray}{\textit{Moncost}}^{*}_{t} &=& \frac{m}{1-m}\eta \mu^{E\times} G^{E\times}\left(\tilde{\omega}^{E\times}_{t}\right) R^{E}_{t} \frac{Q_{t-1}K_{Ft-1}}{S_{t}} + \mu^{E*} G^{E*}\left(\tilde{\omega}^{E*}_{t}\right)R^{E*}_{t} Q_{t-1}^{*}K_{t-1}^{*} \nonumber\\ && + \mu^{B*} G^{B*}\left(\tilde{\omega}^{B*}_{t}\right) R^{B*}_{t} X_{t-1}^{*}.\end{eqnarray}

3.6 Market Clearing

Goods markets clear. Goods are consumed, invested, and wasted in the monitoring of failing banks and entrepreneurs. Therefore, for $M = \{ C, I, {\textit{MonCost}} \}$ :

(28) \begin{eqnarray} mY_{t} &=& m \sum_{M} M_{Ht} + (1-m) \sum_{M} M_{Ht}^{*}.\end{eqnarray}

3.7 Central Bank

The center sets the nominal interest rate according to the following monetary policy rule:

(29) \begin{eqnarray} R^{N*}_{t} &=& \beta^{-1} \left( \frac{\Pi_{Ft}^{*}}{\bar{\Pi}_{F}^{*}}\right)^{\phi_{\pi *}} \left( \frac{Y_{t}^{*}}{\bar{Y}^{*}}\right)^{\phi_{Y *}} e^{\epsilon_{R^{*}t}},\end{eqnarray}

where $\Pi^{*}_{Ft}\equiv P_{Ft}^{*}/P_{Ft-1}^{*}$ denotes producer price index inflation, and $\epsilon_{R^{*}t}$ is an i.i.d shock. As the center is large, its monetary policy does not react to prices and quantities in the emerging economy.

The emerging economy sets its nominal interest rate with the following rule:

(30) \begin{eqnarray} R^{N}_{t} &=& \beta^{-1} \left( \frac{\Pi_{Ht}}{\bar{\Pi}_{H}}\right)^{\phi_{\pi}} \left( \frac{Y_{t}}{\bar{Y}}\right)^{\phi_{Y}} \left( \frac{\mathscr{E}_{t}}{\mathscr{E}_{t-1}}\right)^{\phi_{\mathscr{E}}}, \end{eqnarray}

where $\Pi_{Ht} \equiv P_{Ht}/P_{Ht-1}$ , and the coefficients $\phi_{\pi}$ , $\phi_{Y}$ , and $\phi_{\mathscr{E}}$ denote inflation, output, and exchange rate sensitivities to the policy rate. The small open economy is assumed to use a general form of the interest rate rule which nests flexible $(\phi_{\mathscr{E}}=0)$ and fixed $(\phi_{\mathscr{E}} \rightarrow \infty)$ exchange rate regimes. We will examine various combination of sensitivity parameters $\{\phi_{\pi}, \phi_{Y}, \phi_{\mathscr{E}}\}$ in the emerging economy in the following sections.

5.1 Foreign Interest Rate Shock

Figure 3 presents the impulse response functions of selected macroeconomic variables in the emerging economy to a one standard deviation rise in the policy rate in the center economy. All variables except the external finance premium are expressed as a percentage of their steady-state values. The external finance premium is expressed as an annualized percentage point deviation from the steady state.

Figure 3.

Impulse responses to a one standard deviation rise in the interest rate in center. Blue dashed lines correspond to a calibration without cross-border lending $\eta = 0$ . Red solid lines correspond to the baseline calibration, where the share of financing from global banks is $\eta = 15\%$ . All values except for the responses of the external finance premia are in percentage deviations from the steady state $(x_{t}-\bar{x})/\bar{x}\times 100$ . The responses of the external finance premia are presented as annualized percentage point deviations from the steady state.

A rise in the policy rate in the center has an amplification effect due to financial frictions and leads to large fall in investment and real activity. The impulse responses in the center (not shown) is similar to that in BGG (1999) due to the center’s overwhelming size. We are interested in the propagation of the shock to the emerging economy, which comes through three channels. The first is a standard expenditure switching channel present as in models such as Backus et al. (Reference Backus, Kehoe and Kydland1992). The external interest rate shock induces a real exchange rate depreciation in the emerging economy, so demand in both economies switches toward goods produced in the emerging economy. This effect tends to generate a negative international comovements between consumption, investment, and output. A second channel, termed by Faia (Reference Faia2007) as a financial spillover channel, has the opposite effect. When aggregate demand increases, the interest rate in the emerging economy rises to clear the goods market. Monetary tightening reduces demand for capital and its price, thus increasing the external finance premium. This works through the financial accelerator effect in the emerging economy.

The presence of these two channels is not related to cross-border lending by global banks. The blue dashed lines in Figure 3 report what happens when $\eta =0$ (i.e. when entrepreneurs in the emerging economy do not borrow from global banks). It shows a rise in the nominal interest rate and the external finance premium. As a result, the increase in output (coming from the expenditure switching channel) is short-lived, and investment falls from the very beginning.

When entrepreneurs borrow from global banks, a third, cross-border lending channel comes into play. The red solid lines show the impulse responses when a share of $\eta=0.15$ of entrepreneurial borrowing comes from global banks. The cross-border lending channel is as follows: an unexpected tightening of monetary policy in the center reduces the return on capital and so the return to global banks and their net worth, and thereby increases their default probability. Because global banks lend to entrepreneurs in both the center and the emerging economy, the external finance premium rises in both countries. Cross-border lending to the emerging economy falls substantially. At the same time, a rise in the external finance premium also reduces the price of capital, which affects local banks through a financial accelerator mechanism in the emerging economy. A comparison with the blue dashed lines (without cross-border lending) reveals the importance of the common-lender effect of financial integration. The global banking network leads to stronger and more volatile spillovers of monetary shocks to the emerging economy, almost doubling the fall in output and tripling the fall in investment. The response in the external finance premium is about 2–3 times more volatile and the fall in the price of capital is also amplified.

5.2. Financial Risk Shocks

An advantage of this framework is the way financial risk shocks are embedded naturally as a disturbance to the dispersion of the return to global banks’ capital. Figure 4 illustrates the dynamic response of selected variables in the emerging economy to a one standard deviation rise in cross-sectional volatility in global bank risk, $s_{t}^{B*}$ . As before, red solid lines (blue dashed lines) display the impulse responses with (without) cross-border lending.

Figure 4.

Impulse responses to a one standard deviation rise in global bank risk. Blue dashed lines correspond to a calibration without cross-border lending $\eta = 0$ . Red solid lines correspond to the baseline calibration, where the share of financing from global banks is $\eta = 15\%$ . All values except for the responses of the external finance premia are in percentage deviations from the steady state $(x_{t}-\bar{x})/\bar{x}\times 100$ . The responses of the external finance premia are presented as annualized percentage point deviations from the steady state.

Recall that financial risk increases the dispersion of the distribution of idiosyncratic shocks. More global banks go bankrupt, and $\rho^{B*}(\tilde{\omega}^{B*})$ rises, which disrupts the supply of credit in the center. As a result, production falls and demand shifts to the emerging economy. When there is no cross-border lending, which corresponds to the blue dashed lines in Figure 4, this demand shifting effect leads to a rise in investment in the emerging market, a modest rise in asset prices and a fall in the external finance premium. However, the negative business cycle comovement is inconsistent with key stylized facts of the global financial cycle.

When the emerging market borrows $\eta = 15\%$ of their funds from global banks (red lines), the investment dynamics are reversed. This effect is driven by a co-movement of the external finance premia in the center and the emerging economy, as shown in the first-order conditions (9) and (10)1. For the emerging economy, a rise in the external finance premium means that the required return on capital rises and the price of capital $Q_{t}$ falls. This triggers an amplification due to financial market imperfection which reduces local banks’ ability to intermediate funds as well. With global financial linkages, the emerging economy is more exposed to external financial risks, with a much deeper and more persistent fall in output. Note also that cross-border lending to the emerging economy drops persistently when financial risk rises in the center, driven by global banks’ financial linkages.

6.1 Sensitivity Analysis

Figure 6 shows the welfare losses in the emerging economy generated by financial risk shocks under different monetary policy regimes. The top panel shows what happens when the degree of financial integration $\eta$ is varied. Under a fixed exchange rate, the policy rate of the emerging economy follows the center. In a flexible exchange rate regime, I assume that the Taylor rule is based on the optimized parameter ( $\phi_{\pi}=1.62$ and $\phi_{Y}=0.22$ ). Under each of the two exchange rate regimes, I also study a specification which allows the emerging market to tax/subsidize global bank outflows according to the capital control rule (32) with $\Upsilon$ fixed at $0.005$ .

Figure 6.

Welfare loss in the emerging economy (in percentage units of steady-state consumption). The top panel shows welfare loss with various degree of financial integration. The bottom panel shows welfare loss with various sensitivities of capital controls to cross-border flows $\Upsilon$ , when financial integration is fixed at $\eta =0.15$ . Under a fixed exchange rate regime, $\{\phi_{\pi}, \phi_{Y}, \phi_{\mathscr{E}} \} = \{0, 0, 999\}$ . Under the flexible exchange rate regime, $\{\phi_{\pi}, \phi_{Y}, \phi_{\mathscr{E}}\}=\{1.62,0.22,0\}$ . In the top panel, when tax or subsidy is available, the degree of capital controls is set to $\Upsilon=0.005$ .

As $\eta$ increases from 0 to $0.4$ , although the flexible exchange rate regime always fares better than a peg, the welfare loss triples (from $0.0022$ to $0.0067$ ). This is because cross-border lending is an additional channel through which shocks from the center affect the emerging economy, and monetary policy cannot smooth the business cycle and capital flows at the same time. In this way, financial integration weakens the stabilization effect of independent monetary policy. Indeed, as Rey (Reference Rey2018) and Obstfeld (Reference Obstfeld, Raddatz, Saravia and Ventura2015) point out, a larger degree of financial integration reduces the welfare gap between flexible and fixed exchange rate regimes.

Temporary capital controls improve welfare in a flexible exchange rate regime. This agrees with the observation that capital controls smooth fluctuations in the impulse response functions. Moreover, capital controls improve welfare in a fixed exchange rate regime as well. This policy works from the bank lending channel in (33) and is independent of the choice of exchange rate regime. The extent to which temporary capital controls improve welfare depends crucially on the financial integration of the emerging economy. The more financially integrated the economy is, the more useful the capital controls are. When the emerging market is sufficiently open (above $0.3$ ), capital account policies appear to be more useful than monetary policy.

The bottom panel of Figure 6 displays how much welfare improves when capital controls with different sensitivities to cross-border lending $\Upsilon$ are implemented, while financial openness is fixed at $\eta=0.15$ . Two results emerge. First, for either regime, welfare loss is monotonically decreasing in the sensitivity of capital controls. The reason for this is similar to Aoki et al. (Reference Aoki, Benigno and Kiytoaki2016). Capital controls, modeled in this way, only impact the bank lending channel, and have no direct effect on households’ consumption smoothing decision, so welfare is always increasing with the capital control parameter $\Upsilon$ . ^{Footnote 18} As discussed above, this channel operates independently of the exchange rate regime, so the welfare gap between two regimes is almost constant. Second, capital controls need not be very sensitive to cross-border flows. When the sensitivity parameter $\Upsilon$ is large (say, above 0.005), the marginal welfare improvement is limited.