Global Banking, Financial Spillovers, and Macroprudential Policy Coordination

UAA

BIS Working Papers

No 764

 

Global Banking, Financial Spillovers, and Macroprudential Policy Coordination

by Pierre-Richard Agénor and Luiz A. Pereira da Silva

 

Monetary and Economic Department

January 2019

 

JEL classification: demography, ageing, inflation, monetary policy

Keywords: E31, E52, J11

 

This publication is available on the BIS website (www.bis.org).

 

© Bank for International Settlements 2017. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated.

ISSN 1020-0959 (print)

ISSN 1682-7678 (online)

 

Global Banking, Financial Spillovers, and Macroprudential Policy Coordination

Pierre-Richard Agénor Luiz A. Pereira da Silva

 

Abstract

The gains from international macroprudential policy coordination are studied in a two-region, core-periphery macroeconomic model with imperfect financial integration and cross-border banking. Financial frictions occur at two levels: between firms and banks in each region, and between periphery banks and a global bank in the core region. Macroprudential regulation takes the form of a countercyclical tax on bank loans to domestic capital goods producers, which responds to real credit growth and is subject to a cost in terms of welfare. Numerical experiments, based on a parameterized version of the model, show that the welfare gains from macroprudential policy coordination are positive, albeit not large, for the world economy. In addition, these gains tend to increase with the degree of international financial integration. However, depending on the origin of financial shocks, they can also be highly asymmetric across regions.

JEL Classification Numbers: E58, F42, F62


  • ∗Hallsworth Professor of International Macroeconomics and Development Economics, University of Manchester; ∗∗Deputy General Manager, Bank for International Settlements. We are grateful to participants at the BIS-PIIE Round Table on Global Interdependence: Rethinking International Policy Coordination (Washington DC, April 2018) and various seminars for helpful discussions, and especially Gianni Lombardo for comments on a previous draft. However, we bear sole responsibility for the views expressed in this paper. Timothy Jackson provided outstanding research assistance. Appendices B and C are available upon request.

 

Introduction

There is growing evidence that international financial spillovers have become a two-way street—they occur not only from the major advanced economies to the rest of the world, as in decades past, but also, and increasingly, from a group of large middle-income countries to advanced economies. Indeed, these countries are now more interconnected financially than ever before. As documented by Cerutti and Zhou (2017), McCauley et al. (2017), and World Bank (2018), this process has been partly the result of banking globalization, which has taken the form of growing networks of foreign branches and subsidiaries centered on global parent banks—despite the retrenchment of major global and non-major European banks operations in the immediate aftermath of the Global financial crisis. Studies such as Bruno and Shin (2015), Temesvary et al. (2018), Avdjiev et al. (2018), and Buch et al. (2019) have found robust evidence that changes in monetary policy in the United States—in large part due to the role of the US dollar as a global funding currency—have a strong impact on cross-border lending by US banks, consistent with the existence of an international bank lending channel. Similar results have been established by Grab and Zochowski (2017) in the case of euro area banks in response to monetary policy accommodation by the European Central Bank.

The fact that cross-border spillovers operate in both directions and have become more significant does not prima facie create a case for greater coordination of policies across countries. Indeed, spillovers (financial or otherwise) do not necessarily reduce global welfare, and coordination is not always needed to improve welfare. In a global recession for instance, uncoordinated expansionary fiscal policies in a core group of countries with small budget deficits and low public debt ratios can benefit all coun­tries. But because financial markets are prone to amplification effects, and because business and financial cycles remain imperfectly synchronized across countries—even when they share a common currency, as in the euro area—this new environment creates the potential for shocks in one jurisdiction to be magnifiedandtransmittedtoothers through short-term capital flows, with the possibility that these flows may exacerbate financial instability in both source and recipient countries.

These risks have led policymakers in some large middle-income countries to issue pleas for policymakers in major advanced economies to go beyond their institutional mandate—which normally requires them to take account of the external impact of their policies only insofar as they feed back onto their own economies—and internalize the cross-border spillover effects associated with their monetary policy decisions and the possible risks that they create (see Mishra and Rajan (2016)). Some observers have gone further and have argued in favour of greater coordination of macroprudential policies (both in their structural and countercyclical components) across countries, to mitigate the adverse effects of capital flows and promote global financial stability.

The foregoing discussion suggests that the analytical case for macroprudential pol­icy coordination across countries rests fundamentally on the fact that financial risks represent negative externalities that tend to increase with the magnitude of spillovers and spillbacks, and the degree to which business and financial cycles are unsynchronized across countries. Conversely, effective domestic macroprudential policy that helps to contain systemic risks in one country may help promote financial stability elsewhere by reducing the scope for negative trade and financial spillovers, creating therefore positive externalities. From that perspective, as noted by Engel (2016), coordination is desir­able when it enables countries to improve their policy trade-offs. At the same time, to make an empirical case for international coordination of macroprudential policies it must be shown that there are potentially significant gains for participating countries, and the world economy as a whole, from doing so. Indeed, these gains must be suffi­ciently large quantitatively to mitigate incentives to renege and ensure that countries remain voluntarily in a cooperative agreement.

Yet, even though much can be learned from the early literature (reviewed by Frankel (2016) for instance) on international monetary policy coordination, research on this issue remains very limited. Among the few contributions available, based explicitly on a game-theoretic approach, are Agenor et al. (2018b), Agenor et al. (2018c), and Chen and Phelan (2017). Agenor et al. (2018b) study the effects of coordinated and non­coordinated macroprudential policies in a model with financial frictions as in Gertler and Karadi (2011) and where global banks in a core region lend domestically and to banks in the periphery. A global benevolent policymaker chooses the constrained efficient allocation in order to maximize the expected present value of the population- weighted sum of household utilities in the cooperative case, or own domestic households’ utility in the non-cooperative (Nash) equilibrium, subject to a cost associated with the use of distortionary policy instruments. Their results show that the global welfare gain from coordination can be relatively large (of the order of 1-2 percent of steady-state consumption), essentially because it mitigates significantly the cross-border spillovers of country-specific shocks. At the same time, however, the distribution of gains across countries tends to be highly asymmetric, implying therefore that coordination may not be Pareto-improving.

For their part, Agenor et al. (2018c) focus on the case of a currency union where investment in each member country is financed by credit from national banks only, sub­ject to collateral-based frictions. Monetary policy is conducted by a common central bank, whereas macroprudential policy can be conducted either by national regulators or a common, union-wide regulator. In either case macroprudential policy (in the form of a simple, implementable countercyclical rule) aims to smooth credit fluctuations in order to maximize welfare. Thus, their focus is on the properties of two alternative, in­stitutional mandates to achieve financial stability: delegation of macroprudential policy to individual member countries (the noncooperative Nash equilibrium or decentralized regime) and delegation to a common regulator (the cooperative equilibrium or central­ized regime), with the common central bank retaining full control of monetary policy in both cases. Their results show that in response to asymmetric real and financial shocks cooperation does generate positive gains relative to the noncooperative outcome at the level of the union but coordination does not necessarily benefit all members. Fi­nally, Chen and Phelan (2017), dwelling on the continuous-time framework developed by Brunnermeier and Sannikov (2015), formulate a symmetric two-country model in which countries have limited ability to issue state-contingent contracts in international markets. As a result, the relative share of global wealth held by each country affects its own level of output. Because of market incompleteness, national macroprudential regu­lation of each country’s borrowing position (in the form of restrictions on capital flows) can improve national welfare. But tight regulation in one country creates incentives for the other one to reciprocate to avoid being relatively poorer on average. Coordination, by eliminating these incentives, therefore generates gains for both countries.

Adopting also a game-theoretic approach, this paper contributes to the literature by focusing on a two-region, core-periphery dynamic stochastic general equilibrium model with imperfect financial integration and a global bank in the core region lending to banks in the periphery. As in some of the contributions alluded to earlier, our analysis considers two levels of financial frictions: between firms and banks in each region, and between periphery banks and the global bank. Periphery banks are not constrained on how much they can borrow from the global bank but they must pay a premium that increases with the amount borrowed. A higher premium, in turn, tends to reduce incentives to borrow. The model is parameterized for two groups of countries, the major advanced economies and a group of large (systemically important) middle- income countries, which have been identified in recent studies as generating significant reverse spillovers, also referred to as spillbacks, on advanced economies. Our focus is on credit spread shocks occurring in both regions.

Numerical experiments show that the welfare gains from macroprudential policy coordination—a regime under which a benevolent regulator internalizes the conse­quences of policy interdependence—are positive, albeit not large (of the order of 0.2-0.9 percent of steady-state consumption, depending on the origin of the financial shock), for the world economy. In addition, consistent with the evidence alluded to earlier, these gains increase with the degree of international financial integration. However, depending on the origin of shocks, they can also be asymmetric across regions. This result is consistent with those reported in Agenor et al. (20186,2018c), albeit in a very different setting. Although our analysis considered only a single (but representative) financial shock, the fact that gains are not large and that coordination is not necessar­ily Pareto-improving raises a general question about incentives for countries to remain voluntarily in a cooperative agreement.

The remainder of the paper proceeds as follows. Section 2 describes the model. In the spirit of a number of recent contributions, and to enhance analytical tractability, macroprudential regulation is introduced as a time-varying tax on bank loans. Such atax canbeviewedasagenericspecification consistent with the price-based channel through which two major instruments of macroprudential policy, capital requirements and dynamic provisions, operate in terms of their impact on the cost of borrowing. A simple implementable macroprudential rule, linking the tax on loans to deviations in the credit-to-output ratio, is defined. The equilibrium and some key features of the steady state are briefly discussed in Section 3, and a benchmark parameterization is presented in Section 4. To illustrate the functioning of the model, the impulse response functions associated with asymmetric and symmetric financial shocks are described in Section 5. The gains from coordinating macroprudential policies across borders are evaluated in Section 6. Sensitivity analysis is reported in Section 7, in order to examine how the model’s structural features affect the gains from coordination. We consider, in particular, the impact of a greater degree of financial integration and the case of a perfectly integrated world housing market, which implies that policy responses to house price shocks occurring in one region may generate a pecuniary externality for other regions—thereby potentially enhancing the scope for coordination to improve welfare. The last section discusses the broad policy implications of the analysis and some potentially fruitful extensions.

 

The World Economy

The world economy consists of two regions, called core and periphery, of normalized economic size n G (0,1) and 1 — n, respectively. Population size in both parts of the world is normalized to unity. Each region is populated by a representative household, a continuum of monopolistic (IG) firms producing intermediate goods, a representative final good (FG) producer, a representative capital good (CG) producer, a government, and a central bank, which also operates as the macroprudential regulator. A single global bank operates in the core economy, whereas a continuum of commercial banks operate in the periphery. In line with the original sin argument, banks in the periph­ery cannot borrow in their own currency. They are also unable to fully hedge against foreign exchange risk. In addition, the cost at which banks in the periphery borrow from the global bank is increasing in the amount borrowed. Regions trade in (inter­mediate) goods and government bonds, but markets in cash and credit are segmented. In particular, firms in either region cannot directly lend or borrow internationally.

  1. Core Economy

In what follows we describe the behavior of households, the global bank, the central bank, and the government in the core economy. Because households and the govern­ment behave essentially in the same way in both regions, we subsequently describe only the behavior of banks and the central bank in the periphery. The structure of production is also the same in both regions, and details for these sectors are provided in Appendix A.

  1. Households

The objective of the representative household in the core economy is to maximize  where Ct is consumption of the core final good, N. the number of hours provided to IG producer j, xt a composite index of real monetary assets.

Image 1m4p

 HtC the stock of housing, Л e (0,1) a discount factor, <; > 0 the intertemporal elasticity of substitution in consumption, 'фN the inverse of the Frisch elasticity of labor supply, Et the expectation operator conditional on the state of nature at the beginning of date t,and vn ,Vx,Vh > 0 are preference parameters. Households derive utility from housing services, which are proportional to their stock of dwellings.

The composite monetary asset consists of real cash balances, mf, and real bank deposits, df, both measured in terms of the price of core final output, Ptf:

Image ar07

where Nt = f0 N/ dj, p^H = PtcH/Ptc is the real price of housing (with PtcH denoting the nominal price), 1 = Ptc/Ptf 1, bfC (z_1b) real holdings of one-period, non­ contingent core (periphery) government bonds, zt = EtPtc /PtP, the real exchange rate measured from the perspective of the periphery, with PtP the price of the periphery’s final good and Et the nominal exchange rate (expressed in terms of units of periphery currency per unit of core currency, so that an increase in Et is a depreciation), ifD the interest rate on bank deposits, ifB the interest rate on core government bonds, ip the premium-adjusted (or effective) interest rate on periphery government bonds measured in the core region’s currency, wt the economy-wide real wage, Tt real lump-sum taxes, J/, JtK, and Jf, end-of-period profits of the IG producer, the CG producer, and the global bank, respectively. For simplicity, housing does not depreciate.

Core households face intermediation costs when acquiring periphery bonds. The effective rate of return on these bonds is given by

Image x4yo

where i^ is the (unadjusted) periphery bond rate and 6fP an intermediation premium, which increases with the core household’s own stock of periphery bonds:

Image sjeu

The representative household maximizes (1) with respect to sequences {Ct+s, Nt+s,

m?+s+l, df+s+1, ablesaswellas wt, Tt and real profits as given. The first-order conditions are ogether with appropriate transversality conditions. These results are standard, with the exception of the last two which define core household demand for housing services and periphery bonds.

Image 4zdh

  1. Global Bank

Image lk4k

where i«R is the marginal cost of borrowing from the central bank, i«P the interest rate on loans to periphery banks, rC £ (0,1) the tax rate on the gross value of domestic loans imposed for macroprudential reasons, q £ (0,1) the repayment probability of core firms on their loans, and q^ £ (0,1) the repayment probability of periphery banks on their loans, which is determined (as discussed later) by conditions in that region. The first term in (14) is expected repayment when there is no default by domestic firms, whereas the second is the value of collateral seized in case of default, corresponding to afraction к £ (0,1) of the expected value of the housing stock, which is assumed to be in fixed supply HC. We assume that the global bank cannot seize collateral if periphery banks choose to default; these banks therefore have effectively limited liability, so that when they default (which occurs with probability 1 — qpc) the global bank gets nothing. Expected repayment (the third term in (14)) is therefore only qpc( 1 + i<jcP)l<jcp. The fourth term is repayment to depositors and the fifth repayment to the central bank, neither of which is state contingent. The global bank also incurs a convex cost that increases with the amount of international lending to periphery banks, as measured by 0.57c(lCP)2, where 7е > 0. The last term, Q<jc, represents the proceeds of the loan tax; in order we abstract from the fiscal effects of macroprudential policy, we assume that these proceeds are rebated to each bank in lump-sum fashion.

The bank has monopoly power in the deposit and domestic credit markets, whereas the market for periphery loans is competitive. Thus, it sets the deposit and lend­ing rates, and chooses the amount of lending to periphery banks, so as to maximize expected profits:

Image riz9

where vd ,Vl > 0 are gross interest elasticities of the supply of deposits and the demand for loans, respectively. Thus, the wedge between the policy rate and the loan rate depends on both the risk of default and macroprudential regulation. In particular, equation (17) shows that a higher tax on loans raises the lending rate. In addition, equation (18) indicates that the supply of loans to periphery banks is increasing in the expected return on these loans, as measured by qpc(1 + icP).

The repayment probability on loans to local firms depends positively on the ex­pected value of collateral relative to the volume of loans, and the cyclical position of the economy:

Image e9fz

where Yc is the steady-state level of core final output. Agenor and Pereira da Silva (2017) formally derive an equation similar to (19) as part of the bank’s optimization problem, by assuming that monitoring costs are endogenous and that ex ante monitor­ing effort is directly related—as in Allen et al. (2011) and Dell’Ariccia et al. (2014), for instance—to the probability of repayment. The collateral-loan ratio reflects a moral hazard effect, whereas the cyclical position of the economy reflects the fact that (unit) monitoring costs tend to be relatively low in good times.

In Appendix A we relate loans to local firms (the representative CG producer) to investment. Thus, given (17), the supply of these loans is perfectly elastic. In addition, because the supply of deposits is determined by households (given (16)), and that the supply of loans to periphery banks is set in (18) on the basis of the net return to lending, borrowing from the core central bank is determined residually from (13).

  1. Central Bank

The central bank operates a standing facility, which involves a perfectly elastic supply of (uncollateralized) loans to the global bank, l<jcB, at the prevailing cost of borrowing. It does not intervene in the foreign exchange market and supplies cash, in quantity m, to households and firms. Setting its (constant) stock of foreign reserves to zero, its balance sheet is thus

Image 0vyb

The core central bank supplies liquidity elastically to the global bank at a cost г^, which is set on the basis of an inertial Taylor rule:

Image sb9v

where %cR is the steady-state value of the refinance rate, > 0 the inflation target, Xc € (0,1),an,ec > 0.

As noted earlier, macroprudential regulation takes the form of a time-varying tax on bank loans to domestic firms.  We consider a simple implementable rule whereby changes in the tax rate are related to an operational target for systemic risk, the credit growth rate. The focus on that variable is consistent with the evidence which suggests that (excessive) credit growth has often been associated with financial crises. It also reflects the assumption that inefficient credit fluctuations are not directly observable, which implies that in practice regulators can

Image jcpb

only adopt policies that are based on noisy indicators of financial risks. Specifically, where x1 E (0,1) is a persistence parameter and xf > 0 is the response parameter to the credit growth rate. Thus, from (17) and (22), borrowing is more costly during episodes of credit booms and this in turn helps to mitigate macroeconomic fluctuations.

  1. Government

Income received by the central bank on its lending to the global bank is transferred to the government, whereas (as noted earlier) revenue from the macroprudential tax is returned lump-sum to the global bank. The core government budget constraint is thus given by

Image 6u1n

In what follows the government in each region is assumed to keep its real stock of debt constant and to balance its budget by adjusting lump-sum taxes.

  1. Periphery
  2.  
  3. 1.2 Households

Periphery households have the same utility function as core households. They also face a resource allocation problem similar to the one faced by core households, with the effective rate of return on core government bonds if defined as, symmetrically to

Image nrnb

Equations (12) and (27) imply therefore that uncovered interest parity, 1 + ips — (1 + ifB)Et(Et+1/Et), obtains when 6^ ^ 0. Thus, as discussed later, the impact of increased financial integration on the gains from coordination can be assessed by lowering 6B.

  1. 1.3 Commercial Banks

The balance sheet of periphery bank i £ (0,1) is given by

Image 2er

where ljfK,i is loans to periphery firms, dp’1 deposits (determined analogously to (9)), ^ £ (0,1) the required reserve ratio on these deposits, ztlpc,i borrowing from the global bank (with lpc,i measured in foreign-currency terms), at the rate ifP,i, and lpBi borrowing from the periphery central bank. Thus, due to the absence of hedging instruments, periphery banks are exposed to exchange rate risk; fluctuations in the real exchange rate generate balance sheet effects.

The market for deposits is competitive, and deposits and central bank liquidity are perfect substitutes. this ensures therefore that, Vi, the following no-arbitrage condition holds:

Image s4e2

Expected profits of bank i at the end of period t are given by where i^ is the marginal cost of borrowing from the central bank, тP G (0,1) the macroprudential tax rate, and qp G (0,1) the repayment probability of periphery CG producers. As before, the first two terms represent expected income (net of taxes) from lending, the third interest paid on deposits, the fourth reserve requirements held at the central bank and returned to bank i at the end of the period, the fifth repayment on loans from the central bank, and the sixth expected repayment to the global bank (given limited liability). In addition, periphery banks incur a convex cost that increases with the amount of borrowing abroad, as measured by 0.57Pzt(lpC,i)2, where 7P > 0. The last term fiPi represents the revenue of the loan tax, which again is transferred back in lump-sum fashion to bank i.

Each bank maximizes profits with respect to their loan rate and their demand for foreign loans:

Image jwo1

Image tmau

Equation (32) shows once again that a tighter macroprudential response raises the cost of loans, whereas equation (33) indicates that a higher cost of borrowing from the global bank (adjusted for expected depreciation) reduces the demand for foreign loans—and vice versa for an increase in the marginal cost of borrowing domestically. As before, borrowing from the central bank is determined residually from (28).

The repayment probability of firms depends once again positively on the expected value of collateral relative to the volume of loans and the cyclical position of the economy:

Image tiwg

where Ytp is the periphery’s final output and Yp itssteady-statevalue.

As noted earlier, the global bank cannot effectively secure collateral against its loans to periphery banks. Yet these banks can suffer from lender-enforced penalties, or a reputational cost, which creates an incentive to repay. We assume, in line with the standard literature on foreign borrowing and sovereign default risk, that the repay­ment probability on core loans is negatively related (due to banks’ opaqueness) to the economy-wide debt-to-output ratio:

Image z3nr

    Central Bank and Regulator

Analogously to (20), the balance sheet of the periphery central bank is given by

Image sfj7

The periphery central bank also operates a standing facility. Its supply of liquidity to local banks is perfectly elastic at the rate ipR, which is set through a Taylor rule similar to (21): where ^p > 0 is the inflation target, Xp e (0,1) and £i Yp > °.

Image iblc

The tax on loans is also set according to a rule similar to (22):

Image 6kt1

where xp G (0,1) and xp > 0.

Interest income received by the central bank is once again transferred to the gov­ernment. The periphery government budget constraint takes therefore the same form as (23), with now bf = blfP + bfp and interest payments of (1 + ^f )-1(1 + if__31)bf_-1.

The production structure and the main real and financial flows between agents (abstracting from the government) and regions are summarized in Figure 1.

            Equilibrium and Steady State

As shown in Appendix A, in a symmetric equilibrium all IG firms in both regions produce the same output, prices are the same across firms, and total output of core and periphery intermediate goods must be equal to world demand for these goods. In addition, equilibrium in the market for final goods requires that output be equal to domestic absorption, inclusive of price adjustment costs.

Assuming for simplicity that loans to firms are made exclusively in the form of cash, the equilibrium condition of the currency market in the core region is given by

Image mndb

Equilibrium in the market for periphery loans requires equating (18) and (33), that is, I^p = IfC, which can be solved for the equilibrium loan rate. Alternatively, rewriting (18) as

Image qrjn

shows that an increase in the amount borrowed by periphery banks, as given by (33), raises the cost at which they borrow from the global bank both directly and indirectly, through a reduction in the repayment probability on periphery loans, as implied by. Thus, in the model 1/qplays the same role as the country risk premium externality in the literature on sovereign debt and foreign borrowing. The equilibrium condition of the housing market for the core region is

Image zpp3

which can be solved, using (10), to determine the dynamics of house prices. A similar condition holds for the periphery.

In equilibrium, net trade in government bonds (or, equivalently, the world net supply of bonds) must be zero, so that

Image g9ox

where PtCC is the price of core intermediate goodssoldonthe peripherymarket(that is, the price of core exports), YfP are core exports of intermediate goods, which cor­respond also to the periphery’s imports of these goods, PtPC = E—1PtPP the price of periphery intermediate goods sold in the core region (equal, under local currency pric­ing, to the price of periphery intermediate goods adjusted for the exchange rate), and YtPC core imports of intermediates, which correspond also to the periphery’s exports. The third term in (44) is the interest income from loans to the periphery by the global bank, and the fourth (fifth) term interest income (payment) on holdings of periphery (core) bonds by core (periphery) households. By definition, the current account is also

Image kfy4

The steady-state solution of the model, assuming a zero target inflation rate, is briefly described in Appendix B. Several of its key features are fundamentally similar to those described in Agenor et al. (2014, 2018a) for a small open economy, so we refer to thosepapersfor amoredetailed discussion.

            Parameterization

To assess the properties of the model and evaluate the gains from coordination we parameterize it for two groups of countries, corresponding to the core and periphery, respectively: major advanced economies (MAEs) and systemically important middle- income countries (SMICs). As defined in Agenor and Pereira da Silva (2018), MAEs consist of the United States, the euro area, and Japan, whereas SMICs consist of Brazil, China, India, Indonesia, Mexico, Russia, South Africa, and Turkey. As identified by the International Monetary Fund (2016), these groups of countries represent those who have exerted the largest financial spillovers and spillbacks to each other in recent years.

Our benchmark parameterization uses standard values used in the literature on small open-economy and two-country models. In addition, a number of asymmetries across regions are imposed. In particular, we account for the fact that, as documented elsewhere (see Agenor (2019, Chapter 1)), financial frictions are more pervasive in middle-income countries. In addition, for some of the parameters that are deemed critical from the perspective of this study, sensitivity analysis is reported later on.

The discount factor Л is set at 0.98 for MAEs and 0.95 for SMICs, which gives a steady-state annualized interest rate (real and nominal, given zero inflation in the steady state) of about 2.0 percent in the firstcaseand 5.3 percent in the second. Thus, consistent with the evidence, real interest rates are significantly higher in SMICs. The intertemporal elasticity of substitution is uniformly set at 0. 5, in line with the empirical evidence discussed by Braun and Nakajima (2012) and Thimme (2017). The preference parameter for leisure, qN, is set at 16, to ensure that in the steady state households in both regions devote one third of their time endowment to market activity—a fairly common benchmark in the literature (see Christoffel and Schabert (2015) and Boz et al. (2015) for instance). The Frisch elasticity of labor supply is set at 0.33 for both regions (implying that ^N is equal to 3), in line with the empirical evidence.

The parameter for composite monetary assets, qx, is set at a low value, 0.01, to capture the common assumption in the literature that their weight in household pref­erences is negligible (see for instance Coenen et al. (2009) and Christoffel and Schabert (2015)). For the housing preference parameter, qH, we use the same value as in No- tarpietro and Siviero (2015), 0.1. The share parameter in the index of money holdings, v, which corresponds to the relative share of cash in narrow money, is set at 0.2 to capture the predominant use of deposits in transactions in both regions. The cost parameter related to core (periphery) bond holdings by core (periphery) households, 6P, is set initially at 0.8. This value is consistent with a relatively low degree of capital mobility. Sensitivity analysis is performed later on.

The distribution parameter between core and periphery intermediate goods in the production of the final good (or, equivalently, the degree of home bias), А/, is set at 0.8 for MAEs and 0.6 for SMICs, to reflect the fact that the latter group is relatively more open than the former. The elasticity of substitution between baskets of domestic and imported composite intermediate goods used in the production of the final good, , is set at 6, which implies that these goods are substitutes in the production of the final good. This value is close to the one used by Bergin et al. (2007). The elasticities of substitution between core intermediate goods among themselves, всс, and imported periphery goods among themselves, врр, are both set equal to 10. Quint and Rabanal (2014), for instance, use the same value. This implies a steady-state mark-up of 20 percent. The share of capital in output of intermediate goods, o,isset at a fairly standard value, 0.35, for both regions. The adjustment cost parameter for prices of domestic intermediate goods, , is also set uniformly at 74.5 to capture a relatively high degree of nominal price stickiness. This value is close to the average value initially estimated by Ireland (2001, Table 3) and implies a Calvo-type probability of not adjusting prices of approximately 0.71 percent per period, or equivalently an average period of price fixity of about 3. 5 quarters. These figures are consistent with the point estimates of Quint and Rabanal (2014, Table 2) and Christoffel and Schabert (2015, Table 2) for advanced economies, and Agenor et al. (2018a) for middle-income countries. The capital depreciation rate, 5k, is set at a quarterly rate of 0.01 for the core and 0.025 for the periphery, which are within the span of values typically used in the literature. The adjustment cost incurred by the CG producer for transforming investment into capital, ©k ,isset at 14, in order to match the fact that the standard deviation of the cyclical component of investment is 3 to 4 times more volatile as output in most countries (see Hnatkovska and Koehler-Geib (2018) for instance).

Regarding the global bank and periphery banks, the collateral-loan ratio, к, is set at 0. 4 for MAEs and at 0. 2 for SMICs, to capture the relatively higher costs associated with recovery of collateral and more generally debt enforcement procedures in the latter group of countries, as documented by Djankov et al. (2008). For both regions, the elasticity of the repayment probability with respect to the effective collateral-loan ratio is set initially at =0.05 for MAEs and фf = 0.1 for SMICs, whereas the elasticity with respect to deviations in output from its steady state is set initially at ф^ = 0.1 for the core and, consistent with Agenor et al. (2018a), фf = 0.2 for the periphery. The cost parameters 7c and 7f are set at 0.05 and 0.1, respectively, in order to generate sensible values for initial interest rates. The elasticities , ^L and (L are set equal to 2.5, 25 and 25, respectively. This gives a mark-down of the policy rate relative to the policy rate of about 58 basis points in the core region, and a mark-up of the loan rate over the policy rate (given repayment probabilities of 0.966 in the core and 0.936 in the periphery) of about 464 basis points in the core and 823 basis points in the periphery. The latter results are in line with the evidence for MAEs and SMICs, which suggests significantly higher default rates and higher lending spreads for the latter group of countries. The parameter ф^, which measures the sensitivity of the repayment probability on loans by the global bank to periphery banks, is set at 0. 3.

The degree of persistence in the core central bank’s policy response, y, is set at 0.7, whereas the responses of the policy rate to inflation and output deviations, £1 and £2, are set at 1.7 and 0.1, respectively, as in Coenen et al. (2009). For the periphery central bank, the corresponding values are у = 0.8, £ = 2.0, and £2 = 0.4, based on the evidence for upper middle-income countries reported by Federico et al. (2014). In particular, the weight on output fluctuations in SMICs is significantly higher than in MAEs, a well-documented fact in the literature. The required reserve ratio, ^, is set at 0.3, consistent with the evidence for some Latin American countries like Brazil (Agenor et Pereira da Silva (2017)).

The share of noninterest government spending in final output, , is set at 0.2 for the core (as in Coenen et al. (2009), again, and Alpanda and Aysan (2014)) and 0.25 for the periphery, as in Agenor et al. (2018a). These values are consistent with actual data for MAEs and SMICs and close to those used in a number of other contributions.

Parameter values are summarized in Table 1, whereas initial steady-state values for some key variables are shown in Table 2. In particular, they indicate that the shares of (intermediate good) exports are relatively high for both regions (22.6 and 18.9 percent for the core and the periphery, respectively), and that the amount of loans from the global bank to the periphery banks is relatively large in proportion of the region’s output. The countercyclical tax rates on loans, тc and тр,are set at 0 initially in both regions.

           Asymmetric Credit Spread Shocks

To characterize the properties of the model in terms of the cross-border transmission of financial shocks, we consider asymmetric credit spread shocks occurring in both regions when there is no countercyclical macroprudential policy (x = Xp = 0). To do so we introduce a multiplicative shock to the loan rate in equations (17) and (32), 6Jt, which reflects a shock to the elasticity of the demand for loans. Moreover, is assumed to follow a first-order autoregressive process of the form e^ = (e^_exp(<^), where ff £ (0,1) and a - N(0,CTjp), with j = C, P. The autocorrelation coefficients ff areset at thesamevalue, 0.85, which implies a fairly high degree of persistence.

ThecontinuouslineinFigure2showstheresultsfor aonepercentagepointnega- tive shock in the core region. The direct impact of the shock is a reduction in the loan rate and an increase in investment in that region. This leads to a gradual increase in the capital stock and an expansion in aggregate demand, which translate into higher marginal production costs and inflation. In response to the increase in cyclical output and inflation the central bank raises its policy rate, which leads to a higher deposit rate and a shift toward deposits. To induce a reduction in the demand for cash, its opportunity cost, the nominal bond rate, must increase. Given our calibration, this increase dominates the rise in (one-period ahead) inflation, so that the (expected) real bond rate increases, thereby leading through intertemporal substitution to a reduction in current consumption by core households. Gross complementarity between consump­tion and leisure implies that labor supply increases, but because labor demand rises as well, wages tend to increase, thereby raising further marginal costs and inflation. The increase in the bond rate and the drop in current consumption also combine to reduce the demandfor housing, whichinturntranslatesinto afall in houseprices—andthus a reduction in collateral values, which is large enough to induce a reduction in the re­payment probability, despite the positive effect associated with the increase in cyclical output. This drop in the repayment probability mitigates, but does not reverse, the initial fall in the loan rate and the increase in investment.

The increase in the bond rate in the core region is such that the demand for periph­ery bonds by core households falls, whereas the demand for core bonds by periphery households increases. At the same time, the impact increase in the marginal cost of borrowing from the central bank induces the core bank to cut lending to periphery banks. From the perspective of the periphery, the net effect is thus a capital outflow and an initial depreciation of the nominal and real exchange rates. On the one hand, this makes imported intermediate goods from the core more expensive; on the other, it makes exports from the periphery cheaper. The second effect dominates from the perspective of the periphery and this translates into a current account surplus for that region and a deficit for the core.

The increase in the domestic-currency price of imported inputs associated with the exchange rate depreciation translates into higher inflation in the periphery, which leads to an increase in the policy rate there as well. As a result, however, the loan rate increases now, and consequently investment falls. At the same time, the increase in (expected) inflation is larger than the increase in the nominal bond rate—which occurs through the same mechanism described earlier, related to the shift toward deposits— implying a fall in the real bond rate, which weakens incentives to save and induces an increase now in current consumption. This tends to increase housing demand and real house prices which, through higher collateral values and a higher repayment probability, tend to mitigate the rise in the loan rate and the drop in investment. However, the net effect on aggregate demand is negative and output of final goods falls.

The continuous line in Figure 3 shows the results for a one percentage point negative credit spread shock in the periphery. The results are largely opposite to those described earlier: the expansion in investment and output occurs initially in the periphery, but is transmitted through an inflow of capital and a real appreciation of the periphery’s currency to the core region. This time, lending by the global bank increases and serves in part to finance the investment boom that occurs in the periphery. The positive correlation between the policy rate in the periphery and borrowing by periphery banks is consistent with the empirical evidence provided by Avdjiev et al. (2018) on lending in global funding currencies.

In sum, the results show that a credit spread shock in one region is transmitted to the other through portfolio, trade and exchange rate channels, as well as changes in lending by the core global bank to periphery banks. In addition, there is no much co-movement across regions with respect to real and financial variables, except for inflation and portfolio flows. An interesting aspect of our results is that an expansion in the core does not translate into more lending to the periphery; the key reason is that the policy rate in the core (the marginal cost of borrowing for the global bank) rises in response to higher output and inflation and this tends to reduce the supply of loans. Of course, these outcomes are specific to the type of shocks considered. But given that cross-border transmission creates more volatility, in both regions, the issue is whether cooperation between regulators can promote stability and generate welfare gains, compared to a policy setting where they act independently, based on their own strategic interests.

            Gains from Coordination

In the absence of international coordination, each region’s regulator sets its instrument taking as given the reaction function of the other regulator. In doing so, each regulator j = C,P seeks to maximize its own country’s welfare only, adjusted for the cost of changing its macroprudential instrument, in similar fashion to Rudebusch and Svensson (1999), Taylor and Williams (2010), and Debortoli et al. (2017), in the context of monetary policy, and Angelini et al. (2014), with respect to macroprudential policy:22

Image j1rb

where kw > 0 is a parameter that measures the welfare cost (assumed quadratic) associated with the use of the macroprudential instrument and u() the truncated period utility function given by u(Ct.Nt) = ( 1 — ^-1)-1С,1-<1 — ^N(1 + фм)-1nI+^n.23

Thus, under independent policies, the central bank in each region takes as given the behavior of the other regulator and determines the optimal value of the response parameter x2 in the rules (22) and (38), denoted x2’N,sothat, for 3 = C.P,

Image 4ih4

where W, is the second-order approximation to the objective function W, defined in (46).

In contrast, under coordination, regulators—or a benevolent global policymaker working on their behalf—jointly determine the optimal response parameters, denoted X'° and x^’°, so as to maximize a weighted sum of each region’s welfare, again defined as in (46):

Image pnri

where the persistence parameter x1 in (22) and (38) is assumed to remain the same under both regimes. Thus, higher welfare for each region taken individually in the coordination regime relative to the uncooperative regime is a sufficient, but not neces­sary, condition to generate a net gain for the world as a whole; this also depends on the magnitude of the relative gain (or loss) for each region and the relative weight of each of them, as measured by n, inthe commonwelfare function.  

To assess the gains from coordination, we compare the two regimes—the Nash equilibrium, under which regions pursue independent policies and set unilaterally the tax rate on loans (or more accurately, the response parameter xi in the own tax rule), and the cooperative regime, under which the regions set together a common policy, with differentiated tax rates for each of them, so as to maximize their weighted welfare function. Policies are computed under commitment, that is, under the assumption that regulators (individually and jointly) have the ability to deliver on past promises—no matter what the current situation is today. As in de Paoli and Paustian (2017) for instance, under non-cooperation we solve for the closed-loop or feedback equilibrium. Given the pre-determined nature of the feedback rules (22) and (38), each regulator has full knowledge of the other regulator’s reaction function; their best responses reflect therefore this knowledge.

In line with Lucas (1990) and the subsequent literature, we evaluate welfare gains in terms of compensating variations in consumption. Abstracting from the cost of instrument manipulation (so that kw = 0), the welfare gain at the level of each region is thus obtained by solving for ftг, the fraction of the (expected) consumption stream that would make households equally well off, in each period, under noncooperation as under cooperation:

Image 8kid

where {C/+f }O=0 and (N/+ }O=0 are solution paths under the Nash equilibrium, based once again on the maximized value of each region’s welfare (that is, at the optimal own response parameter xi’W), and {C/+2}O=0 and {N/+f}O=0 solution paths under co­ordination, based on the maximization of the weighted sum of each region’s welfare. Thus, a positive value of ft3 indicates that households in region i prefer the coordi­nation regime—they would need additional consumption under noncooperation to be indifferent between the two regimes.

Similarly, the welfare gain for the world as a whole is calculated by solving for ft in the expression

Image 9bur

where again ft > 0 indicates a welfare gain under coordination. As discussed in Ap­pendix C, (49) and (50) are evaluated using second-order approximations to both the household’s (truncated) period utility function and the model, conditional on the initial steady state being the deterministic steady state. The relative weight of each region is initially set at n = 0.5, to capture the case where although their economic weight may differ, political equality prevails when it comes to evaluating world welfare.

Theupper partof Table3show theresultsfor theasymmetriccoreand periphery shocks discussed earlier, as well as for the joint shock, for the benchmark set of pa­rameters. In all cases, the adjustment cost parameter kw is set uniformly to a very low value of 0.01. The degree of persistence in the regulatory policy rules, Xi, is set to 0.8. A gridstepof 0.01 is used to search for the optimal response parameters X27 and Xй in (22) and (38). This is sufficient for our purpose. Compensatory variations, both with and without adjustment for the cost of instrument use, are reported for both individual regions and the world. Figures 4, 5 and 6 show relative welfare levels (nor­malized by the level of welfare when there is no countercyclical response, that is, when X2 = Xй = 0) for both regions and the world, for the core, periphery, and joint shocks, respectively. The value of (relative) welfare at the Nash and cooperative solutions in these figures can therefore be interpreted as the gain from activism. The dotted (red) lines in Figures 2 and 3 show the impulse response functions under coordination. Fi­nally, Table 4 shows the asymptotic standard deviations of a range of macroeconomic variables under the three policy regimes—no countercyclical policies, noncooperation, and coordination, for both types of shocks and for the joint shock.

The results show first that welfare in the region where an asymmetric shock origi­nates, as well as in both regions when there is a joint shock, has an inverted U-shape form, both under Nash and under coordination. The intuition is as follows. Initially, as countercyclical regulatory policy is implemented, volatility falls at first, because it stabilizes credit, investment and aggregate demand. As a result, social welfare in­creases. However, as the policy becomes more aggressive, its cost increases as well. This eventually dominates the initial gains, entailing therefore a marginal reduction in social welfare. Thus, there exists an optimal value for the response parameters xi to credit growth, both under Nash and under coordination.

Second, in response to an asymmetric shock in each regulator’s own region, it is optimal under the Nash regime for the regulator in the other region not to react. This is also the case under coordination for the periphery shock. By contrast, when the shock occurs in the core region, coordination involves a more aggressive response by both regulators. Intuitively, under coordination regulators internalize the effects of credit fluctuations (occurring through spillovers to the periphery and spillbacks to the core) in both regions by pursuing a more aggressive policy and this generates a superior outcome for the world as a whole. Thus, coordination does not involve burden sharing, a situation where the region where the shock occurs (say, the core) reacts less, whereas the other (say, the periphery) reacts more. Nevertheless, there is still a net benefit for the world economy. When the shock occurs simultaneously in both regions, coordination entails naturally a reaction by both regulators—in both cases by more than under the Nash equilibrium.

Third, the more aggressive the response under coordination by the region where the shock originates means also that the cost of instrument manipulation is higher—so much so that, in fact, compensating variations that account for the cost of instrument manipulation are actually negative for the core for both asymmetric and joint shocks. This loss with respect to the Nash equilibrium means that the gains from coordina­tion are highly asymmetric, particularly so when the shock occurs in the core region. Put differently, policy coordination is not Pareto improving—at least with respect to the type of financial shocks considered here. To the extent that credit spread shocks are representative of those that tend to occur in practice, our results highlight a po­tential challenge in terms of generating incentives for countries to engage in a formal arrangement to cooperate in setting their macroprudential policy instruments.

Fourth, the results indicate that the gains from coordination depend on whether the cost of instrument manipulation is accounted for or not when evaluating welfare. For instance, with a core shock only, the compensating variation is 0.2 percent in the first scenario (the standard case where welfare is based solely on the discounted present value of the household utility) and 4.4 percent in the second. This difference is quite large, despite the fact that kw , at 0.01, is fairly small. In addition, when the instrument adjustment cost is accounted for, the gain is not large. Again, in the case of a core shock only, ahouseholdwithanannual consumption stream of $50,000 would need to receive compensation of about $100 to be indifferent between cooperation and noncooperation. This gain is even lower when the shock originates in the periphery. Prima facie, these relatively small gains create concerns regarding the ability to provide incentives for countries to join and remain voluntarily in a cooperative agreement. At the same time, however, it is important to keep in mind that in the real world, there could be a variety of financial shocks occurring simultaneously; the gain from coordination could be larger as a result. This is indeed the case when the shock occurs simultaneously in the two regions.

Finally, the results displayed in Table 4 show that while the reduction in volatility is quite large between the last two regimes and the first (no countercyclical regula­tion) when the shock occurs in the core region, this reduction is much smaller for the periphery shock and for both regions. In fact, for a number of variables there are no discernible differences between outcomes under noncooperation and coordination. These results are consistent with those reported in Table 3, and discussed earlier, re­garding the small welfare gain associated with coordination in response to a financial shock occurring in the periphery.

        Sensitivity Analysis

To assess the robustness of the previous analysis, we perform sensitivity analysis with respect to four features of the model: the degree of international financial integration (as measured by the size of intermediation costs on world capital markets), the cost of instrument manipulation, the relative weight of each region in evaluating global welfare, and the case where the housing market is perfectly integrated across regions. In all of these cases we focus on the welfare gain from coordination (as measured by adjusted compensating variations), rather than the transmission mechanism.

1.1 Financial Integration

First, consider the case where the cost parameter associated with financial intermedi­ation on world capital markets, , falls from its benchmark value of 0.8 to 0.6. As a result of greater financial integration, changes in interest rates become more closely correlated across jurisdictions. This implies that shocks in one region are transmitted to a greater extent to the rest of the world, implying therefore larger spillovers and potentially larger gains from international coordination, given that this regime allows regulators, acting together, to internalize cross-border effects.

The results are displayed in the lower part of Table 3. They show that when the financial shock originates in the core region, both regulators react (when they do at all) slightly less aggressively, both under Nash and under coordination. The same occurs for the regulator in the periphery, when the shock occurs in that region, again both under Nash and under coordination. But while the welfare gain (including the instrument adjustment cost) is smaller for the core region in the first case, the policy loss is smaller for the periphery in both cases. Welfare for the world economy falls in the case of a core shock and increases in the case of a periphery shock. Thus, with greater financial integration, coordination is more beneficial to the periphery and the world as a whole when financial shocks originate in that region. This larger gain for the world economy is consistent with the recent evidence, reviewed by Agenor and Pereira da Silva (2018), which suggests that greater financial interconnectedness in the world economy has increased the potential benefits of macroprudential policy coordination— although these benefits, once again, appear to be asymmetric across regions.

 1.2 Instrument Cost and Welfare Weights

As notedearlier, the gainsfrom coordinationdependonwhether thecost of instrument manipulation, as measured by kw, is accounted for or not when evaluating welfare. The results shown in Table 3 are based on a very low value of kw ; the upper part of Table 5 displays those obtained with a higher value of kw = 0.05.

The first point to note is that, with a higher cost, the optimal values for the response parameters xi are lower, under both under Nash and coordination. This negative correlation, which is also verified for higher values of kw , is simply the consequence of policymakers internalizing the effect of their policy choices on their objectives. As a result, the stabilization effect is now weaker; this is clearly illustrated by the dashed (blue) lines in Figures 2 and 3, which show again the impulse response functions under coordination.

The second point is that when compensating variations do not account for the instrument adjustment cost, the core benefits less from coordination when the shock occurs there (either individually or jointly) and benefits slightly more when it occurs in the periphery. At the same time, for the world economy, the gain is uniformly lower under coordination, regardless of where the shock occurs and whether the occur simul­taneously or not. The third point is that when compensating variations account for the cost of instrument manipulation, the core region benefits a bit more from coordina­tion when the shock occurs in the periphery alone or in both regions, but the gain for the world economy is weaker. Overall, a higher cost of instrument manipulation does have an adverse effect on the magnitude of the welfare gain associated with interna­tional macroprudential policy coordination—inclusive or not of instrument adjustment costs—both at the level of the individual parties and the world economy as a whole.

Alternatively, keeping kw at 0.01, consider the case where instead of equal weights in the global welfare function, based on political considerations (one country, one vote), weights are based on economic strength. Specifically, suppose that n is calculated on the basis of the total GDP of the two regions. World Bank data indicate that SMICs accounted for a share of 18.2 percent over the period 2010-17, up from 12.8 percent during 2000-09. Thus, we set the size of the core region to n = 1 — 0.812 = 0.818. The results associated with the same experiments as before are shown in the lower part of Table 5. With respect to the optimal response parameters, the most noticeable result relates to the response of the regulator in the periphery under coordination, when the shock occurs in the core region; this response is now much higher. For the core region, the gain (based on the compensating variation inclusive of the instrument adjustment cost) is now significantly higher regardless of the origin of the shock. For the periphery, the reverse holds. Nevertheless, given the higher weight of the core now, the gain for the world economy increases in all cases. For instance, if the shocks occur in both regions at the same time, a household with an annual consumption stream of $50,000 would need now to receive compensation of about $470 to be indifferent between cooperation and noncooperation. Yet, because the periphery is now worse off, the enforcement problems highlighted earlier are magnified.

 1.3 Globally Integrated Housing Market

Finally, we consider the case where the housing market is globally integrated. In this setting, housing services can now be traded across regions, even though dwellings themselves are immovable assets. This is consistent with growing evidence that house price fluctuations have become highly synchronized across countries, as documented by Hirata et al. (2013), Cesa-Bianchi (2013), Jorda et al. (2018), and most importantly in a comprehensive study by the International Monetary Fund (2018, Chapter 3), which considers a large sample of high- and middle-income economies.

A simple way to account for a globally integrated housing market in our model consists of treating households as global property owners and replacing the region- specific housing market equilibrium conditions, equation (41) for the core region and the equivalent for the periphery, by the single equilibrium condition:

Image 7bz8

where 6H E (0,1) is the share of the global housing stock held in the core region, together with the equilibrium price condition:

Image 62t6

where for simplicity we abstract from region-specific real estate transactions costs and other regulations, such as restrictions on land use or foreign buyers, limits on loan-to-
value ratios, and so on.

A globally integrated housing market may transmit and amplify shocks by increas­ing the exposure of local markets to global financial conditions. In our model, more specifically, it implies that house price changes in one region are now transmitted di­rectly through collateral effects to the other region. The question is whether, in a setting where regulators operate on the basis of a simple domestic credit-output policy rule to maximize welfare, this additional channel creates room for coordinated policy responses to be Pareto-improving.

Consider for instance, as before, a negative credit spread shock in the core region. As discussed earlier, this translates into a fall in house prices in that region, due to a reduction in the demand for housing services there. This also lowers the value of collateral that core firms can pledge to the global bank, which in turns tends to increase the loan rate (or, more precisely, mitigate its initial fall), thereby dampening the expansion in investment and output.

With an integrated housing market, and because the depreciation of the real ex­change rate documented earlier is not large, house prices in the periphery fall as well, instead of increasing as before. Thus, the model now generates co-movement in house prices across countries, in line with the evidence on price synchronicity reported earlier. As a result of that drop, the loan rate in the periphery rises further, investment falls by more on impact, and so does output. This implies also that the policy and bond rates increase by less than in the case of separate housing markets, thereby dampen­ing capital outflows. Put differently, given the shock that we consider, an integrated housing market does generate stronger spillover effects from the core to the periphery, although not necessarily stronger spillbacks from the periphery to the core. Neverthe­less, to the extent that these fluctuations lead to higher volatility in consumption and employment, thereby reducing welfare, the regulator in the periphery has an incentive to intervene to stabilize lending. At the same time, however, under non-cooperation, the regulator in each region sets the tax on loans solely on the basis of the behavior of the credit-to-output ratio in its own jurisdiction; the regulator in the region where the shock occurs (the core) does not internalize the fact that it amplifies fluctuations in the periphery. Thus, a globally integrated housing market may generate a cross-border pecuniary externality, which can be internalized under coordination.

Nevertheless, numerical results show that this additional channel is relatively weak in our model: although housing prices in the periphery do fall now instead of increasing, the repayment probability falls by more, and the lending rate rises by more, than in the benchmark case of segmented housing markets, Figure 7 shows that the impact on investment is muted. This is largely due to the fact that the arbitrage condition with respect to the rate of return on capital (see Appendix A, equation (A19)) involves the expected loan rate. In turn, as can be inferred from (17) and 32), the expected loan rate depends only on changes in monetary and regulatory policy instruments. As a result, an assessment of the gains from coordination leads to results that are not discernibly different from those reported in the upper part of Table 3. However, it is very possible that, in a more general model with housing collateral and a globally integrated housing market, the cross-border pecuniary externality discussed earlier could be the source of significant gains from international macroprudential policy coordination. In our view, this is an important issue for future research.

      Concluding Remarks

The purpose of this paper was to study the extent to which international coordination of macroprudential policy (in the form of a countercyclical tax on bank loans) can generate welfare gains, in a two-region, core-periphery model with a global bank, im­perfect financial integration, and financial frictions occurring at both the national levels (between firms and banks in each region) and international level (between periphery banks and the global bank in the core region). Our key results were summarized in the introduction.

Our contribution can be extended in a number of directions. First, a key issue that our analysis raised relates to the need to identify what type of incentives can ensure that countries do not renege on a commitment to coordinate their macroprudential policies. Such incentives relate to side payment mechanisms and the perceived ex post cost of reneging on a cooperative agreement. Second, our analysis was limited to a narrow (albeit representative) set of financial shocks and a particular type of finan­cial frictions. In the real world, of course, there are a number of alternative sources of shocks and financial frictions; it is possible that accounting for a combination of financial frictions could make the gains from coordination significantly larger. Third, as is well known from game theory, the choice of policy instruments can matter signif­icantly in a non-cooperative game. Our focus has been on a tax on bank loans as a generic macroprudential instrument, which captures the typical cost effect associated with price-based macroprudential tools (such as capital requirements). However, there is a range of other, quantity-based tools (such as loan-to-value or debt-to-income ra­tios), whose effects operate through different channels; it is possible that the welfare effects of these instruments may differ substantially under non-cooperation. Fourth, the coordination issue could be cast in the context of leadership games, which would involve one regulator leading the decision-making process. Given that these games involve within-period timing, they are difficult to model fully in existing models, al­though leadership can be thought of as within-period commitment by one player, which clearly makes the leader better off (de Paoli and Paustian (2017)). However, it is in general not the case that a leadership setup improves welfare compared to the case where both players move simultaneously. Similarly, rather than one-shot games, one could focus on modeling repeated games between regulators. From the experimental literature reviewed by Dal Bo and Frechette (2018), one can surmise that as long as these games are sufficiently robust to strategic uncertainty—that is, uncertainty re­garding the behavior of regulators in an interactive setting—reputational gains can be large enough to make macroprudential policy coordination a preferable strategy.

Finally, there is now significant evidence that macroprudential policies are subject to leakages across countries and can generate significant credit spillover effects of their own, as a result of global banks shifting targeted activities across countries in response to changes in prudential regulation where they are based, essentially outside the scope of the instrument’s application and enforcement. These spillover effects can operate not only through direct lending to foreign-country borrowers (firms or households) but also through lending locally to foreign branches, as well as through a “rebooking” of loans—whereby credit is originated by subsidiaries, but then booked on the balance sheet of the parent institution. If increased lending induced by cross-border regula­tory arbitrage by foreign banks contributes to a credit boom or asset price pressures in the recipient economies, depending on the stage of their financial cycles a counterbal­ancing macroprudential response by regulators there may also be called for to mitigate systemic financial risks. If delays in policy responses can magnify these risks, or if manipulating policy instruments is costly, ex ante coordination may improve global welfare. The model presented in this paper could be extended to account for these ef­fects, possibly by considering economies of scope between domestic and foreign lending by global banks.

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