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Macroprudential Policy in a Monetary Union.

Introduction

The experience of the euro area over the last decade has shown that a single monetary policy does not necessarily promote convergence of economies belonging to a monetary union. For example, since 1999, the gap between the ECB's interest rate and the interest rate that would have resulted from the application of a Taylor rule in the core and peripheral countries was very large. (1) In fact, monetary policy was relatively loose in the periphery (see the left-hand panel of Fig. 1), mainly between 2002 and 2007, which could have contributed to the building up of financial and economic imbalances (Altunbas et al. 2014). (2)

This calls for the use of macroprudential (henceforth MaP) policy as a complementary instrument to monetary policy. The global financial crisis has made it clear that financial stability has a macroprudential or systemic dimension that cannot be ignored. Treating the financial system as merely the sum of its parts leads one to overlook the system's tendency to swing from boom to bust.

There is indeed a growing literature that claims that monetary policy should factor in financial stability considerations. Monetary policy should "lean against the wind" (LATW, Borio and Lowe 2002; Gambacorta and Signoretti 2014) to prevent financial imbalance, rather than merely "clean up afterwards" (Bernanke and Gertler 1999). Blinder (2010) notes the emergence of a new consensus on the responsibility of central banks to combat asset price bubbles, by using targeted regulatory tools, rather than interest rate, which is considered as a blunt tool (Svensson 2016). In the meantime, many economists think that the central bank's interest rate could play a major role to ensure financial stability, (3), in order to avoid leakages overseas and notably to shadow banking. In addition, LATW is also a way to take into consideration the banks' risk-taking channel (Adrian and Shin 2009; Borio and Zhu 2012) especially when many asset types show signs of overpricing. However, MaP policy can revisit this debate in the case of a monetary union where financial shocks could be asymmetric and a (common) LATW policy could be not successful.

From the standpoint of the "optimum currency area" theory developed by Mundell (1962), MaP policy may be interpreted as a complementary adjustment tool that enhances the degree of optimality of a monetary union, specifically when economic cycles are out of sync. This is particularly the case of the Eurozone which suffers from low mobility of production factors, the absence of fiscal transfers between countries (Kenen 1969), and heterogeneous real-estate cycles (Krugman 2012). Additionally, business and financial cycles are divergent among European countries (Stremmel 2015). Figure 1 (right-hand panel) illustrates that the core and the periphery have divergent financial conditions, that have been amplified since 2010. It also shows also that the credit spread between the lending rate and the ECB interest rate has been increasing since 2010, particularly in the periphery.

Within the European Union, the European Systemic Risk Board (ESRB) is responsible for the MaP oversight of the financial system primarily by issuing warnings and recommendations. (4) The Single Supervisory Mechanism (SSM) designates the ECB as an important player of the MaP framework for the countries that participate in the banking union, mostly those of the Eurozone. According to Article 5(2) of the SSM Regulation (ESRB 2014), (5) the ECB has the power to set tighter (not looser) regulatory requirements (6) than national authorities. The asymmetric nature of the ECB's powers reflects the potential inaction bias of national authorities. In fact, the costs of applying MaP tools are felt immediately (constraints on demand), while benefits are long-term (reduction in the probability, frequency and severity of financial crisis). Nevertheless, other MaP measures, mainly related to housing stock, such as loan to value (LTV) ratios and debt to income (DTI) ratios, remain under national competence and are not coordinated at the Union level.

The complex decision-making process (7) in the European Union (the ECB, national authorities, and the ESRB) calls for adequate coordination, information sharing, and communication.

Our contribution to the literature is threefold. First, our paper analyses how macroprudential policy could enhance the degree of optimality of a monetary union. Second, it identifies some key general principles for the conduct of a policy mix that combines a single monetary policy and a MaP policy. Third, despite its simplicity, the model can analyse simultaneously the effects of some financial frictions: countercyclical credit spreads, financial shock and imperfect transmission of monetary policy to financial conditions (pass-through).

Our study emphasises that a better policy mix promotes not only financial but also macroeconomic stability, particularly when core and periphery economies are hit by asymmetric shocks. A single monetary policy conducted at the Union level reacts only to average conditions, which mask differences in member countries (Constancio 2015b). For example, the unintended accommodative (restrictive) effect of monetary policy for countries that record higher (lower) inflation may be counteracted by country-adjusted restrictive (loose) MaP measures, such as an increased (reduced) countercyclical capital buffers or lower (higher) LTV/DTI caps.

Our analysis also shows that unless economies and shocks are completely symmetric, a national implementation of MaP policy, adapted to the situation of each member state, is more appropriate than a federal implementation that reacts to the average situation.

The reminder of the paper is organised as follows: The "Literature Reviews" section presents literature, "A Simple New Keynesian Model with Credit Intermediation" section presents the model, "Monetary and Macroprudential Policy Mix" section discusses optimal policy mix under different scenarios and the last section concludes.

Literature Review

Several papers have demonstrated the potential stabilising role of MaP policy. Some MaP tools may complement and in some cases even replace monetary policy (Cecchetti and Kohler 2014), as they transit through similar channels (Beau et al. 2011). For example, N'Diaye (2009) stresses that increased regulatory capital requirements during economic upswings can act as a brake on the financial accelerator mechanism. As a result, MaP policy may contribute to economic stability and facilitate the task of the monetary authority. In the case of the Eurozone, many papers, using DSGE modelling framework, highlight the ability of MaP policy to moderate regional imbalances. For example, Angelini et al. (2012) stress that MaP policy may improve macroeconomic stability when economic fluctuations are caused by housing markets or financial shocks, especially when the central bank and the MaP authority cooperate closely. Brzoza-Brzezina et al. (2015) and Rubio (2014) show that countercyclical MaP tools can help deploying a more uniform monetary policy in the Eurozone, whereas Quint and Rabanal (2014) emphasise that the introduction of a national MaP policy reduces macroeconomic volatility and palliates partially the absence of autonomous monetary policies.

On the empirical side, since systemic risk has both structural and cyclical dimensions and appears in several guises (excessive credit and leverage, illiquidity and balance sheet mismatches, interconnectedness and moral hazard), ESRB (2014) suggests that using a toolkit may be more effective than using a single instrument. However, the effectiveness of MaP policy is still an open issue, especially when more than one tool is activated. MaP policy effectiveness should be analysed with respect to the specific goal that they are aimed to achieve, which is increasing the resilience of the financial system or, more ambitiously, taming financial booms and busts. Currently the evidence is mixed, with most of the work analyses the impact of macroprudential tools on bank lending rather than on the ultimate goal of containing systemic risk. For instance, recent evidence suggests that DTI and, probably to a lesser extent, LTV caps seem to be comparatively more effective than capital requirements as a tool for containing credit growth (Claessens et al. 2013; Kuttner and Shim 2016). Indeed, the recent activation of the Basel III countercyclical capital buffer (to risk-weighted domestic residential mortgages) in Switzerland, while having some effects on mortgage pricing, seems to have had little impact on credit extension (Basten and Koch 2015). As clarified by the Basel HI framework, the main objective of the Basel III countercyclical capital buffer is to increase the resilience of the banking system. Tuning the cycle is rather a difficult task to achieve (Drehmann and Gambacorta 2012). Some instruments may work better to achieve the narrow aim of increasing financial system resilience rather than the broader aim of constraining the cycle.

A Simple New Keynesian Model with Credit Intermediation

We use a reduced-form New Keynesian model, (8) augmented by an additional equation that captures financial frictions (credit spreads, financial shock and imperfect transmission of monetary policy to lending rates). The model is written as log-linear deviations from the steady state.

We use this framework to analyse the potential benefits of MaP policy in a monetary union by means of comparative statics. The model consists of four building blocks representing the three "New Keynesian" equations, in addition to a financial friction equation (FF) that introduce the credit market. The first three equations are an IS aggregate demand curve, a Phillips supply curve (PC), and a monetary policy "Taylor rule" (TR) representing the central bank's policy interest rate (Table 1 reports the list of symbols):

IS: y = [beta]([i.sub.c] - i) + [[epsilon].sub.d] (1)

PC: [pi] = [[pi].sup.e] + [[lambda].sub.y]y + [[epsilon].sub.s] (2)

TR: [i.sub.n] = i + [[alpha].sub.y]y + [[alpha].sub.[pi]]([pi] - [pi]*) (3)

The first equation is a simplified IS demand curve where economic agents borrow from banks to consume or invest. It links output gap y, defined as the percentage deviation of aggregate output from its potential level, to the difference between the real credit rate ([i.sub.c] - [Z.sup.e]) and real natural rate (i - [[pi].sup.e]) (9) The output gap y is also affected by a demand shock [[epsilon].sub.d], which represents an exogenous shift in demand that arise from changes in consumption and/or investment.

The second equation represents the Phillips supply curve (PC) linking inflation rate to its expected future value, the output gap and a supply shock [[epsilon].sub.s] which represents an unexpected change to production. The third equation is the Taylor rule, which describes how the central bank sets the policy rate by taking into account the nominal natural rate, and responding to inflation and output gaps.

The last equation introduces financial frictions (FF) and determines the lending rate which reacts to the policy rate, output gap, financial shocks and to MaP policy:

FF: [i.sub.c] = [[gamma].sub.in] - [[gamma].sub.y]y + [[gamma].sub.MaP]MaP + [[epsilon].sub.f] (4)

As in the IS-LM-CC model developed by Bernanke and Blinder (1988), we distinguish between two interest rates: [i.sub.n] the policy interest rate and [i.sub.c] the credit rate. The novelty with respect to the usual modelling is that: (a) it is the credit rate that enters the IS equation rather than the policy rate; and (b) the credit rate is determined by a fourth equation that equalises the demand and supply of credit. The credit rate represents the cost of borrowing (financial conditions) and includes the credit spread or risk premium beyond the policy rate. (10) It is the differential between the real credit rate and the real natural rate (Wickselian rate that equalises saving and investment and keeps the economy on a stable path) that matters for the output gap. Financial conditions are looser if ([i.sub.c] < i) and restrictive if ([i.sub.c] > i). The FF equation captures many financial frictions: countercyclical credit spreads (11) ([[gamma].sub.y]), transmission of monetary policy to lending rates (12) ([[gamma].sub.n]) and financial shocks ([[epsilon].sub.f]) such as a decrease in the value of collateral or in lender's capital.

Following Minsky's financial instability hypothesis (1975) where credit risk is usually underestimated (overestimated) during boom (bust) periods, we hypothesise that the credit rate and-by extension-the credit spread ([i.sub.c] - [i.sub.n]) are countercyclical (negative relation between [i.sub.c] and y). This is also what we observe from the literature on the risk-taking channel (Gambacorta 2009). For example, as output increases, the value of collateral is likely to rise and the expected probability of default to decrease, which leads banks to supply more credit and vice versa. This mechanism is similar to the "external finance premium" concept developed by Bernanke and Gertler (1999), in which asymmetric information represents a financial friction that amplifies financial and economic cycles (financial accelerator mechanism).

It is worth noting that in the absence of financial frictions (if [[gamma].sub.n] = 1, [[gamma].sub.y] = 0 and [[epsilon].sub.f] = 0), we obtain a conventional "three equation" New Keynesian model where IS: y = -[beta]([i.sub.n] - i) + [[epsilon].sub.d] (see Mankiw (2016)).

We derive the FF equation by equalising the supply and demand of credit, for which we try to introduce some micro-foundations (Cecchetti and Li 2008). Loan supply depends positively on equity K = [v.sub.y]y (which is linked to the output gap through retaining earnings) and deposits D. (13) Deposits D = [n.sub.y]y - [[eta].sub.n][i.sub.n] are positively correlated with the output gap (increase in savings via the income effect) and negatively correlated with the policy rate (14) (opportunity cost for investing in remunerated securities;Bernanke and Blinder 1988). Loan supply also depends positively on the mark up, which is the difference between the lending rate and the cost of funding, or the opportunity cost of investing in risk-free assets ([i.sub.c] - [i.sub.n]). (15) Lastly, macroprudential policy denoted MaP is aimed to tighten (ease) the supply of credit during an upswing (downswing) through banks' balance sheets (CGFS 2012). MaP policy could operate on loan supply using different tools such as countercyclical capital requirements, leverage restrictions, general or dynamic provisioning, the establishment of liquidity requirements. (16) Here, for simplicity, we consider only one tool but we could interpret it also as a weighted average of tools that impact on loans' supply.

The credit supply is represented by the following equation:

[L.sup.s] = K + D + [[omega].sub.sc] ([i.sub.c] - [i.sub.n]) - [[omega].sub.Map]MaP (5)

We replace K and D by their respective equations and simplify as follows:

[L.sup.s] = [V.sub.y]y + [[eta].sub.y]y - ([[eta].sub.n] + [[omega].sub.cs])[i.sub.n] + [[omega].sub.cs][i.sub.c] - [[omega].sub.Map]MaP

The demand for loans reacts positively to the output gap as agents have a greater willingness to borrow if the expected future income is higher (an increase in the project's probability of success) but reacts negatively to the real credit rate (the cost of borrowing):

[L.sup.d] = [[mu].sub.y]y - [[mu].sub.c]([i.sub.c] - [[pi].sup.e]) (6)

In order to simplify the model, we follow Cecchetti and Kohler (2014) by assuming that monetary policy is credible ([[pi].sup.e] = [[pi].sup.*]) and that agents have rational expectations, so expected inflation can be normalised to zero ([[pi].sup.e] = [pi]* = 0) (17). By imposing a clearing condition for the loan market ([L.sup.s] = [L.sup.d]) we can obtain the lending rate or cost of borrowing ic:

FF' : [i.sub.c] = [[gamma].sub.n][i.sub.n] - [[gamma].sub.y]y + [[gamma].sub.Map]MaP,

where [[gamma].sub.n] = [[eta].sub.n] + [[omega].sub.cs]/[[mu].sub.c] + [[omega].sub.cs], [[gamma].sub.y] = ([v.sub.y] + [[eta].sub.y]) - [[mu].sub.y]/[[mu].sub.c] + [[omega].sub.cs] and [[gamma].sub.MaP] = [[gamma].sub.MaP]/[[mu].sub.c] + [[omega].sub.cs],

Equation FF is slightly different from FF' since we introduce an exogenous financial shock (18) [[epsilon].sub.f] to the credit rate [i.sub.c].

Figure 2 describes how credit market clears. [L.sup.s] and [L.sup.d] curves indicate, respectively, the supply and demand of credit. Credit institutions do not accept any interest rate that is below the policy rate, that is their refinancing cost. For example, during a period characterised by an excessive credit supply, a restrictive macroprudential policy [MaP.sup.+] shifts the [L.sup.s] line to the left, which means a reduction in the supply of credit. This raises the equilibrium cost of borrowing, which could moderate imbalances.

We assume that the lending rate is countercyclical and that [[gamma].sub.y] = ([v.sub.y] + [[eta].sub.y]) - [[mu].sub.y]/[[mu].sub.c] + [[omega].sub.cs] > 0. The main hypothesis here is that credit demand's elasticity to output [[mu].sub.y] (19) is lower to the sum of elasticities of equity and deposits (credit supply) to output ([v.sub.y] + [[eta].sub.y]). This hypothesis simplifies the analysis, but it is not essential. We will show below that MaP policy is still useful even if theoretically credit spread is procyclical since it compensates any reaction of lending rate to output.

In what follows, our model will help us explaining how a monetary union could benefit from a country-specific MaP policy in the case of asymmetric shocks (e.g. [[epsilon].sub.f]), imperfect pass-through and countercyclical credit spreads that cannot be fully neutralised using a single monetary policy or a federal MaP that reacts to average conditions. Figures 2 and 3 illustrate how MaP policy influences output through its effect on financial conditions. Following a tightening of MaP measures (shift of the credit rate to [i.sub.c]([MaP.sup.+])), output declines because agents reduce consumption and investment.

Monetary and Macroprudential Policy Mix

In this section, we analyse the optimal policy mix in a monetary union composed of two countries (core and periphery, with subscript c for the former and p for the later) in the presence of asymmetric and symmetric shocks. We first consider a single monetary policy set by the ECB and then interest rates that are decided by the national central banks (henceforth NCBs) and account for different situations of the core and the periphery separately. In particular, we consider the cases where authorities: (a) do not react to financial instability; (b) react only with the interest rate or (c) react with interest rate and federal or country-targeted MaP policy. It is worth stressing that in our simplified framework the "separation principle" holds: macroprudential policy is fully effective and always able to perfectly insulate the real macroeconomy. Besides, both policies are conducted independently, abstracting from potential conflicts (see Paoli and Paustian (2017) on the coordination of monetary and macroprudential policies).

The nominal rate is set by a central bank (ECB) that minimises a quadratic loss function (LF) for the monetary union, without taking into consideration financial stability:

[LF.sup.ECB] = 1/2 [y.sup.2] + [theta]/2 [[pi].sup.2] (7)

where [theta] denotes the central bank's relative weight on inflation stabilisation. Without loss of generality, but to simplify the algebra, we assume that the central bank weights both objectives equally ([theta] = 1). For simplicity, we also assume, in a first step, that the transmission of monetary policy to the credit market is complete ([[gamma].sub.n] = 1). (20) Since the ECB reacts to the average variables of the core and the periphery, we rewrite our model as follows:

[mathematical expression not reproducible]

MaP policy could be implemented at a federal or national level. We focus in what follows mainly on the policy mix in the presence of a financial shock. However, demand shocks have also an (indirect) effect on the credit rate and hence on the credit spread through the output gap.

Asymmetric Shock

In the first policy experiment, we assume that the periphery and the core are hit by a fully asymmetric financial shock (respectively [[epsilon].sup.p.sub.f] = -[[epsilon].sup.c.sub.f]), where the periphery for example suffers a positive financial shock (financial stress), while the core experiences a negative one (favourable financial conditions).

Comparison of the ECB's Interest Rate with Theoretical National Interest Rates

The ECB ignores financial shocks since they are fully asymmetric ([[epsilon].sup.c.sub.f] + [[epsilon].sup.p.sub.f])/2 = 0. The interest rate is therefore fixed by minimising Lagrange subject to the Phillips curve (PC): L = 1/2 [y.sup.2] + 1/2 [[pi].sup.2] + [chi]([[gamma].sub.y]y + [[epsilon].sub.s] - [pi]). After solving for the optimal interest rate (see the annex for details), the expression for [i.sub.n] is:

[i.sup.ECB*.sub.n] = i [[lambda].sub.y]([beta][[gamma].sub.y] - 1)/[beta](1 + [[lambda].sup.2.sub.y]) [[epsilon].sub.s] + 1/[beta] [[epsilon].sub.d]

The policy rate reacts to the natural rate, but also to shocks (supply and demand). To verify whether the ECB's interest rate corresponds to both economies, we compare it with theoretical rates that are consistent with each region need separately.

When calculated in a similar manner, the theoretical NCBs' rates are:

[mathematical expression not reproducible]

NCBs counterfactual policy rates are different from the ECB rate because they consider the financial shock. In fact, the ECB's monetary stance is simultaneously tighter for the periphery [mathematical expression not reproducible] and looser for the core [mathematical expression not reproducible]. MaP policy would improve economic conditions of the monetary union by compensating for different monetary stances and by insuring homogeneous financial conditions.

Policy Mix with a Single Monetary Policy and Macroprudential Policy

Following Cecchetti and Kohler (2014), we introduce a credit spread in the loss function.

Country-Targeted Macroprudential Policy

The loss functions of national MaP authorities are:

[LF.sup.c.sub.MaP] 1/2[([i.sup.c.sub.c] - [i.sup.ECB*.sub.n]).sup.2] and [LF.sup.p.sub.MaP] = 1/2 [([i.sup.p.sub.c] - [i.sup.ECB*.sub.n]).sup.2]

In each country, the MaP authority minimises any deviation of the credit spread from its optimal level [i.sup.c,p.sub.c] - [i.sup.ECB*.sub.n] = 0 using the financial frictions equation, taking the policy rate as given.

F[F'.sub.NCB] : [i.sup.c.sub.c] - [i.sup.ECB*.sub.n] = [[gamma].sub.y][y.sup.c] + [[gamma].sub.Map][MaP.sup.c] - [[epsilon].sub.f] and [i.sup.p.sub.c] - [i.sup.ECBB*.sub.n] = -[[gamma].sub.y][y.sup.p] + [[gamma].sub.MaP][MaP.sup.p] + [[epsilon].sub.f]

In each country, the MaP policy rule contains the financial shock and reacts to the countercyclical impact of the output gap on the credit spread. This helps to minimise the MaP authority's loss function and ensure economic convergence between the core and the periphery.

The value of MaP that minimises the loss function (FOC: [i.sup.c,p.sub.c] - [i.sup.ECB*.sub.n] = 0) is:

[MaP.sup.c*] = [[gamma].sub.y]/[[gamma].sub.MaP] [y.sub.c] + 1/[[gamma].sub.MaP] [[epsilon].sub.f] and [MaP.sup.p*] = [[gamma].sub.y]/[[gamma].sub.MaP] [y.sup.p] - 1/[[gamma].sub.MaP] [[epsilon].sub.f]

In order to avoid imbalances, MaP policy is respectively tighter in the core and looser in the periphery. We may notice that MaP reacts not only to the financial shock but also to the demand shock through the output gap. By plugging [MaP.sup.c*] and [MaP.sup.f*] in the FF equations we obtain: [FF.sub.NCB]: [i.sup.c.sub.c] = [i.sup.p.sub.c] = [i.sup.ECB*.sub.n]. Thanks to country-targeted MaP policy, we reach the same output gap as in the absence of financial frictions:

[y.sup.c] = -[beta]([i.sup.c.sub.c] - i) + [[epsilon].sub.d] and [y.sup.p] = -[beta]([i.sup.p.sub.c] - i) + [[epsilon].sub.d]

[y.sup.c] = -[beta]([i.sup.ECB*.sub.c] - i) + [[epsilon].sub.d] and [y.sup.p] = -[beta]([i.sup.ECB.sub.n] - i) + [[epsilon].sub.d]

Federal Macroprudential Policy

The value of MaP that minimises the loss function ([LF.sup.F.sub.MaP] = 1/2 [([i.sup.c.sub.c] + [i.sup.p.sub.c]/2 [i.sup.ECB*.sub.n]).sup.2] = 1/2 [(-[[gamma].sub.y] ([y.sup.c] + [y.sup.p]/2) [[gamma].sub.MaP]MaP).sup.2]) is:

[MaP.sup.F*] = [[gamma].sub.y]/[[gamma].sub.MaP] [y.sup.c] + [y.sup.p]/2

We note that an implementation of MaP policy at a federal level ([LF.sup.F.sub.MaP] = 1/2 [([i.sup.c.sub.c] + [i.sup.p.sub.c]/2 - [i.sup.ECB*.sub.n]).sup.2] = 1/2[(-[[gamma].sub.y] ([y.sup.c] + [y.sup.p])/2 [[gamma].sub.MaP]MaP).sup.2]) ignores the financial shock. In this case, economic imbalances emerge since output gaps of core and periphery deviate in opposite direction:

[y.sup.c] = -[beta]([i.sup.ECB*.sub.n] - [[epsilon].sub.f] - i) + [[epsilon].sub.d] and [y.sup.p] = -[beta]([i.sup.ECB*.sub.n] + [[epsilon].sub.f] - i) + [[epsilon].sub.d]

In order to avoid the building up of imbalances in the euro area, the MaP authority (i.e. the ECB with/or national MaP authorities (21)) should fine-tune with country-targeted MaP policy to compensate the tight or loose stance of the single monetary policy.

Symmetric Shock

In the previous section, we have analysed the extreme case in which countries are hit by a full asymmetric shock. What does it happen in the more general case where the two countries are hit by the same shock? To this end, we assume that core and periphery are hit by a fully symmetric financial shock [[epsilon].sub.f]. The only change from the previous section is the presence of the financial shock in the ECB's financial friction's equation FF':

FF': [i.sub.c] = [i.sup.c.sub.c] + [i.sup.p.sub.c]/2 = [i.sub.n] - [[gamma].sub.y] ([[gamma].sup.c] + [y.sup.p])/2 + [[epsilon].sub.f]

After solving for the optimal interest rate (see the annex for details), the resulting expression is: [i.sup.ECB*.sub.c] = i - [[lambda].sub.y]([beta][[gamma].sub.y] + 1)/[beta](1 + [[lambda].sup.2.sub.y]) [[epsilon].sub.s] + 1/[beta] [[epsilon].sub.d] - [[epsilon].sub.f], which is different from the previous ECB's rate in the presence of an asymmetric shock since it takes into account [[epsilon].sub.f].

In this case, the financial shock can be neutralised through: (a) the single interest rate, (b) MaP policy, or even (c) a combination of monetary and MaP policies. (22) However, the impact of such policies on the economy is not similar in practice. For example, a monetary authority that reacts only to a financial shock has to modify its nominal interest rate aggressively, which may have destabilising effects on inflation and output (23) (Svensson 2016).

In this setup, the MaP policy for the core, the periphery and the Union are:

[MaP.sup.c*] = [[gamma].sub.y]/[[gamma].sub.MaP] [y.sup.c] + 1/[[gamma].sub.MaP] [[epsilon].sub.f] and [gamma].sub.y]/[[gamma].sub.MaP] [y.sup.p] + 1/[[gamma].sub.MaP] [[epsilon].sub.f]

[MaP.sup.F*] = [[gamma].sub.y]/[[gamma].sub.MaP] [y.sup.c] + [y.sup.p]/2 + 1/[[gamma].sub.MaP] [[epsilon].sub.f]

We can notice that federal and country-targeted MaP policies give similar outcomes only when both countries and shocks are fully similar. Otherwise, country-targeted MaP policies are more appropriate since a federal policy reacts to averages.

Heterogeneous Transmission of Monetary Policy to Financial Conditions

In this section, we analyse whether the federal implementation of MaP could be appropriate when the transmission of monetary policy to financial conditions is not the same in the two countries. To do that, we modify the financial friction equation (FF) by introducing heterogeneous transmission of monetary policy (Gambacorta 2003). This distinction in the pass-through (denoted [[gamma].sub.n]) could be justified for example by different bank lending conditions such as differences in prevalent mortgage contracts, for example fixed vs variable interest rates. (24) The monetary transmission is more direct when the lending rate applied to mortgage contract is variable because banks adjust their rates as the cost of funding (policy rate) is modified. Suppose, for example, that the pass-through is not complete in the core [[gamma].sup.c.sub.n] = 1/2 [[gamma].sup.p.sub.n] = 1 and to simplify the analysis that the credit rate does not react to y ([[gamma].sub.y] = 0). The FF' equations are:

[i.sup.c.sub.c] = 1/2 [i.sup.ECB*.sub.n] + [[gamma].sub.MaP][MaP.sup.c] + [[epsilon].sub.f]

[i.sup.p.sub.c] = [i.sup.ECB*.sub.n] + [[gamma].sub.MaP][MaP.sup.p] + [[epsilon].sub.f]

For a given policy rate, all things being equal, the spread between the rate credit and the policy rate is wider for the core ([i.sup.c.sub.c] - 1/2 [i.sup.ECB*.sub.n] > [i.sup.p.sub.c] - [i.sup.ECB*.sub.n]). This calls for more aggressive MaP policy in the core, compared to the situation where the transmission was complete, to minimise the loss function [LF.sup.c.sub.MaP] = 1/2 [([i.sup.c.sub.c] - 1/2 [i.sup.ECB.sub.n]).sup.2] > [LF.sup.p.sub.MaP] = 1/2[([i.sup.p.sub.c] - [i.sup.ECB*.sub.n]).sup.2].

Suppose for example that following a period of financial stress ([[epsilon].sub.f]), the central bank eases it's policy by (-[[epsilon].sub.f]) to neutralise the impact of the financial shock on the cost of borrowing. In the presence of imperfect transmission in the core, financial conditions will be eased by only 1/2 [[epsilon].sub.f]. So, MaP constraints should be released further to complement the action of the central bank.

[mathematical expression not reproducible]

In this case, MaP policy is complementary to monetary policy since it could help to ensure a better transmission of the monetary stance to financial conditions. As mentioned before, since MaP policy should be differentiated through countries [MaP.sup.F*] [not equal to] [MaP.sup.c*] to stabilise the economy, any federal implementation is not a first best policy.

Conclusion

In this paper, we show that a monetary union could benefit from adopting a policy mix that combines a single monetary policy and a macroprudential policy adjusted to the economic and financial situation of each member state. Since macroprudential policy shares many transmission channels with monetary policy, it may compensate some limits of the common monetary policy by responding to asymmetric financial shocks and moderating macroeconomic imbalances related to endogenous and countercyclical credit spreads. This policy mix becomes even more useful when economies belonging to the monetary union are hit by asymmetric shocks or out of sync economic cycles: some countries require a tight policy stance, others a loose stance. In case of symmetric financial shock, a monetary authority could react alone, but has to modify the policy interest rate aggressively, which may potentially have other destabilising effects. In this case, a policy mix that also uses macroprudential tools would promote not only macroeconomic, but also financial stability.

The implementation of a new framework for financial stability raises several challenges, which are not captured in our simple model. From a practical perspective, the activation of macroprudential policies is undoubtedly not an easy task, since it optimally requires both coordination with microprudential and monetary authorities. This point is particularly relevant for the euro zone regarding the multiple stockholders (ECB, ESRB, national micro and macroprudential authorities) involved in the macroprudential framework and the complex architecture of financial supervision (national vs supranational level). An additional challenge is the possibility of spillovers and leakages to relatively less regulated activities (Cizel et al. 2016) or to other countries (Reinhardt and Sowerbutts 2015; Buch and Goldberg 2017) following the adoption of macroprudential measures. Moreover, the evaluation of the effectiveness of MaP tools remains problematic given the wide range of possible measures, their interactions, and a scarcity of data and practical experiences to appraise results. Policy makers should be careful to avoid overestimation of and overreliance on MaP policy effectiveness. Macroprudential policy execution remains highly contingent on institutional framework and instruments effectiveness (BIS 2018). MaPs are more effective if embedded in a broader macrofinancial stability framework and coordination with other policies.

Appendix: Solution for the Central Bank's Optimal Interest Rate

Interest rate is set by minimising the quadratic loss function [LF.sup.ECB] subject to the Phillips curve (PC) equation. The central bank minimises the Lagrange: L = 1/2[y.sup.2] + 1/2[[pi].sup.2] + [chi]([[lambda].sub.y]y + [[epsilon].sub.s] - [pi]). First-order conditions (FOCs) are:

[partial derivative]L/y = 0 [??] y + [chi] [[lambda].sub.y] = 0

[partial derivative]L/[pi] = 0 [??] [pi] = [chi]

By solving the FOCs, we obtain an optimal value of the output gap [y.sup.op] = [([y.sup.c] + [y.sup.p]).sup.op]/2 = [[lambda].sub.y][pi]. We can replace the latter equation in the PC equation and then back into the (reduced-form) output gap. We can derive in this way the optimal value of the output gap:

y = [y.sub.c] + [y.sup.p]/2 = -[[lambda].sub.y]/(1 + [[lambda].sup.2.sub.y]) [[epsilon].sub.s]

By plugging this formula into the PC equation and solving for inflation, we obtain:

[pi] = 1/(1 + [[lambda].sup.2.sub.y]) [[epsilon].sub.s]

[LF.sup.ECB] = 1/2 [(- [[lambda].sub.y]/(1 + [[lambda].sup.2.sub.y]) [[epsilon].sub.s]).sup.2] + 1/2 [(1/(1 + [[lambda].sup.2.sub.y])[[epsilon].sub.f]).sup.2]

In order to find the optimal interest rate, we insert y into FF' [i.sub.c] = [i.sup.c.sub.c] + [i.sup.p.sub.c]/2 = [[gamma].sub.n][i.sub.n] + [[gamma].sub.y][[lambda].sub.y]/(1 + [[lambda].sup.2.sub.y]) [[epsilon].sub.s] + ([[epsilon].sup.c.sub.f] + [[epsilon].sup.p.sub.f])/2 and then combine y and [i.sub.c] in the IS equation y = [y.sup.c] + [y.sup.p]/2 = -[beta] ([i.sup.c.sub.c] + [i.sup.p.sub.c])/2 [beta]i + [[epsilon].sub.d]. We can then solve the resulting expression for i

[i.sup.*.sub.ECB] = 1/[[gamma].sub.n] - [[lambda].sub.y] ([beta][[gamma].sub.y] - 1)/[beta][[gamma].sub.n] (1 + [[lambda].sup.2.sub.y]) [[epsilon].sub.s] + 1/[beta][[gamma].sub.n] [[epsilon].sub.d] - 1/[[gamma].sub.n] [[epsilon].sub.f]

For the special case analysed in "Asymmetric Shock" section, where the passthrough is complete [[gamma].sub.n] = 1 and the financial shock is asymmetric ([[epsilon].sup.c.sub.f] + [[epsilon].sup.p.sub.f])/2 = 0, we have:

[i.sup.*.sub.ECB] = [[lambda].sub.y]([beta][[gamma].sub.y] - 1)/[beta](1 + [[lambda].sup.2.sub.y]) [[epsilon].sub.s] 1/[beta] [[epsilon].sub.d]

https://doi.org/10.1057/s41294-019-00085-0

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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Salim Dehmej [1] * Leonardo Gambacorta [2] (iD)

The authors thank Paul Wachtel (NY Stern), Pierre-Richard Ag6nor (University of Manchester), Maria Canelli, Boris Hoffman (BIS), Jezabel Couppey Soubeyran (University Paris 1), Andres Murcia Pabon (Banco de la Republica-Colombia), Tomislav Ridzak (Croatian National Bank), Carmelo Salleo (ECB), and all participants in seminars and conferences (Bank of England, Labex ReFi, Universite Paris 1, Universite Paris Nanterre, CEPII, Bank Al-Maghrib, Stony Brook University, Dubrovnik Economic Conference) for their careful reading and helpful comments and suggestions. The opinions expressed in this paper are those of the authors only and do not necessarily reflect those of the Bank for International Settlements or the International Monetary Fund.

[mail] Leonardo Gambacorta

Leonardo.Gambacorta@bis.org

Salim Dehmej

sdehmej@imf.org

[1] International Monetary Fund, Washington, D.C., USA

[2] Bank for International Settlements (BIS) and CEPR, Basel, Switzerland

(1) We follow the standard distinction between core (Germany, the Netherlands, Finland, Austria, France) and periphery (Greece, Spain, Italy, Portugal, Ireland). See among others Quint and Rabanal (2014).

(2) Those divergent interest rates do not depend upon the fact that financial indicators are not taken into consideration by a standard Taylor rule. Interestingly, Couppey-Soubeyran and Dehmej (2016) illustrate, using a static counterfactual analysis, that augmenting the Taylor rule by a financial indicator (credit or housing) to ensure financial stability would have led to more divergent (Taylor) interest rates from the main interest rate and between countries.

(3) See Smets (2014), Carre et al. (2015) or Adrian and Liang (2016) for a survey.

(4) The ESRB was established in January 2011. At the national level, there are four institutional models for the allocation of macroprudential powers: the government, the central bank, the financial authority and a committee with representatives from these three bodies (ESRB 2014).

(5) The ECB is required however to notify the national authorities (Article 5(4)) which can object to the measures, even though objections are not legally binding (ESRB 2014). Furthermore, national authorities must notify the ECB of their intention to implement MaP tools (Article 5(1)) and the ECB can object to them.

(6) Those falling within the scope of the Capital Requirement Regulation (CRR) and Capital Requirement Directive 4 (CRD4) that implement the Basel III banking regulation.

(7) The degree of complexity depends on the type of macroprudential instruments.

(8) The model adapts the static IS/LM-AS/AD model developed by Bofinger et al. (2006) or Mankiw (2016). It takes into account the critic of Romer (2000) about the need to replace the quantity instrument (LM) by interest rate as monetary policy main tool (IS-MP). Poutineau and Vermandel (2015) used this framework to study how MaP policy has an impact on the economy through its effects on credit rate and how it can increase welfare, taking into account different possible interaction between monetary and MaP policies.

(9) Expected inflation cancel out in the IS equation. For simplicity, we assume that the elasticities of the output gap with respect to the two interest rates are equal.

(10) The coexistence of two different interest rates could also be justified by the fact that some firms have access to the financial market, and fund their activities at the risk-free policy rate, while others must rely on banks, and get finance at a slightly higher rate due to the existence of imperfections on credit markets.

(11) Credit spread is considered as barometer of financial instability (Curdia and Woodford 2010)

(12) The transmission is sometimes imperfect (pass-through different from one). Constancio (2015a) highlights that ECB's interest rate cuts (95 basis points) from June 2012 to 2014 was transmitted partially to the effective borrowing costs faced by firms (30 basis points).

(13) We can also introduce reserve requirements since banks (supply of credit) could be constrained by reserve requirements [tau]. In this case, we replace deposits by available deposits (1 - [tau])D. We ignore the reserve requirement ratio ([tau] = 0) in order to simplify the model and because it represents only 1% in lite Eurozone (ECB Monthly Bulletin, 2/2012).

(14) For simplicity, we suppose that deposits are not remunerated and that savers do not hoard money.

(15) We can think either about real or nominal margins since inflation cancel out ([i.sub.c] - [i.sub.n] = ([i.sub.c] - [[pi].sup.e]) - ([i.sub.n] - [[pi].sup.e])).

(16) Loan to value ratios and debt to income ratios are usually considered as macroprudential tools that constraint borrowers (Blanchard et al. 2013). However, they also have an effect on banks' lending, since they limit the amount that a bank can lend against a specific collateral. For a review see, among others, Cerutti et al. (2017).

(17) As a result, the following equations are simplified PC: [pi] = [[gamma].sub.y]y + [[epsilon].sub.s]: TR: [i.sub.n] = i + [[alpha].sub.y]y + [[alpha].sub.[pi]][pi] and [L.sup.d] = [[mu].sub.y]y - [[mu].sub.c][i.sub.c].

(18) In a recent paper, Peersman and Wagner (2015) argue that financial shocks are an important source of macroeconomic fluctuations, accounting for at least 30% of the United States output's variation. They identify three types of financial shocks: a risk-taking shock, a securitisation shock and a lending shock.

(19) Calza et al. (2006) find that the elasticity of credit demand to real GDP for the euro area is 1.48.

(20) [[gamma].sub.n] = 1 if [[eta].sub.n] = [[mu].sub.c]. We relax this assumption in "Heterogeneous Transmission of Monetary Policy to Financial Conditions" section.

(21) Schoenmaker (2013) distinguish between: (a) a decentralised model, in which the ECB would set the macroprudential framework and the NCAs would apply the tools in their respective countries or (b) a centralised model, where the ECB would set and directly apply the macroprudential tools in cooperation with the NCAs.

(22) On this aspect, see the theoretical paper by Paoli and Paustian (2017) on the coordination of monetary and macroprudential policies. Cecchetti and Kohler (2014) distinguish between three possibilities: no coordination; full coordination; and partial or leader-follower coordination.

(23) Several simulations have indeed shown that an augmented Taylor rule alone does not constitute a welcome alternative, since it would be necessary in certain situations to raise the interest rate to very high levels to offset asset price inflation (BoE 2009).

(24) See Rubio (2014) for a DSGE model that study the coordination of monetary and MaP policies in a monetary union with different mortgage market structure.

Caption: Fig. 1 Euro area financial [conditions.sup.1] (in per cent). [sup.1]Core countries include Germany, the Netherlands, Finland, Austria and France, while the periphery countries are Greece, Spain, Italy, Portugal and Ireland. The aggregated cost of borrowing for non-financial corporations is based on short-term loans. Sources: ECB; authors' calculations

Caption: Fig. 2 Supply and demand for credit

Caption: Fig. 3 Credit spread vs output gap
Table 1 List of symbols

Variable            Description              Parameter

y                   Output gap               [beta]
[i.sub.c]           Loan interest rate       [[lambda].sub.y]
i                   Natural interest rate    [[alpha].sub.y]
[i.sub.n]           Policy interest rate     [[alpha].sub.[pi]]
[pi]                Inflation                [[gamma].sub.n]
MaP                 Macroprudential policy   [[gamma].sub.y]
[L.sup.s]           Supply of loans          [[gamma].sub.MaP]
[L.sup.d]           Demand of loans          [[omega].sub.cs]
K                   Bank's capital           [[omega].sub.MaP]
D                   Deposits                 [v.sub.y]
[[epsilon].sub.d]   Demand shock             [[eta].sub.y]
[[epsilon].sub.s]   Supply shock             [[eta].sub.n]
[[epsilon].sub.f]   Financial shock          [[mu].sub.y]
[tau]               Reserve requirement      [[mu].sub.n]

Variable            Responsiveness of

y                   Output gap to credit minus natural rates
[i.sub.c]           Inflation to output gap
i                   Policy rate to output gap
[i.sub.n]           Policy rate to inflation
[pi]                Credit rate to policy rate
MaP                 Credit rate to output gap
[L.sup.s]           Credit rate to MaP policy
[L.sup.d]           Supply of loans to credit spread
K                   Supply of loans to MaP policy
D                   Bank's capital to output gap
[[epsilon].sub.d]   Deposits to output gap
[[epsilon].sub.s]   Deposits to policy rate
[[epsilon].sub.f]   Demand for loans to output gap
[tau]               Demand for loans to credit rate
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Date:Jun 1, 2019
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