Risky banks and macro-prudential policy for emerging economies

Review of Economic Dynamics 30 (2018) 125–144

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Risky banks and macro-prudential policy for emerging economies Gabriel Cuadra a , Victoria Nuguer b,c,∗ a

Bank of Mexico, General Directorate of Financial Stability, Directorate of Macrofinance Risk Analysis, Av. 5 de Mayo #1, 06059 Ciudad de México, Mexico b Bank of Mexico, General Directorate of Economic Research, Directorate of Economic Studies, Av. 5 de Mayo #18, 06059 Ciudad de México, Mexico c Inter-American Development Bank, Department of Research and Chief Economist, 1300 New York Ave. NW, Washington, DC 20016, United States of America 1

a r t i c l e

i n f o

Article history: Received 12 August 2015 Received in revised form 30 April 2018 Available online 8 May 2018 JEL classification: G28 E44 F42 G21

a b s t r a c t We develop a two-country DSGE model with financial intermediaries to analyze the role of cross-border bank flows in the transmission of a U.S. bank’s balance sheet shock to emerging market economies (EMEs). In the model, banks in both countries face an agency problem when borrowing from domestic households. EME banks might also be constrained in borrowing from U.S. banks, what we call risky EME banks. A negative quality of capital shock in the United States generates a global financial crisis. EME’s macro-prudential policy that targets non-core liabilities (cross-border bank flows) makes the domestic economy resilient to the volatility of cross-border bank flows and makes EME’s households better off. © 2018 Elsevier Inc. All rights reserved.

Keywords: Cross-border bank flows Emerging market economies Financial frictions Macro-prudential policy DSGE models

1. Introduction The 2008 global financial crisis demonstrated that adverse financial shocks in advanced economies (AEs) generate spillovers to emerging market economies (EMEs). Cetorelli and Goldberg (2011) find evidence that the main channel of transmission of the 2008 financial crisis from AEs to EMEs was the reduction in cross-border lending by foreign banks. Moreover, scholars and policymakers in EMEs have expressed concern regarding negative spillover effects of AEs’ events through cross-border flows (see Sánchez, 2013; Powell, 2013; Rajan, 2014), particularly cross-border bank flows (see Takáts and Vela, 2014). EMEs are thus required to deal with the risks of these spillover effects, and in recent years there has been extensive discussion of macro-prudential policies. However, in order to assess the use of these policies as a response to AEs’ financial shocks, it is necessary to have a better understanding of how adverse financial events in AEs are transmitted to

* 1

Corresponding author. E-mail addresses: [email protected] (G. Cuadra), [email protected] (V. Nuguer). Current address.

https://doi.org/10.1016/j.red.2018.05.001 1094-2025/© 2018 Elsevier Inc. All rights reserved.

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EMEs. This requires additional empirical studies on the subject and the development of quantitative models that capture the relevant transmission channels. This paper aims to contribute to that discussion. First, we present new VAR-based evidence of spillovers from the United States to EMEs. Second, we develop a theoretical model to explain this empirical evidence. Third, we analyze a macroprudential policy carried out by an EME to mitigate the negative impact of AEs’ financial shocks on the EME. The VAR-based evidence suggests that a shock to the quality of capital in the United States, captured by an increase in the net charge-offs of U.S. commercial banks, negatively affects output and credit in EMEs. To explain this evidence, we build a two-country model with banks in both the United States and the EME where AE banks lend to EME banks, thus allowing for cross-border bank flows. The model additionally contains financial frictions, in particular an agency problem that constrains how much banks can borrow from households. Finally, we consider a macro-prudential policy that targets cross-border bank flows. We show that this policy improves welfare for EMEs’ households. In the empirical part of the paper, we examine how a shock to U.S. banks’ net charge-offs is transmitted internationally through cross-border bank flows. Net charge-offs represent the value of loans that banks know will not be repaid, and we assume that they have a direct impact on the other variables in the exercise; because we are analyzing the Great Recession episode, we assume that this shock drives events. We estimate two VARs, the first using U.S. and Mexican data and the second using U.S. and Turkish data. The difference between the two EMEs lies in their banking regulation: Mexico has had prudential banking regulation in place since the 1990s, while Turkey only implemented it after the 2008 financial crisis. Four important findings emerge from the VAR-based evidence. First, in response to an increase in their net charge-offs, U.S. banks decrease how much they lend to EME banks. Second, the EME experiences a decrease in credit and in GDP. Third, there is asset price co-movement across countries. Fourth, the estimated VAR with Turkish data shows a deeper fall in domestic credit and GDP than the estimated VAR with Mexican data. We propose a framework that accounts for these four empirical facts, building on the open-economy framework of Nuguer (2016). In the baseline model, there are two countries (AE and EME), and we assume that there are domestic financial frictions in both economies à la Gertler and Kiyotaki (2010) and Gertler and Karadi (2011) and cross-border bank flows. The EME is a relatively small country with a small banking sector, such as Mexico or Turkey, while the AE is a relatively big economy with a big banking sector, such as the United States. Banks in both countries use their net worth and local deposits (core bank liabilities) to finance domestic non-financial businesses. In particular, banks purchase securities issued by local businesses, and we assume that there are no financial frictions between banks and non-financial business. However, we introduce an agency problem and assume that banks face a financing constraint in raising domestic deposits from households. AE banks have a larger net worth (relative to the size of their economy) than EME banks and consequently lend to EME banks using cross-border bank flows (non-core bank liabilities) and actively participate in financing EME projects.2 In order to account for the difference in the results between the estimated VAR for Mexico and the estimated VAR for Turkey, we extend our baseline model and introduce an additional friction: banks in the EME are constrained in how much they borrow from AE banks. We refer to this extension of the model as risky EME banks, in contrast to safe EME banks that correspond to the financial intermediaries in the baseline model. Once we have the empirical results from the VAR analysis and a theoretical framework that allows us to interpret them, we proceed to evaluate the model’s ability to replicate the empirical facts in response to shocks to the quality of capital in the AE. We compare the impulse response functions of the model with the ones from the estimated VAR. The quality of capital shock resembles the U.S. banks net charge-offs shock implemented in the VAR analysis, and the baseline model with safe EME banks replicates the first three facts that result from the VAR-based evidence. In response to a reduction in the value of capital (and securities) in the AE, banks in this economy become more constrained in raising deposits. Therefore, they have to reduce lending to domestic AE businesses, which further depresses the value of securities and banks’ net worth in the AE. In addition, AE banks also contract lending to EME banks. Accordingly, EME banks’ net worth falls and their liability side shrinks. Since EME banks are now more financially constrained, they reduce lending to domestic EME firms, which leads to a fall in asset prices. In this way, shocks originating in the AE are transmitted to the EME through cross-border bank flows. In the extension of the model we assume that EME banks are risky. Therefore, in response to an adverse financial shock, AE banks further reduce lending to risky EME banks; in our baseline calibration, on impact, cross-border bank flows fall 58% more in the model with risky EME banks, this translates into a 9% further decrease in credit to domestic firms, 8% lower asset prices, and a 10% larger fall in output. Accordingly, the impact on the EME is larger, which allows us to replicate the fourth finding from the VAR estimation. The baseline and the extended model reproduce the shape and the magnitudes of the two estimated VARs. Furthermore, we show that a model without cross-border bank flows, i.e., in financial autarky, does not replicate the findings from the VAR evidence. Overall, the above results suggest that the framework presented in this paper is useful for studying the transmission of AE financial shocks to the EME. To mitigate the effects that these AE shocks prompt in the EME, we propose a macro-prudential policy. The main purpose of the policy is to smooth the effect of cross-border bank flows’ volatility on the EME financial system through a levy on non-core bank liabilities. In particular, when bank credit is growing faster than bank deposits,

2 In the model, we assume that international flows are only bank-to-bank for three main reasons. First, financial systems in EMEs are bank based. Second, the prudential regulation implemented in Mexico in the 1990s focused on the banking system. Third, EME non-financial firms are mainly financed through domestic bank credit, as shown for Mexico in Appendix A.3.

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EME banks pay a tax on non-core liabilities, and the magnitude of this tax depends on the ratio of bank credit growth to growth in bank deposits. This restricts the risk of widespread disruptions from the AE to the EME, limiting the negative consequences for the small economy. With the policy in place and after a shock, cross-border bank flows react 25% less on impact and the transmission of the shock is mitigated. EME banks experience a smoother reaction of their net worth, which translates into a 20% reduction in the decrease in credit and a 19% reduction in the fall of asset prices on impact. In addition, EME households cut their consumption 12% less and the labor response is smoother. EME households are better off, while the AE is slightly affected by the EME macro-prudential policy. Welfare for EME consumers is 8.35 basis points higher under the macro-prudential policy than without it, while for the AE it is 0.68 basis point lower. What is new in this framework is the interaction between the transmission of financial shocks from AEs to EMEs through cross-border bank flows and macro-prudential policy in the EME. We need to include non-core liabilities in the model to match the VAR-based evidence because cross-border bank flows lead to co-movement between EME and AE variables. There are international co-movements in asset prices, banks’ net worth, and total final demands, which are exacerbated by the introduction of a financial friction that constrains AE banks’ lending to EME banks, which we call risky banks.3 Moreover, the macro-prudential policy protects the EME from shocks originating in the AE and propagated by banks’ non-core liabilities. To the extent that our model is a good representation of both the interaction between financial shocks in the AE and their transmission to the EME through cross-border bank flows, and of the regulatory differences between Mexico and Turkey, we believe the model provides a useful framework for evaluating the use of macro-prudential policy in EMEs as a response to AE financial shocks. The rest of the paper is organized as follows. In the next section, we present the historical background on macroprudential policy and the VAR-based evidence. In Section 3, we describe in detail the two-country model with cross-border bank flows. In Section 4, we incorporate into our framework the EME macro-prudential policy in the form of a levy on non-core liabilities. In Section 5, we study the role of cross-border bank flows in the transmission mechanism of an AE quality of capital shock, and we compare the impulse response functions from the model with those from the VAR-based evidence. Furthermore, we present the EME’s policy response and its welfare implications. Finally, in Section 6, we discuss the main results of the paper and conclude. 2. Historical background on macro-prudential policy and empirical evidence In this section, first, we briefly explain the historical background that brought macro-prudential policy to the front of the stage. We want to understand why bank flows from AEs to EMEs have been highly volatile in the last years and why macro-prudential policy carried out by EMEs might help to mitigate its consequences. Additionally, we explain the prudential regulation implemented in Mexico in the nineties. Second, we show new VAR-based evidence for two EMEs: Mexico and Turkey. The VAR presents evidence that foreign claims on U.S. banks play a key role in the transmission of a shock to the value of U.S. bank assets to EMEs. We also find that there is a difference between a country that has had prudential regulation for more than a decade, such as Mexico, versus one that only started to carry out policy after the latest financial crisis, such as Turkey: after the shock, the lack of regulation prompts a larger fall on foreign claim to the EME bringing about a deeper decrease in domestic credit and output. 2.1. Historical background on macro-prudential policy The 2008 international financial crisis revealed the role that global banks can play in spreading financial shocks across economies. In 2007, the problems in the U.S. housing sector hit financial institutions and many banks found themselves in distress. This, in addition to the failure of Lehman Brothers in September 2008, triggered a severe liquidity crisis in the interbank market. Assets in the United States started to lose value. U.S. banks decreased their loans, including their cross-border bank claims on EMEs counter-parties. EMEs banks saw an outflow of capital; their liability side shrunk. In turn, EMEs banks decided to decrease loans domestically, and the crisis transmitted from the United States to EMEs.4 To mitigate the effects of the crisis, many AEs implemented the so-called “unconventional” monetary policies. These actions contributed to an episode of large capital flows to EMEs. The magnitude and speed at which these financial flows moved, raised some financial stability concerns in the recipient economies, see Sánchez (2013), Powell (2013), and Rajan (2014). The consequences of the financial crisis and the AEs response prompted a deep discussion regarding macro-prudential policy. The financial crisis reminded policy makers around the globe about the costs of a systemic disruption in financial markets. Macro-prudential policy aims to reduce the systemic risk of the financial system. The BIS (2010a) defines a macro-prudential tool as the one whose main objective is to promote stability of the financial system as a whole.

3 The co-movement across the two countries that we see in the data and in this paper contrasts with the theoretical results of Justiniano and Preston (2010)’s small open economy analysis. The difference comes from the two-country setup with financial openness. Leblebicioglu and Hernandez (2012) have a similar setup to ours, but in theirs, firms borrow from abroad and banks do not, so they do not model cross-border bank flows. 4 It is important to remark that the crisis was not only transmitted to EMEs by banks. The trade channel also played a significant role in the transmission mainly because the EMEs banks did not hold U.S. mortgage backed securities and in general the financial deepness is low in comparison to AEs. Chudik and Fratzscher (2011) find that, unlike for AEs, for EMEs the key transmission channel of the financial crisis was the real side.

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Although the global financial crisis led to a broad discussion on macro-prudential policy, it is important to note that many EMEs implemented prudential regulation at the end of the nineties in response to several EMEs crisis. EMEs have strengthened their regulatory framework with respect to maturity mismatches on the balance sheet of financial institutions, limited short-term foreign borrowing, and strengthened the supervision of foreign currency exposures. These measures have ensured a resilient financial system (BIS, 2010b). In Mexico, after the so-called Tequila Crisis in 1995, the Bank of Mexico started to implement prudential regulation. One of the main changes in the regulation was to require financial intermediaries offering banking services in Mexico to do it through subsidiaries, instead of branches.5 Other prudential regulation measures included: regulation of banks’ foreign currency operations (maturity and currency); a cap on exposure to related counter-parties; caps on interbank exposures and higher limits on value at risk for pension fund portfolios at times of high volatility (Guzmán Calafell, 2013). The prudential measures implemented in the nineties helped Mexican banks to be more resilient than other financial intermediaries during the 2008 financial crisis. With the financial crisis and the Basel III Agreement, some new measures were implemented, however there is still room for working on targeting the sources of instability in the financial system. 2.2. Empirical evidence: VAR analysis The magnitude of the effects prompted by the 2008 financial crisis was different across EMEs because of country-specific characteristics. In this paper, we look at Mexico, an EME that started to improve financial regulation and supervision after the 1995 crisis, and Turkey, a stylized EME that had not implemented prudential regulation until the 2008 financial crisis (see Central Bank of the Republic of Turkey, 2014). We provide new VAR-based evidence on the role of cross-border bank flows on the transmission of financial shocks in the U.S. to EMEs. To exploit the difference in regulation between Mexico and Turkey, we compare a VAR estimated with U.S. and Mexican data to one with U.S. and Turkish data. In order to be in line with our theoretical model, we follow Lambertini and Uysal (2013) and use shocks to the U.S. commercial banks net charge-offs as trigger of the financial crisis. To the extent that net charge-offs correspond to the value of those loans that will not be paid, shocks to this variable represent a fall in the value of banks’ assets. In our model, loans granted to non-financial firms to buy capital are banks’ assets. In turn, a shock to the quality of capital leads to a decrease in the value of such assets. Therefore, a shock to the quality of capital in the model is similar to a shock to net charge-offs in the empirical exercise. The core VAR consists of seven variables: real net charge-offs on all loans and leases of U.S. banks, the S&P500 index, real foreign U.S. banks’ claims on EME counter-parties, real EME GDP, real EME banks’ credit to the private non-financial sector, exchange rate of EME currency per U.S. dollar, and EME stock market index. The first two variables emphasize the shock and the effect on the financial system of the United States. We use U.S. banks’ foreign claims on EME counter-parties to model the transmission channel of the shock in the AE to the EME, as we do in our theoretical model.6 ,7 We choose EME banks’ credit and the stock market index to model the financial sector. The EME GDP captures the effects on the real side of the economy. The identifying assumption implicit in the recursive ordering of the VAR implies that U.S. net charge-offs shocks have an immediate impact on the other variables. Moreover, we assume that EME variables might influence U.S. series with one lag. We assume this structure and not an exogenous block because we want to be as close as possible to our model which is a two-country one. Nevertheless, the estimated parameters of U.S. series to changes in EME series are smaller than the reaction of EME variables to domestic ones. We have tried with different orderings, especially for the variables that are new, such as foreign claims of U.S. banks and domestic bank credit, and the main results hold. For Mexico, the data for the estimated VAR goes from 2002Q1 until 2015Q1. For Turkey, we estimate the VAR for the 2000Q2–2015Q1 period.8 All data are in log and detrended using the Hodrick–Prescott filter. The starting point corresponds to the availability of the EMEs data. The Cholesky ordering corresponds to the order of the listed variables.9 Fig. 1 shows the orthogonalized impulse response functions of the variables to a positive shock to the real net charge-offs on all loans and leases of U.S. banks. The blue-dashed-dotted line is the mean of the estimated VAR with U.S. and Mexican data, the gray-solid line is the one for Turkey; the shaded area represents the one standard deviation confidence interval of the estimation with Turkish data. The results for both EMEs are qualitatively similar. The shock captures one of the initial

5

Subsidiaries are separate entities from their parent bank with their own capital. In Figure A.1 in Appendix A.1, we show the relevance of Mexican and Turkish claims for U.S. banks. 7 In Appendix A.2, we document that commercial banks in Turkey and Mexico fund their activities mainly with domestic households’ deposits. Moreover, we show data on foreign agents lending to Turkish and Mexican banks. We do not use these data for the VAR-based evidence because it is available for a brief time frame. 8 See Appendix B for the definition and the sources of the data, we plot the variables in Figure A.5 in the Appendix. We use Mexican banks’ credit to the private non-financial sector rather than the new loans of Mexican banks because the former starts before. Moreover, the data that we use is comparable to the one for Turkish banks. 9 The Akaike information criterion (AIC) suggests the use of one lag. Given the comments of Kilian (2011), we performed different robustness checks. Changing the order for the Cholesky decomposition of the Mexican variables does not alter the behavior of the IRF. Including the difference between the Mexican interest rate on new loans and the interest rate on deposits before the Mexican stock market index prompts a similar reaction of the VAR with the spread increasing after a positive shock to the net charge-offs of U.S. banks. The results are also robust to allowing for a contemporaneous impact of the S&P 500 in the U.S. net charge-offs, we present this result in the Appendix, Figure A.6. 6

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Fig. 1. VAR evidence. Impulse response functions to Cholesky one standard deviation innovation to U.S. commercial banks net charge-offs. Note: Mexican VAR (blue-dashed-dotted lines represent the mean) estimated from 2002Q1 to 2015Q1. The Cholesky ordering is U.S. net charge-offs, S&P500, U.S. banks’ foreign claims on Mexican banks, Mexican GDP, Mexican banks credit to the private non-financial sector, exchange rate of Mexican pesos per U.S. dollar and the Mexican stock market index. Turkish VAR (gray-solid lines represent the mean and shaded areas represent one standard deviation confidence interval) estimated from 2000Q2 to 2015Q1. The Cholesky ordering of the variables is the same to the Mexican VAR. The vertical axis shows the percent deviation from the trend, while the horizontal axis corresponds to quarters. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

characteristics of the financial crisis: the decrease in the value of the U.S. banks’ loans. The shock suggests a decrease in the S&P 500 index and a decrease in the loans that U.S. banks make to the EME. Then, the crisis is transmitted to the EME, where the GDP, the total loans to the private non-financial sector, and the stock market index fall. The exchange rate between EME currency and U.S. dollar increases suggesting a deterioration of the EME currency because of the loans flying away from the EME. The VAR evidence highlights a significant and negative reaction of the EME (real and financial) to an increase in the U.S. banks’ net charge-offs on all loans and leases; as we can infer from the time series, that we plot in the Appendix, Figure A.5, the results are mainly driven by the 2008 episode. There are four relevant findings that result from the two estimated VARs. First, while U.S. loans go down because of the shock, U.S. banks decrease loans to the EME. Second, this emphasizes the co-movement across countries prompting GDP and credit to fall in the EME. Third, there is also co-movement of the stock indexes suggesting a strong cross-country relation of asset prices. The two EMEs show a similar response to the initial shock. However, and fourth, the VAR estimated with Turkish data presents a larger impact on EME variables. This highlights how the Turkish economy, one without prudential regulation, is hit harder by a financial AE shock than the Mexican economy, an economy that started to improve financial regulation and supervision in the mid-nineties. In the next section we build a DSGE model that accounts for these empirical facts. 3. The model The model builds on the work of Gertler and Kiyotaki (2010) and Nuguer (2016). Our focus, as in Nuguer (2016), is on the international transmission of a simulated financial crisis. However, in this paper we look at countries that are net borrowers from the United States and face a premium on borrowing from an AE, such as an EME. In particular, we introduce banks’ non-core liabilities in the form of cross-border bank flows and imperfect global integration of the capital markets, i.e., risky banks; they both contribute to the international spread of the crisis. We keep the framework as simple as possible to analyze the effects of cross-border bank lending. In line with the previous literature, we focus on a real economy, abstracting from nominal frictions. We introduce banks that intermediate funds between households and non-financial firms. Financial frictions constrain the flow of funds from households to banks. A new feature of this model is that AE banks can invest in the EME by lending to EME banks. Moreover, in an extension of the baseline model we assume that EME banks are constrained in how much they borrow from AE banks. Households and non-financial firms (intermediate goods producers, final goods producers, and capital goods producers) are standard and we describe them briefly, while we explain in more detail the banks. In what follows, we describe the AE; otherwise specified, the EME is symmetric and EME variables are expressed with an ∗ . We present all equations in Appendix C. 3.1. Households There are two countries in the world: the AE and the EME. Each country has a continuum of infinitely lived households. The household is composed of a continuum of members. A fraction f are bankers, while the rest are workers. Workers

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supply labor to intermediate goods producers, and return their wages to the household. Each of the bankers manages a financial intermediary and transfers non-negative profits back to its household, subject to its flow-of-funds constraint. Within the household, there is perfect consumption insurance. The representative household chooses consumption, C t , deposits, D t , and labor, L t , to solve the following problem

max E 0

∞ 

 β t ln C t −

t =0

χ 1+γ

1 +γ

Lt

 ,

where E t is the expectation operator conditional on information available at date t, β is the discount factor, and inverse of Frisch elasticity, subject to the following flow-of-funds constraint:

C t + D t +1 = W t L t + R t D t + t − T t ,

(1)

γ is the (2)

where W t is the wage rate, t are the profits from ownership of banks and non-financial firms, and T t are lump-sum taxes. We assume that households deposit funds in a bank, i.e., they cannot hold capital directly. Deposits are riskless one period securities, and they pay a return R t , determined in period t − 1. The first order conditions are standard. 3.2. Intermediate goods producers In the model, there is also a continuum of firms of unit mass. A fraction m corresponds to the AE, while a fraction 1 − m to the EME. Intermediate goods producers operate at a local level with constant returns to scale technology with domestic capital, K t , and domestic labor, L t , as inputs and they are perfectly competitive. Their production is used locally, X tA , and abroad, X tA ∗ .10 The production function of the intermediate good, X t , is:

X t = K tα L t1−α .

(3)

The maximization problem of these agents is described in Appendix C. From the first order conditions, we define the gross profits per unit of capital as

Z t = α P tA L t1−α K t α −1 ,

(4)

P tA

where is defined in the next subsection and is the price of the advanced good consumed in the AE. Intermediate producers acquire new capital from capital producers via frictionless markets, however in order to buy it they need to borrow from banks. To simplify, we assume that intermediate goods firms do not face any financial friction when obtaining funds from banks and they can commit to pay all future gross profits to the creditor bank. An intermediate producer will issue new securities at price Q t to obtain funds to buy new capital. Each unit of security is a state-contingent claim to the future returns on one unit of investment. By perfect competition, the price of new capital equals the price of the security and intermediate goods producers earn zero profits state-by-state. With K t as the capital stock at the end of period t and S t as the aggregate capital stock “in process” for period t + 1, we define

S t = I t + (1 − δ) K t

(5)

as the sum of investment, I t , and the undepreciated capital, (1 − δ) K t .11 Capital in process for the next period is transformed into final capital, K t +1 , after receiving the quality of capital shock, t +1 ,

K t +1 = S t t +1 .

(6)

Following the previous literature, the quality of capital shock introduces an exogenous variation in the value of capital. This disruption refers to economic obsolescence, in contrast with physical depreciation. Moreover, the AE quality of capital shock serves as a trigger of the financial crisis.12 3.3. Final goods producers As in Heathcote and Perri (2002), there are local perfectly competitive distributor firms (or final goods producers) that combine domestic, X tA , and imported, X tE , intermediate goods to produce the final good, Y t . These are produced using a constant elasticity of substitution technology. Final good producers maximize their profits subject to the aggregator for the final good,

10 11 12

The capital letter A (E) indicates that the good is produced in the AE (EME), while the ∗ indicates that the good is sold in the EME. Note that we include adjustment costs in the resource constraint, and not in the law of motion of capital. The problems are equivalent. The process of the shock is log t = ,t , where ,t ∼ N (0, σ ).

 Yt =

ν

1

η

η −1 A η Xt

+ (1 − ν

1

)η

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η η −1  η −1 E η Xt

(7)

,

where η is the elasticity of substitution between domestic (advanced) and imported (emerging) goods and ν is the parameter on home bias (see Sutherland, 2005). The law of one price holds for each good. However, because of home bias, it does not hold in the aggregate; then, the P ∗ NER

real exchange rate is defined by εt = t P t , where NERt is the nominal exchange rate. We define the terms of trade, ToT t , t as the price of imports relative to exports. An increase in ToT t implies a deterioration (appreciation) of the terms of trade for the AE (EME). 3.4. Capital producers Capital producers use final output, Y t , to make new capital subject to adjustment costs. They sell new capital to goods producers at price Q t . The objective of capital producers is to maximize their expected discounted profits, choosing I t

max E t

∞ 

It







t , j Q j I j − 1 + f

j =t

Ij I j −1



Ij .

The first order condition yields the price of capital goods, which equals the marginal cost of investment

 Qt = 1 + f

It I t −1

+

It I t −1

f





It I t −1



 − E t t ,t +1

I t +1 It

2 f





I t +1 It

.

(8)

Profits, which arise only out of the steady state, are redistributed lump sum to households. 3.5. Banks To finance their lending, banks in the AE and the EME get funds from domestic households, dt and dt∗ , and use retained earnings from previous periods, nt and nt∗ , respectively. In addition, EME banks get funds from AE banks, bt∗ . Banks in both economies are constrained in how much they borrow from households. In order to limit the bankers’ ability to save to overcome their financial constraint, we allow for turnovers between bankers and workers inside the household. We assume that with i.i.d. probability σ a banker continues being a banker next period, while with probability 1 − σ it exits the banking business. If it exits, it transfers retained earnings back to its household, and becomes a worker. To keep the number of workers and bankers fixed, each period a fraction of workers becomes bankers. Given that a bank needs positive funds to operate, every new banker receives a start-up constant fraction ξ of total assets of the bank. To motivate cross-border bank flows, we assume that AE banks are relatively larger than the size of their economy, and EME banks are relatively smaller than the size of the domestic economy, so AE banks lend to EME banks. We call flows between AE and EME banks non-core liabilities, in contrast with core liabilities or deposits. After obtaining their liabilities and combining them with their net worth, AE and EME banks decide how much to lend to intermediate firms. In the case of AE banks, they also lend to EME banks. Since there is no friction when transferring resources to intermediate goods producers, neither for AE or EME banks, firms offer banks a perfect state-contingent security. The price of the security (or loan) is Q t , which is also the price of bank assets. In other words, Q t is the market price of the bank’s claims on the future returns on one unit of present capital of intermediate goods firms at the end of period t, which is in process for period t + 1. Next, we describe the characteristics of the AE and the EME banks. 3.5.1. Advanced economy banks For an individual AE bank, its balance sheet states that the value of the loans funded in that period, Q t st plus Q bt bt , where Q bt is the price of cross-border bank flows, has to equal the sum of bank’s net worth and domestic deposits

Q t st + Q bt bt = nt + dt . Let R bt be the cross-border bank flows rate of return from period t − 1 to period t. The net worth of an individual AE bank at period t is the payoff from assets funded at t − 1, net borrowing costs:

nt = [ Z t + (1 − δ) Q t ]st −1 t + R b,t Q bt −1 bt −1 − R t dt −1 , where Z t is the dividend payment at t on loans funded in the previous period, and is defined in Equation (4). At the end of period t, the bank maximizes the present value of future dividends taking into account the probability of continuing being a banker in the next periods; the value of the bank is defined by

V t = Et

∞  i =1

(1 − σ )σ i −1 t ,t +i nt +i .

(9)

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Following the previous literature, we introduce a simple agency problem to motivate the limited ability of the bank to obtain funds. After the bank obtains deposits, it may transfer a fraction θ of assets back to its own household. In this way, households limit the funds lent to banks. If a bank diverts assets, it defaults on its debt and shuts down. Its creditors can re-claim the remaining 1 − θ fraction of assets. Let V t (st , bt , dt ) be the maximized value of V t , given an asset and liability configuration at the end of period t. The following incentive constraint must hold for each bank individually to ensure that the bank does not divert funds:

V t (st , bt , dt ) ≥ θ ( Q t st + Q bt bt ) .

(10)

The borrowing constraint establishes that for households to be willing to supply funds to a bank, the value of the bank must be at least as large as the benefits from diverting funds. Rewriting Equation (9), at the end of period t − 1, the value of the bank satisfies the following Bellman equation



V (st −1 , bt −1 , dt −1 ) = E t −1 t −1,t (1 − σ )nt + σ





max V (st , bt , dt )

(11)

.

st ,bt ,dt

The problem of the bank is to maximize Equation (11) subject to the borrowing constraint, Equation (10). In Appendix C we show the complete set of first order conditions. We guess and verify that the form of the value function of the Bellman equation is linear in assets and liabilities,

V (st , bt , dt ) = ϑst st + ϑbt bt − ϑt dt ,

(12)

where ϑst is the marginal value of assets at the end of period t, ϑbt is the marginal value of cross-border bank lending, and ϑt is the marginal cost of deposits. Rewriting the incentive constraint, we define the leverage ratio net of cross-border bank lending as

φt =

ϑt , θ − μt

(13)

where μt is the excess value of a unit of assets relative to deposits, individual bank is written as

μt =

ϑst Qt

− ϑt . Therefore, the balance sheet of the

Q t st + Q bt bt = φt nt .

(14)

The last equation establishes how tightly the constraint is binding. The leverage has negative co-movement with the fraction that banks can divert, θ , and positive with the excess value of bank assets, μ. These interactions imply that when banks can divert a higher fraction of their assets (they are more borrowing constrained), the ratio between assets and net worth falls, mainly because there are fewer assets. When the value of an extra unit of assets increases relative to the cost of holding deposits, the leverage falls, due to the accumulation of assets. We verify the conjecture regarding the form of the value function. The shadow value of net worth at t + 1 yields

t +1 = (1 − σ ) + σ (ϑt +1 + φt +1 μt +1 ),

(15)

where the first term corresponds to the probability of exiting the banking business, and the second term represents the marginal value of an extra unit of net worth given the probability of survival. For a survivor banker, the marginal value of net worth corresponds to the sum of the benefit of an extra unit of deposits ϑt +1 plus the payoff of holding assets, the leverage ratio times the excess value of loans, φt +1 μt +1 . Because the leverage ratio and the excess return varies counter-cyclically, the shadow value of net worth varies counter-cyclically, too. In other words, because the banks’ incentive constraint is more binding during recessions, an extra unit of net worth is more valuable in bad times than in good times. For the conjecture of the value function to be correct, the cost of deposits and the excess value of bank assets have to satisfy:

ϑt = E t t ,t +1 t +1 R t +1 and  μt = E t t ,t +1 t +1 R kt +1 − R t +1 ,

(16) (17)

where t ,t +1 is the household’s stochastic discount factor, and R kt +1 is the gross rate of return on bank assets,

R kt +1 = t +1

Z t +1 + Q t +1 (1 − δ) . Qt

(18)

Then, from Equation (16), the marginal value of deposits is equal to the expected augmented stochastic discount factor (the household’s discount factor times the shadow value of net worth) times the risk free interest rate, R t +1 . According to Equation (17), the excess value of a unit of assets relative to deposits is the expected value of the product of the augmented stochastic discount factor and the difference between the risky and the risk free rate of return, R kt +1 − R t +1 . The spread is also counter-cyclical.

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The first order conditions yield that the marginal value of cross-border bank lending is equal to the marginal value of assets in terms of AE final good,

ϑst

ϑbt

=

Qt

Q bt

,

which implies that the discounted rate of return on AE assets has to be equal to the discounted rate of return on crossborder bank loans

E t t ,t +1 t +1 R kt +1 = E t t ,t +1 t +1 R bt +1 ,

(19)

where R bt is defined in the next section and is also related to the return on loans from EME banks to EME intermediate goods producers. AE banks are indifferent between providing funds to intermediate goods AE firms and to EME banks because the expected return on both assets is equalized. 3.5.2. Emerging market economy banks The problem of EME banks is similar to the one of AE banks, except for two features. The first feature is that the cross-border bank flows, bt∗ , are a liability. Therefore, the balance sheet of the bank reads ∗ ∗ Q t∗ st∗ = nt∗ + dt∗ + Q bt bt .

The net worth of an individual EME bank is the payoff from assets funded at t − 1, net of borrowing costs which include the cross-border loans, ∗ ∗ ∗ nt∗ = [ Z t∗ + (1 − δ) Q t∗ ]st∗−1 − R t∗ dt∗−1 − R bt Q bt −1 b t −1 .

The second feature corresponds to the EME banks’ agency problem. Similar to AE banks, EME banks might run away with a fraction of households’ deposits. However, EME banks have an additional source of finance: cross-border bank flows. Under the baseline model, or safe global banks case, EME banks pay back all the cross-border bank flows before running away. In contrast, under the extended model, or risky global banks case, EME banks might pay back only a fraction ω of cross-border bank flows before running away.  We incorporate this additional friction into the EME banks’ incentive constraint. Let V t∗ st∗ , bt∗ , dt∗ be the maximized value of V t∗ , the value of the bank, given an asset and liability configuration at the end of period t. The following incentive constraint must hold for each bank individually to ensure that a bank does not divert funds,







∗ ∗ V t∗ st∗ , bt∗ , dt∗ ≥ θ ∗ Q t∗ st∗ − ω Q bt bt



with 0 < ω ≤ 1.

(20)

In the equation above, θ ∗ measures how tightly the constraint binds for households’ deposits, while

ω relates to the default on cross-border bank flows. The baseline case corresponds to ω = 1, safe EME banks, an EME bank pays back its debt to AE banks. The extended model corresponds to 0 < ω < 1, risky EME banks, an EME bank can default on a fraction (1 − ω) of cross-border flows. However, in equilibrium the above constraint holds with equality and there is no default. EME banks maximize its value function, similar to Equation (11), subject to constraint (20). From the first order conditions, that we present in Appendix E, it can be shown that the shadow value of domestic assets is equal to the shadow cost of cross-border bank flows minus a term that depends on the friction (ω ) on cross-border bank flows; that is ϑst∗

Q t∗

 =

∗ ϑbt

∗ Q bt

− (1 − ω)ϑt∗



1

ω

On the one hand, in the baseline model, the last equation becomes

ϑst∗

Q t∗

=

∗ ϑbt

∗ Q bt

(21)

.

ω = 1, EME banks pay in full cross-border bank debt before running away and

. In terms of returns:

∗ ∗ ∗ ∗ E t t∗,t +1 t∗+1 R kt +1 = E t t ,t +1 t +1 R bt +1 .

(22)

Under this setup, after a shock in the AE, the return on the cross-border bank flows transmits the impact to the EME through the return on the domestic asset. Furthermore, the expected discounted rate of return on the cross-border bank asset equalizes to the one on loans to non-financial AE firms, see Equation (19). In turn, both AE and EME loan market behave in a similar way. On the other hand, in the extended model, when 0 < ω < 1, Equation (21) implies that the cost of holding cross-border bank flows,

∗ ϑbt

∗ Q bt

, is smaller than the marginal value of holding assets,

ϑst∗

Q t∗

. As a result, the interest rate on cross-border bank

ω > 0). We ∗ ∗ ∗ = ϑbt − ϑ ∗ . μt∗ = ϑQst∗ − ϑt∗ and the excess return on cross-border bank flows as μbt ∗ t Q t bt ∗ . The last equation also reads: Moreover, using Equation (21), ωμt∗ = μbt flows is lower than the rate of return on domestic capital, but higher than the deposit interest rate (because define the excess return on capital as

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∗ ∗ ∗ ∗ ∗ ∗ ω E t t∗,t +1 t∗+1 R kt +1 − R t +1 = E t t ,t +1 t +1 R bt +1 − R t +1 .

(23)

Under this setup, the rate of return on domestic assets is larger than the rate on cross-border flows. Actually, after a shock in the AE, the extra term in the equation above makes the return on cross-border flows more volatile than the return on domestic assets, which will prompt a larger reaction of the EME to an AE shock, in comparison to the baseline case. 3.5.3. Aggregate bank net worth Finally, aggregating across AE banks, from Equation (14):

Q t S t + Q bt B t = φt N t ,

(24)

where capital letters indicate aggregate variables. The law of motion of the AE banking system’s net worth results in





N t = (σ + ξ ) R k,t Q t −1 S t −1 + R b,t Q b,t −1 B t −1 − σ R t D t −1 .

(25)

The first term in the second parenthesis represents the return on loans made last period. The second term is the return on funds that the banks invested in the EME. Both loans are scaled by old bankers (that survived from the last period) plus the start-up fraction of loans that young bankers receive, σ + ξ . The last term in the equation is the total return on households’ deposits that surviving banks need to pay back. For EME banks, the aggregation yields ∗ ∗ ∗ N t∗ = (σ ∗ + ξ ∗ ) R k∗,t Q t∗−1 S t∗−1 − σ ∗ R t∗ D t∗−1 − σ ∗ R bt Q bt −1 B t −1 .

(26)

The balance sheet of the aggregate EME banking system can be written as ∗ ∗ Q t∗ S t∗ − ω Q bt B t = φt∗ N t∗ .

(27)

3.5.4. Cross-border bank flows At the steady state, AE banks invest in the EME because the AE has excess resources in comparison to what the AE needs; this is translated into the agency parameter of each banking system that results in a stronger constraint on the EME. Then, there are cross-border bank flows in the model. The smaller (and riskier) economy is an EME and we assume that banks in the economy need to pay a premium on borrowing from AE banks. Following Schmitt-Grohé and Uribe (2003), the interest rate paid by EME banks on the international debt is debt elastic. Specifically, we assume that Equation (19) becomes



E t t ,t +1 t +1 R kt +1 = E t t ,t +1 t +1 R bt +1 +  exp ( B t − B¯ ) − 1 .

(28)

The new term in Equation (28) is the risk premium associated with the EME. The parameter  reflects the elasticity of the ¯ Note that at the steady state the risk premium is difference between the international asset and its steady state level, B. zero.13 εt +1 ∗ Regarding the interest rate, the return on loans to EME banks made by AE banks is E t ( R bt +1 ) = E t ( R bt +1 εt ). The return on cross-border flows is equalized to the return on loans to AE firms, R kt , in expected terms plus a risk premium, as in Equation (28); AE banks at the steady state are indifferent between lending to AE firms or to EME banks. When EME banks are safe, in other words ω = 1, Equation (22) relates the rate of return on cross-border bank loans to the rate of return on EME loans and there is perfect asset market integration. However, when EME banks are risky, 0 < ω < 1, there is imperfect asset market integration and there is an extra cost specified in Equation (21). The EME bears all the exchange rate risk: we assume that the contract between EME banks and AE banks is in AE’s currency. As we are going to see in Section 5, there is an exchange rate channel on the international transmission of shocks. When the EME currency depreciates, the EME collateral expressed in foreign currency falls, then AE banks lend less to EME banks, because the risk of running away with AE money is higher (especially when there are risky EME banks). Cesa-Bianchi et al. (2015) document empirically the effects of the exchange rate movements on the collateral for EME, which go in line with ours. It is important to notice that cross-border bank flows are different from the so-called “outside” equity in Gertler et al. (2012) in two aspects. First, EME banks prefer financing their activity with deposits rather than cross-border bank flows because at the steady state, the interest rate that they have to pay on core liabilities is lower than the one for non-core liabilities. However, the latter is state-contingent while the former is predetermined. In contrast, outside equity is preferred to deposits because the interest rate is not only state contingent, but also lower than the one for deposits. Second, an increase in cross-border bank flows makes the borrowing constraint, Equation (20), less binding because EME banks have a lower gain from running away. On the contrary, an increase in outside equity prompts a tightening on the borrowing constraint. Even though cross-border bank flows and outside equity are both a kind of debt, they have different implications on the optimal decision of the banks.

13 The reason to change Equation (19) for Equation (28) is that the model without it becomes highly volatile when we decrease the size of the EME by reducing 1 − m. Moreover, the parameter  helps to match the volatility of cross-border bank flows of the model with the VAR-based evidence.

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3.6. Market clearing and equilibrium The final output is used for domestic households’ consumption, C t , domestic investment, I t , and domestic government consumption, G t ,





Y t = Ct + It 1 + f

It I t −1



+ Gt .

(29)

As in Christiano et al. (2005), we assume convex adjustment costs in the gross rate of investment for capital goods producers. The intermediate-competitive goods are used locally and abroad,

X t = X tA +

1−m m

X tA ∗ .

(30)

The market for securities is in equilibrium when we combine Equation (5) with Equation (6). The equilibrium in the labor market is given by the standard equations. If the economies are in financial autarky, i.e., no cross-border bank flows, the net exports for the AE are zero in every period; the current account results in

C At = 0 =

1−m m

X tA ∗ − T oT t X tE .

(31)

However, if there are cross-border bank flows, the current account is

C A t = Q b,t B t − R bt Q b,t −1 B t −1 = X t∗ A

1 − m P tA m

Pt

− X tE T oT t

P tH Pt

,

(32)

m with the cross-border bank asset in zero net supply B t = B t∗ 1− . We formally define the equilibrium of the model in m Appendix D.

4. Macro-prudential policy in the EME We allow the EME policy maker to carry out macro-prudential policy. We incorporate a levy on non-core liabilities, in our model they correspond to cross-border bank flows.14 Since October 2010, the Bank of Korea has introduced several macro-prudential measures to address the risk factors of capital inflows and outflows generated on the demand and the supply side. Here we focus on the macro-prudential stability levy. The objective of the levy is to reduce the increase in banks’ non-core liabilities (non-deposit liabilities). The levy rate varies according to the maturity of the liability. This measure contributed to reducing banks’ foreign borrowing and improving their maturity structures (Kim, 2014 and Shin, 2010). Levy on non-core liabilities. In the framework that we have developed in this paper, the systemic risk or the contagion across financial institutions for the EME comes from the cross-border bank flows. The policy is a tax on non-core liabilities, the magnitude of the tax is related to the ratio between the banks’ credit growth and the banks’ deposits growth,

⎛ ⎜ ∗ ϑ gt =⎝

S t∗+1 − S t∗ S t∗

D t∗ − D t∗−1 D t∗−1

⎞τ g∗ ⎟ ⎠

.

(33)

We focus on this ratio because Lane and McQuade (2014) highlight that behind the divergence between domestic bank deposit growth and bank credit growth, banks are using wholesale cross-border funding, mainly borrowing short-term on the international interbank and money markets and by issuing bonds. We show evidence of the divergence in this ratio for the Turkish and Mexican economies in Appendix A.4. The size of the tax has an exogenous (arbitrary) component τ g∗ and an endogenous one that corresponds to the one in the parenthesis. In Section 5.4.2 we do a welfare analysis for different levels of τ g∗ . EME banks pay the tax from their net worth, Equation (26) is now

14 Hanson et al. (2011); Beau et al. (2012); Quint and Rabanal (2014), among others, develop models to study the role of macro-prudential policy and its interaction with monetary policy. Mohanty (2014) expresses the policy makers’ general agreement: macro-prudential policy in EMEs helps to reduce the volatility generated by international spillovers. Moreover, Cerutti et al. (2017), for a large set of countries, show that macro-prudential policies are effective in reducing the growth rates of overall credit, and household and corporate sector credit. However, there is no specific analysis of the relation between cross-border bank flows and macro-prudential policy.

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Table 1 Calibration. AE

β

γ χ α δ

κ g¯

ν η m

ξ θ

σ 

EME

Source or target

ω=1

ω = 0.50

discount factor inverse elasticity of labor supply relative utility weight of labor effective capital share depreciation adjustment cost steady state gov expenditure

0.990 0.100 2.000 0.330 0.018 3.000 0.196

0.990 0.100 2.000 0.330 0.023 3.000 0.111

0.990 0.100 2.000 0.330 0.023 3.000 0.105

Gertler and Kiyotaki Gertler and Kiyotaki target valuea Gertler and Kiyotaki target valueb Gertler and Kiyotaki target valuec

(2010) (2010)

home bias elasticity of substitution country size

0.775 1.556 0.900

0.975 1.556 0.100

0.975 1.556 0.100

target valued target valuee target valuef

start-up fraction of div assets survival rate country-specific risk premium

0.002 0.407 0.972

0.002 0.412 0.972 0.010

0.002 0.408 0.972 0.040

Gertler and Kiyotaki (2010) target valueg Gertler and Kiyotaki (2010) target valueh

(2010) (2010)

a

Targeted to match the consumption to GDP ratio in EME, see Table 2. Targeted to match the investment to GDP ratio in EME, see Table 2. Targeted to match the government expenditure to GDP ratio, see Table 2. d Targeted to match the U.S. to EME GDP ratio. e Targeted to match the net imports to GDP ratio in EME, see Table 2. f Chosen to have the AE bigger than the EME. g Targeted to match that the average interest rate premium is 110 basis point per year. h Targeted to match the largest fall of cross-border-banking flows EME data with the VAR results, see Figs. 2 for Mexico and 3 for Turkey. b

c





∗ ∗ ∗ N t∗ = (σ ∗ + ξ ∗ ) R kt Q t∗−1 S t∗−1 − σ ∗ R t∗ D t∗−1 + ϑ gt R bt Q b∗,t −1 B t∗−1 .

On the one hand, when assets are growing faster than deposits, assets are being financed with non-core liabilities, or cross-border bank flows. Because it is a credit boom, the policy is a tax paid by EME banks; the tax smooths the quantities borrowed from abroad. On the other hand, during periods of financial crisis, the policy works as a subsidy. The EME’ government budget constraint becomes ∗ ∗ G t∗ = T t∗ + (ϑ gt − 1) R bt Q b∗,t −1 B t∗−1 .

In this framework, macro-prudential policy helps to limit exposures arising from cross-border bank flows and moderates adverse consequences associated with them. The policy tool is a levy on non-core liabilities. This is in line with the BIS (2010b) and Shin (2011)’s suggestions regarding macro-prudential measures in EMEs. Finally, it is important to note that the policy is different from the prudential regulation that we interpret in the model as a difference in ω . The policy is an instrument that moves over the financial cycle and aims at reducing the volatility of cross-border bank flows to mitigate the spillovers from AE shocks, while the regulation is a set of rules that do not vary over the financial cycle and contribute to the contract enforcement of the banking system as a whole. 5. Crisis experiment In this section, we present numerical exercises to show how the model captures key aspects of the international transmission of a financial crisis. First, we present the calibration. We include two different set of parameters, the first one for the model with safe EME banks that matches certain ratios of the Mexican economy; while the second one corresponds to the model with risky EME banks that matches Turkish ratios. Second, we assume that the U.S. banks’ net charge-offs on all loans and leases that we include in the VAR-based evidence can be thought of as the quality of capital shock in the AE, we use the data as the path of the shock and we compare the models with the empirical evidence. We show that the model with safe banks and the model with risky banks replicate the VAR-based evidence for Mexico and Turkey, respectively; while a model without cross-border bank flows does an insufficient job. Third, we explore the transmission mechanism by analyzing the impulse response functions to a crisis experiment without a response from the government and we highlight the role of banks’ non-core liabilities in the transmission of the crisis. We show how cross-border bank assets in the AE work as an insurance when the economy is hit by a shock. Moreover, we explore the difference between risky and safe EME banks. Finally, we look at the consequences of the macro-prudential policy carried out by the EME. 5.1. Calibration Table 1 lists the values of the models’ parameters for the calibration of the main exercise of the paper: the comparison between the model and the VAR analysis for Mexico and Turkey. We calibrate ω = 1 for the Mexican case, and 0 < ω < 1

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137

Table 2 Deterministic steady state, model and data. Source: own calculations with data from FRED 2002Q1–2014Q4. For Mexico, the cross-border bank flows to deposits ratio is the ratio between deposits from financial institutions from abroad and deposits from households for the period 2004Q2–2015Q2, CF445, Bank of Mexico. For Turkey, it is the ratio between total deposits from financial foreign institutions and total deposits from households in TRY for the same time period, Central Bank of Turkey. Safe EME banks Model

ω=1

Data CI 2sd

Risky EME banks Model

ω = 0.5

Data CI 2sd

Advanced economy: Consumption/GDP Investment/GDP Government spending/GDP

0.6115 0.1924 0.1961

0.6753 0.1558 0.1909

United States 0.6820 0.6728 0.1774 0.1980 0.2013 0.1961

0.6753 0.1558 0.1909

0.6820 0.1774 0.2013

Emerging market economy: Consumption/GDP Investment/GDP Government spending/GDP Exports/GDP Imports/GDP Cross-border bnk fl/Deposits

0.6771 0.2120 0.1109 0.2465 0.2301 0.0196

Mexico 0.6576 0.2083 0.1094 0.2749 0.2722 0.0105

0.6682 0.2193 0.1124 0.3008 0.3025 0.0273

Turkey 0.6782 0.2158 0.1022 0.2436 0.2573 0.0082

0.6969 0.2453 0.1087 0.2570 0.2852 0.0793

0.6817 0.2128 0.1055 0.2479 0.2339 0.0670

for the Turkish case. The model is calibrated to a quarterly frequency, as the VAR exercise, with most parameters taken from Gertler and Kiyotaki (2010)’s work. The parameters that do not follow Gertler and Kiyotaki (2010) are generally chosen to fit the deterministic steady state of the model to the two standard deviations’ confidence interval of the data; the comparison between those two are in Table 2. We try to change as fewer parameters as possible between the AE and the 2 different EME’s specifications to minimize any asymmetries that could otherwise cloud the driving mechanism. The parameters that correspond to the non-financial part of the model, i.e., households and non-financial firms, are common in the literature. The discount factor, the inverse of the Frisch elasticity of labor supply, the capital share, and the adjustment cost are taken from Gertler and Kiyotaki (2010). They set the parameters to reasonably conventional values, except for the labor supply elasticity, for which they use a low value to compensate partly for the absence of labor market frictions. The calibrated parameter values are: β = 0.99, γ = 0.1, α = 0.33, and κ = 3, respectively. We calibrate the relative utility weight of labor, χ , to match the consumption to GDP ratio in the EME, resulting in 0.6771 for Mexico while the 2 standard deviation confidence interval of the data is [0.6576; 0.6682] and 0.6817 for Turkey, while the data correspond to [0.6782; 0.6969]. The depreciation rate of capital, δ , equals 0.18 for the AE, and 0.023 for the two cases of EME; we are targeting the investment to GDP ratio in the EME, which results in 0.2120 for Mexico, while in the data the interval is [0.2083; 0.2193], and 0.2128 for Turkey, while in data the interval is [0.2158; 0.2453]. The steady state government expenditure matches the mean of the data for each of the countries. The open economy parameters are chosen to match certain data ratios. Regarding the parameters that enter into the CES aggregator, we choose ν to match the ratios between the U.S. and the EME GDP. The size of the AE is set to be clearly bigger than the EME, we chose 0.9 for the AE and 0.1 for the EME. The elasticity of substitution between the AE and the EME goods in the production of the final good, η , is set to be greater than one. This implies substitutability between emerging and advanced goods; we choose it to control the net imports to GDP ratios, which result to be almost negligible in the data and in the model: −0.0164 for ω = 1, while the mean of the data for Mexico is 0.005, and −0.014 for 0 < ω < 1, while the mean for the Turkish data is 0.015.15 The financial parameters (the transfer to entering bankers, ξ , and the survival rate of bankers, σ ) are taken from Gertler and Kiyotaki (2010). They equal 0.0018 and 0.972, respectively. The  fraction of gross assets that the banker can run away, θ , is set such that the average interest rate spread, E R kt +1 − R t +1 , is 110 basis point per year for the AE and the EME. For the AE it is a rough approximation of the different spreads for the pre-2007 period.16 The parameter is different across the models because the capital to net-worth ratio in each on the set-ups is different. Finally, the cross-border bank flows to deposit ratios of the models match the data, we choose them to be 0.0196 for ω = 1, and 0.670 for 0 < ω < 1, while in the data they are [0.0105; 0.0273] for Mexico and [0.0082; 0.0793] for Turkey. For the shock process we follow Gertler and Kiyotaki (2010) and assume a negative i.i.d. quality of capital shock that occurs in the AE. For the VAR comparison between the data and the model, the shock follows the path and the size of the U.S. net charge-off series of the VAR exercise. For the analyzes of the effects of cross-border bank flows on the different

15 Even-though the EMEs are net importers in the model by construction, we try to reduce the difference between imports and exports as much as possible, a lower value of η prompts that the steady state of the model is not properly specified. 16 The literature for EME usually assumes higher spreads for these economies, we avoid it at the steady state to minimize the differences across countries that prompt the different behavior of the economies. A higher spread at the steady state level does not change the dynamics of the models. Moreover, in the dynamics the spread turns out to be higher on impact because of the parameter  that enters into Equation (28).

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Fig. 2. Mexico: response of the model and the data to an increase in the U.S. commercial banks net charge-offs. Note: Mexican VAR (blue-dashed lines represent the mean and the shaded areas correspond to the one standard deviation confidence interval) estimated for 2002Q1 to 2015Q1. The Cholesky ordering is U.S. net charge-offs, S&P500, U.S. banks’ foreign claims on Mexican banks, Mexican GDP, Mexican banks credit to the private non-financial sector, exchange rate of Mexican pesos per U.S. dollar and the Mexican stock market index. The variables that correspond to the model are, in order: AE quality of capital shock (negative), , AE asset price, Q t , cross-border bank flows, Q t∗ B t∗ , EME total final domestic demand, Y t∗ , EME total credit, Q t∗ S t∗ , real exchange rate (EME currency per AE currency), εt , and EME asset price, Q t∗ . The vertical axis shows the percent deviation from the trend or from the steady state, while the horizontal axis shows quarters after the shock.

models, we give a 5% decrease in the quality of capital, similar to Gertler and Kiyotaki (2010). All the shocks are unexpected and do not have an auto-regressive component. 5.2. Response to a quality of capital shock in the AE: the VAR evidence and the model Our main experiment consists of comparing the responses of three different models to a temporary decrease (increase) in the quality of capital of the AE (the net charge-offs of U.S. commercial banks). The first model is the baseline one, with cross-border bank flows and safe EME banks, the second model is the one with risky EME banks, while the third one corresponds to one in financial autarky. To evaluate the fitness of the models with cross-border bank flows, we compare the VAR-based evidence for Mexico and Turkey with the model with safe and risky EME banks, respectively. We show that a model in financial autarky does a deficient job on explaining the transmission of a quality of capital shock in the AE to the EME. On the contrary, when we add cross-border bank flows, the models replicate the behavior of the variables in the VAR-based evidence. Therefore, introducing cross-border bank flows is essential for understanding the spillovers of a financial shock in the AE to an EME. To do this exercise, we assume that the real net charge-offs on all loans and leases of U.S. banks, that we have used previously in the VAR exercise, are a good approximation to the quality of capital shock in the AE.17 Fig. 2 shows the comparison for Mexico, while Fig. 3 presents the results for Turkey. Fig. 2 and 3 show that our framework can replicate the differential response of EME variables between safe and risky banks, especially when we compare the responses to the model in financial autarky (red-dashed line) facing quality of capital shocks. The models with cross-border bank flows replicate the general patterns of the data well. Relative to the model in financial autarky, the models with international flows generate a decrease in cross-border bank flows that translates into a larger contraction of GDP,18 a fall on EME’s credit, and a strong correlation of the asset price across countries. These three characteristics are important findings from the VAR exercise. The intuition for the results is straightforward: a temporary increase in the U.S. net charge-offs (decrease in the quality of capital in the AE) makes AE banks more financially constrained. They reduce loans and asset prices fall. As a consequence, when we model cross-border bank flows, AE banks contract lending to EME banks. This results in EME banks facing tighter financial constraints, which pushes banks to reduce how much they lend in the domestic market, prompting a decrease in credit that brings about a fall in the asset price. The exchange rate depreciates for the EME because there are less flows going into the economy.

17 As we show on the plots corresponding to the U.S. net charge-offs for Mexico and Turkey, we scale the shock that we fit into the model to get impulse responses of similar magnitude. The path of the shock is the same. 18 We compare the data to total final domestic demand and not total production because the latest is more volatile.

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Fig. 3. Turkey: response of the model and the data to an increase in the U.S. commercial banks net charge-offs. Note: Turkish VAR (solid lines correspond to the mean while shaded areas represent one standard deviation confidence interval) estimated for 2000Q2 to 2015Q1. The Cholesky ordering is U.S. net charge-offs, S&P500, U.S. banks’ foreign claims on Turkish banks, Turkish GDP, Turkish banks credit to the private non-financial sector, exchange rate of Turkish lira per U.S. dollar and the Turkish stock market index. The variables that correspond to the model are, in order: AE quality of capital shock (negative), , AE asset price, Q t , cross-border bank flows, Q t∗ B t∗ , EME total final domestic demand, Y t∗ , EME total credit, Q t∗ S t∗ , real exchange rate (EME currency per AE currency), εt , and EME asset price, Q t∗ . The vertical axis shows the percent deviation from the trend or from the steady state, while the horizontal axis shows quarters after the shock.

We now turn to the underlying mechanism that explains the differential response between the model in financial autarky and the ones that have cross-border bank flows. Moreover, we study the different behavior of safe and risky EME banks. 5.3. Response to a quality of capital shock in the AE: safe and risky EME banks Fig. 4 shows the impulse responses to a one time decline in the AE quality of capital of 5% in period t comparing the same three models presented in the previous section. The comparison of these models shows how the transmission mechanism across countries changes given the different assumptions. The model in financial autarky presents international spillover due to the trade channel of intermediate goods. The two models with cross-border bank flows have financial openness and are able to replicate the VAR-based evidence.19 In the model in financial autarky, when there is a decrease in the AE quality of capital, the reaction of the AE is similar to the closed-economy model of Gertler and Kiyotaki (2010). Banks are financially constrained; when their asset (capital) goes down, banks face a decrease in their net worth. Because banks are more constrained in how much they can borrow, there is a fire-sale of asset that prompts its price, Q t , to go down. The interest rate spread between the AE rate of return on capital and the risk free rate, E ( R k,t +1 ) − R t +1 , widens. This behavior is characteristic of the crisis period. Moreover, it is a result of the fall in capital that prompts the expected rate of return on capital to increase. As a consequence of the decrease in capital, the AE production and consumption shrink. There are fewer advanced goods and they are relatively more expensive, then, the terms of trade slightly improve for the AE. Hence, EME goods are cheaper and their production increases. However, the depreciation of the EME currency makes EME households to cut down on consumption which will prompt a decrease in the EME capital, net worth of the banks, and the asset price. Nevertheless asset prices and production co-move across countries, the interest rate spread does not. The AE quality of capital shock’s spillover to the EME is negligible. When we allow for cross-border bank flows, AE banks lend to EME banks. AE banks diversify their assets and pool a country-specific shock. These international asset market characteristics have been discussed by Cole and Obstfeld (1991) and Cole (1993). As in the model in financial autarky, the decrease in the value of assets and securities in the AE prompts AE banks to be more financially constrained. The mechanism that takes place for the AE variables is the same in both setups. However,

19 For this exercise, we take the calibration that corresponds to ω = 0.5 for all the 3 models. This allows us to look at the consequences of having cross-border bank flows in comparison to the financial autarky case, and then, to a change in ω , ceteris paribus. In Appendix G, we show a complete set of impulse response functions. In Appendix F, we compare these models to the case in which there are no banks in the economy.

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Fig. 4. Impulse response functions to a 5% decrease in the AE quality of capital, t . Note: y axis: percentage deviation from the steady state; x axis: quarters from the shock.

final domestic demand is less affected by the shock when there are cross-border flows because the AE can partially pool the country-specific shock. In the model with safe EME banks, ω = 1, the return on EME assets equalizes to the return on EME cross-border debt. EME banks face a reduction in their net worth because of a country-specific shock in the AE. The collateral of EME banks in foreign currency falls due to the depreciation of the exchange rate and AE banks lend less to the EME. EME financial intermediaries are more financially constrained and reduce lending to domestic businesses, as a result investment and the price of capital shrink. Thereby, cross-border bank flows transmit the crisis from the AE to the EME. Two types of spillovers disturb the EME: the demand and the cross-border bank flows effects. The demand effect prompts an increase in production because the exchange rate is depreciating for the EME. The cross-border bank flows effect generates a tightening of the EME borrowing constraint because there is a decrease in the value of cross-border flows. The cross-border bank flows effect predominates, the net worth of EME banks falls and households cut down on consumption. In the model with cross-border bank flows, AE and EME consumption, asset price, and total demand co-move, while production does not (on impact). The asset markets across countries are integrated when ω = 1 because of the equalization of returns between the assets in the AE and in the EME. The AE banks’ lending to EME banks does not imply a risk for the AE. When we allow for risky EME banks, 0 < ω < 1, the shock hits harder the EME because AE banks further reduce crossborder flows to EME banks. The possibility of running away with money from AE banks prompts a difference in the risk perception of lending to EME banks when a shock hits. This is also reflected in how the interest rate spread of the EME reacts to the shock. Consequently, the AE experiences a deeper crisis when EME banks are riskier. When the shock hits, a lower ω prompts a more abrupt reduction on lending to EME banks, and there is deeper fall in credit and in output in the EME. As we showed in the previous section, the qualitative behavior of the models with cross-border bank flows matches the VAR evidence. In the data, a decrease in U.S. loans prompts a reduction in cross-border flows that is then transmitted to the EME. This leads to a contraction in credit, asset price, and final domestic demand in the EME. The EME has a larger co-movement with the AE in a framework with financial openness than without it. The EME experiences a deeper fall in credit, asset prices, and GDP because of the quality of capital shock abroad, as shown by the VAR evidence and the model. Moreover, through the cross-border bank flows, the AE manages to partially insure itself against the country-specific shock. The EME experiences a deeper fall in output when domestic banks can run away with resources from AE banks. We understand the difference between safe and risky EME banks as having or not having prudential regulation in place before the Great Recession, like Mexico and Turkey, respectively.

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Fig. 5. Impulse response functions to a 5% decrease in the AE quality of capital, t , macro-prudential policy by the EME Central Bank. Note: y axis: percentage deviation from the steady state; x axis: quarters from the shock.

5.4. Response to a quality of capital shock in the AE: macro-prudential policy 5.4.1. Impulse response functions We introduce EME macro-prudential policy. The macro-prudential intervention targets the ratio between the growth rate of credit and deposits of EME banks. When credit is growing faster than deposits, the assets are funded using non-core liabilities, and so EME banks pay a tax on them. When there is a financial crisis, deposits grow faster than credit and so the policy is a subsidy and EME banks adjust non-core liabilities much less than without the levy. We only show the results for risky EME banks to be brief. Fig. 5 shows a small set of variables with two models.20 The dotted-green line is the same model with risky EME banks and without policy shown in previous figures. The solid-black line is the model with macro-prudential policy in the EME.21 When the macro-prudential policy is in place, the net worth of domestic banks falls less, which prompts loans and capital to be cut by less. The price of the capital does not fall as much and so investment moves in a smoother way; even the household’s consumption shows a smaller reaction. The interest rate premium also displays a better scenario. Note that the effect on the AE of having the levy is small. So far, we have studied the first order approximation of the model. This is useful when studying the impact of unexpected shocks to the economy, however, it is not an adequate setup to study welfare. In the next subsection we evaluate the welfare implications of the macro-prudential policy by looking at the second order approximation of the model. 5.4.2. Welfare analysis We look at the advanced and emerging consumers’ welfare given the level of intervention of the EME macro-prudential policy through the policy parameter, τ g∗ . The welfare criterion considered here is the one used by Gertler and Karadi (2011) and developed by Faia and Monacelli (2007). The household’s welfare function is given by

Welf t = U (C t , L t ) + β E t Welf t +1 ,

(34)

20

In Appendix G, we show the rest of the variables. For the macro-prudential policy, the calibrated parameter, exemplify the mechanism through which the policy works. 21

τ g∗ , is set to 19, very closed to the optimal one—as we show in the next section—, to

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Fig. 6. Consumption equivalent under different intensity of macro-prudential intervention and

σ = 0.05.

where the utility function comes from Equation (1). Welfare is defined as the lifetime utility of consumers. We compare the different interventions using the consumption equivalent, i.e., the fraction of household’s consumption that would be needed to equate the welfare of the no-policy steady state to the welfare under policy, in the case of the macro-prudential intervention. We use Schmitt-Grohé and Uribe (2007)’s definition of consumption equivalent. We define the stochastic steady state as the ergodic mean in the absence of shocks.22 We follow Carrillo et al. (2013) in the way to calculate it: it is the place where the model stands after 2500 periods, given the deterministic steady state as starting point and the policy functions approximated up to a second order (see Kim and Kim, 2003; Schmitt-Grohé and Uribe, 2004). We do not give shocks in the process of going from the deterministic to the stochastic steady state but the variances of the perturbations are taken into account in the solution of the model. Fig. 6 shows the consumption equivalent of the AE and the EME for different intensity levels of macro-prudential intervention by the EME. It turns out that for τ g∗ between 0 and 40, the EME is better off with the policy. The gains for EME consumers are approximately 10 times larger than the losses for AE households; this highlights the fact that the policy does not have a relevant impact on the AE. Furthermore, there is a maximum for the EME households’ consumption equivalent when τ g∗ = 23.9. This corresponds to a tax of 0.0284% on the volatility of non-core liabilities. The results show that the macro-prudential intervention makes EME consumers better off. We only plot the results for shocks in the AE because the model turns out to be highly sensitive to the size and the quantity of the shocks. 6. Concluding remarks We have presented a two-country DSGE model with financial intermediaries that captures part of the challenges that non-core liabilities, in particular cross-border bank flows, prompt for EMEs. In the model, banks in the AE and in the EME are constrained in obtaining funds from households. AE banks invest in the EME through banks using cross-border bank flows. Additionally, EME banks might be constrained in how much they borrow from AE banks. Comparing a model in financial autarky with one with cross-border bank flows suggests that the latter generates a higher co-movement when the AE faces an increase in commercial banks net charge-offs (or a decrease in the quality of capital). This matches qualitatively the behavior seen in the data, as shown in the VAR-based analysis. When a quality of capital shock hits the AE, AE and EME experience a crisis both in real and financial variables; the cross-border bank flows prompt the international transmission. The net worth of EME banks drops because the price and the quantities of cross-border bank flows fall. EME banks face a reduction in their liabilities and they are more constrained on lending to domestic non-financial firms. The price of EME domestic assets drops prompting a fall in investment, consumption, and total demand. When EME banks are also constrained in how much they can borrow from AE banks (risky EME banks), the crisis is deeper in the EME, in comparison to the case in which there is no such friction. A model without cross-border bank flows cannot replicate the VAR-based evidence when facing shocks to the net charge-offs of AE commercial banks. Banks that intermediate funds across borders and in different currencies entail relevant challenges in terms of policy and regulation. For open EMEs the non-core liabilities, such as cross-border bank flows, imply significant challenges for their financial stability. We study the introduction of a macro-prudential policy by the central bank of the EME with the objective of reducing the financial and real volatility that banks’ non-core liabilities might prompt. The policy is effective in smoothing the impact of external shocks; the levy is related to the ratio between the credit growth and the deposits growth. Moreover, an ex-ante policy makes EME consumers better off. The paper focuses on one type of non-core liabilities: the cross-border bank flows. One tool that EMEs can use to address the challenges related to these flows is macro-prudential policy. In future research, we plan to extend the model to agency

22 Fernández-Villaverde et al. (2011) and Born and Pfeifer (2014) define the stochastic steady state as: “the point of the state space where, in absence of shocks in that period, agents would choose to remain although they are taking future volatility into account” (Born and Pfeifer, 2014, footnote 2).

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problems when banks lend to non-financial firms, with particular interest in EMEs. Moreover, macro-prudential policy has many possible instruments that have not been studied in this paper and that are of relevance for policy makers. In the model, the AE can only invest in the EME through the banks and we only look at the cross-border bank capital. In reality, non-financial firms issue dollar denominated debt that for the case of Mexico is of extreme relevance; this makes the cross-country relation much more complicated. We believe that this model captures one aspect of the cross-country relations that helps to understand the risks of external shocks for EMEs. Acknowledgments Any views expressed herein are those of the authors and do not necessarily reflect those of Banco de México or the Inter-American Development Bank, their Executive Boards, or their Management. We are grateful to Julio Carrillo for his advice and guidance. We also thank Ana María Aguilar and Jessica Roldán for their time to discuss and Cristina Arellano, Georgia Bush, Luca Dedola, Andrés Fernández Martin, Patrick Fève, Luisa Lambertini, Santiago Bazdresch, Gabriel Tenorio, Martín Tobal, Pinar Uysal, and two anonymous referees for their helpful comments. María del Carmen Hernández Ruiz provided excellent research assistance. Victoria Nuguer specially thanks the Directorate of Economic Studies at the General Directorate of Economic Research from Bank of Mexico, where she did most of the work for this project while she was a Researcher at the institution. We thank seminar participants at the Brownbag Seminar at Bank of Mexico, XVIII Workshop in International Economics and Finance, Sixth BIS CCA Research Conference, Spring 2015 Midwest Macro Conference, 21st International Conference on Computing in Economics and Finance, IBEFA Day-Ahead Conference Summer 2015, and 2nd ITAM-Pier Conference on Macroeconomics. All remaining errors are our own. 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