Global Liquidity, Leverage, House Prices and Exchange Rates9...Ambrogio Cesa-Bianchiy Andrea Ferreroz Alessandro Rebuccix March 25, 2016 ... Panel VAR for 56 advanced and emerging

Global Liquidity, Leverage, House Prices and Exchange Rates9

NOT FOR CIRCULATION

PLEASE DO NOT SHARE WITHOUT THE AUTHORS’ PERMISSION

Ambrogio Cesa-Bianchi† Andrea Ferrero‡ Alessandro Rebucci§

March 25, 2016

Abstract

Exchange rates and house prices can potentially amplify the expansionary effects of capitalinflows by inflating the value of collateral. We first document that, during a boom in capitalinflows, real exchange rates, house prices and equity prices appreciate; the current accountdeteriorates; and consumption and GDP expand; while in a bust these dynamics reverse sharply.Next we show that an identified change to the international supply of cross-border credit in aPanel VAR for 56 advanced and emerging countries has a similar transmission. The intensityof the consumption response to such a shock, however, differs significantly across countriesand it is associated with country characteristics of both the housing finance system and themonetary policy framework. We finally set up an open-economy model of housing consumptionwith domestic and international financial intermediation in which a shock to the internationalsupply of credit is expansionary. In this model environment, we illustrate how the evidenceuncovered may be interpreted in terms of relative importance of exchange rate and house priceappreciations in emerging and advanced economies.

Keywords: Capital Flows, Credit Supply Schock, Leverage, Global Liquidity, Exchange Rates,and Balance Sheet Effects, House Prices.JEL codes: C32, E44, F44.

9Alessandro Rebucci thanks the Black & Decker Research Fund for partial financial support for this paper. Theviews expressed in this paper are solely those of the authors and should not be taken to represent those of the Bankof England.†Bank of England. Email: [email protected].‡University of Oxford. Email: [email protected].§Johns Hopkins University Carey Business School and NBER. Email: [email protected].

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1 Introduction

Appreciating asset prices can potentially amplify the expansionary effects of capital inflows by in-

flating the value of collateral and expanding the borrowing capacity of the economy. Monetary and

macro-prudential policies geared toward stabilizing these dynamics may differ widely depending on

which asset price is responsible for the collateral expansion. If house prices are relaxing domestic

borrowing constraints, inward-looking macro-prudential tools, such as loan-to-value (LTV) require-

ments or leverage caps for financial intermediaries, may be appropriate. However, if the source of

amplification is the exchange rate, official reserve accumulation, sterilized intervention, or capital

controls may be effective in containing a boom.

In this paper, we first document that, during a boom associated with a capital inflow, all

asset prices (real exchange rates, house prices, and equity prices) appreciate, the current account

deteriorates, and consumption and GDP expand, while in a bust these dynamics reverse sharply.

Next, we show that an identified shock to the international supply of credit generates similar

responses for consumption, house prices, exchange rates, and the real short term interest rate.

The transmission, however is heterogenous across countries and the impact of this shocks is much

stronger in economies with larger share of foreign currency denominated liabilities. We then set up

a model in which an international credit supply shock is expansionary for the receiving country, and

study the characteristics of the economy under which the exchange rate channel of amplification

can dominate the house price channel, as we find in the empirical evidence that we report.

We start by describing the behavior of financial and macroeconomic variables during episodes

of boom and bust in capital flows, as for instance in Mendoza and Terrones (2008). We construct

an event study by identifying boom-bust episodes in cross-border bank credit. We then observe the

behavior of the economy around the peak of those boom-bust cycles. This unconditional analysis

shows that, during a capital flows boom, the exchange rate appreciate, house and equity prices

increase, the current account balance goes into deficit, and consumption and GDP expand, while

in the bust these dynamics reverse.

Next, we establish causation by identifying an exogenous change to the international supply

of credit, i.e. a global liquidity shock, in a panel Vector Autoregressive model (PVAR) for house

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prices, the real exchange rate, consumption and the real interest rate. We identify such a shock by

aggregating cross-border credit flows across all sending and receiving countries in our sample, and

by using the external instrumental variable approach of Stock and Watson (2012) and Mertens and

Ravn (2013). We find that the causal effects of an increase in the international supply of credit are

consistent with the unconditional associations documented in the event study.

However, the intensity of this transmission differs significantly across countries. We study this

heterogeneity investigating the association between the VAR responses to the shock and country

characteristics of the system of housing finance and the monetary policy framework. As far as the

system of housing finance is concerned, we consider measures of mortgage market depth, underlying

determinants of financial development, maturity and pricing (the share of variable-rate mortgages),

tax incentives (a measure of possible tax distortions), as well as home ownership rates. As far as

the monetary policy regime is concerned, we consider the degree of exchange rate regime flexibility,

the extent to which the system is fungicidally repressed, the presence of capital controls as well as

macroprudential regulation (i.e., LTV limits), and the share of foreign currency liabilities in total

liabilities. We find that the amplitude of the cyclical variations in consumption triggered by a

international credit supply shock is closely associated with a few of these characteristics, but the

direction of the association differ depending wether the economy is emerging or advanced.

In order to interpret this evidence, we set up a model in which both the exchange rate and

house prices can relax the collateral constraint. In a two-country world, a relatively patient econ-

omy channels funds to a relatively impatient one via competitive financial intermediaries operating

in global markets. The model features two types of financial frictions. First, impatient households

in the domestic country are subject to a borrowing constraint as in Kiyotaki and Moore (1997). Sec-

ond, financial intermediaries are subject to a leverage constraint as in Brunnermeier and Sannikov

(2014) and He and Krishnamurthy (2013).

A simplified version of the model is analytically tractable. The combination of the two financial

frictions delivers a powerful mechanism that fits the evidence rather well. In particular, a relaxation

of the leverage constraint on global financial intermediaries generates a global credit boom, which

leads to a current account deficit and a consumption increase in the domestic economy. If the shock

is sufficiently large, or the borrowing constraint in the domestic economy is already binding, the

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higher supply of credit reduces the real interest rate and fuels house prices. The full blown version

of the model cannot be solved analytically, but allows us to isolate the role of the exchange rate and

the house price channel of transmission quantitatively. The model, therefore, provides a framework

to interpret the VAR evidence and also to explore the impact of alternative policy responses to the

capital inflow.

The paper contributes to the recent literature on capital flows, housing and macroeconomic

dynamics along two dimensions. On the empirical side, we extend the analysis in Cesa-Bianchi,

Cespedes, and Rebucci (2015) by documenting the heterogeneity of the responses to a global credit

supply shock, and provide a model-based counterfactual and interpretation of the results. On the

theoretical side, the model goes beyond the typical assumption of frictionless international financial

markets (e.g. Ferrero, 2015), and introduces a role for global financial intermediation. To the best

of our knowledge, this is the first open economy model of housing and macroeconomic dynamics

with both domestic and international financial frictions.1

Our results are consistent with the recent findings of Mian, Sufi, and Verner (2016), who find

that a higher private debt to GDP ratio is associated with domestic booms and a deterioration of the

current account. The empirical analysis in our paper is able to attribute these dynamics to global

liquidity shocks. More precisely, we extend the idea that institutional changes and innovations in

financial markets may be a key driver of domestic housing booms (Favilukis, Kohn, Ludvigson,

and Van Nieuwerburgh, 2013) by studying the international spillovers of domestic liberalizations

via global financial intermediaries. Furthermore, our model disentangles the relative importance of

house prices and foreign-denominated liabilities in amplifying the shock. The theoretical analysis,

thus, delves one step deeper into the mechanism through which collateral constraints magnify the

effects of fundamental shock (Almeida, Campello, and Liu, 2006).

The rest of the paper is organized as follows. Section 2 reports some novel stylized facts on

house prices and capital flows. Section 3 describes the empirical model and reports the estimation

results. Section 4 sets up a DSGE model consistent with the facts in the previous sections. Section 5

describes the properties of the model in response to foreign credit supply shock. Section 6 concludes.

1Gabaix and Maggiori (2014) also develop a tractable model with a financial friction in international financialintermediation. Differently from ours, their work is primarily theoretical, focuses on exchange rate dynamics, andabstracts from housing.

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2 Capital Flows, Asset Prices and Economic Activity

In this section we document the behavior of asset prices and the real economy during boom-bust

cycles in international capital flows in a large sample of advanced and emerging markets.

We consider the following variables: GDP, private consumption, short-term interest rates, equity

prices, the effective exchange rate, the exchange rate vis-a-vis the US Dollar, cross-border credit to

the non-banking sector, and the current account as a share of GDP. All variables are expressed in

real terms.

We analyze the behavior of macroeconomic and financial variables around boom-bust episodes

in cross-border credit. To identify boom-bust episodes we define a boom (bust) as a period longer

than or equal to three years in which annual cross-border credit growth is positive (negative).2

The peak (trough) is defined as the last period within the episode in which the annual rate of

growth of cross-border credit is positive (negative). We use annual data to avoid the noise of

quarterly movements in cross-border bank credit. We then define boom-bust episodes as boom

episodes followed by a bust episode.

This procedure identifies 134 booms, 81 busts, and 50 boom-bust episodes.3 Figure 1 reports

the event study: we report the mean, median and interquartile range (solid line, dotted line and

shaded area, respectively) across all episodes, using a 9-year window that goes from three year

before the peak to five years after the peak. In each panel, time 0 marks the peak of the boom-

bust cycle in cross-border bank credit (i.e., the last period of a boom in which cross-border bank

credit displays a positive growth rate), which is also depicted with a vertical line. All variables are

expressed in percentage changes, with the exception of the short-term interest rate and the current

account over GDP which are expressed in percentage point changes.

Figure 1 shows that a boom in cross-border credit is associated with a large boom in the real

economy, as both GDP and consumption display positive and elevated rate of growth (about 5-

2This procedure is similar to the one commonly used in the literature (Gourinchas, Valdes, and Landerretche,2001, Mendoza and Terrones, 2008, Cardarelli, Elekdag, and Kose, 2010, Caballero, 2014, Benigno, Converse, andFornaro, 2015)The literature typically defines these episodes as periods in which credit (or capital inflows) rise morethan one standard deviation above their trend level. Our results are robust to using the traditional approach. Theadvantage of our approach is that we do not need to detrend the data, whic introduces spurious variation over timein the analysis.

3The summary statistics for these episodes (such as duration and amplitude) are reported in the Appendix.

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3 percent per year). The boom is also accompanied by very high house price and equity price

inflation. Real interest rates increase only the year before the peak and are associated with a fall in

asset prices and a slowdown in economic activity. On average, the real exchange rate does seems to

be unaffected by the capital inflow, but about half of the episodes are associated with very large real

appreciations. The current account deteriorates sharply for most episodes, and it starts to adjusts

gradually in about half of them before the boom is over during the last year of the expansion.

During the bust phase, these dynamics are partially reversed. The economy experiences a

contraction, with both GDP and to a lesser extent consumption falling. House prices and equity

prices collapse. The real exchange rate depreciates abruptly, and the current account reverts

abruptly and temporarily to a large surplus. While both GDP and consumption stabilize quickly,

both house prices and cross-border bank credit remain depressed for several years.

3 The Impact of a Global Liquidity Shock

In this section, we investigate the causal link from capital flows to house prices and the broader

macroeconomy, using a panel-vector autoregressive model (PVAR) that embeds both “pull” and

“push” factors, as usually assumed in the literature (e.g., Calvo, Leiderman, and Reinhart, 1996).

We establish causality by identifying a shock to a particular push factor: an exogenous shift in the

international supply of credit that we dub “global liquidity shock.” We then trace its impact on

house prices, consumption, the exchange rate, and interest rates.

3.1 A PVAR Model

The PVAR model that we specify includes a small set of variables for which we have a direct

counterpart in the model that we set up in section 4. We include two external variables and three

domestic variables. In addition to cross-border credit to the non-banking sector, we include the

real exchange rate vis-a-vis the US Dollar, the real (ex-post) short-term interest rate, real private

consumption, and real house prices. To keep the size of the VAR model as small as possible, we

do not include inflation and nominal interest rate separately. Thus, the real ex-post short-term

interest rate is meant to reflect the monetary policy stance. A stabilizing monetary policy response

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should manifests itself with a change in the real interest rate. Real private consumption is the

measure of economic activity that we focus on.

We specify the following VAR model for each country i:

xit = ai + bit+ cit2 + F1ixi,t−1 + uit, (1)

where xit is a vector of endogenous variables; ai is a vector of constants; t and t2 are vectors of

deterministic trends; F1i is a matrix of coefficients; and uit is a vector of residuals with variance-

covariance matrix Σiu. All variables considered enter in log-levels, except the interest rate, which

enter in levels. The model is the same for all countries to avoid introducing differences in country

responses due to different specifications, and because it would be difficult to find a perfectly data-

congruent specification for all country in the sample.

We estimate the model using the mean group estimator of Pesaran and Smith (1995) and

Pesaran, Smith, and Im (1996).4 In the estimation, we drop all countries which have less than 40

observations or have unstable dynamics (i.e., with eigenvalues larger than 1). This leaves us with

48 of the original 57 countries in our event study.5

3.2 Identification

While cross-border banking credit can be affected by both demand and supply factors, the shock

that we want to identify is a shift in the international supply of credit. First, we attenuate the

influence of country-specific pull factors by aggregating lending across all sending countries. As long

as countries are relatively small, innovations to this variable cannot be contaminated by domestic

shocks. Second, to rule out that demand factors common among all countries in the sample, or

that any particular country affects the aggregate measure, we also use the external instruments

identification approach proposed by Stock and Watson (2012) and Mertens and Ravn (2013).6

The candidate instruments that we consider are the US effective federal funds rate, the log of

4This is because pooled estimators may be inconsistent in a dynamic panel data model with heterogeneous slopecoefficient (i.e., slope coefficients that vary across countries).

5Specifically, we drop the following countries from our original sample: Brazil, Germany, India, Korea, Mexico,Morocco, Spain, and Uruguay.

6The Appendix reports the details of this identification strategy.

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US M2, the log of US broker-dealers’ leverage, the slope of the US yield curve, the VIX index, and

the TED spread. Note that, since the candidate instruments are all US variables, we exclude the

US from the PVAR.

Equipped with the reduced-form residuals from the OLS estimation of the VAR system (1)

country-by-country, we can regress them on the instruments above (i.e., the first stage regressions

described by equation (A.6) in the Appendix).7 For each country, we select the instrument that

maximizes the F -Statistic associated with the first stage regression, and drop from the analysis

all countries for which the F -statistic of the first stage regression is below 5, leaving us with 33

countries out of the 48 for which we estimated the VAR model.8,9 For each country-specific VAR,

both the R2 and the F -statistic associated with the first stage regressions are reasonably high,

averaging 0.73 and 8.7 across all countries, respectively.

3.3 The Typical Response of a Small Open Economy to a Global Liquidity

Shock

We are now ready to discuss the impulse response functions to this global liquidity shock (i.e., an

exogenous shift in the international supply of credit). Figure 2 reports the mean group estimator

computed across all countries in our sample.10 The size of the shock is normalized so that it

corresponds to an increase in cross-border credit of 1 percent (to consider a 10 percent shock we

can just scale the parameter estimates accordingly as the model is linear). The dark and light

shaded areas represent the one- and two-standard deviation confidence intervals, respectively. The

dashed line is the uncensored impulse response function.

In the typical small open economy represented here, a global liquidity shock leads to a statisti-

cally significant and persistent increase in real consumption and real house prices, a hump shaped

7We enter the instruments both in levels and first differences.8To check the robustness of our results, in the Appendix we conduct two additional exercises. First we keep all

48 countries in the mean group estimator irrespective of their F -statistic. Second, we drop all countries for which theF -statistic is smaller than 10 (as recommended by Stock, Wright, and Yogo (2002) to avoid problems related to weakinstruments). The results from these exercises display little difference from our baseline.

9Specifically, we drop the following countries: China, Czech Republic, Israel, Latvia, Lithuania, Luxembourg,Malta, Peru, Poland, Russia, Serbia, Slovenia, Slovakia and South Africa.

10We use a simple average of the country-specific estimates to construct the mean group estimates. We also censorthe responses included in this average at the 10 percent level (5 percent each side) to eliminate the possible influenceof any outlier on the averages.

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response of real interest rate, a very prolonged real exchange rate appreciation. Consumption and

real house prices increase by about 0.2% and 0.3% above their long-run levels, respectively, within

a year. The real exchange vis-a-vis the US Dollar appreciates on impact by about 0.8 percent, ar-

guably driven by the nominal exchange rate, and then reverts to its equilibrium level over time very

slowly. The response of the short-term real interest rate is initially muted, if not accommodative.

The real interest rate then increases more slowly than consumption and house prices, but steadily

for about two years, peaking at about 6 basis points above its long-run level (or 60 basis point for

a 10 percent increase cross border credit).

This transmission is consistent with an expansionary effect of the capital flow shock that we

identified, possibly mitigated by a tightening monetary policy response, both qualitatively and

quantitatively.

3.4 Understanding Heterogeneity in the Response to Global Liquidity Shocks

As we can see from Figure 2 the house price and, to a lesser, extent the consumption responses

have relatively wide error bands, therefore masking significant heterogeneity across countries. In

this section we investigate whether this heterogeneity follow specific patterns.

We conjecture that asset prices might amplify the impact of an increase in the international

supply of credit through different channels in different countries. Consider for instance the following

collateral constraint on borrowing, which is similar to the one in our model in the second part of

the paper:

dt ≤ θ (qtht) ,

where dt is borrowing, qtht is the value of the house, and θ represents the maximum admissible loan-

to-value (LTV) ratio. An increase in the house price leads to an increase in the borrowing capacity

through increased collateral value. However, if borrowing is denominated in foreign currency, an

exchange rate appreciation can would play a similar role by increasing the foreign currency value of

qtht. In what follows, therefore, we try to better understand the importance of these two channels

by exploring the association between the characteristics of the housing finance system and the

monetary policy framework and strength of the consumption response to the global liquidity shock.

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The list of cross section variables that we consider is reported in Table X in Appendix. As far

as the system of housing finance is concerned, we consider measures of mortgage market depth,

underlying determinants of financial development, maturity and pricing (the share of variable-

rate mortgages), tax incentives (a measure of possible tax distortions), as well as home ownership

rates. As far as the monetary policy regime is concerned, we consider the degree of exchange rate

flexibility, the extent to which the system is financially repressed, the presence of capital controls

on inflows or outflows as well as macroprudential regulation (i.e., LTV limits), and the share of

foreign currency liabilities in total liabilities.

We want to investigate how the country characteristics are associated with the intensity of the

response to the global liquidity shock.11 Tables 2 and 3 report a battery of univariate OLS regres-

sions of the peak response of all variables in the VAR on each of these country characteristics and

a dummy variable for emerging market status. We report results for the full sample, and also two

sub-samples: the group of emerging market and the group of advanced economies. Distinguishing

between advanced and emerging markets economies is a way to capture the role of the quality of

institutions in a clear cut way (indeed our dummy has a correlation of 0.73 with per capita income

level in 1990 – not reported). As we can see, different characteristics often have a different sign

in the two group of countries. For example, higher home ownership is associated with a stronger

consumption response to the global liquidity shock in emerging markets, but has no association

with it in advanced economies. Exchange rate flexibility seems to contain consumption responses

in advanced economies, but is either not associated or has a weak positive association with the con-

sumption response in emerging economies. In general, however, our sample is too small to obtain

reliable estimates from the split of the sample in two.

To gain statistical power, 4 reports the same battery of univariate OLS regressions adding a

dummy variable for emerging market status. The dummy enters the regression interacted with the

specific characteristics considered. The dummy takes the value of 1 when the country is advanced

and 0 when it is emerging. So the estimated coefficient for emerging markets is the first column of

each block. The estimated coefficient for advanced economies is given by the sum of the coefficients

in the first and the third column in each block.

11Table E.1 reports a correlation matrix among all these characteristics, and also between the country characteristicsand the peak response of the 4 variables in the VAR system.

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The results suggests that housing finance characteristics might matter more for emerging

economies, while monetary policy framework characteristics might be more relevant for emerg-

ing markets. In particular, the share of foreign currency liability in total liability is significantly

associated with stronger consumption responses in emerging markets while is not associated with

it in advanced economies. So we now explore this specific characteristics in more details.

3.5 Response to Global Liquidity Shock with Balance Sheet Effects

Using BIS confidential data, we rank all countries in our sample based on the share of cross-border

bank credit in foreign currency over total cross-border bank credit. We then split our sample in two

groups of equal size, depending on whether a country’s share of foreign currency liabilities is above

or below the median. Finally, we compute the mean group estimator on the two groups separately.

The impulse responses for each group are reported in Figure 3.

The impact of the global liquidity shock in the typical ‘low share of foreign currency liabilities’

economy (panel (a) of Figure 3) is relatively similar to the impact that on the typical economy. Real

consumption, house prices and the exchange rate increase in response to the shock, even though

by a smaller magnitude than in Figure 2.

Differently, the response of the short-term real interest rate is now initially mute and then

positive. In contrast, the global liquidity shock has a much stronger impact on the typical ‘high

share of foreign currency liabilities’ economy (panel (b) of Figure 3). Consumption increases on

impact by 0.35 percent and house price by 0.6 percent. These impacts are three times larger than

in the low foreign currency liabilities economy. Differently, the response of the exchange rate is

slightly smaller at 0.8 percent, with the wide error bands revealing large heterogeneity around the

mean group estimate.

This is consistent with the behavior of the short-term interest rate, which falls much more

sharply than in panel (a) of Figure 3.

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4 Model

This section presents a two-country model with financial frictions to interpret the empirical evidence

reported in the previous section. The model, which follows Justiniano, Primiceri, and Tambalotti

(2015), is admittedly very simple, and abstracts from several realistic features, such as aggregate

uncertainty and endogenous production. The great benefit of this approach is that, in a simplified

version of the model, we can obtain clear analytical results that guide our intuition in the more

general framework.

Time is discrete and indexed by t. The world consists of two countries, denoted by H (Home)

and F (Foreign) of size n ∈ (0, 1) and 1−n, respectively. Each country is endowed with one good. In

each country, the representative household consumes a bundle of the two goods, as well as housing

services, assumed to be proportional to the stock of housing.

The two countries only differ in the degree of patience. In particular, the domestic represen-

tative household is relatively impatient. Housing purchases are subject to a standard collateral

constraint. The foreign representative household saves via deposits and equity in a “global” fi-

nancial intermediary. The financial intermediary channels funds internationally from lenders to

borrowers and is subject to a leverage constraint (or, equivalently, a capital requirement).

4.1 Goods Markets

The representative household in country H consumes a basket that combines Home and Foreign

goods according to a Cobb-Douglas aggregator:

ct ≡(cHt)

α(cFt)1−α

αα(1− α)1−α .

The weight on imported goods in the Home consumption basket is a function of the relative size of

the foreign economy (1− n) and of the degree of openness λ ∈ (0, 1), which is assumed to be equal

in both countries:

1− α ≡ (1− n)λ.

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This assumption implies α ∈ (n, 1] and generates home bias in consumption.12

Expenditure minimization determines the optimal allocation of consumption across home and

foreign goods given their price in Home currency (PHt and PFt, respectively):

cHt = α

(PHtPt

)−1

ct and cFt = (1− α)

(PFtPt

)−1

ct. (2)

The price of a unit of the aggregate consumption basket is:

Pt = PαHtP1−αFt . (3)

The consumption basket for the representative household in the foreign economy is defined analo-

gously (foreign variables are denoted by an asterisk), with α∗ ≡ nλ.

The Law Of One Price (LOOP) holds, that is, Pit = EtP ∗it, for i = {H,F}. From the perspective

of country H, the terms of trade (the price of imports relative to the price of exports) are

τt ≡ EtP ∗Ft/PHt = PFt/PHt = P ∗Ft/P∗Ht.

Therefore, an increase in τt represents a depreciation of the terms of trade. Given the expression

of the price index, the relations between the terms of trade and the relative price of each good are

pHt = τα−1t and pFt = ταt ,

where pit ≡ Pit/Pt.

The real exchange rate, also from the perspective of country H, is the price of the foreign

consumption bundle in terms of the home consumption good:

st ≡EtP ∗tPt

. (4)

As for the terms of trade, an increase in st corresponds to a real exchange rate depreciation for

12The size of home bias decreases with the degree of openness and disappears when λ = 1 (Sutherland, 2005). Thisspecification encompasses the small open economy case when n→ 0.

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home consumers. In spite of the LOOP, purchasing power parity does not hold because of home

bias, that is the real exchange rate is generally different from one. However, the (log) real exchange

rate is proportional to the (log) terms of trade:

st = τα−α∗

t = τ(t 1− λ). (5)

Therefore, we can characterize the equilibrium indifferently with respect to the real exchange rate

or of the terms of trade only.

4.2 Domestic Households (Impatient Borrowers)

The representative domestic household consists of a continuum of members of measure n. All mem-

bers are identical and maximize the present discounted value of an instantaneous felicity function

defined over consumption of non-durable goods and housing services, assumed to be proportional

to the housing stock ht:

max{ct,ht,dt}

Ut =∞∑t=0

βt [u(ct) + v(ht)] , (6)

where β ∈ (0, 1) is the individual discount factor, u′ and v′ > 0, and u′′ and v′′ ≤ 0.

Impatient households are subject to the following budget constraint:

ct + qtht − stdt = −stRt−1dt−1 + pHtyt + qtht−1, (7)

where qt is the price of houses in terms of the consumption good, yt is the per-capita endowment

of domestic consumption goods, and dt is the amount of one period debt (in units of foreign

consumption goods) accumulated by the end of period t, and carried into period t+ 1, with gross

real interest rate Rt.

Following Kiyotaki and Moore (1997), a collateral constraint limits debt to a fraction θ ∈ (0, 1)

of the value of the owned housing stock:

stdt ≤ θqtht. (8)

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A common interpretation of this constraint is that the parameter θ represents the maximum admis-

sible loan-to-value (LTV) ratio. We depart from most of the literature by expressing the borrowing

constraint in terms of foreign-denominated liabilities. Because debt is denominated in foreign

goods, an appreciation of the real exchange rate relaxes the borrowing constraint, holding constant

the value of housing. This mechanism provides an additional amplification channel on top of the

standard one due to house prices. The data suggest that both play a role, with the cross-sectional

evidence favoring the foreign-liabilities channel. The quantitative analysis allows for a horse race

between these two mechanisms.

The problem for the domestic representative household is to maximize (6) subject to (7) and

(8). Let µtu′(ct) be the normalized Lagrange multiplier on the borrowing constraint. The first

order condition for the optimal choice of debt is:

1− µt = βRtEt[u′(ct+1)

u′(ct)

st+1

st

]. (9)

Expression (9) is the consumption Euler equation that relates the marginal benefit of higher con-

sumption today to the marginal cost of lower consumption tomorrow. The equation shows how a

tighter borrowing constraint (i.e., a higher µt) reduces the marginal benefit of higher consumption

today.

The first order condition for the optimal choice of housing services is:

(1− θµt)qt =v′ (ht)

u′(ct)+ βEt

[u′(ct+1)

u′(ct)qt+1

]. (10)

Expression (10) prices housing. This equation shows that house prices are higher when (i) the

maximum loan-to-value ratio is higher and (ii) the borrowing constraint is tighter.

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4.3 Foreign Households (Patient Lenders)

The representative foreign household consists of a continuum of members of measure 1 − n who

derive utility from consumption (c∗t ) and maximize the following utility function:

max{c∗t ,d∗t ,e∗t }

Ut =

∞∑t=0

β∗tu(c∗t ), (11)

with β∗ ∈ (β, 1).13

Foreign households are subject to the following budget constraint:

c∗t + d∗t + et + ψ(et) = pFty∗t +Rdt−1d

∗t−1 +Ret−1et−1 + πt, (12)

where d∗t are deposits in a financial intermediary in period t−, which pay a gross interest rate Rdt ,

et represents the amount of equity capital in the financial intermediary, with gross rate of return

Ret , ψ(et) represents a convex cost of changing equity position, and y∗t is the per-capita endowment

of non-durable F consumption goods. As in Jermann and Quadrini (2012), this cost function is

positive (and so are its first two derivatives), and creates a pecking order of liabilities whereby debt

is always preferred to equity.

The problem for the foreign representative household is to maximize (11) subject to (12). The

first order conditions for the optimal choice of deposits and equity are:

1 = β∗RdtEt[u′(c∗t+1)

u′(c∗t )

], (13)

and

1 + ψ′(et) = β∗RetEt[u′(c∗t+1)

u′(c∗t )

]. (14)

13Because of this assumption, the borrowing constraint of the foreign household is never binding in equilibrium. Forsimplicity, we abstract from foreign housing purchases altogether. The only difference from explicitly incorporatingforeign housing decisions would be to price housing in the lending country—something our empirical evidence haslittle to say about.

16

4.4 Global Financial Intermediary

A representative global financial intermediary finance loans to impatient domestic households with

a mix of equity and deposits collected from the patient foreign savers. Deposits and loans are

denominated in Foreign goods to capture the idea that global financial intermediaries do not bear

the costs of currency exposure, either by directly matching the denomination of assets and liabilities,

or by using financial instruments to hedge their positions. Given borrowers and lenders’ decisions,

Table 1 describes the balance sheet of the global financial intermediary at time t.

Table 1 Global Financial Intermedi-aries’ Balance Sheet

Assets Liabilities

Loans: ndt Deposits: (1− n)d∗tEquity: (1− n)et

Next period’s profits are:

max{dt,d∗t ,et}

Πt+1 = Rt ndt −Rdt (1− n)d∗t −Ret (1− n)et. (15)

The financial intermediary is subject to a leverage constraint:

ndt ≤ χ(1− n)et, (16)

where χ ∈ (0, 1) captures the maximum leverage ratio either markets or regulatory authorities

are willing to tolerate.14 The problem for the representative global financial intermediary is to

maximize (15) subject to the balance sheet constraint

ndt = (1− n)d∗t + (1− n)et, (17)

and to the leverage constraint (16).

Let φt be the Lagrange multiplier on the leverage constraint. The first order conditions for

the optimal choice of loans (after substituting for d∗t in the profit function from the balance sheet

14Gabaix and Maggiori (2014) obtain a similar constraint assuming financiers can divert part of the funds inter-mediated through their activity.

17

constraint) is:

φt = Rt −Rdt . (18)

The first order condition for the optimal choice of equity is:

Ret −Rdt = φtχ. (19)

Replacing φt from (18) into (19) we get:

Rt =

(1− 1

χ

)Rdt +

1

χRet

The last equation shows that the interest rate on loans to impatient households is a weighted

average of the cost of funding these loans with a combination of equity and deposits.

4.5 Assumptions, Functional Forms, and Equilibrium

In equilibrium, the assumption of a relative impatient domestic household implies that the Home

country borrows from the Foreign country at the prevailing market interest rate. Therefore, bor-

rowers can use their endowment, together with new loans, to buy non-durable consumption goods

and new houses, and to repay principal and interest rates on old loans. Additionally, we assume

that the supply of housing is fixed and normalized to 1 (ht = h = 1), and that the equity adjustment

cost function is of the form:

ψ(et) = ηe(ete

)γ,

where e is steady state equity, η > 0, and γ > 1.

We solve for an equilibrium in which the leverage constraint is binding. An equilibrium is a set

of stationary processes

{qt, µt, Rt, Rdt , Ret , dt, et, τt, st, ct, c∗t , cHt, c∗Ht, cFt, c∗Ft}

for t ≥ 0 such that:

18

1. Domestic households maximize their utility subject to their budget and collateral constraint

cHt = ατ1−αct,

cFt = (1− α) τ−αct

1− µt = βRtEt[u′(ct+1)

u′(ct)

st+1

st

],

(1− µtθ)qt =v′ (h)

u′(ct)+ βEt

[u′(ct+1)

u′(ct)qt+1

],

stdt ≤ θqt,

ct = τα−1t yt + st(dt −Rt−1dt−1).

with µt ≥ 0.

2. Foreign households maximize their utility subject to their budget constraint

c∗Ht = α∗τ1−α∗t c∗t

c∗Ft = (1− α∗) τ−α∗t c∗t ,

1 = β∗RdtEt[u′(c∗t+1)

u′(c∗t )

],

1 + ψ′(et) = β∗RetEt[u′(c∗t+1)

u′(c∗t )

].

3. Financial intermediaries maximize their profits subject to their balance sheet and leverage

constraints

Rt =

(1− 1

χ

)Rdt +

1

χRet ,

ndt = χ(1− n)et.

4. Goods market clear

nyt = ncHt + (1− n)c∗Ht

(1− n)y∗t = ncFt + (1− n)c∗Ft.

19

Finally, the relation between the real exchange rate and the terms of trade is

st = τα−α∗

t .

5 A Foreign Credit Supply Shock

This section studies the response of the domestic economy to a foreign shock that is consistent

with the “global liquidity shock” identified in the empirical analysis of section 3. Specifically,

we consider a foreign credit supply shock caused by the relaxation of the financial intermediary’s

leverage constraint (χ). We focus on this shock because, according to the instrument selection

procedure described in section 3, US broker dealers’ leverage turns out to be the most relevant

instrument to identify global liquidity shocks. Specifically, leverage is chosen as external instrument

in 42 out of 48 cases.

We first present the results from a simplified version of the model to build intuition on how the

foreign credit supply shock transmits to the domestic economy. We then consider the full version

model to conduct a quantitative exercise.

5.1 Analytical Results

We consider a simplified version of the model that allows us to characterize analytically the equi-

librium of the economy. Consider a symmetric (n = 0.5), one-good (st = τt = 1) world economy,

in which the representative households of both countries are risk-neutral (u′(ct) = u). In this case,

the marginal rate of substitution between housing services and consumption is constant and the

equilibrium is fully static (the Appendix reports the full derivation).

Under these assumptions, we can derive the credit demand and the credit supply schedules, and

characterize the equilibrium in the credit market.

The combination of the first order condition for financial intermediaries and the first order

20

conditions for the Foreign representative household gives the supply of funds:

R =1

β∗

[1 + Θ

(d

χ

)γ−1], (20)

where Θ = γηe1−γ . In the space {d,R}, the supply is an increasing and convex function (as long

as γ > 1), which crosses the vertical axis at 1/β∗.

The combination of the first order conditions for the Home representative household gives the

demand of funds:

R =

1/β if d < θp

θ−(1−β)βθ − mrs

βd if d = θp(21)

Credit demand is a piecewise function in the space {d,R}. The first portion is flat: When debt is

low, the collateral constraint is not binding. Hence, the shadow price of the collateral constraint is

zero. The second part of the demand schedule is downward-sloping. The borrowing constraint at

equality pins down the kink of the demand function.

Finally, we can derive an expression for house prices that depends on whether the collateral

constraint is binding or not:

q =mrs

1− µθ − β, (22)

while the Home household budget constraint yields domestic consumption:

c = y − (R− 1)d. (23)

The intersection of demand and supply of funds determines an equilibrium quantity of credit d

that flows from the foreign to the domestic economy, and an associated interest rate R. As Figure

4 shows, depending on the parameter values, two equilibria may arise. If the borrowing constraint

does not bind (point A in Figure 4), the interest rate is equal to the inverse of the home households’

discount factor (R = 1/β), house prices equal the present discounted value of the marginal rate of

substitution (q = mrs/(1−β)), and credit is low. Vice versa, if the borrowing constraint is binding

(point B in Figure 4), the interest rate is “low,” and lies somewhere in between the inverse of the

two individual discount factors (1/β∗ ≤ R < 1/β), while credit and house prices are high. Given

21

the value of credit and the interest rate, equity equals credit divided by the leverage constraint

parameter χ. Finally, the budget constraints determine consumption of the two representative

households.

Consider now an increase in χ that leads to an increase in leverage for financial intermediaries.

Since equity is sticky, the shock shifts the supply of credit, which leads to increased cross-border

bank lending. In response to the shock, consumption increases. Depending on the starting point

and the size of the shock, the interest rate and house prices respond differently.

5.1.1 Case 1: Small Shock in a Low Credit Economy

The first case corresponds to an economy that starts in the equilibrium with low credit and high

interest rate (as in point A depicted in Figure 4). If the shock is small, the supply schedule shifts

right (dashed line in Figure 5), but not enough to cross the downward sloping portion of the demand

schedule (point A′). The increase in credit availability is not enough to make agents in the domestic

economy willing to increase their housing purchases. Instead, the additional funds are fully spent

on consumption of non-durable goods. As a result, the shock has no effect on interest rates and

house prices.

5.1.2 Case 2: High Credit Economy

The second case sees the domestic economy starting in an equilibrium in which credit supply is

relatively high and the interest rate relatively low (as in point B depicted in Figure 4). As in the

previous case, the shock shifts the supply schedule to the right (dashed line in Figure 6). But

now the additional availability of credit pushes down on the interest rate and induces domestic

households to further purchase housing (point B′). As the interest rate falls, the shadow value of

housing increases and magnifies the effect on house prices.

5.1.3 Case 3: Large Shock in a Low Credit Economy

The most interesting case occurs when a large credit shock hits an economy that starts with low

credit and a high interest rate (as in point A depicted in Figure 4). In this case, the supply

22

schedule shifts enough to cross the downward sloping portion of the demand schedule (dashed

line in Figure 7), pushing the economy to the new equilibrium denoted by A′. As a result, the

adjustment is similar to the previous case, but all the effects are obviously larger. In particular,

this scenario shows how a relaxation of the collateral constraint via increased house prices can

amplify the foreign-ignited domestic boom caused by the foreign credit supply shock. This result

is qualitatively in line with the VAR evidence, especially for the those countries that have a large

share of foreign currency liabilities. As cross-border credit increases, so do consumption and house

prices. If borrowing is limited by a collateral constraint, the foreign credit supply shock relaxes the

tightness of the constraint by increasing the value of the collateral.

The simplified model, however, abstracts from international relative price movements. As we

have seen in section 3, the data suggest that foreign-denominated liabilities are a powerful source of

amplification that competes with house prices in relaxing collateral constraints following a foreign

credit supply shock. This consideration pushes us toward a model that allows us to study a horse

race between these two amplification channels.

In the next section, we return to the full model and consider the relative importance of the two

candidate explanations for amplification of foreign credit supply shocks.

5.2 Quantitative Results

Besides returning to a two-good world economy in which countries can differ in size, we depart

from the assumption of risk neutrality and assume that preferences for both Home and Foreign

representative households are:

u(ct) =c1−υt − 1

1− υ,

where υ > 0 is the coefficient of relative risk aversion. Next, we provide a short description of

the calibration. The Appendix reports the complete list of the equations that characterize the

equilibrium, together with the derivation of the steady state.

Table 5 summarizes the parameter values. We set the discount factor in the foreign economy

β∗ to 0.992, consistent with an annualized interest rate on deposits (Rdt ) of 3.25%. The discount

factor for home consumers (β < β∗) is assumed to be 0.985.

23

We choose a coefficient of risk aversion υ equal to 1.5, and then set the (constant) marginal

utility of housing services to an arbitrarily low number.

We parametrize the equity adjustment cost function to obtain a return on equity (Ret ) of about

6.4%, which implies η = 0.005 and γ = 1.5. We set steady state leverage (χ) to 5, which gives an

interest on borrowed funds for home consumers equal to about 4%. The maximum allowed LTV

ratio (θ) is set to 0.75.

In line with the empirical exercise, we assume that the domestic economy is small relative to

the foreign economy. We therefore set n = 0.01. We also assume a substantial degree of home bias

in consumption (α = 0.6). Home bias in consumption for the foreign economy is set symmetrically.

As in the previous sections, we consider a foreign credit supply shock caused by the relaxation

of the financial intermediary’s leverage constraint (χ), which is assumed to follow the stationary

autoregressive process

χt = χ(1−ρχ)χρχt−1 exp (εχ,t) , (24)

where ρχ > 0 is the persistence parameter and εχt ∼ N (0, σ2χ) is an exogenous i.i.d. innovation.

We solve and log-linearize the model around its non-stochastic steady state using Dynare,

focusing on the case in which the collateral constraint is always binding (Case 2 in the previous

section).

5.3 Baseline

Figure 8 reports the impulse responses to a shock to εχt. To facilitate the comparison with the

impulse responses from the VAR in section 3, we normalize the shock as to generate a 1% increase in

Home borrowing. As in the simple model, the shock corresponds to an outward shifts of the credit

supply schedule. The additional availability of credit pushes down on the interest rate and induces

domestic households to further purchase non-durable goods and housing services. As the interest

rate falls, the shadow value of housing increases and magnifies the effect on house prices. Differently

from the simplified model, however, the real exchange rate now plays an additional amplification

role. The increase in domestic demand, together with home bias, implies an appreciation of the

real exchange rate. Therefore, ceteris paribus, the value of collateral in units of domestic goods

24

increases, further relaxing the borrowing constraint.

5.4 Counterfactuals

[To be completed]

Address relative role of house prices and real exchange rate in amplifying foreign credit supply

shock.

Estimate the model by matching impulse responses to the data.

Counterfactual 1: Keep house prices at their steady state value.

Counterfactual 2: Keep real exchange rate at its steady state value.

6 Conclusions

[To be completed]

25

Table 2 Cross-country Determinants of Impulse Response to Global Liquidity Shock

CONSUMPTION HOUSE PRICES

Coeff t-Stat R2 N Coeff t-Stat R2 N

Full Sample

MortgDebt / GDP (Avg) -0.05 -0.94 0.03 33 -0.20 -1.45 0.06 33MortgDebt / GDP (Max) -0.10 -1.95 0.11 33 -0.20 -1.53 0.07 33HousLoan Penetr. (2011) -0.12 -2.34 0.15 33 -0.20 -1.43 0.06 33Tenure : Owner-occupied units 0.08 1.60 0.08 33 0.28 2.17 0.13 33Legal Right Index 0.04 0.66 0.01 33 0.07 0.44 0.01 33Credit Info Index 0.08 0.94 0.03 33 0.10 0.42 0.01 33Cost of Registering Property -0.09 -1.68 0.08 33 -0.23 -1.71 0.09 33Term to Maturity 0.07 1.35 0.06 33 0.01 0.11 0.00 33Int. Type Interest Type 0.01 0.05 0.00 33 0.56 1.57 0.07 33Tax Deduction (yes=1, no=0) 0.19 1.68 0.08 33 0.05 0.17 0.00 33Full Recourse (yes=1, no=0) -0.08 -0.49 0.01 33 -0.03 -0.07 0.00 33LTV (typical) 0.01 0.24 0.00 33 0.16 1.12 0.04 33Max LTV -0.06 -1.23 0.05 33 -0.09 -0.68 0.01 33ExchRate FLEX (Avg 2000-10) 0.02 0.36 0.00 33 -0.07 -0.53 0.01 33Shar of FC Liab (Avg) 0.21 4.69 0.42 33 0.45 3.55 0.29 33Average KCO 95-05 0.11 1.67 0.09 30 0.12 1.08 0.04 30Average KCI 95-05 0.09 1.56 0.08 30 0.08 0.76 0.02 30Average REO 95-05 0.08 1.21 0.05 30 0.10 0.94 0.03 30

Emerging Markets

MortgDebt / GDP (Avg) 0.12 1.02 0.06 19 0.13 1.20 0.08 19MortgDebt / GDP (Max) 0.06 0.85 0.04 19 0.14 2.16 0.22 19HousLoan Penetr. (2011) 0.00 0.00 0.00 19 0.09 1.30 0.09 19Tenure : Owner-occupied units -0.09 -1.09 0.07 19 0.04 0.51 0.02 19Legal Right Index 0.12 1.57 0.13 19 0.16 2.15 0.21 19Credit Info Index 0.02 0.27 0.00 19 0.09 1.28 0.09 19Cost of Registering Property 0.03 0.25 0.00 19 -0.04 -0.37 0.01 19Term to Maturity -0.04 -0.70 0.03 19 -0.09 -1.55 0.12 19Int. Type Interest Type 0.11 1.84 0.17 19 0.06 1.05 0.06 19Tax Deduction (yes=1, no=0) -0.12 -0.77 0.03 19 -0.01 -0.05 0.00 19Full Recourse (yes=1, no=0) 0.12 0.77 0.03 19 -0.02 -0.15 0.00 19LTV (typical) 0.00 -0.04 0.00 19 0.01 0.08 0.00 19Max LTV 0.01 0.09 0.00 19 0.06 1.04 0.06 19ExchRate FLEX (Avg 2000-10) 0.02 0.33 0.01 19 0.03 0.47 0.01 19Shar of FC Liab (Avg) 0.05 0.92 0.05 19 0.09 1.68 0.14 19Average KCO 95-05 0.23 3.19 0.38 19 0.24 3.72 0.45 19Average KCI 95-05 0.28 0.79 0.04 19 0.26 0.76 0.03 19Average REO 95-05 0.36 1.37 0.10 19 0.46 1.90 0.18 19Average REI 95-05 0.15 0.50 0.01 19 0.35 1.29 0.09 19

Advanced Economies

MortgDebt / GDP (Avg) 0.00 -0.02 0.00 14 -0.18 -0.41 0.01 14MortgDebt / GDP (Max) 0.02 0.14 0.00 14 -0.10 -0.21 0.00 14HousLoan Penetr. (2011) 0.08 0.51 0.02 14 0.51 0.80 0.05 14Tenure : Owner-occupied units 0.00 -0.02 0.00 14 0.21 0.85 0.06 14Legal Right Index 0.08 1.17 0.10 14 0.11 0.39 0.01 14Credit Info Index 0.15 1.48 0.16 14 0.28 0.66 0.03 14Cost of Registering Property -0.18 -2.42 0.33 14 -0.57 -1.69 0.19 14Term to Maturity 0.07 1.00 0.08 14 0.13 0.44 0.02 14Int. Type Interest Type 0.06 0.22 0.00 14 1.37 1.45 0.15 14Tax Deduction (yes=1, no=0) 0.38 2.99 0.43 14 0.37 0.56 0.03 14Full Recourse (yes=1, no=0) 0.03 0.15 0.00 14 0.41 0.54 0.02 14LTV (typical) 0.06 0.80 0.05 14 0.45 1.47 0.15 14Max LTV -0.06 -0.79 0.05 14 0.16 0.47 0.02 14ExchRate FLEX (Avg 2000-10) -0.17 -2.02 0.25 14 -0.85 -2.76 0.39 14Shar of FC Liab (Avg) 0.24 1.53 0.16 14 0.83 1.28 0.12 14Average KCO 95-05 -0.02 -0.20 0.00 11 -0.39 -1.61 0.22 11Average KCI 95-05 -0.03 -0.47 0.02 11 -0.36 -1.86 0.28 11Average REO 95-05 -0.05 -0.69 0.05 11 -0.30 -1.42 0.18 11

Note. OLS regressions of the peak response of the variables in the VAR on a set of country-specific characteristics.We report results for the full sample, and also two sub-samples: the group of emerging market and the group ofadvanced economies. 26

Table 3 Cross-country Determinants of Impulse Response to Global Liquidity Shock

EXCHANGE RATE INTEREST RATE

Coeff t-Stat R2 N Coeff t-Stat R2 N

Full Sample

MortgDebt / GDP (Avg) 0.02 0.17 0.00 33 -0.08 -1.13 0.04 33MortgDebt / GDP (Max) -0.04 -0.37 0.00 33 -0.07 -1.13 0.04 33HousLoan Penetr. (2011) 0.07 0.70 0.02 33 -0.07 -1.08 0.04 33Tenure : Owner-occupied units 0.05 0.48 0.01 33 0.08 1.25 0.05 33Legal Right Index -0.07 -0.70 0.02 33 0.04 0.60 0.01 33Credit Info Index 0.04 0.27 0.00 33 0.17 1.53 0.07 33Cost of Registering Property 0.03 0.27 0.00 33 -0.05 -0.79 0.02 33Term to Maturity 0.04 0.39 0.00 33 -0.08 -1.21 0.05 33Int. Type Interest Type -0.20 -0.78 0.02 33 0.15 0.83 0.02 33Tax Deduction (yes=1, no=0) -0.03 -0.13 0.00 33 -0.18 -1.16 0.04 33Full Recourse (yes=1, no=0) -0.07 -0.22 0.00 33 0.16 0.73 0.02 33LTV (typical) -0.06 -0.63 0.01 33 -0.05 -0.65 0.01 33Max LTV 0.09 0.95 0.03 33 -0.02 -0.25 0.00 33ExchRate FLEX (Avg 2000-10) 0.08 0.79 0.02 33 -0.07 -0.97 0.03 33Shar of FC Liab (Avg) 0.11 1.09 0.04 33 0.10 1.32 0.05 33Average KCO 95-05 -0.08 -0.58 0.01 30 0.05 0.46 0.01 30Average KCI 95-05 -0.09 -0.67 0.02 30 0.03 0.32 0.00 30Average REO 95-05 -0.16 -1.20 0.05 30 0.00 0.02 0.00 30

Emerging Markets

MortgDebt / GDP (Avg) 0.14 0.66 0.03 19 0.00 -0.04 0.00 19MortgDebt / GDP (Max) 0.05 0.35 0.01 19 0.01 0.49 0.01 19HousLoan Penetr. (2011) -0.01 -0.10 0.00 19 0.00 -0.19 0.00 19Tenure : Owner-occupied units 0.06 0.44 0.01 19 0.01 0.41 0.01 19Legal Right Index 0.32 2.37 0.25 19 0.03 1.84 0.17 19Credit Info Index 0.07 0.53 0.02 19 0.00 0.28 0.00 19Cost of Registering Property -0.16 -0.76 0.03 19 0.00 0.17 0.00 19Term to Maturity -0.04 -0.38 0.01 19 -0.01 -0.63 0.02 19Int. Type Interest Type 0.14 1.24 0.08 19 0.03 2.45 0.26 19Tax Deduction (yes=1, no=0) 0.02 0.07 0.00 19 0.06 1.67 0.14 19Full Recourse (yes=1, no=0) -0.24 -0.87 0.04 19 0.03 0.97 0.05 19LTV (typical) -0.06 -0.48 0.01 19 0.00 -0.20 0.00 19Max LTV -0.02 -0.17 0.00 19 0.00 -0.02 0.00 19ExchRate FLEX (Avg 2000-10) 0.23 1.85 0.17 19 0.01 0.63 0.02 19Shar of FC Liab (Avg) 0.07 0.71 0.03 19 0.01 0.48 0.01 19Average KCO 95-05 0.38 2.80 0.32 19 0.03 1.84 0.17 19Average KCI 95-05 0.68 1.07 0.06 19 -0.03 -0.42 0.01 19Average REO 95-05 0.37 0.76 0.03 19 0.04 0.63 0.02 19Average REI 95-05 -0.01 -0.02 0.00 19 -0.01 -0.22 0.00 19

Advanced Economies

MortgDebt / GDP (Avg) -0.46 -2.10 0.27 14 -0.22 -0.88 0.06 14MortgDebt / GDP (Max) -0.50 -2.23 0.29 14 -0.22 -0.83 0.05 14HousLoan Penetr. (2011) -0.49 -1.44 0.15 14 -0.34 -0.95 0.07 14Tenure : Owner-occupied units -0.05 -0.38 0.01 14 0.09 0.66 0.03 14Legal Right Index -0.26 -1.75 0.20 14 0.10 0.62 0.03 14Credit Info Index 0.24 0.98 0.07 14 0.34 1.47 0.15 14Cost of Registering Property 0.19 0.95 0.07 14 -0.17 -0.81 0.05 14Term to Maturity -0.20 -1.21 0.11 14 -0.24 -1.47 0.15 14Int. Type Interest Type -0.57 -1.02 0.08 14 0.27 0.48 0.02 14Tax Deduction (yes=1, no=0) 0.19 0.51 0.02 14 -0.44 -1.22 0.11 14Full Recourse (yes=1, no=0) -0.46 -1.13 0.10 14 0.35 0.82 0.05 14LTV (typical) -0.18 -1.01 0.08 14 -0.11 -0.61 0.03 14Max LTV -0.22 -1.21 0.11 14 0.02 0.11 0.00 14ExchRate FLEX (Avg 2000-10) 0.17 0.76 0.05 14 -0.35 -1.75 0.20 14Shar of FC Liab (Avg) 0.72 2.20 0.29 14 0.33 0.88 0.06 14Average KCO 95-05 0.00 0.01 0.00 11 -0.14 -0.47 0.02 11Average KCI 95-05 -0.04 -0.19 0.00 11 -0.12 -0.50 0.03 11Average REO 95-05 -0.15 -0.63 0.04 11 -0.19 -0.75 0.06 11

Note. OLS regressions of the peak response of the variables in the VAR on a set of country-specific characteristics.We report results for the full sample, and also two sub-samples: the group of emerging market and the group ofadvanced economies. 27

Table 4 Cross-country Determinants of Impulse Response to Global Liquidity Shock - In-teraction with EM Dummy

CONS RHP

Coeff t-Stat EM t-Stat R2 Coeff t-Stat EM t-Stat R2

MortgDebt / GDP (Avg) -0.11 -0.95 0.09 0.59 0.04 -0.46 -1.55 0.38 1.00 0.09MortgDebt / GDP (Max) -0.07 -0.65 -0.03 -0.21 0.11 -0.41 -1.33 0.29 0.75 0.09HousLoan Penetr. (2011) -0.07 -0.50 -0.07 -0.39 0.15 -0.20 -0.52 0.00 0.00 0.06Owner-occupied units 0.01 0.19 0.16 1.56 0.15 0.25 1.45 0.07 0.24 0.13Legal Right Index 0.08 0.94 -0.08 -0.67 0.03 0.10 0.47 -0.07 -0.24 0.01Credit Info Index 0.15 1.24 -0.14 -0.81 0.05 0.29 0.89 -0.39 -0.84 0.03Cost of Registering Property -0.19 -1.93 0.14 1.24 0.13 -0.59 -2.30 0.49 1.62 0.16Term to Maturity 0.06 0.65 0.02 0.17 0.06 0.09 0.38 -0.11 -0.39 0.01Int. Type Interest Type 0.19 1.28 -0.35 -2.60 0.18 1.12 3.16 -1.06 -3.31 0.32Tax Deduction (yes=1, no=0) 0.45 3.44 -0.39 -3.14 0.31 0.68 1.84 -0.96 -2.74 0.20Full Recourse (yes=1, no=0) 0.10 0.57 -0.27 -2.30 0.16 0.58 1.26 -0.88 -2.95 0.22LTV (avg, if missing max) 0.22 1.12 -0.22 -1.05 0.04 0.36 0.68 -0.34 -0.61 0.02LTV (typical) 0.06 0.62 -0.07 -0.59 0.01 0.43 1.83 -0.42 -1.44 0.10Max LTV -0.14 -1.79 0.15 1.29 0.10 -0.15 -0.68 0.10 0.33 0.02ExchRate FLEX (Avg 2000-10) -0.15 -1.43 0.22 1.83 0.10 -0.79 -3.12 0.94 3.22 0.26Shar of FC Liab (Avg) 0.19 1.71 0.02 0.16 0.42 0.87 2.79 -0.62 -1.46 0.34Average KCO 95-05 -0.02 -0.17 0.29 1.41 0.15 -0.36 -2.09 1.11 3.44 0.33Average KCI 95-05 -0.04 -0.43 0.36 2.01 0.20 -0.33 -2.44 1.13 4.07 0.39Average REO 95-05 -0.03 -0.35 0.33 1.59 0.13 -0.24 -1.67 1.05 3.23 0.30

RXUSD RS

Coeff t-Stat EM t-Stat R2 Coeff t-Stat EM t-Stat R2

MortgDebt / GDP (Avg) -0.32 -1.52 0.48 1.80 0.10 -0.24 -1.61 0.23 1.22 0.09MortgDebt / GDP (Max) -0.29 -1.31 0.35 1.27 0.06 -0.23 -1.54 0.22 1.16 0.08HousLoan Penetr. (2011) -0.18 -0.69 0.35 1.02 0.05 -0.31 -1.72 0.33 1.42 0.10Owner-occupied units -0.08 -0.63 0.30 1.51 0.08 0.10 1.11 -0.04 -0.29 0.05Legal Right Index -0.26 -1.75 0.35 1.72 0.10 0.10 0.94 -0.11 -0.72 0.03Credit Info Index 0.23 1.03 -0.37 -1.18 0.05 0.34 2.27 -0.34 -1.64 0.15Cost of Registering Property 0.20 1.04 -0.24 -1.05 0.04 -0.17 -1.28 0.16 1.02 0.05Term to Maturity -0.18 -1.20 0.35 1.80 0.10 -0.24 -2.36 0.26 2.00 0.16Int. Type Interest Type -0.40 -1.37 0.37 1.42 0.08 0.24 1.18 -0.18 -0.95 0.05Tax Deduction (yes=1, no=0) -0.11 -0.38 0.12 0.45 0.01 -0.20 -1.01 0.03 0.18 0.04Full Recourse (yes=1, no=0) -0.34 -0.98 0.39 1.73 0.09 0.32 1.31 -0.23 -1.43 0.08LTV (avg, if missing max) 0.27 0.73 -0.33 -0.85 0.02 -0.13 -0.51 0.13 0.48 0.01LTV (typical) -0.18 -1.02 0.17 0.81 0.03 -0.12 -0.97 0.11 0.73 0.03Max LTV -0.10 -0.68 0.36 1.73 0.12 -0.03 -0.31 0.03 0.19 0.00ExchRate FLEX (Avg 2000-10) 0.14 0.71 -0.09 -0.38 0.02 -0.34 -2.59 0.36 2.38 0.18Shar of FC Liab (Avg) 0.00 0.01 0.16 0.46 0.04 0.27 1.48 -0.25 -1.04 0.09Average KCO 95-05 -0.06 -0.24 -0.05 -0.11 0.01 -0.12 -0.69 0.37 1.16 0.05Average KCI 95-05 -0.09 -0.47 0.02 0.04 0.02 -0.10 -0.71 0.36 1.22 0.06Average REO 95-05 -0.17 -0.84 0.03 0.07 0.05 -0.15 -1.04 0.45 1.42 0.07

Note. OLS regressions of the peak response of the variables in the VAR on a set of country-specific characteristics.We report results for the full sample, and also two sub-samples: the group of emerging market and the group ofadvanced economies.

28

Table 5 Model’s Parameters

Parameter Description Value

α Weight of H good in H consumption 0.6n Size of H economy 0.01α∗ Weight of H good in F consumption 1− αν Relative risk aversion 1.5vh Marginal utility of housing 0.0006β H discount factor 0.985β∗ F discount factor 0.992θ LTV ratio 0.75y H endowment 1y∗ F endowment 1ρχ Persistence of leverage shock 0.25χ Steady state leverage 5γ Equity adj. cost (1) 1.5η Equity adj. cost (2) 0.005

Note. Parameter values in the baseline calibration.

29

GDP

−3 −2 −1 0 +1 +2 +3 +4 +5−10

−5

0

5

10

Consumption

−3 −2 −1 0 +1 +2 +3 +4 +5−5

0

5

10

House Price

−3 −2 −1 0 +1 +2 +3 +4 +5−20

−10

0

10

20

Real Short−term Int. Rate

−3 −2 −1 0 +1 +2 +3 +4 +5−6

−4

−2

0

2

4

Equity Price

−3 −2 −1 0 +1 +2 +3 +4 +5−60

−40

−20

0

20

40

Real Eff. Exch. Rate

−3 −2 −1 0 +1 +2 +3 +4 +5−10

−5

0

5

10

15

Real Exch. Rate (USD)

−3 −2 −1 0 +1 +2 +3 +4 +5−20

−10

0

10

20

Cross−border Credit

−3 −2 −1 0 +1 +2 +3 +4 +5−40

−20

0

20

40

Current Account / GDP

−3 −2 −1 0 +1 +2 +3 +4 +5−4

−2

0

2

4

6

Mean Median 25/75 Iqrt range

Figure 1 Event Study On Cross-border Bank Credit. Note.

30


Perc

ent

Quarters5 10 15 20 25 30 35 40

0

0.2

0.4

0.6

0.8

1

Consumption

Perc

ent

Quarters5 10 15 20 25 30 35 40

0

0.05

0.1

0.15

0.2

0.25

House Price

Perc

ent

Quarters5 10 15 20 25 30 35 40

0

0.1

0.2

0.3

0.4

Real Int. Rate

Perc

ent

Quarters5 10 15 20 25 30 35 40

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

Real Exch. Rate

Perc

ent

Quarters5 10 15 20 25 30 35 40

0

0.2

0.4

0.6

0.8

1

Figure 2 IRFs to a global liquidity shock - All Countries. Censored impulseresponses to a shock to global liquidity that raises cross-border credit by 1 percent.The dark and light shaded areas are the one and two standard deviation confidenceintervals. The dashed line reports the uncensored impulse responses.

31

(a) Low foreign currency liabilities


Perc

ent

Quarters5 10 15 20 25 30 35 40

0

0.2

0.4

0.6

0.8

1

Consumption

Perc

ent

Quarters5 10 15 20 25 30 35 40

0

0.05

0.1

0.15

House Price

Perc

ent

Quarters5 10 15 20 25 30 35 40

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Real Int. Rate

Perc

ent

Quarters5 10 15 20 25 30 35 40

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

Real Exch. Rate

Perc

ent

Quarters5 10 15 20 25 30 35 40

0

0.2

0.4

0.6

0.8

1

(b) High foreign currency liabilities


Pe

rce

nt

Quarters5 10 15 20 25 30 35 40

0

0.2

0.4

0.6

0.8

1

Consumption

Pe

rce

nt

Quarters5 10 15 20 25 30 35 40

0

0.1

0.2

0.3

0.4

0.5

House Price

Pe

rce

nt

Quarters5 10 15 20 25 30 35 40

0

0.2

0.4

0.6

0.8

1

Real Int. Rate

Pe

rce

nt

Quarters5 10 15 20 25 30 35 40

−0.3

−0.2

−0.1

0

0.1

Real Exch. Rate

Pe

rce

nt

Quarters5 10 15 20 25 30 35 40

0

0.2

0.4

0.6

0.8

1

1.2

Figure 3 Impulse Responses To A Global Liquidity Shock – Low And HighShare Of Foreign Currency Debt. Censored impulse responses to a shock toglobal liquidity that raises cross-border credit by 1 percent in “high” and “low” for-eign currency liabilities countries. The dark and light shaded areas are the one andtwo standard deviation confidence intervals. The dashed line reports the uncensoredimpulse responses.

32

d

R

Demand of fundsSupply of funds

A

B

1/β*

θmrs/(1‐β)

1/β

Figure 4 Graphical Representation Of The Equilibrium. Equilib-rium in the credit market of the simplified model.

d

R

Demand of fundsSupply of funds

A

1/β*

θmrs/(1‐β)

d0 d1

A’R0=1/β

Figure 5 Relaxation Of The Leverage Constraint (Small Shock)In An Economy Starting With Low Credit And High InterestRate. Comparative statics in the simplified model. The shock correspondsto an increase in χ, i.e. an increase in the financial intermediary’s leverage.

33

d

R

Demand of funds

Supply of funds

B

1/β*

θmrs/(1‐β)

B’

d0 d1

R0

R1

1/β

Figure 6 Relaxation Of The Leverage Constraint (Small Shock)In An Economy Starting With High Credit And Low InterestRate. Comparative statics in the simplified model. The shock correspondsto an increase in χ, i.e. an increase in the financial intermediary’s leverage.

d

R

Demand of funds Supply of funds

A

1/β*

θmrs/(1‐β)

d0 d1

A’

R0=1/β

R1

Figure 7 Relaxation Of The Leverage Constraint (Large Shock)In An Economy Starting With Low Credit And High InterestRate. Comparative statics in the simplified model. The shock correspondsto an increase in χ, i.e. an increase in the financial intermediary’s leverage.

34


Perc

ent

Quarters5 10 15 20

0

0.2

0.4

0.6

0.8

1

Consumption

Perc

ent

Quarters5 10 15 20

0

0.1

0.2

0.3

0.4

House Price

Perc

ent

Quarters5 10 15 20

0

0.1

0.2

0.3

0.4

0.5

Real Int. Rate

Perc

ent

Quarters5 10 15 20

−0.5

−0.4

−0.3

−0.2

−0.1

0

Real Exch. Rate

Perc

ent

Quarters5 10 15 20

−2.5

−2

−1.5

−1

−0.5

0x 10

−3

Figure 8 Relaxation Of The Leverage Constraint. Impulse responses obtainedfrom the full model. The shock corresponds to an increase in χ, i.e. an increase inthe financial intermediary’s leverage, that leads to an increase of home consumersborrowing by 1 percent.

35

References

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Benigno, G., N. Converse, and L. Fornaro (2015): “Large capital inflows, sectoral allocation, andeconomic performance,” Journal of International Money and Finance, 55(C), 60–87.

Brunnermeier, M., and Y. Sannikov (2014): “A Macroeconomic Model with a Financial Sector,”American Economic Review, 104, 379–421.

Caballero, J. A. (2014): “Do Surges in International Capital Inflows Influence the Likelihood of BankingCrises?,” The Economic Journal, -, 1–36.

Calvo, G. A., L. Leiderman, and C. M. Reinhart (1996): “Inflows of Capital to Developing Countriesin the 1990s,” Journal of Economic Perspectives, 10(2), 123–139.

Cardarelli, R., S. Elekdag, and M. A. Kose (2010): “Capital inflows: Macroeconomic implicationsand policy responses,” Economic Systems, 34(4), 333–356.

Cesa-Bianchi, A., L. F. Cespedes, and A. Rebucci (2015): “Global Liquidity, House Prices, andthe Macroeconomy: Evidence from Advanced and Emerging Economies,” Journal of Money, Credit andBanking, 47(S1), 301–335.

Favilukis, J., D. Kohn, S. Ludvigson, and S. Van Nieuwerburgh (2013): “International CapitalFlows and House Prices: Theory and Evidence,” in Housing and the Financial Crisis, ed. by E. Glaeser,and T. Sinai, chap. 6. University of Chicago Press.

Ferrero, A. (2015): “House Price Booms, Current Account Deficits, and Low Interest Rates,” Journal ofMoney, Credit and Banking, 47(S1), 261–293.

Gabaix, X., and M. Maggiori (2014): “International Liquidity and Exchange Rate Dynamics,” NBERWorking Papers 19854, National Bureau of Economic Research, Inc.

Gourinchas, P.-O., R. Valdes, and O. Landerretche (2001): “Lending Booms: Latin America andthe World,” Economia, 1(Spring), 47–100.

He, Z., and A. Krishnamurthy (2013): “Intermediary Asset Pricing,” American Economic Review, 103,732–770.

Jermann, U., and V. Quadrini (2012): “Macroeconomic Effects of Financial Shocks,” American Eco-nomic Review, 102(1), 238–71.

Justiniano, A., G. E. Primiceri, and A. Tambalotti (2015): “Credit Supply and the Housing Boom,”NBER Working Papers 20874, National Bureau of Economic Research, Inc.

Kiyotaki, N., and J. Moore (1997): “Credit Cycles,” Journal of Political Economy, 105(2), 211–48.

Mendoza, E. G., and M. E. Terrones (2008): “An Anatomy Of Credit Booms: Evidence From MacroAggregates And Micro Data,” NBER Working Papers 14049, National Bureau of Economic Research, Inc.

Mertens, K., and M. O. Ravn (2013): “The Dynamic Effects of Personal and Corporate Income TaxChanges in the United States,” American Economic Review, 103(4), 1212–47.

Mian, A., A. Sufi, and E. Verner (2016): “Household Debt and Business Cycles Worldwide,” Unpub-lished, Princeton University.

Pesaran, M. H., and R. Smith (1995): “Estimating long-run relationships from dynamic heterogeneouspanels,” Journal of Econometrics, 68(1), 79–113.

36

Pesaran, M. H., R. Smith, and K. Im (1996): “Dynamic Linear Models for Heterogenous Panels,” inThe Econometrics of Panel Data, ed. by L. Mtys, and P. Sevestre, chap. 8, pp. 145–195. Kluwer AcademicPublishers, Dordrecht, The Netherlands.

Stock, J., and M. Watson (2012): “Disentangling the Channels of the 2007-2009 Recession,” BrookingsPapers on Economic Activity, Spring, 81–135.

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Sutherland, A. (2005): “Incomplete pass-through and the welfare effects of exchange rate variability,”Journal of International Economics, 65(2), 375–399.

37

A Appendix. Identification

Consider the following reduced form VAR (with only one lag and no constant or trend for simplicity):

xt = Fxt−1 + ut, (A.1)

where xt is a (m× 1) vector of endogenous variables; F is a (m×m) matrix of coefficients; and ut

is a (m× 1) vector of residuals with variance-covariance matrix Σu. The objective is to recover the

structural form of the above VAR, i.e.:

Axt = Bxt−1 + εt, (A.2)

where A and B are (m × m) matrices of coefficients; and εt is an (m × 1) vector of structural

residuals with variance-covariance matrix Σε = I. Note that the reduced form residuals are a linear

combination of the structural residuals. Specifically, letting A = A−1, we have that ut = Aεt.

If we partition the vector of endogenous variables xt as (GL′t, x′p,t)′ —where GLt is global

liquidity and xp,t is the (m− 1× 1) vector of remaining endogenous variables— we can re-write the

reduced-form VAR as:[GLt

xp,t

]=

[f11 f12

f21 f22

][GLt−1

xp,t−1

]+

[a11 a12

a21 a22

][εGLt

εxpt

], (A.3)

where f11 and a11 are scalars; f12 and a12 are (1 × m − 1) vectors; f21 and a21 are (m − 1 × 1)

vectors; f22 and a22 are (m − 1 ×m − 1) matrices; and εGLt and εxpt are the structural residuals

associated to global liquidity and the remaining endogenous variables, respectively.

For the sake of argument, let’s assume that the structural matrix A is known. Then, we would be

able to compute the impulse response to a global liquidity shock. Specifically, the contemporaneous

responses of GL and xp to a unit shock to εGL would be given by:[IRFGL0

IRFxp0

]=

[a11

a21

],

which, since the model is linear, can be normalized to:[IRFGL0

IRFxp0

]=

[1a21a11

]. (A.4)

Finally, the impulse response functions at longer horizons can be computed as:

IRFn = Fn−1 · IRFn−1 for n = 2, ..., N. (A.5)

Note that if we are interested in computing the impulse responses to the global liquidity shock only

38

we do not need to know all the coefficients of A, but rather only the elements of the first column

of A, namely a1.

We now consider the case of A unknown. To achieve identification, we follow the external

instrument identification approach pioneered by Stock and Watson (2012) and Mertens and Ravn

(2013). Let uGL and uxp be the OLS estimates of the reduced form residuals in (A.1). Also, let Zt

be a (z × 1) vector of instrumental variables that satisfy:

E[εGLZ ′t

]= φ,

E[εxpZ ′t] = 0,

i.e., the instruments are correlated with the global liquidity shock (εGL) but are orthogonal to all

the other domestic shocks (the elements of εxp). We can obtain consistent estimates of a1 from

the two-stage least squares regression of uxp on uGL using Zt as instruments. In other words, since

the reduced form residuals of the global liquidity equation (uGLt ) are an imperfect measure of true

structural shock (εGL), in the first stage we regress them on the set of instruments (Zt):

uGLt = βZt + ξt, (A.6)

to construct the fitted values uGLt . Then we regress the reduced form residuals of the domestic

equations (uxpt ) on the fitted values (uGLt ) to get a consistent estimate of the ratio a21/a11:

uxpt =

a21

a11uGLt + ζt, (A.7)

where note that uGLt is orthogonal to ζt under the assumption that E[εxpZ ′t] = 0.

Finally, we can use the OLS estimates of the matrix F to compute the impulse response functions

of all variables to a global liquidity shock using the formula in (A.5).

B Appendix. Steady state of the full model

First substituteconsumption demands and definition of exchange rate into goods market equilib-

rium:

nyt = τ1−αt [αnct + stα

∗(1− n)c∗t ] (1− n)y∗t = τ−αt [(1− α)nct + st(1− α∗)(1− n)c∗t ].

39

The equilibrium simplifies to a set of stationary processes {qt, µt, Rt, Rdt , Ret , dt, et, τt, st, ct, c∗t } for

t ≥ 0 subject to the equilibrium equations below:

(1) 1− µt = βRtEt[u′(ct+1)u′(ct)

st+1

st

](2) (1− µtθ)qt = v′(h)

u′(ct)+ βEt

[u′(ct+1)u′(ct)

qt+1

](3) stdt = θqt

(4) 1 = β∗RdtEt[u′(c∗t+1)

u′(c∗t )

](5) 1 + ψ′(et) = β∗RetEt

[u′(c∗t+1)

u′(c∗t )

](6) Rt =

(1− 1

χ

)Rdt + 1

χRet

(7) ndt ≤ χ(1− n)et

(8) st = τα−α∗

t

(9) nyt = τ1−αt [αnct + stα

∗(1− n)c∗t ]

(10) (1− n)y∗t = τ−αt [(1− α)nct + st(1− α∗)(1− n)c∗t ]

(11) ct = τα−1t yt + st(dt −Rt−1dt−1)

with µt ≥ 0. Remove time subscripts and plug in assumed functional forms:

(1) 1− µ = βR,

(2) (1− θµ)q = vhcυ + βq =⇒ q = vhcυ

1−θµ−β(3) sd = θq,

(4) 1 = β∗Rd

(5) 1 + γη = β∗Re

(6) R =(

1− 1χ

)Rd + 1

χRe

(7) nd ≤ χ(1− n)e

(8) s = τα−α∗

(9) ny = τ1−α[αnc+ sα∗(1− n)c∗]

(10) (1− n)y∗ = τ−α[(1− α)nc+ s(1− α∗)(1− n)c∗]

(11) c = τα−1y + sd(1−R)

From (4):

Rd =1

β∗.

From (5):

Re =1 + γη

β∗.

From (6):

R =

(1− 1

χ

)Rd +

1

χRe.

From (1)

µ = 1− βR.

40

Substitute s from (8) everywhere

(2) (1− θµ)q = vhcυ + βq =⇒ q = vhcυ

1−θµ−β(3) τα−α

∗d = θq,

(7) nd ≤ χ(1− n)e

(9) ny = τ1−α[αnc+ τα−α∗α∗(1− n)c∗]

(10) (1− n)y∗ = τ−α[(1− α)nc+ τα−α∗(1− α∗)(1− n)c∗]

(11) c = τα−1y + τα−α∗d(1−R)

Substitute q from (2) into (3):

(3) τα−α∗d = θ vhcυ

1−θµ−β ,

(7) nd ≤ χ(1− n)e

(9) ny = τ1−α[αnc+ τα−α∗α∗(1− n)c∗]

(10) (1− n)y∗ = τ−α[(1− α)nc+ τα−α∗(1− α∗)(1− n)c∗]

(11) c = τα−1y + τα−α∗d(1−R)

Now forget about (7) for the moment and note that if we substitute d from (3) into (11), we get a

system of 3 equations (9)-(10)-(11) in three unknowns c, c∗, and τ :

(9) ny = τ1−α[αnc+ τα−α∗α∗(1− n)c∗]

(10) (1− n)y∗ = τ−α[(1− α)nc+ τα−α∗(1− α∗)(1− n)c∗]

(11) c = τα−1y + θ vhcυ

1−θµ−β (1−R)

We can solve this system in Matlab. Now we can use (2) to recover q

q =vhcυ

1− θµ− β,

and (3) to recover d:

d = θqτ−α+α∗ .

Finally we can find a value for e from (5):

et =ndt

χ(1− n),

and a value for s from (3)

s = τα−α∗.

41

C Appendix. The simplified model

We consider a simplified verison of the model that allows us to characterize the equilibrium of the

economy analytically. To do that we make three auxiliary assumptions: (i) there is a single good

in the economy (i.e., st = τt = 1); (ii) utility is linear in consumption (i.e., u′(ct) = u for both H

and F consumers); and (iii) the two countries have equal size (i.e., n = 0.5).

The equilibrium conditions of the simplified model are very similar to the ones of the full

model. The exchange rate (st) drops out from the budget and collateral constraints of the impatient

household. The problem of the patient household is not affected. Given the assumption of countries

of equal sizes (i.e., n = 0.5), the problem of the global financial intermediary also simplifies and n

disappears from balance sheet and leverage constraints. An implication of imposing that utility is

linear in consumption and that the supply of housing is fixed and equal to 1 (ht = h = 1), is that

the marginal rate of substitution between housing services and consumption is constant:

mrs =v′(1)

u.

This also implies that the equilibrium is fully static. Therefore, in what follows, we drop the time

indexes. The equilibrium of this simple economy can be characterized by the following system of

equations:

(1) 1− µ = βR

(2) (1− µθ)q = mrs+ βq

(3) d = θq

(4) 1 = β∗Rd

(5) 1 + ψ′(e) = β∗Re

(6) R =(

1− 1χ

)Rd + 1

χRe

(7) d ≤ χe(9) c = y + (d−Rd)

C.1 Analytical derivation of the equilibrium in the credit market

Risk neutrality gives that the return on deposits is equal to the inverse of the individual discount

factor of the foreign representative household:

Rd =1

β∗,

while the return on equity is:

Re =1 + ψ′(e)

β∗,

42

which implies that that the return on equity is larger than the return on deposits. We can now

rewrite the optimality condition for the global financial intermediary as:

R =1

β∗

(1 +

ψ′(e)

χ

).

Finally, note that

ψ′(e) = Θeγ−1,

where Θ = γηe1−γ . Finally, we assume that the leverage binds with equality to obtain:

R =1

β∗

(1 + Θ

(d

χ

)γ−1). (C.1)

Equation (C.1) constitutes the supply of funds. In the space {d,R}, the supply is an increasing

and convex function (as long as γ > 1), which crosses the vertical axis at 1/β∗.

To obtain an expression for the demand of funds, we can use the domestic representative house-

hold optimality condition

R =1− µβ

The demand of funds is a piecewise function in the space {d,R}. The first portion is flat: when

debt is low the collateral constraint is not binding and, hence the shadow price of the collateral

constraint is zero. The second part of the demand schedule is downward-sloping. The borrowing

constraint at equality pins down the kink of the demand function. To obtain the expression for

demand in this case, we can recover an expression for the Lagrange multiplier from the first order

condition for house prices (i.e., (1−µθ)q = mrs+βq) assuming that the collateral constraint holds

with equality (i.e., d = θq). We can finally write:

R =

{1/β if d < θpθ−(1−β)

βθ − mrsβd if d = θp

(C.2)

The intersection of demand and supply of funds determines an equilibrium quantity of credit d

that flows from the foreign to the domestic economy, and an associated interest rate R.

D Appendix. Data Sources

This appendix provides a description of the data used in the empirical analysis and on their sources.

We consider 57 countries in our empirical analysis: 24 advanced economies (Australia, Austria,

Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan,

Luxembourg, Malta, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland,

43

UK, and US) and 33 emerging economies (Argentina, Brazil, Bulgaria, Chile, China, Colombia,

Croatia, Czech Republic, Estonia, Hong Kong, Hungary, India, Indonesia, Israel, Korea, Latvia,

Lithuania, Malaysia, Mexico, Morocco, Peru, Philippines, Poland, Russia, Serbia, Singapore, Slo-

vakia, Slovenia, South Africa, Taiwan, Thailand, Ukraine, and Uruguay).

We collect data over the 1990:Q1 – 2012:Q4 (subject to data availability) for the following

variables:

• House prices. Nominal house prices deflated by consumer price inflation. Source: OECD

house price database, BIS Residential property price statistics, Dallas FED International

House Price Database, National Central Banks, National Statistical Offices, academic and

policy publications. More details on the definitions and the sources are reported in Table

D.1.

• Total cross-border banking flows. Foreign claims (all instruments, in all currencies) of

all BIS reporting banks vis-a-vis all sectors deflated by US consumer price inflation. Source:

BIS.

• Global liquidity. Foreign claims (loans and deposits, in all currencies) of all BIS reporting

banks vis-a-vis the banking sector deflated by US consumer price inflation. Source: BIS.

• GDP. Real index. Source: OECD, IMF IFS, Bloomberg.

• Consumption. Real private final consumption index. Source: OECD, IMF, IFS, Bloomberg.

• Consumer prices. Consumer price index. Source: OECD, IMF IFS, Bloomberg.

• Short-term interest rates. Short-term nominal market rates. A real ex-post interest rate

is obtained by subtracting consumer price inflation. Source: OECD, IMF, IFS, Bloomberg.

• Equity prices. Equity price index deflated by consumer price inflation. Source: OECD,

IMF IFS, Bloomberg.

• Exchange rate vis-a-vis US dollar. US dollars per unit of domestic currency. A real ex-

change rate is obtained with US and domestic consumer price inflation. Source: Datastream.

• Real effective exchange rate. Index (such that a decline of the index is a depreciation).

Source: IMF IFS, BIS, Bloomberg.

• Current account to GDP ratio. Current account balance divided by nominal GDP.

Source: OECD, IMF IFS, Bloomberg.

44

Table D.1 House Price Data: Definitions and Sources

Country Definition Source

Argentina House Apartments in Buenos Aires City, average price per sqm (USD). ArklemsAustralia House Price Indexes: Eight Capital Cities. OECDAustria Residential property prices, new and existing dwellings. OECDBelgium Residential property prices, existing dwellings, whole country. OECDBrazil Residential Real Estate Collateral Value Index. Central BankBulgaria Residential property price, existing flats (big cities), per sqm. BISCanada Average existing home prices. OECDChile HPI general, houses and apartments. Central BankChina House price index. OECDColombia House Price Index. Central BankCroatia House price index Dallas FEDCzech Rep. Residential property prices, existing dwellings, whole country. OECDDenmark Price index for sales of property. OECDEstonia Residential property prices, all dwellings, per sqm. BISFinland Prices of dwellings. OECDFrance Indice trimestriel des prix des logements anciens. OECDGermany Residential property prices in Germany. OECDGreece Prices of dwellings. OECDHong Kong Residential property price, all dwellings, per sqm. BISHungary Residential property price, all dwellings, per sqm. BISIceland Residential property price, all dwellings (Reykjavk), per sqm. BISIndia Residex. National Housing BankIndonesia Residential property prices, new houses (big cities), per dwelling. BISIreland Residential property price index. OECDIsrael Prices of dwellings. OECDItaly Residential property prices, existing dwellings, whole country. OECDJapan Urban Land Price Index. OECDKorea House price index. Dallas FEDLatvia Residential property prices, new and existing flats, whole country. ECBLithuania Residential property price, all dwellings, per sqm. BISLuxembourg House price index. Dallas FEDMalaysia Residential property prices, all dwellings, per sqm. BISMalta Property Prices Index (based on advertised prices). Central BankMexico Residential property prices, all dwellings, per dwelling. BISMorocco Residential property prices, existing dwellings, per sqm. BISNetherlands House Price Index for existing own homes. OECDNew Zealand House price index. OECDNorway House price index. OECDPeru Residential property prices, per sqm. BISPhilippines Residential and commercial property prices, flats (Makati), per sqm. BISPoland Residential property prices, (big cities), per sqm. BISPortugal Residential property prices, new and existing dwellings. BISRussia Residential property prices, existing dwellings, per sqm. BISSerbia Average prices of dwellings in new construction, per sqm. National Stat. OfficeSingapore Average prices of dwellings in new construction, per sqm. BISSlovak Rep. Residential property prices, existing dwellings. OECDSlovenia House price index. OECDSouth Africa Residential property price. BISSpain Precio medio del m2 de la vivienda libre (> 2 anos de antiguedad). OECDSweden Real estate price index for one and two dwelling buildings for permanent living. OECDSwitzerland Real estate price indices. OECDTaiwan National House Price Index. SynyiThailand Residential property prices, average of all detached houses, per sqm. BISUkraine Average Price of Apartments, Kiev, per sqm (USD). BlagovestUK Mix-adjusted house price index. OECDUS Purchase and all-transactions indices. OECDUruguay Precio promedio del metro cuadrado de compraventas, Montevideo (USD). National Stat. Office

Note. See the extended appendix on the sources of house price series extended with historical data.

45

E Appendix. Additional Results

46

Table

E.1

CorrelationMatrix

ofCountryCharacteristics

EM

MortgDe

btGDP

Avg_std

MortgDe

btGDP

Max_st

d

Mortgagelo

ansend

ofye

aras_std

HousLoanPe

netr20

11_st

d

Tenu

reinurb

anareasO

wn

er_std

LegalRightIn

dex_std

Cred

itInfoIn

dex_std

CostofRe

gist

eringPrope

rty_std

Term

toMat

urity

_std

Interest

Type

Tax

Dedu

ction

(yes=1,

no=0)

Full

Recourse

(yes=1,

no=0)

LTVa

vgifm

issin

gmax_std

LTVtypical_s

tdMaxLTV_

std

ExchRa

teFLE

XAvg20

001

0_std

SharofFCLia

bAvg_std

kco1

0_std

kci10_std

reo_

std

rei_std

RS_avg95

_05_std

IRF_CO

NS_

max_std

IRF_RH

P_m

ax_std

IRF_RX

USD

_max_std

IRF_RS_m

ax_std

EM Dum

my

1

GDP

pc_90_std

0.74

MortgDe

btGDP

Avg_std

0.71

1

MortgDe

btGDP

Max_std

0.68

0.95

1

Mortgageloansen

dofyearas_std

0.72

0.9

0.88

1

HousLoanPe

netr20

11_std

0.72

0.75

0.75

0.77

1

Tenu

re_O

wne

r_std

‐0.33

‐0.33

‐0.32

‐0.28

‐0.23

1

LegalRightInde

x_std

0.07

0.41

0.43

0.35

0.34

‐0.17

1

Cred

itInfoInd

ex_std

‐0.03

0.02

0.01

‐0.08

‐0.18

‐0.14

0.28

1

CostofRe

gisteringPrope

rty_std

0.05

‐0.16

‐0.16

‐0.14

0‐0.09

‐0.26

‐0.21

1

Term

toMaturity

_std

0.22

0.39

0.33

0.31

0.38

0.16

0.3

‐0.05

‐0.18

1

Interest Type

‐0.26

‐0.14

‐0.12

‐0.11

‐0.07

0.36

0.07

0.1

0.03

0.04

1

Tax De

duction (yes=1, no=

0)0.08

0.08

0.08

0.12

0.09

0.06

‐0.06

0.02

‐0.05

0.23

‐0.02

1

Full Re

course (yes=1, no=

0)0.27

0.23

0.2

0.32

0.26

0.01

0.13

‐0.15

‐0.12

0.07

‐0.08

‐0.13

1

LTVa

vgifm

issingm

ax_std

‐0.05

0.13

0.13

0.08

0.04

‐0.06

0.14

‐0.04

‐0.03

0.43

‐0.04

0.16

‐0.26

1

LTVtypical_std

0.11

0.29

0.31

0.29

0.22

0.12

0.18

‐0.14

0.06

0.37

0.06

0.08

0.05

0.44

1

MaxLTV_

std

0.2

0.18

0.21

0.2

0.21

‐0.03

0.15

0.18

0.04

0.24

‐0.15

0.13

‐0.06

0.26

0.44

1

ExchRa

teFLEXAv

g200

010_std

‐0.23

0.06

‐0.02

‐0.07

‐0.22

0.01

0.16

0.22

‐0.29

0.22

0.11

‐0.09

‐0.15

0.11

‐0.04

0.05

1

SharofFCLiabAv

g_std

‐0.73

‐0.49

‐0.49

‐0.49

‐0.64

0.37

‐0.07

‐0.02

‐0.26

‐0.05

0.11

‐0.1

‐0.06

0.08

‐0.03

‐0.13

0.34

1

kco1

0_std

‐0.67

‐0.6

‐0.56

‐0.58

‐0.59

0.21

‐0.15

‐0.14

‐0.04

‐0.13

0.01

‐0.01

‐0.43

0.22

‐0.04

0.02

0.24

0.47

1

kci10_std

‐0.63

‐0.55

‐0.52

‐0.52

‐0.53

0.17

‐0.17

‐0.16

‐0.16

‐0.12

0.03

‐0.01

‐0.47

0.23

‐0.07

‐0.03

0.26

0.5

0.93

1

reo_

std

‐0.55

‐0.39

‐0.35

‐0.41

‐0.42

0.24

0.01

‐0.25

‐0.06

‐0.03

0.02

0.07

‐0.28

0.24

0.07

‐0.02

0.18

0.38

0.85

0.78

1

rei_std

‐0.16

0‐0.04

00.02

0.2

0.18

‐0.27

‐0.44

0.24

0.09

0.07

‐0.05

0.13

0.05

‐0.03

0.23

0.27

0.31

0.46

0.39

1

RS_avg95

_05_std

‐0.26

‐0.16

‐0.16

‐0.31

‐0.31

0.09

‐0.26

0.16

0.11

‐0.05

0.06

‐0.21

‐0.05

0.05

‐0.08

‐0.18

0.21

0.29

0.03

0.03

‐0.03

‐0.19

1

IRF_CO

NS_max_std

‐0.42

‐0.17

‐0.33

‐0.24

‐0.39

0.28

0.12

0.17

‐0.29

0.24

0.01

0.29

‐0.09

0.07

0.04

‐0.21

0.07

0.64

0.3

0.28

0.22

0.19

0.12

1

IRF_RH

P_max_std

‐0.47

‐0.25

‐0.27

‐0.2

‐0.25

0.36

0.08

0.07

‐0.29

0.02

0.27

0.03

‐0.01

0.06

0.2

‐0.12

‐0.09

0.54

0.2

0.14

0.18

0.11

‐0.05

0.62

1

IRF_RX

USD

_max_std

0.22

0.03

‐0.07

0.01

0.13

0.09

‐0.12

0.05

0.05

0.07

‐0.14

‐0.02

‐0.04

‐0.03

‐0.11

0.17

0.14

0.19

‐0.11

‐0.13

‐0.22

‐0.1

0.45

0.2

‐0.02

1

IRF_RS_m

ax_std

‐0.18

‐0.2

‐0.2

‐0.17

‐0.19

0.22

0.11

0.27

‐0.14

‐0.21

0.15

‐0.2

0.13

‐0.03

‐0.12

‐0.05

‐0.17

0.23

0.09

0.06

00.21

‐0.14

0.15

0.3

‐0.05

1

47

Global Liquidity, Leverage, House Prices and Exchange Rates9...Ambrogio Cesa-Bianchiy Andrea Ferreroz Alessandro Rebuccix March 25, 2016 ... Panel VAR for 56 advanced and emerging

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