**BIS Working Papers **

**No 661**

**How important is the Global Financial Cycle? Evidence from capital flows **

by Eugenio Cerutti, Stijn Claessens and Andrew K Rose

**Monetary and Economic Department **

August 2017

JEL classification: F32, F36, F65, G15

Keywords: empirical, data, centre, country, panel, fit, VIX, equity, bonds, FDI, credit

BIS Working Papers are written by members of the Monetary and Economic Department of the Bank for International Settlements, and from time to time by other economists, and are published by the Bank. The papers are on subjects of topical interest and are technical in character. The views expressed in them are those of their authors and not necessarily the views of the BIS.

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

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

ISSN 1020-0959 (print)

ISSN 1682-7678 (online)

**How important is the Global Financial Cycle? Evidence from capital flows**

Eugenio Cerutti, Stijn Claessens and Andrew K Rose

**Abstract **

This study quantifies the importance of a Global Financial Cycle (GFCy) for capital flows. We use capital flow data disaggregated by direction and type between Q1 1990 and Q4 2015 for 85 countries, and conventional techniques, models and metrics. Since the GFCy is an unobservable concept, we use two methods to represent it: directly observable variables in centre economies often linked to it, such as the VIX; and indirect manifestations, proxied by common dynamic factors extracted from actual capital flows. Our evidence seems mostly inconsistent with a significant and conspicuous GFCy; the two methods combined rarely explain more than a quarter of the variation in capital flows. Succinctly, most variation in capital flows does not seem to be the result of common shocks nor stem from observables in a central country like the United States.

Keywords: empirical, data, centre, country, panel, fit, VIX, equity, bonds, FDI, credit.

JEL classification: F32, F36, F65, G15.

Cerutti is Assistant to the Director, IMF Research Department, [email protected], www.eugeniocerutti.com; Claessens is Head of Financial Stability Policy, BIS Monetary and Economic Department, www.bis.org/author/stijn_claessens.htm, and CEPR Research Fellow, [email protected]; Rose is Rocca Professor at Berkeley-Haas, ABFER Senior Fellow, CEPR Research Fellow and NBER Research Associate, [email protected], faculty.haas.berkeley.edu/arose.

We thank Nathan Converse and Carmen Reinhart for providing data, and Tamim Bayoumi, Olivier Blanchard, Antoine Bouveret, Steve Davis, Robin Koepke, Maurice Obstfeld, David Reeb, Hyun Song Shin, Anand Srinivasan, Johan Sulaeman, Shang-Jin Wei and workshop participants at ABFER and NUS for comments. Rose thanks the National University of Singapore for hospitality during the course of this research. A current version of the paper, the data set and key output are freely available on Rose’s website. All opinions expressed in this paper are those of the authors, and not of the institutions they are affiliated with.

**1. Introduction and motivation**

This paper seeks to quantify the importance of a Global Financial Cycle (hereafter GFCy), particularly for the variation in international capital flows.^{2} The concept of an important GFCy is closely identified with the work of Rey, who writes:

"There is a global financial cycle in capital flows, asset prices, and in credit growth. This cycle co-moves with the VIX, a measure of uncertainty and risk aversion of the markets."

- Rey (2013, abstract)

"Large gross cross-border flows are moving in tandem across countries regardless of the exchange rate regime, they tend to rise in periods of low volatility and risk aversion and decrease in periods of high volatility and risk aversion, as measured by the VIX ... There is a global financial cycle."

- Passari and Rey (2015, p 693)

The interest in the GFCy is certainly not confined to Rey and her co-authors. For instance, Forbes and Warnock (2012) write:

"Global factors, especially global risk, are significantly associated with extreme capital flow episodes. ... Our analysis indicates that waves of capital flows are primarily associated with global factors. Global risk, which incorporates both risk aversion and economic uncertainty, is the only variable that consistently predicts each type of capital flow episode; an increase in global risk is associated with more stops and retrenchments and fewer surges and flight. ... most domestic factors only have a limited correlation with capital flow volatility ... global factors, and especially global risk, are key to understanding periods of extreme capital flows by domestic and foreign investors. Increases in global risk predict sudden stops in capital flows by foreigners and retrenchments in capital flows by domestic investors

As reflected in a growing literature, it is easy to motivate research on the GFCy. Suppose that the GFCy explains much of the variation in capital flows, particularly for small and emerging economies. In this case, it becomes more difficult for policymakers in these countries to manage their economics, as the GFCy, driven by common shocks including factors emanating from the centre, leads to large capital flow fluctuations (exogenous from the viewpoint of the small and/or emerging economies). They could insulate their economies against the GFCy (with capital controls, macroprudential instruments and the like), but also give up some of the benefits of international financial integration. As Rey (2015, pp 9-10) writes:

"As capital flows respond to US monetary policy, they may not be appropriate for the cyclical conditions of many economies. For some countries, the Global Financial Cycle can lead to excessive credit growth in boom times and excessive retrenchment in bad times. ... The Global Financial Cycle can be associated with surges and dry outs in capital flows, booms and busts in asset prices and crises ... The empirical results on capital flows, leverage and credit growth are suggestive of an international credit channel or risk-taking channel and point towards financial stability issues."

However, if the GFCy does not explain most or even much of the variation in capital flows, then the policy authorities in small and/or emerging economies have greater degrees of freedom to manage their economies, at least in terms of the impact of the GFCy on capital flow fluctuations. For this reason, quantifying the importance of the GFCy for capital flows, our chief concern in this paper, is important. We emphasise at the outset that our approach is conventional, by design. Thus, our data sets, techniques, capital flow models and statistical metrics are widely used and plain vanilla. The focus of this paper is on empirical results, not on our data or methodology.

In the next section, we review related empirical literature, which also helps explain our methodological approach. Section 3 introduces our data. The heart of the paper is in Section 4, which presents our empirical results. We end with a brief summary and conclusion.

In our investigation, we draw on two strands of literature that have analysed the GFCy implicitly or explicitly. One strand involves traditional "push-pull" analyses, which try to explain capital flows with global "push" (ie source country) and "pull" (ie recipient country) factors. The other strand documents the (degree of) commonality in global financial developments, including capital flows, credit creation and domestic asset prices, using factor models and structural time series models (often variants of vector autoregressions (VARs)). We use elements of both strands in such a way that our exploration maximally favours the quantitative importance of the GFCy for international capital flows. Since the literature has also documented differences by type, source and destination of capital flows as well as period of time, we explore the robustness of our results to variations in these dimensions as well.

**Push-pull**

The first strand of literature, started by Calvo et al (1993, 1996), mainly uses panel regressions to investigate the relative roles of push and pull factors in driving capital

flows. Recent contributions include Fratzscher (2011), Forbes and Warnock (2012), Broner et al (2013), Bruno and Shin (2015a), and Cerutti et al (2017). Koepke (2015) provides a recent review of some 40 papers; see also IMF (2014). While results vary, typically a worsening in global risk conditions, as measured by the VIX, is found to lower capital flows, especially to emerging market economies (EMEs).^{3} Evidence on US monetary policy is more mixed. Some papers find capital flows respond negatively to a tightening in US monetary policy, more so for portfolio bond and equity flows; others find that monetary policy variables are not always significant, or do not consistently have the same sign (eg Cerutti et al (2015)), with some even finding opposite signs (eg Correa et al (2016) find that banking flows increase for some countries when US interest rates rise, in part related to the relative level of riskiness comparing US non-bank borrowers and those countries' borrowers).

The explanatory power of these push variables is typically limited, in absolute terms and sometimes also relative to pull variables (when those are included). Bruno and Shin (2015b) investigate banking flows to 46 countries using BIS data and find that "local factors account for only a modest amount of the variation and global factors account for an overwhelming part of the variation", but they report overall R^{2}s of .1 or less. Similarly, Forbes and Warnock (2012, p 244) state in an endnote that it is difficult to fit capital flows: "For example, in a simple logit specification, the pseudo- R2 is only .04 for flight episodes, increasing to .07, .13, and .15 for surges, retrenchments, and stops, respectively." Cerutti et al (2017), regressing a panel of banking flows on domestic factors, spreads and global measures, report R^{2}s less than .1, even when including, besides US VIX and other US measures, conditions in other funding areas (UK, Japan, euro area). Only when including various pull variables as well as country fixed effects do their R^{2}s exceed .5. It seems reasonable to conclude that capital flows are difficult to model empirically in general, especially using only push variables.^{4}

**Factor models and VARs**

The second strand is more recent and limited; it is exemplified by Rey (2013). In her Jackson Hole paper, Rey first documents the (negative) correlations between (various types of) capital flows and the VIX, both globally and for various subregions, varying between -.06 and -.28. Conditional on other push factors (world short-term real interest rate and growth), correlations rise slightly, peaking at -.36 for debt flows to central and eastern Europe, and -.34 for equity flows to East Asia. She then documents, using principal components analysis, the presence of a large single common factor among various asset prices from many countries (some 850), where the first common factor in turn shows a relatively high, negative correlation (about .25) with the VIX. Building on her earlier work with Miranda Agrippino (2015), she then shows, using a VAR (and a BVAR), dynamic relations running from monetary policy in the United States to the VIX, and then on to bank leverage, capital flows and credit, with final effects on US GDP and deflator (which are last in the ordering in the VAR). In the VAR, she explains 4-17% of the variation in VIX by shocks to the federal

A paper along the same lines is Bruno and Shin (2015a). The paper uses a small- scale VAR to study the impact of US monetary policy on leverage and the VIX, and consequently on capital flows over the period Q4 1995-Q4 2007. Their ordering of variables in the VAR is similar to that used by Miranda Agrippino and Rey (2015): (i) federal funds rate; (ii) broker-dealer leverage; (iii) BIS banking flows; (iv) VIX; and (v) US dollar real effective exchange rate (REER). They then show that US monetary policy eventually leaves its mark on the US dollar exchange rate and capital flows funded by the US dollar. The quantitative importance of the global (and other) factors is, however, not noted.^{5}

**Variations, by type of flow, country and source and over time**

Both strands, especially the first one, recognise that sensitivities to global factors can vary between inflows and outflows, between gross and net flows, and by flow type. While the typical focus is on inflows, outflows can also be sensitive to global factors. Not surprisingly, outflows tend to increase when global interest rates rise. At the same time, increases in global risk reduce the probability of outflow-driven stops - maybe signalling capital repatriation by domestic investors in such circumstances (Calderon and Kubota (2013)). Even when gross inflows and outflows are volatile, net flows will be less volatile if the two offset each other.^{6} Since this offset is more common for advanced than for emerging market economies, in part as the private sector in advanced economies typically has larger gross foreign asset positions, global factors are typically more important for the latter (see further IMF (2013) and Forbes and Warnock (2012); Broner et al (2013) provide a comprehensive study).

The impact of global factors may also vary across flow type, ie bank (credit) flows, equity and bond portfolio flows and foreign direct investment (FDI), vs other flows (the latter include a broad residual array of transactions and holdings between residents and non-residents). A common finding is that portfolio flows and credit react more to global factors than FDI flows do.^{7} Related, sensitivities can vary by maturity (short vs long) and currency (US dollar vs others; foreign vs local currency).

All this argues against sweeping generalisations, in the spirit of Claessens et al (1995) and others. And given these differences, as the composition of capital flows changes, the aggregate exposures to global factors are likely to vary both over time and across countries.^{8}

Research has tried to assess whether shifts come along with variations in the importance of specific drivers. Avdjiev et al (2017a) find that the impact of global risk has increased post-GFC for international bond flows and declined for cross-border loan flows. They also report greater sensitivities to US monetary policy, driven mainly by behavioural shifts, with better-capitalised banking systems experiencing smaller rises in sensitivities and larger increases in international lending shares. McCauley et al (2015), focusing on credit denominated in US dollars, find that unconventional monetary policy helped the partial shift from borrowing away from global banks and towards bonds. Cerutti et al (2017) show that changes in banking system conditions since the GFC have affected the importance of US and European drivers of bank flows.

Variations in countries' general exposure to global factors have been studied in both strands of the literature mentioned. Unsurprisingly, more open countries (in both real and financial terms) experience greater effects. Bruno and Shin (2015b) find that global factors have a larger impact than local factors in more financially open countries with bigger banking flows. They report, when using a model with global and local variables, that, for countries subject to large bank inflows, the R^{2} (of 0.21) is 3.6 times higher than for a model with just local variables (still, in countries with lower banking inflows, global factors explain somewhat more than local factors). They find differences, in how much global factors explain, to be small between developing and developed countries, but larger between countries with high and low measures of law and order. Calderon and Kubota (2013), however, document only small differences in how capital flows to EMEs and advanced countries vary in their sensitivity to global factors.

There is less research on how recipient type and source characteristics affect the sensitivities of flows to global factors, and related domestic responses. Using gross capital inflows during 1996-2014 for 85 countries at a quarterly frequency, Avdjiev et al (2017b) show that capital flows into banks and corporations decline in both advanced economies and emerging market economies when the VIX rises, as do flows to EME sovereigns, but not to advanced economies' sovereigns. Baskayay et al (2017) show for one country that, through fluctuations in capital flows, local banks are especially affected by global factors, with a lower VIX leading to lower local borrowing rates and greater credit supply, explaining up to 40% of cyclical credit growth.^{9} Some Lastly, a number of papers have investigated cross-country differences in the independence of domestic monetary policy, the "dilemma vs trilemma" issue first raised by Rey (2013), typically focusing on the determinants of interest rates. While Han and Wei (2016) find that a flexible exchange rate by itself does not confer monetary policy autonomy, Klein and Shambaugh (2015) find that a moderately flexible exchange rate does confer monetary policy autonomy, although partial capital controls do not. And Obstfeld et al (2017) highlight that the transmission of global financial shocks is magnified under fixed exchange rates relative to more flexible regimes. Aizenman et al (2016) also find that economies that pursue greater exchange rate stability and financial openness face stronger links with centre economies' monetary policies. Han and Wei (2016) find that a flexible exchange rate regime confers monetary policy autonomy when the centre country raises its interest rate, but not when it lowers its rate (in their words, "fear of floating" mostly takes the form of "fear of appreciation"); capital controls provide insulation to countries even when the centre lowers its rate. Ghosh et al (2014) find that while global factors act as "gatekeepers" in determining the timing of capital flow surges, local macroeconomic variables determine the magnitudes. More case-based analyses also find that capital flows can vary across countries during periods of global financial stress, but it has proven harder to explain such differences.

Overall, the properties of different types of flows remain an area of ongoing research and debate, as do the relationships between global factors to domestic financial and economic developments and cross-country differences in the sensitivities of capital flows and domestic developments to various global factors. Few of the papers in either strand, however, have analysed the relative importance of global factors, the main objective of this paper.

The chief objective of this paper is to quantify the importance of the GFCy for capital flows; we seek to understand what proportion of the variation in capital flows is explained by the GFCy. To do this, we must be able to measure the GFCy. In this section, we explain the strategy we employ and explore the data we use.

**Strategy**

Our goal is to identify the GFCy, an intrinsically unobservable variable. We are guided by the idea that if the GFCy is consequential for capital flows, it should drive a high proportion of the fluctuations in most types of capital flows, in many places, much of the time.^{11} For the purposes of this paper, we define the GFCy as (high) commonality in financial conditions, manifest in capital flows, driven by observable global determinants. Accordingly, and in the spirit of finding robust evidence, we proceed in two ways, investigating both measurable variables from centre countries and commonality.

First, we examine the role of directly observable "fundamental" GFCy drivers, centre-country macroeconomic and financial determinants of capital flows. But which variables, and for which centre-countries? Our reading of the literature delivers a relatively strong consensus; the VIX is widely considered the favourite direct measure, most closely related to the GFCy. Still, in an effort to be conservative, we cast a wide net, since we are keenly aware that choosing the wrong measures or centre countries could lead us to underestimate the importance of the GFCy. Accordingly, we also include other measures used as drivers in the literature, for both the United States and other potential centre economies.

We proceed conservatively by also taking an indirect approach; we examine observable manifestations of the GFCy via the commonality of capital flows. There is a host of reasons why capital flows could behave similarly across countries at a point in time, and the GFCy is certainly one of them.^{12} If we ascribe *all* common movements in capital flows to the GFCy, we thereby develop an upper bound for the importance of the GFCy on capital flows. Accordingly, we use factor analytic methods to extract common factors in capital flows and use those as manifestations of the GFCy. Finally, in an effort to be extra-conservative, we combine both methods.

**Data: centre-country variables**

The most discussed and plausible centre country is the United States, and whenever we include variables, we include US measures.^{13} However, the euro area is also a potential generator of fluctuations in the GFCy; the same is also true (perhaps less plausibly) of the United Kingdom.^{14} Accordingly, as a robustness check, in some of our analysis we include variables from both Europe and the UK, as well as the US. This is limiting, since the euro area came into existence only in Q1 1999, necessarily reducing the span of study for certain variables (such as euro areaarea interest rates).

We start with the consensus GFCy measure, the VIX (ticker symbol for the Chicago Board Options Exchange (CBOE) volatility index). It measures the implied near-term volatility of S&P 500 index options, calculated and published by the CBOE. We use the last VIX reading of each quarter, downloaded from Bloomberg.^{15} The VIX is extensively used as a measure of the GFCy. For instance, it is explicitly identified by Passari and Rey (2015, p 683) as "our proxy for the global financial cycle".^{16} However, we do not restrict ourselves to purely US volatility measures; we also use a German analogue, the VDAX, which began trading in 1992 (now replaced by the VDAX-NEW), and check that our results are robust to using the VSTOXX, which began in 1999 with the euro area; and the UK analogue (IVI, which measures the volatility of the underlying FTSE 100 index) after 2000.^{17} These VIX analogues are also end-of-quarter measures obtained from Bloomberg.

As with the choice of centre country, we try to be conservative by considering other observable centre-country "fundamentals" above and beyond measures of stock market volatility. We use seven other standard variables: (a) the nominal policy interest rate (the federal funds rate for the United States, the UK base rate and the euro area deposit facility rate, all end-of-period and obtained from Haver); (b) the ex post real policy interest rate, measured as the nominal rate minus the ex post year- over-year realised CPI inflation rate (inflation is obtained from IFSTSUB and GDS); (c) the TED spread (measured as end-of-period three-month Libor minus the government rate - for the latter, we use the Treasury bill rate for the United States, the gilt rate for the UK and the government AAA bill rate for the euro area); (d) the yield curve slope (measured as the end-of-period 10-year minus the three-month government rates); (e) GDP growth (obtained from IMF WEO); (f) the growth in the REER (measured as the quarter-over-quarter percentage change in the IMF's CPI- based REER); and (g) M2 growth (measured as year-over-year growth in local currency, obtained from Haver).^{18}

**Data: capital flows**

For capital flow data, we rely on conventional series from the balance of payments on four types of disaggregated capital flows: foreign direct investment ("FDI"), portfolio equity investment ("Equity"), portfolio debt investments ("Debt") and bank credit ("Credit"; occasionally we sum portfolio equity and portfolio debt flows for an overall measure of portfolio flows).^{19} All these series come from the IMF BOP Statistics. We have data on both inflows and outflows, and all are expressed as percentages of GDP. Our panel data set is unbalanced, and runs from Q1 1990 up to Q4 2015 (since we are interested in quantifying the GFCy over recent history, and as data are of lesser quality in earlier periods). We have data on 85 countries; they are listed in Table A1.^{20} In much of what follows, we focus on a set of 63 "small" countries by excluding other plausible centre countries (US, UK, actual/future members of the euro area, and Japan).^{21} We have checked and corrected the data set using standard techniques.

Figure 1 provides a quick informal peek at the relationships between the standard GFCy proxy (the VIX) and capital flows. It shows scatters of capital flows (on the vertical axis, measured as a percentage of GDP) against the VIX; eight plots are provided for the two directions (in- and outflows) and four types of capital flows. Each scatter includes observations for the five dozen countries and 100 time periods, without conditioning for any influences at all, so the plots should be interpreted cautiously. Still, there is no indication of strong relationships between capital flows and the VIX for any type/direction of flow. While Figure 1 has some non-trivial outliers, the same non-result characterises the data when constrained to smaller values (Figure A1, an analogue for capital flows of less than 5% of GDP, delivers a similar message). Of course, both figures implicitly gloss over many other sources of variation that can be controlled for, so we do not take the negative message from the raw data too seriously.^{22}

**Factors**

Our indirect method of measuring the GFCy is through common movements in capital flows, for which we use factor analysis. Since there is no obvious way to estimate commonality, we estimate common factors in a large number of ways - 180, to be precise - to check that our results are not sensitive to minor perturbations in the methodology or sample.

We begin our analysis using Q1 1990-Q4 2015 to provide a reasonable span of recent data. However, we also generate our factors using Q1 1996-Q4 2015 since that increases the fraction of countries with complete series and restricts the GFCy impact to be estimated over a period of time when arguably financial globalisation had its greatest influence. Similarly, we also generate our factors using data from different groups of countries, to allow for the possibility that phenomena common to advanced economies may not be the same as those relevant for EMEs. We therefore use three sets of countries: advanced economies; emerging market economies; and a mix of advanced and emerging economies, all listed in an Table A1.^{23}

Given specific samples of time and countries, we then construct factors for each direction (capital flows either into or out of a country) and type of capital flow. We use five types of capital flows (FDI, debt, equity, credit and portfolio (debt+equity) flows. For each set of data, we then estimate common factors in three ways. First, we estimate a dynamic factor model with a single lag and extract an unobserved factor from the largest eigenvalue, following eg Miranda Agrippino and Rey (2015).^{24} Second, we estimate a dynamic factor model with two lags, and again extract a single factor from the largest eigenvalue; we do this to check sensitivity to the exact lag length. Third, and again for comparison, we estimate a traditional static factor model and again extract a single factor from the largest eigenvalue. We thus obtain 180 factors, one for each of the (two) samples of time, (three) sets of countries, (two) directions and (five) types of capital flows, and (three) estimation methods. To check that the results are insensitive to our forms of factor analysis, we also use the global factors provided by Miranda Agrippino and Rey (2015).

A ubiquitous GFCy should drive fluctuations in most capital flows for most countries to a significant degree. This should be manifest in our dynamic factors, which should display much commonality. Accordingly, it is useful to look at the factors extracted from capital flows.^{25} Figure 2 displays a matrix of scatter plots which graph factors against each other. Eight factors are portrayed, one for each of the two capital flow directions (in/outflows) and each of the four main types (FDI/debt/equity/credit); all the factors were estimated using a dynamic factor model for advanced economies between Q1 1990 and Q4 2015 using a single lag. The horizontal axis at the extreme left is the date, so that the column on the extreme left contains simple time series plots. The column next to the date contains the VIX, the standard direct measure of the GFCy. Each of the scatter plots contains over 100 points, one for each quarterly observation for our 26-year span.

If the GFCy drives most of the variation in most types and directions of capital flows, then one would expect the eight factors (which measure cross-country commonality in capital flows, and thus include variation due to the GFCy) to be reasonably positively correlated with each other in the scatter plots of Figure 2. If the VIX is highly correlated with the GFCy, it should also be highly correlated with the factors. While some of the scatter plots display positively correlated data (particularly among the outflow factors), most of the scatter plots are clouds without any clear shape. Another striking feature of Figure 2 is that the VIX is not particularly strongly related to any of the factors extracted from capital flows. Of the eight scatters between the VIX and capital flow factors, all have correlations smaller than .5, and three are negatively correlated. Only three of the eight correlation coefficients are significantly different from zero; two of these are actually positive (FDI inflows, .41; and FDI outflows, .34), while one is negative (debt inflows, -.29).^{26}

Figure 2 portrays factors extracted from advanced economies, although much of the interest in the literature lies in the drivers of capital flows to EMEs. Accordingly, Figure 3 portrays factors extracted from (four types of) capital inflows, and implicitly compares factors derived from capital flows to advanced economies and from flows to emerging economies. If capital flows into advanced and emerging economies are driven by similar phenomena - such as the GFCy - this would be manifest in positively correlated scatter plots, particularly those that compare factors derived from advanced and emerging economies for the same type of capital inflow. While this characterises the FDI common factors (the correlation coefficient is .66), the three other factors are only modestly correlated (the coefficients are -.01/.18/-0.1 for debt/equity/credit).

Figures 2 and 3 compare factors extracted from capital flows. However, the literature makes it clear that the GFCy should manifest itself in other phenomena as well, including asset and commodity prices. It is also worth investigating the analogues to the VIX in other potential centre countries. All this is pursued in Figure 4, which includes four factors extracted from stock returns and another from commodity prices as well as the VIX and its counterparts for the UK (IVI) and Germany (VDAX). We display both the long-sample and short-sample stock market factors provided by Miranda Agrippino and Rey (MAR).^{27} We also include factors extracted from the (national) MSCI stock returns of the advanced and emerging market economies, and another extracted from the levels of commodity prices.^{28} While the two factors extracted by MAR are, not surprisingly, strongly correlated with each other (.78), there are few strong positive correlations with other price factors.

Figure A4 examines the effects of different modelling assumptions for the factor models. It shows scatters for capital inflow factors for advanced economies derived from three statistical models: dynamic factor models with both one and two lags, and static factor models. The exact lag length used in a dynamic factor model does not seem to have a large impact on the results, but using a static factor model delivers factors only loosely correlated with those of dynamic factor models. It seems reasonable to set the one-lag dynamic factor as our default.^{29}

The evidence from Figures 2-4 suggests that the factors extracted from different types and directions of capital flows are not strongly related to the VIX or to each other. One would imagine that a substantive GFCy should result in capital flows that are correlated with the VIX, the standard proxy used in the literature for the GFCy; and that capital flows to various countries should be related to each other.30 The more important the GFCy is, the tighter these relationships should be. So the limited relationships between factors extracted from capital flows and the VIX as well as the limited relationships among capital flows revealed in our admittedly quick examination of the data are not easy to reconcile with an important GFCy for capital flows. Since our analysis up to this point has been informal - scatter plots and correlations - we now turn to a more formal statistical examination.

**4. Empirical results **

**Panel regressions**

We begin our analysis by estimating regressions where capital flows are pooled across countries but disaggregated by direction and type. As a first exercise, we begin without any country-specific time-varying regressors at all. Instead, we project capital flows on a comprehensive set of time fixed effects, common across countries. We do this to assess the quantitative importance of *all* possible global phenomena (such as the GFCy), thus working (temporarily) under the assumption that these shocks have an equal impact on all countries. In particular, for a particular direction and type of capital flow, we start with estimating a panel regression with least squares:

- CAPFLOWd,e,i,t represents a capital flow of direction
*d,*type*e*vis-à-vis country*i*in quarter t, as a percentage of GDP of country i; - (9i| and {0t} are comprehensive sets of country- and time-specific fixed effects; and
- £ represents all other determinants of capital flows.

We estimate (1) pooling data across all the countries for which the regressand is available for the entire period of time, Q1 1990-Q4 2015. Our results are presented in Table 1, which has eight rows corresponding to the two directions (d) and four types (e) of capital flows. The first two columns of Table 1 presents two familiar measures of goodness of fit when equation (1) is estimated over the entire sample, the within and overall R^{2} measures.^{31} All 16 of these goodness-of-fit measures are low. The same is true if the data set is extended to the countries which have complete series available only back to Q1 1996; the results are tabulated in the third and fourth columns of Table 1. The result is also similar when the estimation is restricted to small economies, as shown by the last two columns of Table 1. Succinctly, global phenomena specific to a period of time - such as the GFCy - do not seem to have an important effect on capital flows, even if not modelled explicitly, so long as their impact is restricted to having the same effect on all countries.

Table 1 is not particularly revealing, however, for at least two reasons. First, there is no explicit modelling of economic shocks such as the GFCy; instead, the effects of all common phenomena, including the GFCy, are absorbed by the time fixed effects. Second, the response of one particular country's capital flows to a common shock is assumed to be the same as the response of all other countries. We unpack these assumptions in two steps: first, we remove the time effects from (1) and substitute time-varying common phenomena; and next, we allow responses to the latter to vary by country.

We begin by removing the time fixed effects from (1) and replacing them with a standard set of "push" regressors used to model capital flows.^{32} In particular, we use contemporary US values of eight key variables: (a) VIX; (b) real GDP growth rate; (c) nominal policy rate; (d) real policy rate; (e) TED spread; (f) yield curve slope; (g) REER change; and (h) M2 growth. Above and beyond the eight variables and using country fixed effects, we include two dynamic factors extracted from capital flows, each matching the direction and type of capital flow of the regressand: one is extracted from capital flows to/from advanced economies, the other from capital flows to/from emerging economies.^{33} We note that the factors include *all* sources of commonality in capital flows, whether driven by the GFCy or not. As with equation (1), we estimate our regressions with least squares, pooling across countries with data available over the entire time span, and again disaggregated by direction and type of capital flow:

- USFUND
^{i}_{t}is the value of one of the eight US variables indexed by*j;*and - FACd,e
^{k}is the value of one of the two dynamic capital flow factors (one for advanced economies, one for emerging economies, both estimated with one lag) indexed by*k*.

Results are tabulated in Table 2. Again, there are eight rows of results, one for each direction and type of capital flow. Both within and overall R^{2} measure of goodness of fit are presented, although they are (as in Table 1) typically close. The results in the first column show the results when equation (2) is estimated for small countries. The results are necessarily worse than those of Table 1 (since time effects are more flexible than any set of common time-varying regressors), and show that the standard push factors account for only a small fraction of the variation in capital flows. These results are essentially unchanged when the MAR factors are substituted for our default factors.^{34} In the third column, we add a single quarterly lag of each of the US factors; this improves the goodness of fit, but only marginally. In the last column, we add four lags of the US variables; again, this makes only a small difference to the goodness of fit.

We conclude that standard centre-country variables do not seem to explain much of the variation in capital flows, so long as the responsiveness to these phenomena is constrained to be identical across countries. Accordingly, we next allow the effects of centre-country variables on capital flows to vary by country. We retain both dynamic capital flow factors (as always, matching direction/type of capital flow) and country-specific fixed effects. But now we allow for the possibility of country- specific effects of US variables (both contemporary and lagged) on capital flows.

Results are estimated with least squares for small countries and are tabulated in Table 3.

The first column of Table 3 contains results when (3) is estimated with a single US variable, namely contemporaneous values of the VIX (along with common capital flow factors and country-specific fixed effects). The results are similar to those of Table 1; capital flows are not much determined by centre-country phenomena, even when allowing each country to respond differently to the VIX. To test for delayed responsiveness of capital flows to the VIX, we successively add one and then four lags of the VIX (all with country-specific coefficients) in the second and third columns of Table 3; this does not change the fit of the panel equations very much, and the maximum R^{2} remains less than .15.

To check whether the poor fit of the equations in the first three columns of Table 3 is due to our focus on the VIX, in the last two columns we allow for country-specific slopes for all eight US variables, not simply for the VIX only. That is, we let each country respond differently to the (a) nominal and (b) real policy interest rates and (c) TED spread, (d) yield curve slope, (e) output growth, (f) growth of broad money, (g) REER change and (h) VIX. In the fourth column, we allow all eight US variables to have country-specific slopes; in the last column, we allow both the contemporary and a single lag of all eight US variables to have country-specific slopes. At this point, the equations obviously start to fit better, although in no case does the R^{2} approach .5. Further, this improvement comes with a profligate parameterisation. The best-fitting equation in Table 3 is that for FDI inflows, which has a within R^{2} of .42 but over 300 regressors! This equation is estimated with only 5.8 («2016/349) observations per coefficient, and has an overall R^{2} of just .08.^{36} We return to the issue of free parameters below.

**Histograms of R measures from national capital flow equations**

It seems that panel regressions do not offer a particularly good fit in the sense of explaining much of the variation in capital flows across countries and time, even allowing for either common or idiosyncratic national responses to a variety of contemporary and lagged centre-country variables and factors. That said, the goodness of fit measures tabulated in Tables 1-3 are overall summary statistics that could potentially mask considerable variation across countries. Some of the literature reviewed indeed suggests that the importance of the GFCy varies by country (eg because of different exchange rate regimes). It is conceivable that centre-country variables explain much of the variation for a number of countries' capital flows, but little variation for others. We now investigate that possibility by running regressions for individual countries. We do this only for small countries, as these are most likely.

Thus, for each small country in our sample with capital flow data, we estimate up to 10 time series capital flow equations (potentially one for each of the two directions and five types of capital flows: FDI/debt/equity/credit/portfolio debt+equity). Our interest is restricted to the goodness of fit of these equations. Since we have dozens of small countries, we simply provide histograms of the R s. We focus on (adjusted) —2 R rather than R^{2} to provide a penalty for overparameterisation of the model; since R^{2} necessarily rises with the addition of regressors, one can always "model" capital flows well (in-sample) with enough regressors. We note that this penalty is small, since —2 R still rises when a regressor is added with a *t*-statistic exceeding one in absolute value; we also show that our results are robust to using R^{2}. We note in passing that such measures are the standard used in push-pull regression results (eg Bruno and Shin (2015a), Avdjiev et al (2017a)).

We begin by estimating (4) with the standard eight US variables (the VIX, nominal and real policy rates, the TED spread, yield curve slope, output growth, REER change and M2 growth) and two dynamic capital flow factors (advanced and emerging economies, both estimated with a single lag and matched to the direction and type of capital flow). We estimate (4) with these variables and factors using the time series variation for a particular country/direction/type of capital flow combination if there are any non-trivial time series data (it need not be the entire Q1 1990-Q4 2015 span), and record the R for each combination. We then present the resulting set of R statistics graphically; our default results are presented in Figure 5.

Figure 5 contains 12 small histograms, each presenting R statistics for a set of 2 national capital flow equations. The top left-hand histogram presents all the (598) R values that we estimate for all combinations of countries, directions and types of —2 capital flows. Clearly, most of these time series regressions fit poorly; the mean R is —2 only .12, over a quarter of R s are negative, and only a few exceed .5. This pattern is widespread across different subsets. Across the top row of Figure 5 to the right are analogous histograms which cover capital flow regressions for inflows, outflows and portfolio flows, respectively; all three are similar to the top left-hand histogram. In the —2 two rows below are a set of eight histograms presenting R s for capital flows by direction and type. FDI inflows are the easiest capital flows to model statistically, a —2 pattern we find consistently throughout our research, but even there the mean R is only .25.^{38} Thus the evidence from the dozen histograms of Figure 5 indicates that conventional time series models of capital flows do not fit small countries well, even when incorporating eight centre-country variables and two capital flow factors.^{39} Given that the GFCy should be present in both the variables (particularly the VIX) and the capital flow factors, it is hard to reconcile this evidence with a GFCy that explains much variation in capital flows for many countries.

The sensitivity of these results is explored in Figures A6-A15; these are analogues to Figure 5, but each perturbs an aspect of the methodology. Figure A6 is analogous to Figure 5 but presents conventional measures of R^{2} without adjusting the statistic for degrees of freedom. The results are similar; the typical goodness of fit is poor, with the mean R^{2} less than .25. Figure A7 removes the US variables, while retaining the two capital flow factors. Figure A8 restricts the sample to small countries with complete sets of time series capital flow data, from Q1 1990 to Q4 2015. Figure A9 restricts the sample to the countries with above-median capital mobility, as gauged by the Chinn-Ito index of financial openness.^{40} Figure A10 restricts the sample to countries with per capita annual real GDP of at least $5,000.^{41} Figure A11 adds four quarterly lags of the VIX to the regressors of (4), while Figure A12 adds a quarterly lag of all eight US variables to the contemporaneous values. Finally, Figure A13 adds contemporaneous values of the eight UK and euro area variables to the eight US variables, although this restricts the time series span to Q1 2000-Q4 2015.

None of the nine Appendix variations of Figure 5 alters our view substantively; as with the straightforward estimates of equation (4), national capital flow equations typically fit the time series data poorly, even when traditional proxies of the GFCy (like the VIX) are augmented with other centre-country variables as well as capital flow factors. It is easy to find exceptions of course, given the large number of countries, directions and types of capital flows, but those are ... exceptions, which do not rise to the level of a systemic presence of a GFCy.

The histograms in Figure 5 persuade us that centre-country phenomena and common factors do not explain much of the time series variation in capital flows, and the evidence of Figures A6-A13 suggests to us that this conclusion is robust. We consider the histograms to be compelling presentations of the fit of our many time series capital flow regressions. But histograms are also a somewhat inefficient way to —2 convey the many R statistics; a more concise way is through box plots.

**Box plots of R ଶ measures**

Consider the top left-hand panel of Figure 6, more particularly its top row. This contains a wealth of information on the goodness of fit when FDI inflows (measured, as always, as a percentage of recipient's GDP) are regressed on an intercept, capital flow factors for both advanced and emerging market economies, and the standard eight contemporary US variables.^{43} As in Figure 5, a separate time series regression is estimated for each of the small economies with a sufficiently long series of data on to 75th percentiles of the R statistics, with the median marked by a vertical bar. The whiskers extend out to the "adjacent values", defined as the most extreme values within 150% of the interquartile range of the nearest quartile; outliers are individually marked. Immediately below the box plot for FDI inflows are the analogue box plots for debt, equity and credit inflows; immediately below those are the analogues for capital outflows. For continuity and ease of comparison, a vertical line is marked at .25 for each set of box plots, a notional benchmark.

What is the message from these box plots? The boxes in the top left-hand panel of Figure 6 are all located well to the left; seven of the eight interquartile boxes lie below the .25 marker. So while there are the occasional outliers to the right - those clearly marked observations where a particular country has a capital flow that is well modelled by the 11 coefficients in equation (4) - the majority of the equations fit poorly.

Immediately below the box plots in the top left-hand panel of Figure 6 are box plots for R^{2} statistics computed analogously (instead of the R values in the top left- hand panel); these show that the exact choice of statistics makes little difference. The two panels in the middle are constructed similarly, but restrict the sample to countries with complete time series available over the entire 26 years. The two panels on the right are again similar to those on the left, but drop all eight US variables from the estimation. All six panels of box plots in Figure 6 look similar; the GFCy does not seem to explain much variation in capital flows in that it cannot be modelled well with the 10 time-varying regressors of (4).

Figures 7-9 contain a large number of box plot panels with further robustness checks, all constructed similarly to those of Figure 6. Thus Figure 7 changes the specification of (4). The top left-hand panel drops the factors from the right-hand side of (4); the top centre panel substitutes static for dynamic factors; the top right- hand panel substitutes the dynamic factors estimated by Miranda Agrippino and Rey for our dynamic factors. The bottom left-hand box plots add four lags of the VIX to the right-hand side of (4), while the bottom centre panel adds a single lag of all eight US variables as regressors. In the bottom right-hand panel of Figure 7, contemporary values of all eight variables for both the UK and euro area are added (thereby restricting the time series span of the data). None of these changes leads to a really dramatic improvement in the quality of the fits. The highest R statistics are in the bottom right, when 24 US, UK and European variables are used, along with two factors extracted from capital flows, to model the 64 observations available since Q1 2000.

Even in this case a reasonable median R is .25, and there are plenty of negative statistics.

Figure 8 changes the sample in a number of ways to ensure that the results are robust. The top left-hand panel implicitly splits the sample into two by allowing each

This is, of course, unsurprising since the data underlying the top left-hand panel of Figure 6 are drawn from those of Figure 5.

Using US and euro area (but not UK) variables leads to similar results.

of the eight US variables to have a different coefficient from Q1 2009 onwards, following Avdjiev et al (2017a).^{46} The bottom left-hand panel drops outlier observations, defined as those where the residual lies more than 2.5 standard errors from the mean. The top centre panel drops all observations where capital flows exceed 8% of GDP; the bottom centre panel winsorises all observations at 5% of GDP. At the top right, advanced economies are dropped from the sample, leaving only developing and emerging economies, while observations between Q1 1990 and Q4 1995 are dropped in the bottom right. None of these perturbations alters the results substantially.

Finally, to examine findings in the literature that the impact of the GFCy varies by country characteristics, Figure 9 splits the sample on the basis of a number of criteria. In the top left-hand panel, we drop observations which have below-median levels of financial openness, using the Chinn-Ito measure, while in the bottom left-hand panel observations are dropped for countries with annual real GDP per capital below $5,000. In the top centre panel, results are portrayed using only countries from East/Central Asia, the Pacific and Europe; the panel below contains results for the other countries. The panels on the right-hand side of Figure 9 use the Reinhart-Rogoff annual data on exchange rate regimes to split the sample; countries at the top have relatively flexible exchange rates, either floating (managed or freely) or in bands (crawling or moving). The box plots at the bottom have more rigid regimes, being in currency unions or boards or with currency pegs (crawling or not).^{47} Our results do not seem particularly sensitive to the exact region or exchange rate regime: the GFCy is quantitatively not so important.^{48}

**Event study**

The evidence that we have presented thus far indicates that centre-country phenomena, captured by the VIX or other variables, do not typically explain much variation in capital flows. This is true even when the empirical models are augmented by factors that reflect the common movements of capital flows. Perhaps, though, the GFCy is more important during brief periods of crisis than in more typical and longer tranquil times? We investigate this hypothesis briefly with some event studies of subperiods of global financial stress.

Breaking the sample at Q1 2008 instead of Q1 2009 changes the results insubstantially.

We currently have only annual exchange rate regime data, so all four quarters of the year are matched to the single respective annual Reinhart-Rogoff observation.

The focus in this paper has been on the relationship between the GFCy and capital flows. Figure A16 provides an informal peek at the GFCy and credit growth. It is an analogue to Figure 6, reporting box plots of goodness of fit, but when real credit growth replaces capital flows as the regressand in equation (4), with appropriate dynamic factors. Real credit growth seems to be slightly more linked to the GFCy than most types of capital flows, with a median R^{2} of about 0.3. We are pursuing developments in credit, along with asset prices, in a companion paper.

It can well be the case that global events, including the ones we study here, affect capital flows in the very short run. Since we use capital flow data from balance of payments statistics, however, we are limited to quarterly data. Still, even if the GFCy matters a lot for short periods of time occasionally, our point remains that the GFCy is not typically very important from a broader perspective for capital flows.

To define periods of stress, we focus on periods when the VIX is high. During our 26-year sample, the VIX ended the quarter above 30 on eight occasions; we treat these as the events portrayed in Figure 10.^{50} We then plot some of the key movements of capital flows for our sample of (63) small countries during the 12 quarters on either side of the periods with high VIX values.

Consider the top left-hand graph in Figure 10. Starting at the extreme left of the graph, the solid middle line traces out the average size of FDI inflows (relative to GDP) beginning 12 quarters before the event, then progressing, as the eye moves to the right, through the event and 12 quarters afterwards. The dashed lines above and below trace out the (5, 95) confidence intervals for FDI inflows. There is little action in inflows of FDI capital during the periods immediately before, during and after heightened values of the VIX. The three graphs to the right at the top of Figure 10 are analogous but cover inflows of portfolio debt, portfolio equity and credit; analogous outflows are portrayed in the bottom row. All eight graphs in Figure 10 deliver the same message: capital flows do not seem to change systematically and significantly during periods around high VIX values. There are some small changes in flows, but no statistically significant movements.

The results of Figure 10 are robust to minor changes in the empirics. For instance, Figure A17 replaces the (eight) events when the VIX exceeded 30 with (19) events when the VIX ended the quarter exceeding 25. Little of statistical or economic significance seems to change when we use this lower threshold to mark periods of market fear: capital flows just do not seem to change systematically during these periods of market stress. The same is true when we look at the (dozen) periods when the VIX rose by more 5, as shown in Figure A18; in the (seven) quarters when the average (not just the end-of-quarter) value of the VIX exceeded 30, portrayed in Figure A19; or in the (seven) quarters when the US dollar real effective exchange rate appreciated more than 3.5% (Figure A20). We conclude that periods of financial stress - that is, high and/or rapidly rising values of the VIX or the dollar - do not seem to be systematically associated with unusual capital flow movements (at the quarterly frequency) across our sample of countries. If the former are associated with critical moments in the GFCy, then they are not closely linked to capital flows.

**Coefficients**

Our emphasis in this paper diverges from most of the literature in that we focus on the quantitative importance of the GFCy for determining capital flows; we care about an equation's goodness of fit, rather than the sign, size and significance of its coefficient estimates. This biases our approach *towards* finding an important GFCy, since a particular model of capital flows may fit well statistically, without intuitively signed, plausibly sized coefficients. Indeed, in our analysis above, we have not even discussed the sign or size of the coefficient estimates (this would be difficult, since we have estimated literally thousands of capital flow equations). We nevertheless provide a little direct evidence on the matter by tabulating coefficient estimates from (4) in Table A3 for capital flows into five EMEs. While we do not take these estimates particularly seriously - in part because of the specific choices of countries and models estimated - we note that the coefficients and their significance levels vary dramatically across countries and capital flow types. In general, for example, results confirm the literature's general findings (Koepke (2015)) that portfolio flows, especially debt flows, tend to co-move negatively with the VIX more so than other types of capital flows. Nevertheless, the analogous scatter plots of actual against fitted capital flows for these countries, which are portrayed in Figure A21, confirm our general result of limited explanatory power.

**5. Conclusion**

Our goal in this paper has been not to praise the Global Financial Cycle (GFCy), nor to bury it, but merely to quantify it; we are interested in its relevance for understanding capital flows. We have done this quantification with a variety of techniques, including panel regressions, national capital flow equations and event studies. Our data and statistical metrics are as conventional as our models and techniques, falling well within the bounds of the existing literature. We use a broad approach to quantify the GFCy, measuring it both directly via conventional centre- country variables like the VIX, and indirectly via commonality in capital flows extracted from dynamic factor models. Nevertheless, it has been difficult to find consistent manifestations of the GFCy in capital flows, something that is puzzling for a phenomenon viewed by some as conspicuous and significant. More importantly, we find little evidence that the GFCy explains systematically as much as a quarter of the variation in capital flows.

As the measures that we use simply do not explain much variation in capital flows, we are left feeling skeptical about the general quantitative importance of the GFCy in understanding capital flows. This is especially true since we have been conservative in that: (a) we ignore implausible coefficient estimates; and (b) we attribute *all* explanatory power associated with both centre-country variables and commonality to the GFCy, even if the true source lies elsewhere. Our conclusion is, surprisingly, consistent with the literature, which is more concerned with eg estimating coefficients for global interest rates and risk measures than with understanding their quantitative importance for the variation in capital flows. The main message from our analysis is that the empirical importance of the GFCy in determining capital flows is limited, smaller than typically implied by the literature.

Caveats are naturally appropriate. Our empirics are based on conventional models of capital flows that we estimated in straightforward ways with standard data and evaluated with traditional statistics. Future work can plausibly extend our research on any or all of these dimensions. For instance, a claim that the GFCy explains a high proportion of capital flow variation for a particular set of countries or time periods could be evaluated with out-of-sample statistical techniques. Perhaps the country is an inappropriate unit of analysis? Our approach could also be extended to consider non-linear effects of the GFCy on capital flows. Most of our models have no intrinsic dynamics (unlike eg VARs) so that the GFCy explains the same variation at all horizons, another feature that might be worth exploring. We have also ignored endogenous domestic responses to the GFCy, another aspect of the issue worth exploring. Indeed, we have eschewed all domestic influences on capital flows; including these determinants seems likely to reduce the effects of the GFCy further. More generally, our results focus on the potential impact of the GFCy on capital flows, so it could be the case that countries also face the impact of the GFCy in other important variables, such as domestic asset prices or credit. Finally, our analysis was conducted at the quarterly frequency. The GFCy could be more important for capital flows at higher frequencies for short periods of time. Still, the fact that any such effects do not show up strongly at the quarterly frequency simply reinforces our message that the GFCy is not a very important determinant of capital flows.

The conclusion that the GFCy is not that important in understanding capital flows leads to important policy messages which become clear once one considers two possibilities. Suppose that most of the variation in capital flows that most countries experience most of the time is explained by centre-country phenomena through the GFCy. In this case, as Rey and her co-authors have ably pointed out, a periphery country may consider the benefits of financial integration as less than the risks introduced by (volatile) capital flows driven by exogenous events taking place in larger centre countries. If this is the case, the country may choose to insulate itself from the GFCy with, for example, capital controls, macroprudential policies and the like, or seek to avail itself of (self)-insurance mechanisms. In contrast, however: if, as our results suggest, the GFCy explains only a small fraction of the variation in capital flows, then more idiosyncratic phenomena necessarily explain capital flows. To the extent that these are idiosyncratic foreign phenomena, it will be difficult to put in place systematic policies that screen "good" from "bad" capital flows, and the country is thus more likely to give up the gains of international financial integration as it tries to insulate itself. And, regardless, it may be more natural to identify much of this idiosyncrasy with domestic phenomena, making it incumbent on the policy authorities of countries on the periphery to take ownership of and responsibility for these. Since the potential impact of the GFCy can show up in other variables (eg domestic asset prices and credit), however, more analysis is needed before policy conclusions can be reached.

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