## wp1741

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### Definitions and instrument classification
- FDI: “a category of cross-border investments associated with a resident in one economy having control or a significant degree of influence on the management of an enterprise that is resident in another economy”.
- Portfolio flows: “defined as cross-border transactions and positions involving debt or equity securities, other than those included in direct investment or reserve assets”.
- Other flows: “a residual category that includes positions and transactions other than those included in direct investment, portfolio investment, financial derivatives and employee stock options, and reserve assets”, classified in government-related flows and private flows (bank and non-bank flows).
- Definitions are taken from the sixth edition of the Balance of Payments and International Investment Position Manual (BPM6).

### Evolution of inflows by instrument (EMDEs)
- FDI represent the majority of capital inflows for EMDEs.
- The surge and subsequent collapse in inflows during the GFC was mainly driven by other flows, which include bank flows.
- Post-crisis pick-up in capital flows was led by debt-creating (bank and portfolio debt) instruments, with some reversals between 2015 and 2016.
- Expectation: portfolio and other flows are characterized by a higher volatility than FDI.

### Correlation across instruments (EMDEs)
- Correlations across instruments have evolved and are sometimes significantly different from 0.
- The correlation between FDI and portfolio flows has switched sign multiple times; surges coincide with positive FDI-portfolio correlation, and correlation turns negative soon after a stop.
- Co-movements of FDI and portfolio with other investments do not display the same surge-stop pattern.
- Key message: heterogeneity across instruments.
- Significance markers used in Figure 3: estimates significant at 10%, 5% and 1% indicated by grey, blue and red dots respectively.

### Literature review — determinants of capital flows (selected findings)
- Main determinants categorized as country-specific (pull) and global (push) factors.
- Common global push factors: indicators of global risk appetite and US monetary policy.
- Fratzscher (2012): push factors overall main drivers during the crisis; pull factors dominant in 2009 and 2010 for EMDEs.
- Forbes and Warnock (2012): global risk associated with extreme episodes (surges, stops, flight, retrenchment); contagion through trade, banking, geography associated with stops and retrenchments.
- Agrippino and Rey (2014): one global factor explains large share of variance of risky-asset returns; interpret as market wide risk aversion and aggregate volatility (VIX); US monetary policy drives this global factor.
- Passari and Rey (2015): evidence of a global financial cycle in gross cross-border flows, asset prices and leverage; VIX as proxy; significant spillovers from US monetary policy to EMDE capital flows.
- Ahmed and Zlate (2014): growth and interest rate differentials between EMDEs and AEs and global risk appetite important for net private capital inflows; unconventional US monetary policy positively affects EMDE inflows, especially portfolio inflows.
- Ghosh et al. (2014b): US interest rates and VIX crucial for capital surges to EMDEs; surge occurrence and magnitude depend also on external financing need, capital account openness, exchange rate regime.
- Siemer et al. (2015): countries with higher uncertainty betas see capital inflows more sensitive to risk.

### Literature review — volatility of capital flows (selected findings)
- Two strands: (i) volatility differences between emerging and advanced economies; (ii) panel-data analyses of financial integration impact on volatility.
- Rigobon and Broner (2005): higher volatility in EMDEs primarily due to propensity to build up imbalances.
- Alfaro et al. (2007): domestic factors (institutional quality, sound macro policies) important in explaining volatility differences.
- Goldstein and Razin (2006): gap between volatility of FDI and portfolio flows smaller in AEs.
- Albuquerque (2003) and Tesar and Werner (1995): EMDEs show higher share of FDI and higher volatility of portfolio flows.
- Neumann et al. (2009): financial integration increases volatility of FDI in emerging economies while reducing volatility of other debt flows in mature economies.
- Broto et al. (2011): since 2000 global factors increasingly significant; domestic macroeconomic and financial factors can reduce volatility of certain instruments without increasing others.
- Alberola et al. (2016): international reserves stabilize during financial distress; larger reserves linked to higher gross inflows and lower gross outflows and facilitate disinvestment by residents abroad.
- Broner and Ventura (2016): financial globalization in EMDEs can produce three outcomes depending on development, productivity, domestic savings and institutional quality; empirical investigation expands Broto et al. (2011) to include the GFC period.

### Volatility measures — data and methodology
- Dataset: quarterly data spanning from 1970Q1 to 2016Q1; broader set of capital flow instruments than previous literature.
- Three approaches to estimate capital flow volatility:
  - 1) Rolling-window standard deviations (RW)
    - Formula: 휎푖푡 = (1/n ∑(flow푖푘 − μ)2 t k=t−(n−1) )1/2, where μ = 1/n ∑ flow푖푘 t k=t−(n−1)
    - In computations n = 4 quarters.
    - Caveats: data loss at sample start; 휎푖푡 strongly persistent; equal weights overly smooth volatility.
  - 2) GARCH(1,1) estimated standard deviations
    - Process: y푖푡 = ε푖푡 σ푖푡 ; σ푖푡2 = α0 + α1 y푖(푡−1)2 + α2 σ푖(푡−1)2, where y푖푡 ≡ ∆flow푖푡, ε푖푡 Gaussian white noise.
    - Drawbacks: data scarcity may cause convergence errors; ML small-sample biases; stationarity and positivity require α1̂ + α2̂ < 1, α0̂ > 0, α1̂ > 0 and α2̂ > 0.
  - 3) ARIMA(1,1,0) residual-based standard deviations (authors’ preferred benchmark)
    - Estimate ∆flow푖푡 = c + β ∆flow푖(푡−1) + ν푖푡; test residuals for ARCH effects; if heteroscedasticity rejected, σ푖푡2 = 1/4 ∑(ν푖푗)2 t+(n−2) j=t−(n−3); otherwise fit GARCH(1,1) to residuals.
    - Differencing degree set to 1 since series are ~I(1).
    - ARIMA residual heteroscedasticity checks used to improve robustness; ARIMA estimates used as benchmark in regressions.

### Evolution of volatility over time — empirical findings
- Comparison of measures:
  - RW underestimates the spike at crisis onset and overestimates fall after crisis.
  - GARCH tends to lag RW and ARIMA and is on average higher.
  - Broadly, the three estimates show similar results.
- Cross-group comparisons:
  - Net flows to EMDEs are more volatile than net flows to AEs.
  - In AEs, gross outflows dampen impact of gross inflows on net flows; damping weaker in EMDEs, leading to higher net flow volatility in EMDEs.
  - In EMDEs, volatility of inflows is on average higher than outflows, driving up net flow volatility.
- Post-GFC dynamics:
  - Aside from spikes (biggest corresponding to the GFC), current volatility level is comparable to pre-crisis average.
  - EMDEs volatility prone to bouts, rising during global risk-off episodes (notably the taper tantrum).
  - In context of capital flow slowdown (IMF 2016), even small swings can lead to substantial net outflows or sudden stops.
  - When adjusted for level of flows, volatility has either increased or stayed at the same pre-crisis levels.
- Role of China:
  - Excluding China, broad evolution of volatility for World and EMDEs is not very different, though recent increases in volatility are less pronounced when China is excluded.

### Statistical tests: change in volatility pre- vs post-GFC (Geweke’s test)
- Test: Geweke’s separated partial means test applied to Global, AEs, EMDEs and three volatility measures (RW, GARCH, ARIMA) across GIs (Gross Inflows), GOs (Gross Outflows), NIs (Net Inflows).
- Selected table results (Statistic; P-value):
  - Global
    - RW: GIs 9.18; 0.00. GOs 6.83; 0.01. NIs 1.19; 0.28.
    - GARCH: GIs 62.44; 0.00. GOs 53.39; 0.00. NIs 3.66; 0.06.
    - ARIMA: GIs 20.36; 0.00. GOs 15.27; 0.00. NIs 3.05; 0.08.
  - AEs
    - RW: GIs 20.99; 0.00. GOs 21.04; 0.00. NIs 15.17; 0.00.
    - GARCH: GIs 79.31; 0.00. GOs 86.76; 0.00. NIs 0.68; 0.41.
    - ARIMA: GIs 17.69; 0.00. GOs 17.61; 0.00. NIs 6.88; 0.01.
  - EMDEs
    - RW: GIs 7.89; 0.00. GOs 15.84; 0.00. NIs 24.60; 0.00.
    - GARCH: GIs 0.99; 0.32. GOs 12.38; 0.00. NIs 0.06; 0.80.
    - ARIMA: GIs 6.51; 0.01. GOs 15.10; 0.00. NIs 27.76; 0.00.
- Key conclusions:
  - Null of equal means before and after crisis is almost always rejected at 5% or 10% significance levels, indicating shifts in volatility since the GFC, though magnitude generally small.
  - Exceptions (no statistical difference): net flows in World (RW); net flows in AEs (GARCH); GARCH volatility of both gross and net inflows in EMDEs.
  - Broad summary for EMDEs: aftermath of the crisis EMDEs experienced a slight increase in volatility of gross inflows by 0.2% of GDP and a slight decrease in volatility of gross outflows by 0.16% of GDP; combined to slightly decrease volatility of net inflows by an average of 0.02% of GDP.

### Instrument-level and component volatility (aggregate EMDEs)
- Relative volatility (aggregate EMDEs gross inflows):
  - Portfolio flows ~ two times more volatile than FDI.
  - Other investment flows ~ four times more volatile than FDI.
  - Among portfolio flows, portfolio debt more volatile than portfolio equity.
  - Equity flows (FDI and portfolio equity) generally less volatile.
- Time patterns by instrument:
  - FDI: clear upward trend in volatility before the GFC and downward trend afterwards (notably in GARCH and ARIMA estimates).
  - Portfolio (total): GARCH and ARIMA estimates higher than RW; no defined overall trend; lower volatility in 2009-2016 subsample.
  - Portfolio equity: ARIMA and RW show slight upward trend until GFC and downward thereafter.
  - Other investments: highest volatility estimates among instruments; GARCH produces higher values.
- Geweke’s test for EMDEs gross inflows by instrument (Statistic; P-value)
  - RW
    - FDI 153.78; 0.00.
    - Portfolio 4.18; 0.04.
    - Port. debt 17.06; 0.00.
    - Port. equity 1.90; 0.17.
    - Other 10.76; 0.00.
  - GARCH
    - FDI 136.40; 0.00.
    - Portfolio 2.60; 0.11.
    - Port. debt 5.99; 0.01.
    - Port. equity 2.99; 0.08.
    - Other 5.06; 0.02.
  - ARIMA
    - FDI 233.30; 0.00.
    - Portfolio 2.86; 0.09.
    - Port. debt 4.52; 0.03.
    - Port. equity 3.21; 0.07.
    - Other 13.81; 0.00.
- Instrument-level conclusions:
  - Null of equal means rejected for FDI, portfolio debt and other investments across all estimators.
  - Volatility of portfolio inflows (GARCH) and portfolio equity (RW) show no statistically significant mean difference pre- vs post-GFC.
  - ARIMA-estimate average changes in EMDEs’ volatility post-crisis:
    - FDI: 0.086% of GDP
    - Portfolio: -0.014% of GDP
    - Other investments: 0.249% of GDP

### Delving deeper: other investment flows (composition and volatility)
- Classification: i) bank flows; ii) private non-bank flows; iii) official sector flows.
- Composition (levels, % share of group GDP):
  - Private flows constitute most of aggregate other investment flows.
  - Private flows reversed and experienced a temporary stop during the GFC, contributing to sudden stop of aggregate gross inflows to EMDEs.
  - After the GFC, private-sector other gross inflows are markedly lower than before, with reversals in 2015 and 2016.
  - Before the crisis, most other flows were private flows to banking and non-banking sectors; after the GFC both decreased and in certain periods nearly disappeared from the capital account (e.g., second half of 2009).
- Volatility of subcomponents (other gross inflows, % share of group GDP):
  - Volatility of private flows is much higher than volatility of official sector flows; official flows spiked during crisis then stabilized around a level close to 0.
  - Within private sector:
    - Volatility of flows to banks shows a slight decrease toward end of sample.
    - Volatility of flows to non-banking sector stabilized around a lower long-run average after the crisis.
  - Overall: volatility of other investments almost completely driven by volatility of private flows; volatility roughly equally distributed across banking and non-banking private sectors.

### Volatility measures for individual countries (ARIMA preferred)
- RW, GARCH and ARIMA produce very similar estimates; authors focus on ARIMA.
- Uses of country-level volatility measures:
  - Policy diagnostics for country-specific high volatility.
  - Identifying instruments to monitor more closely.
  - Comparative research across countries and regions.
  - Understanding relationship between EMDEs and AEs capital flow volatility.
- Cross-country median and distributional features (median ARIMA volatilities):
  - Skewness: FDI 1.0770; portfolio 2.8565; portfolio debt 2.8875; portfolio equity 1.2858; other investments 2.1120.
  - Kurtosis: FDI 3.3431; portfolio 14.3172; portfolio debt 14.0942; portfolio equity 4.1295; other investments 8.5991.
  - Interpretation: distributions for portfolio and portfolio debt shifted right and exhibit high kurtosis, indicating higher probability of extreme values relative to FDI or portfolio equity.
- Heat-map comparisons pre- (2000Q1-2007Q2) vs post-GFC (2009Q3-2016Q1):
  - Gross inflows: volatility of total gross inflows decreased in countries like Canada and Russia and some smaller Latin American economies, but median volatility in sample has increased over time; on average volatility of gross inflows increased after the GFC.
  - Other gross inflows: volatility decreased in some Latin American economies, increased markedly in North America and Europe; Asia largely unchanged except Japan where other inflows volatility slightly increased.
  - Bank gross inflows: flows to banking sector are major drivers of observed trends; peripheral Euro Area sovereign debt crisis exacerbated volatility of bank flows toward Western European economies.

### Box 1 — Financial development and capital flow volatility (key results)
- Correlations between Financial Development Index and volatility by instrument:
  - Correlation almost 0 for FDI, portfolio and other investments.
  - Correlation positive and more relevant for portfolio equity.
  - GFC increased significance of correlations (higher R2) for all instruments except portfolio equity.
  - For portfolio flows, especially portfolio debt, correlation sign switched from negative to positive during GFC and moved back to negative afterwards.
- Overall conclusion:
  - Hypothesis that more financially developed countries face more volatile capital flows not confirmed except for portfolio equity (whose size in EMDE financial accounts is much reduced).
- Contagion exposure to AEs:
  - Higher and more significant correlation between volatilities of other investments in EMDEs and AEs.
  - This correlation is stronger the more financially developed a country is (higher Financial Development Index).
  - Interpretation: more financially developed EMDEs present higher exposure to developments on international financial markets.
- Panel regression framework (overview):
  - Sample: EMDEs, period 1980Q1-2016Q1.
  - Dependent variables: ARIMA volatility estimates for total flows and instruments.
  - Independent variables: Global factors (US shadow rate, US real GDP growth, S&P 500 volatility, US inflation, log price of oil), Domestic macro factors (real GDP growth, domestic policy rate, GDP per capita), Domestic structural factors (Chinn-Ito index, trade openness, reserves/GDP).
  - Controls: dummy 2007Q3-2009Q2 (GFC), dummy 2009Q3-2016Q1 (post-crisis), country fixed effects, explanatory variables lagged by one quarter; covariance matrix corrected using Driscoll and Kraay (1998); clustered standard errors also reported.
- Key regression coefficients (selected; significance as reported by authors):
  - Global factors:
    - S&P 500 returns volatility (t-1): 0.849*** for Total.
    - US shadow rate (t-1): 0.174** for Total.
    - US growth (t-1): -0.492*** for Total.
    - US inflation (t-1): -0.320** for Total.
  - Oil price (log) (t-1) — semi-elasticities interpretation:
    - 1% increase in oil price lowers volatility of portfolio equity by 0.9% of GDP.
    - 1% increase in oil price lowers volatility of other investments through the official sector by 2.85% of GDP.
    - 1% increase in oil price increases volatility of other investments through the banking sector by 1.34% of GDP.
  - Domestic factors:
    - RGDP growth (t-1): -0.230*** for Total.
    - GDP per capita (t-1): 0.00130** for Total.
    - Chinn-Ito index (t-1): -2.029* for Total.
    - Trade openness (t-1): 0.0845*** for Total.
    - Reserves/GDP (t-1): 0.00708 for Total (some instruments significant).
  - Crisis dummy effects (2007Q3-2009Q2):
    - Total gross inflows volatility higher during the GFC by 1.467** (i.e., 1.47% of GDP).
    - Portfolio equity volatility higher during the GFC by 0.39% of GDP.
    - Other investments through the official sector higher during the GFC by 0.94% of GDP.
    - Other investments through private non-banking sector higher during the GFC by 0.52% of GDP.
- Statistical summary:
  - Observations (Total): 1,405.
  - Number of groups: 25.
  - Within R2 for Total: 0.176.
  - Note: R2 not very high for any instrument (maximum 0.176), normal for volatility regressions.

### Box 1 — Interpretation and policy-relevant takeaways
- Determinants of capital flow volatility differ from determinants of capital flow levels; global risk aversion (push) can be more important than domestic GDP growth (pull) for volatility.
- Trade openness is a major domestic driver: more open economies face higher volatility.
- GDP per capita positively associated with volatility ceteris paribus, suggesting richer EMDEs exhibit greater volatility.
- More financially developed EMDEs are more exposed to international market developments (contagion channel), notably through other investments.
- Oil price movements affect volatility heterogeneously across instruments and sectors; effects largely driven by oil-exporters and their financial institutions’ behavior.
- Robustness: interaction terms with crisis and post-crisis dummies do not change main takeaways; low R2 implies additional drivers remain to be identified.

### Box 2 — The volatility of bank flows versus oil price (key results)
- Identification: elasticity of bank inflows volatility estimated using log oil price as regressor (direct elasticity interpretation).
- Motivation: link between banks’ profitability and oil price, particularly in oil-exporting emerging economies.
- Average elasticity estimates:
  - Pre-crisis period average elasticity: 1.26% (i.e., a 1% increase in the oil price leads to a 1.26% increase in bank inflows volatility).
  - After the GFC: overall average elasticity 0.95%.
- Post-crisis trend by group:
  - Oil-exporting economies: elasticity has increased after the crisis compared to earlier periods.
  - Oil-importing economies: elasticity has decreased after the crisis relative to earlier periods.
- Distributional dynamics:
  - During financial distress (GFC) median values for exporters and importers collapse to around same level, indicating distributions coincide under aggregate shock.
  - Oil importers: median shows little variation after mid-2000; IQR narrowed over time (distribution more concentrated).
  - Oil exporters: distribution shifts observed; median decreased in mid-2000s and during GFC, then increased after crisis with a spike in 2014-2015.
- Sample definition note:
  - Oil exporters in the sample: Brazil, Ecuador, Egypt, Indonesia, Kazakhstan, Mexico, Malaysia, Russia and Saudi Arabia.

*Source: IMF working paper wp1741 (Appendix E, Boxes 1 and 2, and associated analysis).*

### 1. Foreign Direct Investments (FDI), “a category of cross-border investments associated with

### 1. Foreign Direct Investments (FDI), “a category of cross-border investments associated with 

### Definitions and instrument classification
- FDI: “a category of cross-border investments associated with a resident in one economy having control or a significant degree of influence on the management of an enterprise that is resident in another economy”.
- Portfolio flows: “defined as cross-border transactions and positions involving debt or equity securities, other than those included in direct investment or reserve assets”.
- Other flows: “a residual category that includes positions and transactions other than those included in direct investment, portfolio investment, financial derivatives and employee stock options, and reserve assets”, classified in government-related flows and private flows (bank and non-bank flows).
- Definitions are taken from the sixth edition of the Balance of Payments and International Investment Position Manual (BPM6).

### Evolution of inflows by instrument (EMDEs)
- FDI represent the majority of capital inflows for EMDEs.
- The surge and subsequent collapse in inflows during the GFC was mainly driven by other flows, which include bank flows.
- The post-crisis pick-up in capital flows was led by debt-creating (bank and portfolio debt) instruments, with some reversals between 2015 and 2016.
- Expectation: portfolio and other flows are characterized by a higher volatility than FDI.

### Correlation across instruments (EMDEs)
- Correlations across instruments have evolved and are sometimes significantly different from 0.
- The correlation between FDI and portfolio flows has switched sign multiple times over the sample period; episodes of surges coincide with a positive correlation between FDI and portfolio flows, while the correlation turns negative soon after a stop.
- Co-movements of both FDI and portfolio with other investments do not display the same surge-stop pattern.
- The key message: there exists a degree of heterogeneity across instruments.
- Significance markers used in Figure 3: estimates significant at 10%, 5% and 1% indicated by grey, blue and red dots respectively.

### Literature review — determinants of capital flows
- Main determinants categorized as country-specific (pull) and global (push) factors.
- Common global push factors: indicators of global risk appetite and US monetary policy.
- Fratzscher (2012): push factors overall main drivers during the crisis; pull factors dominant in 2009 and 2010 for EMDEs.
- Forbes and Warnock (2012): global risk significantly associated with extreme capital flow episodes (surges, stops, flight, retrenchment); contagion through trade, banking, geography associated with stops and retrenchments.
- Agrippino and Rey (2014): one global factor explains important part of variance of returns of risky assets; interpret this as market wide risk aversion and aggregate volatility (VIX); US monetary policy drives this global factor.
- Passari and Rey (2015): evidence of a global financial cycle in gross cross-border flows, asset prices and leverage; identify the VIX as a suitable proxy and show significant spillovers from US monetary policy to EMDE capital flows.
- Ahmed and Zlate (2014): growth and interest rate differentials between EMDEs and AEs and global risk appetite are statistically and economically important for net private capital inflows to EMDEs; unconventional US monetary policy positively affects EMDE inflows, especially portfolio inflows; greater sensitivity of net inflows to interest rate differentials in the post-crisis period.
- Ghosh et al. (2014b): global factors like US interest rates and VIX crucial for capital surges to EMDEs; surge occurrence and magnitude also depend on external financing need, capital account openness, exchange rate regime; liability-driven surges more sensitive to global factors and contagion.
- Siemer et al. (2015): decompose return volatility into systemic volatility (uncertainty betas) and country-specific volatility; countries with higher uncertainty betas see capital inflows more sensitive to risk.

### Literature review — volatility of capital flows
- Two strands: (i) volatility differences between emerging and advanced economies; (ii) panel-data analyses of financial integration impact on volatility.
- Rigobon and Broner (2005): higher volatility in EMDEs primarily due to propensity to build up imbalances, creating persistent shocks and greater contagion likelihood.
- Alfaro et al. (2007): domestic factors (institutional quality, sound macro policies) important in explaining volatility differences.
- Goldstein and Razin (2006): gap between volatility of FDI and portfolio flows smaller in AEs.
- Albuquerque (2003) and Tesar and Werner (1995): in EMDEs, higher share of FDI in total inflows and higher volatility of portfolio flows.
- Neumann et al. (2009): financial integration increases volatility of FDI in emerging economies while reducing volatility of other debt flows in mature economies.
- Bekaert and Harvey (1997), Lagoarde-Segot (2009), Umutlu et al. (2010): financial liberalization reduces volatility of stock market returns in emerging economies.
- Broto et al. (2011): since 2000 global factors increasingly significant relative to country-specific drivers; identified domestic macroeconomic and financial factors that reduce volatility of certain instruments without increasing others.
- Alberola et al. (2016): international reserves act as stabilizer during financial distress; larger reserves linked to higher gross inflows and lower gross outflows and facilitate financial disinvestment by residents abroad, partially offsetting drops in foreign capital inflows.
- Broner and Ventura (2016): financial globalization in EMDEs can produce three outcomes depending on development, productivity, domestic savings and institutional quality: i) domestic capital flight and ambiguous net flows, investment and growth; ii) capital inflows and higher investment and growth; iii) volatile capital flows and unstable financial markets. This paper empirically investigates aspects by expanding Broto et al. (2011) to include the GFC period.

### Volatility measures — data and methodology
- Dataset: quarterly data spanning from 1970Q1 to 2016Q1; broader set of capital flow instruments than previous literature.
- Three approaches to estimate capital flow volatility (building on Engle et al. (2005) and Broto et al. (2011)):
  - 1) Standard deviations over a rolling window (RW)
    - Formula: 휎푖푡 = (1/n ∑(flow푖푘 − μ)2 t k=t−(n−1) )1/2, where μ = 1/n ∑ flow푖푘 t k=t−(n−1)
    - In computations n = 4 quarters.
    - Caveats: data loss at sample start depends on n; 휎푖푡 strongly persistent (endogeneity, serial correlation); equal weights across window overly smooth volatility (underestimates spike, overestimates subsequent fall).
  - 2) Estimated standard deviations from a GARCH(1,1) model
    - Process: y푖푡 = ε푖푡 σ푖푡 ; σ푖푡2 = α0 + α1 y푖(푡−1)2 + α2 σ푖(푡−1)2, where y푖푡 ≡ ∆flow푖푡, ε푖푡 Gaussian white noise.
    - Drawbacks: data scarcity may cause convergence errors; Maximum-Likelihood in small samples contains biases; stationarity and positivity require α1̂ + α2̂ < 1, α0̂ > 0, α1̂ > 0 and α2̂ > 0; if violated model fails for that country; residuals may not present ARCH effects making GARCH unsuitable.
  - 3) Estimated standard deviations from an ARIMA(1,1,0) model
    - First estimate residuals from ∆flow푖푡 = c + β ∆flow푖(푡−1) + ν푖푡.
    - Test residuals for ARCH effects. If null of heteroscedasticity rejected, σ푖푡2 = 1/4 ∑(ν푖푗)2 t+(n−2) j=t−(n−3). Otherwise fit a GARCH(1,1) to residuals.
    - Choice: AR and MA orders from literature; differencing degree set to 1 since series are ~I(1).
    - The ARIMA residual heteroscedasticity checks deviate from reference literature and are used to improve robustness; authors prefer ARIMA estimates and use it as the benchmark in regressions.

### Evolution of volatility over time — empirical findings
- Comparison of the three measures:
  - RW underestimates the spike in volatility at the onset of the crisis and overestimates the fall after the crisis.
  - GARCH estimates tend to lag slightly behind RW and ARIMA and are on average higher than the other two measures.
  - Broadly, the three estimates show similar results.
- Cross-group comparisons:
  - Net flows to EMDEs are more volatile than net flows to AEs.
  - In AEs, gross outflows tend to dampen the impact of gross inflows on net flows; this damping is weaker in EMDEs, leading to higher volatility of net flows in EMDEs.
  - In EMDEs, the volatility of inflows is on average higher than outflows, driving up net flow volatility.
- Post-GFC dynamics:
  - Aside from several spikes in AEs and EMDEs (biggest corresponding to the GFC), the current level of volatility is comparable to the pre-crisis average.
  - EMDEs volatility has been prone to bouts, rising during global risk-off episodes (notably the taper tantrum).
  - In the context of capital flow slowdown (IMF 2016), even small swings can lead to substantial net outflows or sudden stops.
  - When adjusted for the level of flows, volatility has either increased or stayed at the same pre-crisis levels (Appendix D).
- Role of China:
  - Excluding China, the broad evolution of volatility for World and EMDEs is not very different, though recent increases in volatility are less pronounced when China is excluded (charts in Appendix E).

*Source: https://www.imf.org/-/media/files/publications/wp/2017/wp1741.pdf*

### Appendix E show that this discrepancy is associated with the volatility of other investments.

### wp1741 - Appendix E show that this discrepancy is associated with the volatility of other investments.

### Statistical tests: change in volatility pre- vs post-GFC
- Geweke’s separated partial means test (two separate means, p=2; covariance functions tapered at 2%; limiting distribution chi-squared with 1 dof; H0: means are equal, H1: means are different) was applied to three country groups (Global, AEs, EMDEs) and three volatility measures (RW, GARCH, ARIMA) across GIs (Gross Inflows), GOs (Gross Outflows), NIs (Net Inflows).
- Table 2: Geweke’s test results (Statistic and P-value)
  - Global
    - RW: GIs Statistic 9.18; P-value 0.00. GOs Statistic 6.83; P-value 0.01. NIs Statistic 1.19; P-value 0.28.
    - GARCH: GIs Statistic 62.44; P-value 0.00. GOs Statistic 53.39; P-value 0.00. NIs Statistic 3.66; P-value 0.06.
    - ARIMA: GIs Statistic 20.36; P-value 0.00. GOs Statistic 15.27; P-value 0.00. NIs Statistic 3.05; P-value 0.08.
  - AEs
    - RW: GIs Statistic 20.99; P-value 0.00. GOs Statistic 21.04; P-value 0.00. NIs Statistic 15.17; P-value 0.00.
    - GARCH: GIs Statistic 79.31; P-value 0.00. GOs Statistic 86.76; P-value 0.00. NIs Statistic 0.68; P-value 0.41.
    - ARIMA: GIs Statistic 17.69; P-value 0.00. GOs Statistic 17.61; P-value 0.00. NIs Statistic 6.88; P-value 0.01.
  - EMDEs
    - RW: GIs Statistic 7.89; P-value 0.00. GOs Statistic 15.84; P-value 0.00. NIs Statistic 24.60; P-value 0.00.
    - GARCH: GIs Statistic 0.99; P-value 0.32. GOs Statistic 12.38; P-value 0.00. NIs Statistic 0.06; P-value 0.80.
    - ARIMA: GIs Statistic 6.51; P-value 0.01. GOs Statistic 15.10; P-value 0.00. NIs Statistic 27.76; P-value 0.00.

- Key statistical conclusions:
  - The null hypothesis of equal means before and after the crisis is almost always rejected at 5% or 10% significance levels, indicating shifts in volatility since the GFC, though magnitude is generally small.
  - Exceptions (no statistical difference in mean values) include: net flows in World (RW measure); net flows in AEs (GARCH estimator); GARCH volatility of both gross and net inflows in EMDEs.
  - Broad summary for EMDEs: in the aftermath of the financial crisis, EMDEs experienced a slight increase in the volatility of gross inflows by 0.2% of GDP and a slight decrease in the volatility of gross outflows by 0.16% of GDP; these two effects combined to slightly decrease the volatility of net inflows by an average of 0.02% of GDP.

### Instrument-level and component volatility (aggregate EMDEs)
- Relative volatility across instruments (aggregate EMDEs gross inflows):
  - Portfolio and other investment flows are around two and four times, respectively, more volatile than FDI.
  - Among portfolio flows, portfolio debt is more volatile than portfolio equity.
  - Equity flows (both FDI and portfolio equity) are generally less volatile.
- Time patterns by instrument:
  - FDI: clear upward trend in volatility before the GFC and downward trend afterwards, particularly for GARCH and ARIMA estimates.
  - Portfolio (total): GARCH and ARIMA estimates are higher than RW; no defined trend overall, but volatility for this instrument is lower in the subsample 2009-2016.
  - Portfolio equity: ARIMA and RW show slight upward trend until the GFC and downward trend thereafter.
  - Other investments: highest volatility estimates among all instruments; GARCH produces higher values than other approaches.
- Table 3: Geweke’s test for EMDEs gross inflows by instrument (RW, GARCH, ARIMA)
  - RW
    - FDI Statistic 153.78; P-value 0.00.
    - Portfolio Statistic 4.18; P-value 0.04.
    - Port. debt Statistic 17.06; P-value 0.00.
    - Port. equity Statistic 1.90; P-value 0.17.
    - Other Statistic 10.76; P-value 0.00.
  - GARCH
    - FDI Statistic 136.40; P-value 0.00.
    - Portfolio Statistic 2.60; P-value 0.11.
    - Port. debt Statistic 5.99; P-value 0.01.
    - Port. equity Statistic 2.99; P-value 0.08.
    - Other Statistic 5.06; P-value 0.02.
  - ARIMA
    - FDI Statistic 233.30; P-value 0.00.
    - Portfolio Statistic 2.86; P-value 0.09.
    - Port. debt Statistic 4.52; P-value 0.03.
    - Port. equity Statistic 3.21; P-value 0.07.
    - Other Statistic 13.81; P-value 0.00.

- Instrument-level test conclusions:
  - Null of equal means is rejected for FDI, portfolio debt and other investments across all estimators.
  - Volatility of portfolio inflows (GARCH) and portfolio equity (RW) show no statistically significant mean difference pre- vs post-GFC.
  - Using ARIMA estimates, average changes in EMDEs’ volatility in the aftermath of the financial crisis are:
    - FDI: 0.086% of GDP
    - Portfolio: -0.014% of GDP
    - Other investments: 0.249% of GDP

### Delving deeper: other investment flows (composition and volatility)
- Classification of other investment flows: i) bank flows; ii) private non-bank flows; iii) official sector flows.
- Composition (levels, % share of group GDP):
  - Private flows constitute most of aggregate other investment flows.
  - Private flows reversed and experienced a temporary stop during the GFC, contributing to the sudden stop of aggregate gross inflows to EMDEs in that period.
  - After the GFC, private-sector other gross inflows are markedly lower than before, with reversals in 2015 and 2016.
  - Before the crisis, most other flows were private flows to both banking and non-banking sectors; after the GFC, both decreased and in certain periods nearly disappeared from the capital account (e.g., second half of 2009).
- Volatility of subcomponents (other gross inflows, % share of group GDP):
  - Volatility of private flows is much higher than volatility of official sector flows; official flows spiked during the crisis then stabilized around a level close to 0.
  - Within the private sector:
    - Volatility of flows to banks shows a slight decrease toward the end of the sample.
    - Volatility of flows to the non-banking sector stabilized around a lower long-run average after the crisis.
  - Overall: volatility of other investments is almost completely driven by volatility of private flows; volatility is roughly equally distributed across banking and non-banking private sectors.

### Volatility measures for individual countries (ARIMA preferred)
- The three approaches (RW, GARCH, ARIMA) produce very similar estimates across flow types and instruments; subsequent analysis focuses on ARIMA estimates.
- Uses of country-level volatility measures:
  - Policy diagnostics for country-specific high volatility.
  - Identifying instruments to monitor more closely.
  - Comparative research across countries and regions.
  - Understanding relationship between EMDEs and AEs capital flow volatility and determinants of EMDEs capital flow volatility.
- Cross-country median and distributional features:
  - Median volatility is higher for portfolio flows than for other types.
  - Median variance of overall portfolio flows is lower than the sum of variances of portfolio debt and portfolio equity, suggesting possible negative correlation between portfolio debt and portfolio equity.
  - Significant heterogeneity across countries; examples cited (from figures) where FDI volatility can exceed or match portfolio volatility include Chile, Latvia, Kazakhstan.
  - Empirical distribution features (median ARIMA volatilities):
    - Skewness values: FDI 1.0770; portfolio 2.8565; portfolio debt 2.8875; portfolio equity 1.2858; other investments 2.1120.
    - Kurtosis values: FDI 3.3431; portfolio 14.3172; portfolio debt 14.0942; portfolio equity 4.1295; other investments 8.5991.
    - Interpretation: distributions for portfolio and portfolio debt are shifted right (higher median volatilities) and exhibit high kurtosis, indicating higher probability of extreme values (outliers) relative to FDI or portfolio equity.
- Heat-map (ARIMA) comparisons pre- (2000Q1-2007Q2) vs post-GFC (2009Q3-2016Q1):
  - Gross inflows: volatility of total gross inflows has remarkably decreased in countries like Canada and Russia and some smaller Latin American economies; however, boundary values in legends indicate an upward shift in the entire distribution—median volatility in the sample has increased over time. Overall, on average, volatility of gross inflows has increased after the GFC (conclusion holds also if outliers are excluded).
  - Other gross inflows: volatility decreased in some Latin American economies, but increased markedly in North America and Europe; Asia largely unchanged except Japan, where other inflows volatility slightly increased.
  - Bank gross inflows: flows to the banking sector are major drivers of observed trends. The peripheral Euro Area sovereign debt crisis exacerbated volatility of bank flows toward Western European economies.

*Source: IMF, International Financial Statistics, authors’ computations (content unit: wp1741 - Appendix E).*

### Box 1: Do more financially developed countries have more volatile capital flows?

### Box 1: Do more financially developed countries have more volatile capital flows?

### Relationship between financial development and capital flow volatility
- The analysis uses volatility estimates of capital flows and the Financial Development Index (higher value = more financially developed).
- Correlation findings by instrument:
  - Correlation is almost 0 for FDI, portfolio and other investments.
  - Correlation is positive and more relevant for portfolio equity.
  - The Global Financial Crisis (GFC) increased the significance of these correlations (higher R2) for all instruments except portfolio equity.
  - For portfolio flows, especially portfolio debt, the sign of the correlation switched from negative to positive during the GFC and moved back to negative afterwards.
- Overall conclusion:
  - The hypothesis that more financially developed countries face more volatile capital flows is not confirmed by this exercise, except for portfolio equity flows (whose size in the financial account of EMDEs is much reduced compared to other instruments).
  - This finding is consistent with existing literature cited in the box.

### Contagion exposure to advanced economies (AEs)
- Method: measure of possible contagion derived from the correlation between volatility estimates for EMDEs and volatility estimates for AEs, by instrument.
- Finding:
  - A higher and more significant degree of correlation exists between volatilities of other investments in EMDEs and AEs.
  - This correlation is stronger the more financially developed a country is (i.e., higher Financial Development Index).
  - Interpretation: more financially developed EMDEs present a higher degree of exposure to developments on international financial markets.

### Panel regression framework (overview)
- Sample and dependent variables:
  - EMDEs, period 1980Q1-2016Q1.
  - Dependent variables: ARIMA volatility estimates for total flows and different instruments.
- Independent variables grouped in three categories:
  1. Global factors: US shadow rate, US real GDP growth, S&P 500 volatility (proxy for global risk aversion), US inflation, log price of oil.
  2. Domestic macroeconomic factors: real GDP growth, domestic policy rate, GDP per capita.
  3. Domestic structural factors: Chinn-Ito capital account openness index, trade openness, reserves as a share of GDP.
- Additional controls:
  - Dummy for 2007Q3-2009Q2 (GFC) and dummy for 2009Q3-2016Q1 (post-crisis).
  - Country fixed effects; explanatory variables lagged by one quarter.
  - Covariance matrix corrected using Driscoll and Kraay (1998) to account for serial and spatial correlations; clustered standard errors also reported.

### Key regression results and magnitudes (selected coefficients)
- Global factors:
  - S&P 500 returns volatility (t-1): 0.849*** for Total (DK standard errors in parentheses).
  - US shadow rate (t-1): 0.174** for Total.
  - US growth (t-1): -0.492*** for Total.
  - US inflation (t-1): -0.320** for Total.
- Oil price (log) (t-1):
  - Regression interpretation: coefficient represents semi-elasticity of capital flow volatility to oil price.
  - Econometric magnitudes (discussion):
    - An increase in the oil price by 1% lowers volatility of portfolio equity by 0.9% of GDP.
    - An increase in the oil price by 1% lowers volatility of other investments through the official sector by 2.85% of GDP.
    - An increase in the oil price by 1% increases volatility of other investments through the banking sector by 1.34% of GDP.
- Domestic factors:
  - RGDP growth (t-1): -0.230*** for Total.
  - GDP per capita (t-1): 0.00130** for Total.
  - Chinn-Ito index (t-1): -2.029* for Total.
  - Trade openness (t-1): 0.0845*** for Total.
  - Reserves/GDP (t-1): 0.00708 for Total (some instruments show significance).
- Crisis dummy effects (2007Q3-2009Q2):
  - Total gross inflows volatility higher during the GFC by 1.467** (i.e., 1.47% of GDP).
  - Portfolio equity volatility higher during the GFC by 0.39% of GDP.
  - Other investments through the official sector higher during the GFC by 0.94% of GDP.
  - Other investments through private non-banking sector higher during the GFC by 0.52% of GDP.
- Statistical summary:
  - Observations (Total): 1,405.
  - Number of groups: 25.
  - Within R2 for Total: 0.176.
  - Authors note: R2 is not very high for any instrument (maximum 0.176), which is normal for volatility regressions and indicates other relevant factors remain to be identified.

### Interpretation and policy-relevant takeaways
- Push versus pull factors:
  - Determinants of capital flow volatility differ from determinants of capital flow levels.
  - Global risk aversion (a global "push" factor) can be more important than domestic GDP growth (a "pull" factor) in driving volatility.
- Role of trade openness and financial development:
  - Trade openness is a major domestic driver: more open economies face higher volatility.
  - GDP per capita is positively associated with volatility ceteris paribus, suggesting richer EMDEs exhibit greater volatility.
  - More financially developed EMDEs are more exposed to international financial market developments (contagion channel), notably through other investments.
- Commodity price channel:
  - Oil price movements affect volatility heterogeneously across instruments and sectors, largely driven by oil-exporters and their financial institutions’ behavior.
- Robustness and caveats:
  - Interaction terms with crisis and post-crisis dummies do not change main takeaways.
  - Low R2 implies that additional drivers of volatility exist and are avenues for future research.

*Source: IMF working paper — Box 1 and related regression results (wp1741).*

### Box 2: The volatility of bank flows versus oil price

### Box 2: The volatility of bank flows versus oil price

### Background and identification
- The analysis estimates the elasticity of bank inflows volatility to oil price using the log of oil price on the right-hand side of panel regressions, allowing direct interpretation as an elasticity.
- Motivation: empirical literature highlights a crucial link between banks’ profitability (and banking-system soundness) and oil price, operating mainly through macroeconomic channels and particularly strong in oil-exporting emerging economies.

### Average elasticity estimates
- Overall average elasticity in the pre-crisis period: 1.26% (i.e. a 1% increase in the oil price leads to a 1.26% increase in bank inflows volatility).
- Overall average elasticity after the GFC: 0.95%.
- Post-crisis trend by group:
  - Oil-exporting economies: on average, elasticity has increased after the crisis compared to earlier periods.
  - Oil-importing economies: on average, elasticity has decreased after the crisis relative to earlier periods.

### Distributional patterns and dynamics
- Figure 2.1 (described): displays evolution of elasticity over time, disentangling oil exporters and oil importers; shows gradual decrease until the aftermath of the GFC.
- Figure 2.2 (described): median elasticities for the overall sample, oil exporters, and oil importers:
  - During periods of financial distress (GFC), median values for exporters and importers collapse to around the same level.
  - This suggests distributions of oil price elasticities across groups tend to coincide under an aggregate shock, while they are distinct in more normal times.
- Figure 2.3 (described): evolution of median and interquartile range (IQR) of estimates over time, by group:
  - Oil importers:
    - Median shows little variation after mid-2000.
    - Interquartile range has considerably narrowed over time → distribution more concentrated around the median (lower variance).
  - Oil exporters:
    - Shifts in the entire distribution observed.
    - Median elasticity decreased in the mid-2000s and during the GFC, then increased after the crisis, with a spike in the period 2014-2015.
- Interpretation: changes in group-level averages can reflect either shifts in the entire distribution or movements at distribution tails (outliers); evidence points to different mechanisms for exporters versus importers.

### Sample definition note
- Oil exporters in the sample are: Brazil, Ecuador, Egypt, Indonesia, Kazakhstan, Mexico, Malaysia, Russia and Saudi Arabia.

*Source: Box 2, "The volatility of bank flows versus oil price", IMF Working Paper wp1741.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp1741.pdf_