3.1 Methodology

We estimate a simple model of capital flow:

where d_i,t is the causal variable of interest or treatment effect, x_i,t is the set of controls or confounding factors, µ_i is a country fixed effect, and ε_i,t is the error.

There is potentially a large number of confounding factors. According to the literature on the determinants of capital flows (including sudden stops or capital reversals), there are two broad categories of factors that need to

be accounted for—global and domestic. The global factors are included to account for important co-movements in capital flows across emerging and developing economies. Commonly used variables for this purpose include VIX (as a proxy for global risk aversion), changes in money supply of major advanced economies (as a proxy for global liquidity), growth rates of major advanced economies (as a proxy for the strength of the global economy and perhaps investors’ risk appetite), and the Federal Funds Rate (to account for the special role of the U.S. dollar as a source of liquidity to the global financial system). The domestic factors are country-specific factors that may explain differences across countries in capital inflows. Commonly used variables for this purpose include the level of per capita income, real GDP growth, trade openness, financial openness, the exchange rate regime, exchange rates, foreign reserves, current account balances, bank credit, and sovereign credit ratings.

The large number of potential confounding variables poses a challenge to model selection and estimation. First, where there are many potential confounding variables, it is likely that only some of them are relevant, but empirical studies often do not agree because of their differences in data, models, methodology, as well as researchers’ preoccupations. Second, there is a problem of estimation. Including too many variables in the regression leads to inefficiency; because variables tend to be highly correlated with each other, they need to be included parsimoniously (Eichengreen and Gupta, 2016). Yet failing to control for key confounders leads to omitted variable bias. Third and finally, there is a problem of saturation (or “high dimensionality”). It is possible that the influence of these variables is nonlinear and that there are important interactions effects. But using several permutations of each variable—such as levels, lags, differences at various horizons, and polynomials—or including all pairwise interactions and temporal and spatial effects would be infeasible as it would quickly run into a problem of degrees of freedom.

Faced with these dilemmas, economists are increasingly using machine learning for model selection and estimation. The proposed estimation strategy in this paper is lasso.¹⁰ Lasso is probably the most familiar machine learning technique among economists (Mullainathan and Spiess, 2017). As such, it has a relatively well-developed literature on the statistical properties of its estimates. In the current context, it has the following attractive properties.

First, it is a straightforward extension of linear regression but is good at dealing with the dimensionality problem. Just like ordinary least squares (OLS), lasso minimizes the sum of squared deviations between observed and model predicted values. Unlike OLS, to achieve a dimension reduction, lasso imposes a penalty on model complexity by limiting the sum of the absolute values of the coefficients and forces all but the most important ones to zero. Simply put, lasso does the model selection for us by systematically selecting the most important features and throwing out others that contribute little to the model’s fit (Ahrens, Hansen, and Schaffer, 2019).

Second, it allows causal interpretation of the estimated coefficients for a subset of variables. Since the primary purpose of most supervised machine learning techniques is prediction, the techniques usually do not produce estimates that can be interpreted as causal (Tiffin, 2019). Similarly, lasso, in general, does not produce unbiased estimates of coefficients and standard errors required to perform valid inference.¹¹ However, an extension of lasso, known as double-selection lasso (Belloni, Chernozhukov, and Hansen, 2014a; Urminsky, Hansen, and Chernozhukov, 2016), addresses the problem by adopting a modified estimation procedure and generates unbiased coefficients and standard errors for a subset of variables that are suitable for making causal inferences.

Finally, a recent paper by Belloni, Chernozhukov, and Hansen (2014a) provides a panel data extension of double-selection lasso, accommodating common forms of within-group correlation and heteroskedasticity in errors expected in a panel data context.

3.2 Model

Formally, for the general model

lasso finds a vector of coefficients, β, such that

is minimized for a given value of λ. The last term distinguishes lasso from OLS: there is a cost to including many regressors and we can reduce the objective function by setting β_j = 0 for variables that contribute little to the fit. Thus, lasso does the model selection for us.¹² The parameter λ is called a tuning parameter, which controls the overall penalty level. The larger is λ, the more coefficients are shrunk to zero. If λ = 0 we have an OLS regression (Ahrens, Hansen, and Schaffer, 2019 and Fonti and Belitser, 2017).

Lasso estimator can also be written as

where λ is the tuning parameter that controls the overall penalty level as before and ψ_j are predictor-specific penalty loadings. The latter are predictor-specific to account for the fact that the predictors x_j are not of equal variance. Under a homoskedasticity assumption, lasso sets the penalty loading to

In order to allow for valid inference on the coefficient of a variable of interest (in our case, the dummy variable for gray-listing), we follow the double-selection approach developed by Belloni, Chernozhukov, and Hansen (2014a). Rewriting equation (3), we split the vector x_i into a variable of interest, d_i, and other controls:

We want to be able make a valid inference on the parameter β₀. The double-selection approach estimates the equation (7) in three steps:

1. Use lasso to estimate y_i on x’s without d_i. Denote the set of lasso-selected controls by A.

2. Use lasso to estimate d_i on x’s. Denote the set of lasso-selected controls by B.

3. Estimate the following equation using OLS:

where w_i = A∪B, i.e., the union of the selected controls from Steps 1 and 2 (Ahrens, Hansen, and Schaffer, 2018). Thus, the double-selection approach first uses lasso to select covariates correlated with the outcome (y_i), and second, uses lasso to select covariates correlated with the treatment (d_i). By taking the union of both sets of covariates and including them as controls in a standard OLS regression (in the third stage), it takes account of the joint association that is the source of bias for the treatment effect (Belloni, Chernozhukov, and Hansen, 2014a.)

Finally, the panel data extension of double-selection lasso developed by Belloni et al. (2014b) extends the general model to the panel framework:¹³

Eliminating the fixed effects by subtracting the individual specific intercept leads to the “within model”:

where {\ddot{x}}_{i,t}=x_{i,t}-\frac{1}{T}{\mathrm{\Sigma }}_{t=1}^T{x}_{i,t}. The coefficient estimate is defined by the solution to the penalized minimization problem of the within model:

The approach by Belloni et al. (2014b) to accommodate the non-homoskedastic errors, according to Ahrens, Hansen, and Schaffer (2019), is similar to standard clustered-error adjustments used in OLS models, whereby “observations within clusters are aggregated to create ‘super-observations,’ which are assumed independent, and ... are treated similarly to cross-sectional observations in the non-clustered case” (p. 21). Accordingly, the penalty loading ψ_j is given by

where u_ij is the “super-observation”, defined as u_ij = Σ_tx_ijtε_it for the ith cluster and jth regressor.

3.3 Data

For the empirical implementation of the model in equation (10), the dependent variables are gross capital inflow, FDI inflow, portfolio inflow, and other inflows, all as a share of GDP. The data on capital flows come from the FFA database, as before. We supplement the data on quarterly GDP where it is possible using the data from the IFS and Haver, and exclude extreme values from the data before running the model in equation (10) (see Section 2 for detail).

The explanatory variable of interest is an indicator variable d_it (= 1 for gray-listing), defined over a window [to — k,to + k], where to is the date of the FATF announcement and k is varied between 1 and 3 quarters (see Section 2). Following a standard practice in the literature, we drop post-gray-listing observations for four quarters, so as to avoid the post-gray-listing dynamics in capital flow biasing our estimation of β_o.¹⁴

With regard to control variables x_i,t, there are 15 domestic primary variables: six exchange rate variables (exchange rate vis-a-vis the SDR, nominal effective exchange rate, real effective exchange rate, all for period average and end of period); two official reserves variables (in U.S. dollars and as a share of GDP); two current account balance variables (in U.S. dollars and as a share of GDP); one-year ahead forecast of real GDP growth rate; a measure of capital account openness; a measure of exchange rate flexibility; and credit ratings. Because of endogeneity concerns, all domestic variables are included in the model with four-quarter lags. Missing values in the primary domestic variables reduce the sample size to 81 countries, of which 28 have been gray-listed. See Appendix B for the list of countries. The domestic variables are complemented by 22 international variables: VIX, the U.S. short-term rate, the U.S. 10-year rate, the U.S. Federal Funds rate, two commodity price indexes (one including and one excluding gold), the real GDP growth rate of G4 countries (the U.S., the Euro Area, the U.K., and Japan) in total and individually, the money supply of G4 countries as a share of GDP in total and individually, the growth rate of the money supply of G4 countries in total and individually, and a dummy variable for the GFC. Furthermore, the analysis uses several permutations of each variable—such as levels and differences—as well as interaction effects of each variable with the three categorical variables in the model (a measure of exchange rate flexibility, credit ratings, and the dummy variable for the GFC). Finally, the model includes a full set of year fixed effects. Overall, this yields 2,842 variables. Appendix D describes the variables and sources.

3.4 Results

Table 1 reports the estimates of the impact of gray-listing on capital inflow, with results for different types of capital inflow presented across the columns. With double-selection lasso, the estimates of the coefficient of the variable of interest (β₀) can be interpreted just as they are in a standard linear regression. However, the coefficients of the control variables cannot and therefore are not reported here.¹⁵

^{Table 1:}

Effect of Gray-Listing on Capital Inflows

The table presents estimates of the effect of gray-listing on the type of capital flow, in percent of GDP. Each specification includes additional controls as described in the text and Appendix D and a full set of year and country fixed effects. Robust standard errors clustered by country are in parentheses. Confidence intervals are at the 95 percent confidence level. *, **, *** mean, respectively, significant at the 10, 5, and 1 percent level.

^{Table 1:}

Effect of Gray-Listing on Capital Inflows

	Total	FDI	Portfolio	Other
Coefficient	-7.550***	-3.034***	-2.926***	-3.551***
Standard Errors	(1.522)	(1.016)	(0.981)	(0.685)
Conf. Intervals	[-10.53, -4.57]	[-5.02, -1.04]	[-4.85, -1.00]	[-4.89, -2.21]

The table presents estimates of the effect of gray-listing on the type of capital flow, in percent of GDP. Each specification includes additional controls as described in the text and Appendix D and a full set of year and country fixed effects. Robust standard errors clustered by country are in parentheses. Confidence intervals are at the 95 percent confidence level. *, **, *** mean, respectively, significant at the 10, 5, and 1 percent level.

View Table

^{Table 1:}

Effect of Gray-Listing on Capital Inflows

	Total	FDI	Portfolio	Other
Coefficient	-7.550***	-3.034***	-2.926***	-3.551***
Standard Errors	(1.522)	(1.016)	(0.981)	(0.685)
Conf. Intervals	[-10.53, -4.57]	[-5.02, -1.04]	[-4.85, -1.00]	[-4.89, -2.21]

The table presents estimates of the effect of gray-listing on the type of capital flow, in percent of GDP. Each specification includes additional controls as described in the text and Appendix D and a full set of year and country fixed effects. Robust standard errors clustered by country are in parentheses. Confidence intervals are at the 95 percent confidence level. *, **, *** mean, respectively, significant at the 10, 5, and 1 percent level.

Our point estimate for the effect of gray-listing on total capital inflow is -7.6, meaning that we expect a country’s capital inflow to decline by 7.6 percent of GDP when the country is gray-listed. The coefficient estimate is statistically significant at the 1 percent level based on the robust standard errors. The 95 percent confidence interval is between -10.6 percent of GDP and -4.6 percent of GDP, meaning that most countries experience a decline within this range when gray-listed.¹⁶

Moving on to different components of capital flows, the effect of gray-listing on FDI inflow is estimated to be -3.0 percent of GDP and the effect on portfolio flow is estimated to be -2.9 percent of GDP, both are significant at the 1 percent confidence level (Table 1, columns 2 and 3). The relative magnitude of the coefficients is thus similar for FDI and portfolio inflows– consistent with the finding in the event analysis–although it is possible that dynamics around the time of gray-listing could show different sensitivity both before and after the event (see Section 2).

Looking at different categories of other flows (Table 2), the estimated impact of gray-listing is largest for non-official sector flows (-3.8 percent of GDP). Banking sector flows are somewhat less negatively affected than other (non-bank) private flows (-2.0 percent of GDP and -2.4 percent of GDP). Official sector flows are the least severely affected (-0.9 percent of GDP). All estimates are significant at the 5 percent level or better.

^{Table 2:}

Effect of Gray-Listing on Categories of Other Inflows

The table presents estimates of the effect of gray-listing on the components of other investment flows, in percent of GDP. Each specification includes additional controls as described in the text and Appendix D and a full set of year and country fixed effects. Robust standard errors clustered by country are in parentheses. Confidence intervals are at the 95 percent confidence level. *, **, *** mean, respectively, significant at the 10, 5, and 1 percent level.

^{Table 2:}

Effect of Gray-Listing on Categories of Other Inflows

	Official	Non-Official	Banks	Other Private
Coefficient	-0.925**	-3.796***	-1.964***	-2.372***
Standard Errors	(0.393)	(0.755)	(0.667)	(0.443)
Conf. Intervals	[-1.70, 0.15]	[-5.28, -2.32]	[-3.27, -0.66]	[-3.24, -1.50]

The table presents estimates of the effect of gray-listing on the components of other investment flows, in percent of GDP. Each specification includes additional controls as described in the text and Appendix D and a full set of year and country fixed effects. Robust standard errors clustered by country are in parentheses. Confidence intervals are at the 95 percent confidence level. *, **, *** mean, respectively, significant at the 10, 5, and 1 percent level.

View Table

^{Table 2:}

Effect of Gray-Listing on Categories of Other Inflows

	Official	Non-Official	Banks	Other Private
Coefficient	-0.925**	-3.796***	-1.964***	-2.372***
Standard Errors	(0.393)	(0.755)	(0.667)	(0.443)
Conf. Intervals	[-1.70, 0.15]	[-5.28, -2.32]	[-3.27, -0.66]	[-3.24, -1.50]

The table presents estimates of the effect of gray-listing on the components of other investment flows, in percent of GDP. Each specification includes additional controls as described in the text and Appendix D and a full set of year and country fixed effects. Robust standard errors clustered by country are in parentheses. Confidence intervals are at the 95 percent confidence level. *, **, *** mean, respectively, significant at the 10, 5, and 1 percent level.

4.1 Event Window

Our analysis focuses on the response of capital flows in a period around gray-listing, and to capture the response, we define gray-listing as an event with widow [t₀ – k,t₀ + k] where t₀ is the date of the FATF public announcement and k is varied between 1 and 3 quarters, allowing for the possibility that gray-listing may be foreseen by market participants and that some investors may delay their response due to uncertainty (see Section 2). The size of the window in an event study is an open choice (Choi and Hashimoto, 2017). If the window is too narrow, it may preclude any proper identification of the effect of an event that takes time to materialize. If the window is too wide, other confounding factors may affect the dependent variable. In the baseline, we use k = 3. To check robustness of our estimates reported in Table 1, we re-estimate the model using k = 1, 2, and 4. Results are reported in Table 3.

^{Table 3:}

Robustness: Effect of Gray-Listing using Different Event Windows

The table presents estimates of the effect of gray-listing on total capital inflow, in percent of GDP. Each column corresponds to the size of k in an event window [t₀ -k, t₀ +k]. The column k=3 corresponds to the baseline results in the column “Total” in Table 1. Each specification includes additional controls as described in the text and Appendix D and a full set of year and country fixed effects. Robust standard errors clustered by country are in parentheses. Confidence intervals are at the 95 percent confidence level. *, **, *** mean, respectively, significant at the 10, 5, and 1 percent level.

^{Table 3:}

Robustness: Effect of Gray-Listing using Different Event Windows

	k=4	k=3	k=2	k=1
Coefficient	-8.203***	-7.550***	-5.789***	-4.836***
(Standard Errors)	(1.524)	(1.522)	(1.649)	(1.683)
Conf. Intervals	[-11.19, -5.22]	[-10.53, -4.57]	[-9.02, -2.56]	[-8.14, -1.54]

The table presents estimates of the effect of gray-listing on total capital inflow, in percent of GDP. Each column corresponds to the size of k in an event window [t₀ -k, t₀ +k]. The column k=3 corresponds to the baseline results in the column “Total” in Table 1. Each specification includes additional controls as described in the text and Appendix D and a full set of year and country fixed effects. Robust standard errors clustered by country are in parentheses. Confidence intervals are at the 95 percent confidence level. *, **, *** mean, respectively, significant at the 10, 5, and 1 percent level.

View Table

^{Table 3:}

Robustness: Effect of Gray-Listing using Different Event Windows

	k=4	k=3	k=2	k=1
Coefficient	-8.203***	-7.550***	-5.789***	-4.836***
(Standard Errors)	(1.524)	(1.522)	(1.649)	(1.683)
Conf. Intervals	[-11.19, -5.22]	[-10.53, -4.57]	[-9.02, -2.56]	[-8.14, -1.54]

The table presents estimates of the effect of gray-listing on total capital inflow, in percent of GDP. Each column corresponds to the size of k in an event window [t₀ -k, t₀ +k]. The column k=3 corresponds to the baseline results in the column “Total” in Table 1. Each specification includes additional controls as described in the text and Appendix D and a full set of year and country fixed effects. Robust standard errors clustered by country are in parentheses. Confidence intervals are at the 95 percent confidence level. *, **, *** mean, respectively, significant at the 10, 5, and 1 percent level.

For all values of k, we consistently find negative and statistically significant effects of gray-listing on capital inflows. The absolute size of the coefficient is larger when using a wider event window (k = 4), perhaps as expected. The coefficient becomes smaller in absolute value using a narrower window (k = 2 or k = 1) but remains negative and significant. It is possible that the larger impact we find using the wider window reflects influences of confounding factors; it is also possible that we may not see the full extent of impact on capital inflow using a narrower window, for example, because gray-listing is foreseen by market participants and they adjust their behavior earlier or, conversely, because gray-listing does not initially trigger de-risking among the investors in sufficient numbers within the first few months.

4.2 Small Number of Gray-Listing Observations

In our data, gray-listing observations are a small minority of the sample— about 0.7 percent—and this reduces the model’s accuracy for estimating the impact of gray-listing on capital flows. To check robustness of our estimates reported in Table 1, we re-estimate the model using different resampling techniques to increase the share of gray-listing observations in our sample. The techniques we used are oversampling, which involves adding more observations of the minority class sample; undersampling, which involves removing the majority class observations; and using a combination of the two. In all cases, we boost the share of gray-listing observations up to about 2 percent of the data (for example, see Tiffin, 2019).

The simplest oversampling technique would involve replicating the existing minority class observations (i.e., gray-listing=1) until the desired mix of majority and minority class in the sample is achieved. However, we use an alternative technique known as SMOTE (Synthetic Minority Oversampling Technique).¹⁷ Instead of replicating exact copies of the existing minority class observations, SMOTE creates synthetic copies that are similar to, but not exactly the same as, the existing minority class observations (see Fernandez et al., 2018 for details).

Next, we use random undersampling (RU), which involves randomly selecting and deleting the majority class observations, until the share of gray-listing observations in the data reaches 2 percent.¹⁸

Finally, we use a combination of SMOTE and random undersampling. According to the machine learning literature, the combined approach often results in the model with better out-of-sample performance (Brownlee, 2020).

The results are reported in Table 4. The estimated coefficients of gray-listing remain negative and similar in size to that obtained in the baseline. The standard errors become smaller where a number of the minority-class observations are substantially increased (i.e., under SMOTE) as expected but not where only the share of the minority-class observations is increased (i.e., under random undersampling or a combination of SMOTE and random undersampling). The 95 percent confidence intervals are therefore smaller under SMOTE, ranging from -9 to -4 percent of GDP, but remains similar to the baseline in others (-11 to -4 percent of GDP).

^{Table 4:}

Robustness: Effect of Gray-Listing using Different Event Windows

^{Table 4:}

Robustness: Effect of Gray-Listing using Different Event Windows

	Baseline	SMOTE	RU	SMOTE & RU
Coefficient	-7.550***	-6.316***	-7.245***	-7.504***
Standard Errors	(1.522)	(1.320)	(1.535)	(1.599)
Conf. Intervals	[-10.53, -4.57]	[-8.90, -3.73]	[-10.25, -4.24]	[-10.64, -4.37]

View Table

^{Table 4:}

Robustness: Effect of Gray-Listing using Different Event Windows

	Baseline	SMOTE	RU	SMOTE & RU
Coefficient	-7.550***	-6.316***	-7.245***	-7.504***
Standard Errors	(1.522)	(1.320)	(1.535)	(1.599)
Conf. Intervals	[-10.53, -4.57]	[-8.90, -3.73]	[-10.25, -4.24]	[-10.64, -4.37]