2.1. Data and sample

The main data for the analysis are sourced from the IMF International Financial Statistics (IFS). We obtain quarterly capital flows documented in the official balance-of-payment statistics from the IFS. Reserve accumulation was popularized after many EMEs opened their financial accounts in the 1990s. Hence, we choose the sample period 1999–2019.Footnote ⁹

The sample countries are not chosen arbitrarily. Starting from the full sample of countries in the IFS, we exclude advanced economies and Eurozone countries. Among the remainders, countries with less than 12 quarterly observations of regression variables are excluded. This is necessary because we perform two-step regressions, wherein the first step is a country-by-country time series regression. This sample definition provides us with a total of 34 countries.Footnote ¹⁰

Table 1 provides the summary statistics for our sample. We adjust the nominal value with the US CPI to measure it in the 2010 US dollar value. Reserve accumulation is our dependent variable. The data is obtained from the balance-of-payment statistics; hence, they contain only the transaction component of the international reserve fluctuations. The mean reserve-accumulation-to-GDP ratio recorded in our sample was 0.51% per quarter, showing significant variation across different countries and time periods (standard deviation: 1.68).

Table 1. Descriptive statistics

Notes: This table presents the descriptive statistics for the variables included in the regressions. The sample period is from 1999q1 to 2019q4. A total of 34 emerging economies are included in the sample. See footnote 10 for the full list of countries. Reserve accumulation and other capital flow data are obtained from the IMF International Financial Statistics. Gross capital outflow openness is calculated based on Fernández et al. (Reference Fernández, Klein, Rebucci, Schindler and Uribe2016). It is defined as “1-average of indicators for capital controls on residents’ capital flows.”.

For a shock that induces reserve accumulation, we consider gross capital inflows (non-resident investors’ acquisition of EME assets). We analyze different asset types of gross inflows: direct, equity, bond, and other (banking) investment flows. We normalize the variable using GDP by dividing quarter $t$ capital inflows by the sum of the quarters $t-1$ to $t-4$ GDP. Descriptive statistics show that our sample countries experienced moderate capital inflows during the sample period. An average country received capital inflows amounting to 1.9% of its GDP every quarter. More than half of the inflows were in the form of direct investment (1.0% of the GDP).

We investigate whether there are variations in reserve accumulation responses among countries with different levels of friction that impede residents’ ability to save abroad. We assess these frictions in two dimensions: government restrictions and the underdevelopment of financial institutions.

First, we examine restrictions on gross capital outflows. In many EMEs, financial repression hinders gross capital outflows. To expedite domestic capital accumulation and industrialization, EM governments often want to retain precious capital within their borders. As such, foreign exchange systems in many EMEs are devised to restrict capital outflows. Fernández et al. (Reference Fernández, Klein, Rebucci, Schindler and Uribe2016) note that there is a higher prevalence of outflow controls than of inflow controls, especially for middle- and low-income countries.

In order to assess this friction, we utilize the data on capital controls provided by Fernández et al. (Reference Fernández, Klein, Rebucci, Schindler and Uribe2016). They process the information in the IMF’s Annual Report on Exchange Rate Arrangements and Exchange Restrictions (AREAER) to derive qualitative indicators denoting the presence of capital controls for specific asset classes, distinguishing the residency of the buyer/seller. In our theory, the type of financial friction that necessitates reserve accumulation is that on gross capital outflows (capital flows by residents). Hence, we utilize their indicators on residents. By averaging all the indicators related to residents’ capital flows and subtracting the result from 1, we obtain the index “gross capital outflow openness” (GCO).Footnote ¹¹ This index ranges from 0 to 1, with a value of 0 indicating the lowest level of openness in gross capital outflows, while a value of 1 signifies no restrictions on gross capital outflows. In our sample, the mean of GCO is 0.54, with a standard deviation of 0.39, enabling us to compare between countries with different levels of openness.

Secondly, we examine the underdevelopment of financial institutions. Developed financial institutions are essential for EME residents to invest abroad efficiently. We employ the index of financial institution development from the Global Financial Development Database (GFD) by Čihák et al. (Reference Čihák, Demirgüç-Kunt, Feyen and Levine2012). The GFD index on financial institutions assesses the level of financial institution development based on institutional size, accessibility, efficiency, and stability. This index (FII) also ranges from 0 to 1, with a higher value indicating a greater development. In our sample, the mean is 0.45 with standard deviation 0.17. Both GCO and FII indices are measured on an annual basis. To avoid simultaneity, we use the indices from the preceding year in our investigation of reserve accumulation.

2.2. Empirical strategy

We begin our empirical analysis with a simple two-way fixed effects model. Reserve accumulation is the regressand and gross capital inflows serve as the main regressor. To examine whether the reserve response is stronger for countries with more frictions on gross capital outflows, we interact the capital inflows with the gross capital outflow openness index (GCO) or the financial institution index (FII). This gives us the following specification:

(1) \begin{equation} \texttt {RA/GDP}_{i,t} = \delta _i + \delta _t + \gamma \; \texttt {K/GDP}_{i,t} + \theta \; \texttt {GCO}_{i,t-4} + \phi \; \texttt {GCO}_{i,t-4} \times \texttt {K/GDP}_{i,t} + \varepsilon _{i,t} \end{equation}

where $\delta _i$ and $\delta _t$ are country and quarter fixed effects, respectively. Both reserve accumulation (RA) and gross capital inflows (K) are normalized using GDP to make the results more comprehensible. Considering the potential correlation caused by GDP in both the regressand and regressor, we also examine reserve accumulation per capita as a robustness check. For the types of gross capital inflows, we examine the following categories: direct inflows, equity inflows, bond inflows, and other inflows (bank loans). We also consider total gross capital inflows, which include all these categories as well as financial derivatives inflows.

With the interaction term in Equation (1), we compare the reserve accumulation responses of countries with varying levels of friction. Our conjecture is that reserve accumulation would be more pronounced in countries with more frictions in residents’ investment abroad. In these countries, the private sector cannot channel funds abroad sufficiently in response to massive gross capital inflows, and thus have consumption booms which are not desirable from the social planner’s perspective. In this case, reserve accumulation can help smooth the consumption. Hence, we expect a larger accumulation of reserves for countries with more restrictions on gross capital outflows or with underdeveloped financial institutions. This corresponds to a positive $\gamma$ and a negative $\phi$ coefficient. The friction measures (GCO or FII) are lagged by one year relative to the capital flow variables. In the regression implementation, we winsorize the regressand and regressor to have reasonable value for their kurtosis (below 10). We cluster the standard error at the country level to adjust the error for possible auto-correlation within each country.

In further detail on our hypothesis, capital inflows are the cause, and reserve accumulation is the effect. While the effects can be analyzed by introducing exogenous capital inflows in a theoretical model, it is obviously difficult to address the endogeneity in empirical investigations. From the data, a positive association is expected between gross capital inflows and reserve accumulation. However, it could result from a reverse causality or a third factor affecting both. Reserve accumulation may also influence other private capital flows. Furthermore, many factors considered in international reserve management are correlated with capital flows.

We tackle the identification challenge by employing a two-stage regression method. Using global push factors of capital inflows, we isolate the exogenous parts of gross capital inflows to each country. As our sample consists of only small open economies, we can safely assume that the global push factors are exogenous to domestic fundamentals. For the push factors, we consider two variables: VIX and a US dollar index. The VIX reflects the risk appetites of international investors and is widely used as a representative indicator of the Global Financial Cycle in the literature (Rey, Reference Rey2015). The VIX is highly correlated with portfolio and banking flows. On the other hand, the exchange rate has important influences on direct investment flows and equity flows. Many studies report a close relationship between the exchange rate and FDI (e.g. Matsumoto, Reference Matsumoto2022). Thus, we use changes in the US dollar’s value as the second push factor. Specifically, we measure the value of the dollar using the Real Major Dollar Index (TWEXMPA) offered by the Federal Reserve. This index measures the US real effective exchange rate against major advanced economies (Euro Area, Canada, Japan, U.K., Switzerland, Australia, and Sweden). Notably, the US and these countries are not included in our sample. And we safely assume that the individual EM countries in our sample cannot influence this dollar index.

Specifically, in the first stage, we regress gross capital inflows on VIX and the US dollar index. We conduct the regression country-by-country and obtain the predicted capital inflow series for each country. The first stage regression equation is as follows:

(2) \begin{equation} \texttt {K/GDP} _{i,t} = \alpha _i + \beta _{1,i} \ln \texttt {VIX}_{t-1} + \beta _{2,i}\Delta \texttt {USD}_{t-1} + \gamma _i X_{i,t-4}+\varepsilon _{i,t}\quad \text{for each } i \end{equation}

where $X$ is the covariate (either GCO or FII), and is also included in the second stage regression, identical to Equation (1). The predicted value of regression (2) contains push factor-driven capital inflows. Note that estimating Equation (2) country-wise is the same as estimating the following single panel regression.

(3) \begin{equation} \texttt {K/GDP} _{i,t} = \sum _i \beta _{1,i} \;d_i + \sum _i \beta _{2,i} \;d_i \times \ln \texttt {VIX}_{t-1} + \sum _i \beta _{3,i} \;d_i \times \Delta \texttt {USD}_{t-1} + \sum _i \gamma _i d_i \times X_{i,t-4} +\varepsilon _{i,t} \end{equation}

where $d_i$ is a dummy variable for country $i$ . Therefore, we employ 102 instrumental variables: 34 country dummies and 68 interactions between those country dummies and the VIX and the dollar index. In the actual regression, we perform the above panel regression and obtain the F-statistics that are used to judge the fitness of the first stage. Then, for the second stage, we replace $\texttt {K/GDP}_{i,t}$ in regression (1) with the predicted capital inflow series (push factor-driven capital inflows). Because our regressor is a variable generated by regressions, we calculate the standard error using the bootstrapping method that encompasses both the first and the second stages.

2.3. Results and interpretation

We first present the results of the total gross capital inflows, followed by a discussion of the different asset types of these inflows. See Table 2 for detailed results on total capital flows. Columns (1)–(3) show the standard ordinary least squares (OLS) regression result. As expected, reserve accumulation and gross capital inflows are strongly and positively correlated (Column 1). Furthermore, the positive correlation is stronger for countries with more limitations in residents’ investment abroad (low financial institution development in Column 2 and more restrictions on gross capital outflows in Column 3).

Table 2. Baseline results on total gross capital inflows

Notes: The variable INDEX refers to either the Financial Institution Index (FII) or the Gross Capital Outflow Openness Index (GCO). They are lagged by one year. The sample period is from 1999q1 to 2019q4. The top and bottom 1% of the dependent variables and the top and bottom 3% of the capital flow variable are winsorized. Reported in brackets are the bootstrapped standard errors. Standard errors are clustered at the country level. ^*, ^{* *}, and ^{* * *} indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

Starting from Column (4), we conduct the two-stage regression process: We first isolate the part of the capital inflows explained by the global push factors and then regress reserve accumulation on it. Since the first stage includes 34 regressions (country-by-country), we report only the F-statistics obtained from the combined regression (3) for the first stage. In Column (4) we find that the positive relationship between reserve and gross capital inflows arises from push factor-driven capital inflows and policy responses to it.

Columns (5) and (6) interact the predicted gross capital inflows with the financial institution index and the gross capital outflow openness measure, respectively. We find that reserve accumulation is positively associated with exogenous capital inflows (positive coefficients to K/GDP) but less so for countries with more developed financial institutions or higher levels of gross capital outflow openness (negative coefficients to the interaction terms). Numerically, the results indicate that when countries receive a 1% of GDP capital inflows driven by global factors, a country with the least developed financial institutions ( $\texttt {FII} = 0$ ) or the strictest controls on capital outflows ( $\texttt {GCO}= 0$ ) increases its reserves by 0.75% or 0.86% of GDP, respectively. In contrast, a country with the most developed financial institutions ( $\texttt {FII} = 1$ ) or no capital outflow restrictions ( $\texttt {GCO} = 1$ ) generally does not increase its reserves.

Column (7) does the same regression as in Column (6), but we normalize the reserve accumulation by population instead of GDP, transforming it into a per capita variable. We continue to normalize other capital inflow data using GDP. This approach is adopted to prevent the potential correlation that arises from normalizing both dependent and independent variables using GDP. The population is a relatively stable variable compared to GDP and is less endogenous to business cycles. Hence, many previous studies on economic growth and public debt utilize population normalization for either the dependent variable, the independent variable, or both. See Panizza and Presbitero (Reference Panizza and Presbitero2014) and Eberhardt and Presbitero (Reference Eberhardt and Presbitero2015). We find that our findings are robust to this change.

Next, in Table 3, we investigate different asset types of gross capital inflows. Columns (1)–(4) replicate the regression of Column (5) of Table 2 but examine direct, equity, bond, and other investment inflows, respectively. Likewise, Columns (5)–(8) reproduce the analysis of Column (6) from Table 2, but with different asset types of capital flows. Upon examining various types of gross capital inflows in relation to financial institution development (FII) in Columns (1)–(4), we observe that the coefficients for push factor-driven capital flows are positive, while those for the interaction between capital inflows and FII are negative across all regressions. However, statistical significance is achieved only for direct investment inflows and other inflows.

Table 3. 2SLS results on different types of flows

Notes: The variable INDEX refers to either the Financial Institution Index (FII) or the Gross Capital Outflow Openness Index (GCO). They are lagged by one year. The sample period is from 1999q1 to 2019q4. The top and bottom 1% of the dependent variables and the top and bottom 3% of the capital flow variables are winsorized. Standard errors are clustered at the country level. In Columns (5)–(10), they are obtained by the bootstrapping method. ⁺, ^*, ^{* *}, and ^{* * *} indicate statistical significance at the 15%, 10%, 5%, and 1% levels, respectively.

The subsequent Columns (5)–(8) use gross capital outflow openness index (GCO). The baseline result from Column (6) in Table 2 remains robust across all capital flow types. To identify which inflow type most significantly triggers a reserve accumulation response, we include all four types of gross capital inflows together in one regression in Column (9). We find that countries tend to accumulate reserves when gross capital inflows occur through direct and equity investments, particularly when there are more restrictions on residents’ outward investments. Capital inflows in other asset types are not significant. Column (10) provides a robustness exercise for Column (9) regression. We change the regressand to reserve accumulation per capita to avoid the correlation caused by GDP. While direct investment inflows still remain strongly significant, other types of capital inflows lose significance.

In summary, our empirical findings provide compelling support for the observations that motivate our study. First, we observe that EMEs accumulate reserves in response to capital inflows generated by global push factors. Second, countries with more obstacles in gross capital outflows tend to accumulate larger reserves in response to the same magnitude of capital inflows. This suggests that limitations on residents’ ability to save abroad play a crucial role in shaping the reserve accumulation responses to gross capital inflows. Lastly, these findings are most evident in direct investment inflows, which consistently remain significant while other capital flows provide varying results according to regression specifications. This underscores the nature of direct investment inflows as temporary income shocks, which, in turn, intensifies the need for external savings and strengthens the incentive to accumulate reserves.Footnote ¹²

3.1. Model setup

We consider a small open economy that lasts three periods, t = 0, 1, 2. There are two domestic agents in our model: households and the government. The model also includes two types of international investors: an international financial intermediary who invests in debts issued by residents in the small open economy and direct investors who purchase the capital in this economy. The small open economy faces a credit constraint only in period 1,Footnote ¹⁴ which may or may not bind depending on the states. Therefore, for precautionary purposes, the government accumulates reserves in period 0 when there is no concern over the binding credit constraint. One period in our model corresponds to several years in reality. Period 0 in our model may represent the 2000s when EMEs were receiving massive direct investment inflows, as illustrated in Lane and Milesi-Ferretti (Reference Lane and Milesi-Ferretti2007).

Production The economy has two sectors, the tradable ( $T$ ) and the non-tradable ( $N$ ) sectors. We denote the output of sector $j$ at time $t$ as $Y_t^j$ . Non-tradable goods are endowed, and we assume that they are in the same quantity every period: $y_{0}^{N}=y_{1}^{N}=y_{2}^{N}$ . On the other hand, to introduce direct investment inflows, we consider that tradable goods are produced by AK technology: $y_{t}^{T}=A_{t}K$ . We abstract from capital accumulation or depreciation. Hence, the size of $K$ remains constant while its ownership changes due to direct investment inflows. We assume that $A_{0} \lt A_{1} \lt A_{2}$ , which implies $y_{0}^{T} \lt y_{1}^{T} \lt y_{2}^{T}$ . Therefore, the households need to borrow anticipating higher outputs in the future. This setup allows us to explore how reserve accumulation is linked with the precautionary motive in our model, although reserve accumulation can still occur without this assumption.

Households The overall utility of the representative household is as follows:

\begin{equation*} U=u(c_{0}^{T},c_{0}^{N})+\mathbb{E}_{0}\left [\beta u(c_{1}^{T},c_{1}^{N})+\beta ^{2}u(c_{2}^{T},c_{2}^{N})\right ]. \end{equation*}

The utility function is given as $u(c_{t}^{T},\:c_{t}^{N})=ln\left (\left (c_{t}^{T}\right )^{\alpha }\left (c_{t}^{N}\right )^{1-\alpha }\right )$ , where $\alpha$ is the share of tradable goods. $\beta$ is the discount rate. Given the output streams and direct investment inflows, households determine their borrowing or saving of tradable goods.

Direct investments A direct investor is interested in the capital of this economy. One can imagine direct investments in our model as a merger and acquisition (M&A) process. At the beginning of period 0, the direct investor decides how much capital to purchase depending on the technological features from which we abstract.Footnote ¹⁵ By purchasing capital, direct investors earn claims on the returns generated by that capital, similar to how equities function in reality.Footnote ¹⁶

We assume that the price of capital is determined through a bargaining process similar to M&As. Furthermore, we posit that direct investors value capital more than households do. Therefore, as long as households have some bargaining power, the equilibrium price of capital becomes higher than the valuation of households. Once we denote the price of capital by $Q_{0}$ , then it implies

\begin{equation*} Q_{0}\gt {\sum _{t=0}^{2}}M_{0,t}^{h}A_{t} \end{equation*}

where $M_{0,t}^{h}$ is the stochastic discount factor of households; hence $M_{0,t}^{h}=\beta ^{t}E\frac {u_{t}^{T}}{u_{0}^{T}}$ . $u_{t}^{T}$ is the marginal utility of tradable goods consumption in period $t$ .

Let $\theta$ be the share of capital sold to the direct investor. Then, direct investors obtain $\theta A_{t}K$ from the total returns $A_{t}K$ , while households receive the remaining portion. With the determined price, the direct investment inflows in period 0 are measured as $Q_{0}\;\theta K$ .Footnote ¹⁷

International financial intermediary and household overseas investment We have not explicitly solved the model yet, but we can easily envision that large direct investment inflows induce households to save. As there is no domestic saving technology, households must invest abroad to save. We denote the borrowing (saving) of households at time $t$ by $b_{t+1}$ ; $b_{t+1}\lt 0$ ( $b_{t+1}\gt 0$ ) indicates borrowing (saving). There are foreign assets paying $r^{*}$ unit of net return in the next period. However, households in the EME face lower returns due to frictions regarding overseas investment.

We model the frictions in two dimensions that correspond to those examined in the empirical analysis. The baseline model here captures the underdevelopment of financial institutions by introducing intermediation costs that hinder households from saving abroad. This corresponds to the analysis of the financial institution index (FII) in the empirical section. Detailed micro-foundations are provided in Appendix A.1 In Appendix A.2, we extend the model to include costs incurred by the government in auditing external investment. These costs are ultimately borne by the private sector and serve as the theoretical counterpart to legal restrictions in the empirical analysis.

Low financial development EMEs usually have poor financial development compared to advanced economies. The low financial development should make it more costly to invest abroad as more overseas investments require more financial experts or other costly resources. Thus, we assume that overseas investments incur the intermediation costs increasing in the amount of overseas investments, and furthermore, the marginal cost increases in the investment as well. These give us a quadratic function of the investment cost. That is,

\begin{equation*} C^{0}_{t} = \frac {\Gamma _{s}}{2} b_{t+1}^{2} \:\:\:\:\: ( b_{t+1}\gt 0,\:\: \gamma _{0}\gt 0 ) \end{equation*}

where $C^{0}_{t}$ is the intermediation cost and $\Gamma _{s}$ captures frictions associated with the intermediation of capital outflows. Detailed mircofoundation for this cost is discussed in Appendix A. Please note the return to the investment facing the households is the return minus the marginal intermediation cost. That is,

(4) \begin{equation} r_{t+1} = r^{*} - \Gamma _{s}b_{t+1}\:\:\:\:\:\; ( b_{t+1}\gt 0) \end{equation}

Then, the gross return from the overseas investment, $b_{t+1}\left (1+r^{*}\right )$ is larger than the return to the households and the intermediation cost, $b_{t+1}\left (1+r_{t+1}\right ) + \frac {\Gamma _{s}}{2}b_{t+1}^{2}$ . That is, the overseas investments result in the rents of $\frac {\Gamma _{s}}{2}b_{t+1}^{2}$ . More precisely,

(5) \begin{equation} b_{t+1}\left (1+r^{*}\right )=\underset {\text{returns to households}}{\underbrace {\phantom {\frac {!}{!}}b_{t+1}\left (1+r_{t+1}\right )}}+\underset {\text{rents}} {\underbrace {\frac {1}{2}\Gamma _{s}b_{t+1}^{2}}}+\underset {\text{intermediation costs}}{\underbrace {\frac {1}{2}\Gamma _{s}b_{t+1}^{2}}} \end{equation}

Note that the rents belong to the households as the financial experts are also members of the big family of the households. Nonetheless, we can regard the rents as social cost of overseas investments as the rents matter for income inequality or other various social aspects. Appendix A also discusses the case in which the investment is intermediated by foreign financial intermediaries and the rents belong to the foreign intermediaries.

International financial intermediation and household borrowing We impose imperfect capital mobility on household borrowing as well. For the borrowing of households, we borrow the results in Fanelli and Straub (Reference Fanelli and Straub2021). Assume that there is a continuum of international financial intermediaries with different fixed costs for operation, and also, the individual intermediary’s capacity is limited. If an EME borrows more, the EME needs to attract more international financial intermediaries to the bond market by paying higher rates; international financial intermediaries with higher fixed costs need to join the market. This implies,

(6) \begin{equation} -b_{t+1}=\frac {1}{\Gamma _{b}}\left (r_{t+1}-r^{*}\right )\!. \end{equation}

Hence, the spread $r_{t+1}-r^{*}$ increases with the amount of borrowing ( $-b_{t+1}$ ). Rearranging this yields Equation (7).

(7) \begin{equation} r_{t+1}=r^{*}-\Gamma _{b}b_{t+1}\:\:\:\:\:\; ( b_{t+1}\lt 0) \end{equation}

Credit constraint Households face a credit constraint in period 1.Footnote ¹⁸ That is,

(8) \begin{equation} -b_{2} \leq \phi \left ( y_{1}^{T} (1-\theta )+ p_{1} y_{1}^{N} \right ) \end{equation}

The collateral is GDP in the credit constraint as in the recent capital control literature (e.g. Bianchi, Reference Bianchi2011; Korinek, Reference Korinek2018). $\phi$ is stochastic.Footnote ¹⁹ More formally, $\phi \left (\omega \right )$ depends on the realized state $\omega$ . We assume $\phi$ has the support of an interval and that its CDF and PDF are both continuous.

Government Government accumulates international reserves in period 0. To finance reserve accumulation, government imposes lump-sum taxes $T$ in units of tradable goods. With revenue from the tax, government purchases foreign bonds in period 0, which will earn $1+\overline {r}$ units of tradable goods in period 1 per unit of the bond. Accordingly, the dynamics of international reserves are:

\begin{equation*} T\left (1+\overline {r}\right )=R \end{equation*}

We assume that the return to reserves is lower than that to private foreign assets (i.e., $\overline {r}\lt r^{*}$ ) reflecting the empirical reality that international reserves are typically invested in low-yield, safe assets.Footnote ²⁰ In addition, we assume that reserve accumulation is not subject to any frictions related to overseas investments.Footnote ²¹

3.2. Model equilibrium

3.2.1. Equilibrium without reserve accumulation

We first illustrate the equilibrium without reserve accumulation. We start with household decisions and subsequently introduce our first analytical result showing the existence of a pecuniary externality related to capital outflow frictions.

Utility maximization of households The utility maximization is formally defined below.

\begin{eqnarray*} & \underset {c_{t}^{T},\:c_{t}^{N},\:b_{t}}{\max } &u\left (c_{0}^{T},\:c_{0}^{N}\right )+\mathbb{E}\left [\beta u\left (c_{1}^{T},\:c_{1}^{N}\right )+\beta ^{2}u\left (c_{2}^{T},\:c_{2}^{N}\right )\right ] \\[5pt] & s.t. & \; c_{0}^{T} = \left (1-\theta \right )y_{0}^{T}+p_{0}y_{0}^{N}-p_{0}c_{0}^{N}-b_{1}-T+Q_{0}\theta k\\[5pt] && \; c_{1}^{T} = \left (1-\theta \right )y_{1}^{T}+p_{1}y_{1}^{N}+b_{1}(1+r_{1})+R-p_{1}c_{1}^{N}-b_{2}\\[5pt] && \; c_{2}^{T} = \left (1-\theta \right )y_{2}^{T}+p_{2}y_{2}^{N}+b_{2}(1+r_{2})-p_{2}c_{2}^{N}\\[5pt] && -b_{2} \leq \phi (y_{1}^{T}\left (1-\theta \right )+p_{1}y_{1}^{N}) \end{eqnarray*}

where $u(c_{t}^{T},\:c_{t}^{N})=ln\left (\left (c_{t}^{T}\right )^{\alpha }\left (c_{t}^{N}\right )^{1-\alpha }\right )$ and $R=T(1+\bar {r})$ .

We derive the solution for households via backward induction. There is no dynamic decision of households in the last period. Households consume all available tradable and non-tradable goods after paying back all debts and receiving the remaining reserves from government. As explained later, the government depletes all reserves in period 1, regardless of the realization of $\phi$ . Therefore, household consumption is as follows:

\begin{equation*} c_{2}^{T}=\left (1-\theta \right )y_{2}^{T}+b_{2}\left (1+r_{2}\right ),\;\; c_{2}^{N}=y_{2}^{N} \end{equation*}

In period 1, the households take the states of the economy as given and solve the utility maximization problem. These states include $\phi$ , a random variable whose value is determined at the beginning of period 1.

Market clearing conditions will be given by the pricing functions.

\begin{equation*} p_{t}=\left (\frac {1-\alpha }{\alpha }\right )\left (\frac {c_{t}^{T}}{c_{t}^{N}}\right )\;\;\text{and}\;\;r_{t}=-\Gamma _{j}b_{t}+r^{*}\;\;\text{where}\;j=b,s \end{equation*}

If the credit constraint does not bind, that is, if the realized $\phi$ is sufficiently high, then the household determines its tradable goods consumption according to her Euler equation. The amount of borrowing in period 1 is determined as

(9) \begin{equation} -b_{2}=\frac {-\zeta {}_{1}+\sqrt {\zeta _{1}^{2}-4\left (1+\beta \right )\Gamma \left (\beta \left (1+r^{*}\right )\left (\left (1-\theta \right )y_{1}^{T}+b_{1}\left (1+r_{1}\right )+R\right )-\left (1-\theta \right )y_{2}^{T}\right )}}{2\left (1+\beta \right )\Gamma } \end{equation}

where $\zeta _{1}=\left (1+r^{*}\right )\left (1+\beta \right )\text{+}\beta \Gamma \left (\left (1-\theta \right )y_{1}^{T}+b_{1}\left (1+r_{1}\right )+R\right )$ . The interest rate $r_{2}$ is accordingly determined by $r_{2}=-\Gamma _{b} b_{2}+r^{*}$ .

If the credit constraint binds, the tradable good consumption will be determined by the constraint.Footnote ²³ Plugging in the budget constraint into the credit constraint equation, we haveFootnote ²⁴

(10) \begin{equation} -b_{2}=\left(\frac {1}{1-\,\phi (\frac {1-\alpha }{\alpha })}\right)\phi \Big((1-\theta)y_{1}^{T}+\frac {1-\alpha }{\alpha }\Big((1-\theta)y_{1}^{T}+b_{1}\big(1+r_{1}\big)+R\Big)\Big) \end{equation}

We now turn to the period 0 optimization problem. Since there is no credit constraint, the solution is the Euler equation. By denoting the marginal utility of good $x$ in period $t$ as $u_{t}^{x}$ ,

(11) \begin{equation} u_{0}^{T}=\beta (1+r_{1})\mathbb{E} \big[u_{1}^{T} \big] \end{equation}

Pecuniary externalities We present our first analytical result. We observe that the level of borrowing and saving determined by the Euler equation (11) is not necessarily socially optimal. Externalities arise because agents do not account for the impact of their actions on prices. Such externalities are commonly referred to as pecuniary externality (see Dávila and Korinek, Reference Dávila and Korinek2018).

In our model, two distinct sources of pecuniary externalities are identified: one through the real exchange rate in period 1 ( $p_{1}$ ), and the other through interest rates in period 0, 1 ( $r_{1}$ , $r_{2}$ ). Interestingly, the direction of the externalities in shaping households’ suboptimal decision depends on whether the households borrow or save. When households borrow, the real exchange rate and the interest rate externalities align and act in the same direction. Conversely, when households save, the two externalities diverge and act in opposite directions.

When households borrow, they do not consider that their additional borrowing makes tradables more valuable relative to non-tradables in the next period (i.e. alters the real exchange rate), making it more probable for the credit constraint to bind, thus they overborrow (as in Bianchi, Reference Bianchi2011). At the same time, more borrowing pushes up the interest rate, but it as well is not accounted for by the households, resulting in overborrowing. Therefore, decentralized borrowing by households is always overborrowing in the eye of the social planner.

Conversely, when households save, they do not consider that their additional savings reduce the probability of a sudden stop in the next period by affecting the real exchange rate. Hence, they undersave. At the same time, when they save, their additional savings push down the yields on the savings. Since this is also not considered in household decisions, they oversave. As a result, whether the savings decision of households will be undersaving or oversaving in the eyes of the social planner is indeterministic and depends on the realized state and the values of key parameters; the distribution of $\phi$ and $\Gamma _{s}$ . We formally state these results in the following lemma.

Lemma 1. Assume $ \phi ^{c}\gt \underline {\phi }$ and $\Gamma _{s}, \Gamma _{b} \geq 0$ . $b_{1}^{h}$ be the solution of the households ( 11 ), and $\;b_{1}^{sp}$ be the solution of the social planner.

1. 1) With $\Gamma _{s}=\Gamma _{b}=0$ , we have $b_{1}^{h}\lt b_{1}^{sp}$ .

2. 2) If $b_{1}^{h}\lt 0$ , then $b_{1}^{h}\lt b_{1}^{sp}$ .

3. 3) If $b_{1}^{h}\gt 0$ , then there exists $\gamma _{0}\in \left (0,\infty \right ]$ such that for $\Gamma _{s}\in \left (0,\,\gamma _{0}\right )$ , $b_{1}^{h}\lt b_{1}^{sp}$ . Moreover, if $\gamma _{0}\in \left (0,\,\infty \right )$ , then we can have $\gamma _{1}\in \left (\gamma _{0},\,\infty \right )$ such that for $\Gamma _{s}\in \left (\gamma _{0},\;\gamma _{1}\right )$ , $b_{1}^{h}\gt b_{1}^{sp}$ .

Proof) See Online Appendix B.

Lemma 1 illustrates how the two different externalities induce households’ undersaving or oversaving. First, as long as $\textit {prob}\left (\phi \lt \phi ^{c}\right )\gt 0$ ,Footnote ²⁵ any borrowing (or less savings) by households has the externality of tightening the credit constraint in period 1. Household borrowing reduces tradable goods consumption in period 1, resulting in lower real exchange rates ( $p_{1}$ ). The low exchange rate tightens the credit constraint (see Equation 8). Hence, if there is no friction in capital flows ( $\Gamma _{s}=\Gamma _{b}=0$ ), the economy always suffers from overborrowing or undersaving.

Second, any borrowing or lending abroad results in extra costs of capital flows, which households do not internalize. One unit of borrowing or lending yields $b_{1}\left (1+r_{1}\right )$ in period 1, and $r_1$ is determined by $b_1$ (recall $r_{t}=r^*-\Gamma _{j}b_{t}$ ). Differentiating $b_{1}\left (1+r_{1}\left (b_{1}\right )\right )$ with respect to $b_{1}$ yields

\begin{equation*} \frac {d\left (b_{1}(1+r_{1} (b_{1}))\right )}{db_{1}} \; =\; 1+r^{*}-2\Gamma _{j}b_{1} \; = \; 1+r_{1}\left (b_{1}\right )-\Gamma _{j}b_{1} \end{equation*}

where $j=b,s$ . Households are price takers, and hence, they only consider $1+r_{1}$ as a cost (return) to their borrowing (lending). Thus, any borrowing or lending by households leaves the last term ( $-\Gamma _j b_1$ ) not considered: the second externality through interest rates. An important observation is that the term $-\Gamma _{j}b_{1}$ is positive for $b$ $_{1}\lt 0$ while it is negative for $b$ $_{1}\gt 0$ . These different signs explain reasons why we always have $b_{1}^{h}\lt b_{1}^{sp}$ for $b_{1}^{h}\lt 0$ , but $b_{1}^{h}\gt b_{1}^{sp}$ for $b_{1}^{h}\gt 0$ given a large enough $\Gamma _{s}$ ,Footnote ²⁶ as stated in the second and third statements of the lemma.

Direct investment inflows and equilibrium dynamics As we assumed $y_{0}^{T}\lt y_{1}^{T}\lt y_{2}^{T}$ , the optimum for households is to borrow against larger outputs in the future. However, borrowing creates two externalities, as previously discussed. Direct investment inflows provide a better way of external financing without these externalities since they do not involve costly borrowing or debt repayment.

However, for direct investment inflows above a certain level, households need to save abroad. Then, the friction imposed on capital outflows, $\Gamma _{s}$ , creates a new challenge for households. When $\Gamma _{s}$ is non-negligible, more saving by households leads to lower returns, which in turn leads to insufficient saving (compared to frictionless case) and a consumption boom.Footnote ²⁷

Figure 2 illustrates how the equilibrium changes as direct investment inflows $(\theta )$ vary. In the figure, more capital inflows evidently cause a higher consumption of tradable goods in period 0 and higher real exchange rates. Despite inefficient consumption booms in period 0, direct investment inflows enhance the economy’s resilience to sudden stops: the lower probability of binding credit constraints and the less tight constraint for a given $\phi$ . Hence, as commonly argued, external financing in the form of direct investments is better in terms of macro-prudence. However, the gain strictly diminishes as friction on capital outflows increases. Figure 2 demonstrates that the decline in the probability of sudden stops, denoted as prob ( $\phi \lt \phi ^{c}$ ), decreases rapidly with $\Gamma _{s}$ . For a large enough $\Gamma _{s}$ , an interesting observation is the emergence of a “U-shaped” curve in the sudden stop probability against direct investment inflows. Beyond a certain threshold of direct investment flows, the economy becomes more vulnerable to sudden stops.Footnote ²⁸

Figure 2. Equilibrium without reserve accumulation. Notes: The figure illustrates how the equilibrium without reserve accumulation varies with direct investment inflows $(\theta )$ and different levels of frictions on capital outflows $(\Gamma _s)$ . The parameter values used are as follows: the lower bound of the borrowing rate $r^{*} = 0.05$ ; the interest rate on reserves $\bar {r} = 0.01$ ; the weight on tradable goods $\alpha = 0.35$ ; the discount factor $\beta = 0.94$ ; the distribution of credit constraint coefficient is modeled as a Beta distribution with parameters $(1.2, 5)$ ; and the endowment stream is given by $y_0^T = 0.8$ , $y_1^T = 1$ , $y_2^T = 1.5$ , and $y^{NT} = 1$ .

3.2.2. Equilibrium with reserve accumulation

We then describe the equilibrium with government’s reserve accumulation. Please note that reserve accumulation is the only available policy tool for the government. As such, the equilibrium conditions except for the reserve accumulation, i.e., the household optimality conditions, are identical to the equilibrium without reserve accumulation.

Optimal reserve accumulation To solve for reserve accumulation in period 0, we first need to solve for reserve accumulation (or depletion) in period 1. As expected, the government depletes all reserves regardless of whether or not the credit constraint binds.Footnote ²⁹ Given that the government will deplete all reserves in period 1, we formulate the optimal reserve accumulation as follows:

where $u(c_{t}^{T},\:c_{t}^{N})=ln\left (\left (c_{t}^{T}\right )^{\alpha }\left (c_{t}^{N}\right )^{1-\alpha }\right )$ and $R=T(1+\bar {r}).$ Subsequently, we derive the first-order condition and rearrange the equation, thus yielding Proposition 1.

Proposition 1. The optimal reserve accumulation at t = 0 is characterized by

If $b_{1}^{h}\lt 0$ ,

(12) \begin{align} & \underset {\text{Higher }r_{1}}{\underbrace {{\beta \Gamma _{b}\mathbb{E}\left [u_{1}^{T}\right ]b_{1}\frac {db_{1}}{dR^{*}}}}}+\underset {\text{Consumption Wedge at }\overline {r}}{\underbrace {\left [u_{0}^{T}-\beta \left (1+\overline {r}\right )\mathbb{E}\left [u_{1}^{T}\right ]\right ]}}\nonumber\\& \mathbb{\;\;\;=\;\;} \beta \frac {dw_{1}}{dR^{*}}\Bigg[\underset {\text{Marginal Value of Borrowing}}{\underbrace {\int _{\underline {\phi }}^{\phi ^{c}}\frac {d\left (-b_{2}\right )}{dw_{1}}\left (u_{1}^{T}-\beta\! \left (1+r_{2}\right )u_{2}^{T}\right )d\mathcal{F_{\phi }}}}-\underset {\text{Lower }r_{2}}{\underbrace {\beta \Gamma _{b}\mathbb{E}\left [u_{2}^{T}b_{2}\frac {db_{2}}{dw_{1}}\right ]}}\Bigg] \end{align}

If $b_{1}^{h}\gt 0$ ,

(13) \begin{align} &\underset {\text{Consumption Wedge at }\overline {r}}{\underbrace {\left [u_{0}^{T}-\beta \left (1+\overline {r}\right )\mathbb{E}\left [u_{1}^{T}\right ]\right ]}}\nonumber\\&\mathbb{\;\;=\;\;} \beta \frac {dw_{1}}{dR^{*}}\Bigg[\underset {{\text{Marginal Value of Borrowing}}}{\underbrace {\int _{\underline {\phi }}^{\phi ^{c}}\frac {d\left (-b_{2}\right )}{dw_{1}}\left (u_{1}^{T}-\beta \left (1+r_{2}\right )u_{2}^{T}\right )d\mathcal{F_{\phi }}}}-\underset {\text{Lower }r_{2}}{\underbrace {\beta \Gamma _{b}\mathbb{E}\left [u_{2}^{T}b_{2}\frac {db_{2}}{dw_{1}}\right ]}}\Bigg]-\underset {\text{Higher }r_{1}}{\underbrace {{{\beta \Gamma _{s}\mathbb{E}\left [u_{1}^{T}\right ]b_{1}\frac {db_{1}^{s}}{dR^{*}}}}}} \end{align}

where $w_{1}=R^{*}+b_{1}\left (1+r_{1}\right )$ and $\frac {dw_{1}}{dR^{*}}=\frac {\partial w_{1}}{\partial R}+\frac {\partial w_{1}}{\partial b{}_{1}}\frac {db}{dR}=1+\left (1+r^{*}-2\Gamma _{j}b_{1}\right )\frac {db_{1}}{dR}$ .

Proof) See Online Appendix B.

The proposition above illustrates the underlying considerations for optimal reserve accumulation. The terms in the LHS are the marginal costs of reserve accumulation, and the terms in the RHS are the benefits. The term $u_{0}^{T}-\beta \left (1+\overline {r}\right )\mathbb{E}\left [u_{1}^{T}\right ]$ in the LHS indicates the cost of reserve accumulation due to low returns to reserve in terms of utility.Footnote ³⁰ The two terms in the RHS are the benefits from higher wealth in period 1.Footnote ³¹ Because of the imperfect capital mobility in both capital inflows and outflows, reserve accumulation raises the wealth in the future, which in turn helps with sudden stops and lowers expected borrowing rates in period 1.Footnote ³²

An interesting term is $\beta \Gamma _{j}\mathbb{E}\left [u_{1}^{T}\right ]b_{1}\frac {db_{1}}{dR^{*}}$ . The term is in LHS in Equation (12) whereas it is in RHS in Equation (13): The term is a marginal cost when $b_{1}\lt 0,$ whereas it is a marginal benefit when $b_{1}\gt 0$ . This contrast reflects the reserve accumulation’s effects on the interest rates. As explained already, reserve accumulation increases both the borrowing rates and lending rates. The former—higher borrowing rate—represents the costs, but higher lending rates are benefits. This implies that an interior solution—positive reserve accumulation—is more likely when households save rather than borrow.

We further elaborate on the different efficacy of reserve accumulation, depending on whether households borrow or save. In Figure 3, for $\theta$ such that $b_{1}\lt 0$ , the optimal reserve accumulation is zero. Although our model is too stylized to draw quantitative implications, the results of no reserve accumulation when $b_{1}\lt 0$ in Figure 3 highlight the deficiencies of reserve accumulation in an environment where agents borrow from outside the economy.

Figure 3. Optimal reserve accumulation. Notes: The figure shows how the effectiveness of reserve accumulation varies depending on whether households are borrowers or savers. All parameter values are held constant, except for the wedges in the uncovered interest parity (UIP) condition: $\Gamma _{s} = 0.2$ and $0.5$ , and $\Gamma _{b} = 0.25$ .

Inspecting the mechanism To better understand the mechanism behind Proposition 1 and the numerical results, let us recall Lemma 1, illustrating the inefficiencies facing the small open economy. First, occasionally binding credit constraints induce the overborrowing or undersaving. This calls for the necessity of reserve accumulation by the government, but Ricardian equivalence forces nullify the effects of reserve accumulation. That is, households regard international reserves as their assets and, accordingly, increase (reduce) their borrowing (saving), responding to the reserve accumulation.

The frictions on capital flows, positive $\Gamma _{s}$ and $\Gamma _{b}$ , help the government overcome the Ricardian equivalence problem. Figure 4 well illustrates the difference. When households borrow, households borrow more following the reserve accumulation (shift-left of the foreign borrowing demand curve). The reserve accumulation can increase the net foreign assets because more borrowing following reserve accumulation raises the borrowing rates, discouraging borrowing. However, although higher borrowing rates lead to higher net foreign assets, as borrowing increases less than reserve accumulation, the economy suffers from higher borrowing rates.Footnote ³³

On the contrary, when households save, the fewer private savings due to reserve accumulation raise the returns. Similar shift-left of saving demand curve raises the return to the investment return, as in Figure 4. The higher returns result in more savings, and consequently, the falls in household savings are less than in reserve accumulation. Therefore, the reserve accumulation improves the net foreign asset positions and also reduces the negative externality of lower returns to saving.

Figure 4. Comparative statics of the households decision. Notes: The shift to the left of the curves indicates changes in household borrowing/saving due to reserve accumulation. Reserve accumulation induces more borrowing and less savings for households. More borrowing raises the borrowing rate facing households, whereas less saving raises the return rates facing households.

3.3. Further characterization of the optimal reserve accumulation

In this subsection, we characterize the optimal reserve accumulation from a different angle, highlighting how large direct investment inflows lead to seemingly excessive reserve accumulation. The analytical results establish a clear connection between our model and empirical observations. Furthermore, we provide implications for the ongoing policy debate on currency manipulation with a new proposition.

As a first step, we denote $b_{1}=b_{1}\left (\theta ,R\right )$ . In other words, $b_{1}$ is a function of $\theta$ and $R$ . We also know $\frac {\partial b_{1}}{\partial \theta }\gt 0$ and $\frac {\partial b_{1}}{\partial R}\lt 0$ . Rearranging the FOC of reserve accumulation and using $u_{0}^{T}-\beta \left (1+r_{1}\right )\mathbb{E}\left [u_{1}^{T}\right ]=0$ gives us

(14) \begin{align} & \left [r^{*}-\overline {r}-\Gamma _{s}b_{1}\left (\theta \right )\left (1-\frac {db_{1}\left (\theta \right )}{dR}\right )\right ]\mathbb{E}\left [u_{1}^{T}\right ]\nonumber \\ &\quad \mathbb{\;\;=\;\;} \frac {dw_{1}}{dR^{*}}\left [\int _{\underline {\phi }}^{\phi ^{c}}\frac {d\left (-b_{2}\right )}{dw_{1}}\left (u_{1}^{T}-\beta \left (1+r_{2}\right )u_{2}^{T}\right )d\mathcal{F_{\phi }}-\beta \Gamma _{b}\mathbb{E}\left [u_{2}^{T}b_{2}\frac {db_{2}}{dw_{1}}\right ]\right ] \end{align}

The LHS in Equation (14) decreases in $\theta$ . However, the RHS is always positive as long as $b_{2}\lt 0$ . We can think of the LHS as adjusted marginal costs and RHS as adjusted marginal benefits accordingly. Now define $\theta ^{c}$ such that the LHS in Equation (14) is zero. That is,

(15) \begin{equation} r^{*}-\overline {r}-\Gamma _{s}b_{1}(\theta ^{c})\Big(1-\frac {db_{1}(\theta ^{c})}{dR}\Big)=0 \end{equation}

At $\theta =\theta ^{c}$ , government must accumulate reserves because the marginal cost is zero while the marginal benefit is positive. Thus, $\theta ^{c}$ is the cut-off of direct investment above which the government accumulates reserves. We introduce our second proposition to highlight this finding.

The first statement in the proposition shows the existence of the cut-off, above which government accumulates positive reserves. The second statement shows that the optimal reserve accumulation increases in the measure of direct investment inflows, $\theta$ .Footnote ³⁴ Lastly, the third statement shows that the cut-off decreases in the measure of outflow friction $\Gamma _{s}$ .Footnote ³⁵

The second statement shows that the sizes of reserve accumulation are bounded below, and the bound increases linearly in $\theta$ . We confirm through various numerical experiments that $\delta _{1}$ is large, and the reserve accumulation is close enough to the lower bound.Footnote ³⁶ That is,

(16) \begin{equation} R^{*}\simeq \left (Q_{0}-A_{0}\right )\left (\theta -\theta ^{c}(\Gamma _{s})\right )K \end{equation}

Equation (16) is the theoretical counterpart to the empirical regularity. From the equation, we can see two comparative statics corresponding to our empirical findings in Section 2. First, the optimal reserve accumulation increases linearly in direct investment inflows once the inflows are beyond the threshold $\theta ^{c}$ . Second, the threshold does depend on the measure of outflow frictions, $\Gamma _{s}$ . Therefore, more severe outflow frictions induce more reserve accumulation, given the amounts of direct investment inflows.

In our model, the variable $\Gamma _{s}$ is based on two micro-frictions: underdeveloped financial sector and tax evasion through overseas investment (Appendix A). These correspond to our examinations of the financial institution index and the gross capital outflow openness index in the empirical analysis. We view these two frictions as interconnected in practice. Underdeveloped financial sector may be a reason why EMEs impose capital outflow restrictions. Due to their underdeveloped financial sectors, EMEs incur high costs when interacting with international intermediaries to invest abroad. Recognizing this, EM governments implement outflow restrictions to prevent their valuable resources from turning into rents for international intermediaries and to retain beneficial capital within their own borders. Furthermore, overseas investment facilitates tax evasion in underdeveloped countries, raising enforcement costs for the government. This is modeled explicitly in Appendix A. Both these channels provide theoretical underpinnings for why gross capital outflow openness remains limited in many EMEs.

Overall, once we view direct investment capital flows as exogenous, we can explain the evolution of international reserves of EMEs over the last two decades. That is, as EMEs receive more direct investment flows, many EMEs absorb capital inflows by accumulating reserves.Footnote ³⁷ We summarize the analytical results and the following discussions in the remark below.Footnote ³⁸

Discussion of currency manipulation Another finding from Proposition 2 is that the real exchange rates in period 0 become insensitive to $\theta$ as the government amasses reserves.

(17) \begin{eqnarray}p_{0} &=& \Big(\frac {1-\alpha }{\alpha }\Big)\frac {y_{0}^{T}+(Q_{0}-A_{0})\theta K+b_{1}(\theta)-R (\theta)}{y_{0}^{N}}\nonumber\\[2pt]&\simeq& \Big(\frac {1-\alpha }{\alpha }\Big)\frac {y_{0}^{T}+(Q_{0}-A_{0})\theta ^{c}(\Gamma _{s})K+b_{1}(\theta ^{c}(\Gamma _{s}))}{y_{0}^{N}} \end{eqnarray}

The expression for $p_{0}$ indicates that it is almost invariant to $\theta \in (\theta ^{c},\;1)$ . When confronted with direct investment flows exceeding a certain threshold, the government “passively” absorbs the additional inflows. Consequently, the real exchange rate appears “invariant” to the inflows from direct investments.

Accumulated reserves are often viewed as evidence of currency manipulation intended to gain export competitiveness. For example, one of the criteria that the US Treasury uses to judge whether an EME is manipulating its currency value is the amount of reserve accumulation.Footnote ³⁹ In the literature, it has often been argued that the precautionary view cannot justify international reserve holdings of extraordinarily large sizes, and therefore, large sizes of reserves must be byproducts of the export-oriented growth strategy (i.e., currency manipulationFootnote ⁴⁰ ).

In contrast, we argue that the simple reserve-to-GDP ratio is not a good measure for identifying a currency manipulation. If excessive reserve accumulation occurs when there are large and exogenous capital inflows, then the purpose of reserve accumulation may not be currency manipulation but consumption smoothing. Our theory explains why the sizes of accumulated reserves are not good “litmus” to test currency manipulation. Proposition 2 implies that EMEs facing massive capital inflows make corresponding capital outflows in the form of reserves to maintain a macroeconomic balance. The purpose of reserve accumulation is to reallocate resources from capital inflows to the future. The government in our model does not have mercantilist motives as we do not include any ingredients related to mercantilism, such as positive externalities from exports.

Figure 5 well illustrates this point. First, in the absence of reserve accumulation, direct investment flows generate consumption booms and appreciate the real exchange rate, similar to Figure 2. Therefore, although direct investments lower the probability of a sudden stop, the probability falls slowly as households cannot invest abroad enough. In contrast, once the planner accumulates reserves in response to the inflows, capital outflows are generated enough by the planner, keeping tradable goods consumption almost constant. Consequently, the real exchange rate is almost constant as well. More importantly, the sudden stop probability decreases much faster. As a result, the equilibrium with reserve accumulation is similar to little or no friction on capital outflows (very small $\Gamma _{s}$ ).

Figure 5. Reserve accumulation and currency manipulation. Notes: The figure illustrates how reserve accumulation helps replicate the macroeconomic balance that would be achieved under frictionless capital outflows. Parameter values are the same as in the benchmark case. CE and SP refer to the competitive equilibrium without reserve accumulation and the equilibrium with optimal reserve accumulation, respectively.

In this regard, reserve accumulation is a way to “restore” the macroeconomic balance under frictionless capital outflows. The real exchange rate may be an intermediate target for the planner as it measures over-consumption in the present, but the purpose of the intervention is to prevent “appreciation” of the currency, not to “depreciate” the currency. The current account ( $y_{0}^{T}-c_{0}^{T}$ ) under reserve accumulation (SP) also resembles that under no reserve accumulation but with little friction (CE, $\Gamma =0.01$ ).Footnote ⁴¹

3.4. Reserve accumulation with capital controls

Now, we analyze reserve accumulation in an environment where government has control over capital flows.Footnote ⁴² The analysis here further elucidates the relationship between capital outflow restrictions and reserve accumulation, presented in Section 2. We only consider capital controls on debt flows. The analysis of the relationship between capital controls on direct investment flows and reserve accumulation is introduced in Online Appendix F.

Suppose government can tax or subsidize (negative tax) debt instrument-type capital flows. As well-known in the literature, the optimal tax can achieve the same equilibrium where government directly chooses the capital flow. The optimal tax is characterized as follows.

(18) \begin{align} \tau _{b} & =\frac {1}{\mathbb{E}\left [u_{1}^{T}\right ]}\left [\int _{\underline {\phi }}^{\phi ^{c}}-\frac {db_{2}}{db_{1}}u_{1}^{T}{-{\beta }}\Gamma _{j} b_{2}\frac {db_{2}}{db_{1}}u_{2}^{T}d\mathcal{F}_{\phi }\right ] \end{align}

Thus, the optimal tax increases in the externalities from borrowing or saving of households.Footnote ⁴³

Now, we present two equations characterizing the equilibrium where the government optimally accumulates reserves and taxes (or chooses to borrow or save). Assuming an interior solution, the equilibrium is characterized by the following two equations.

(19) \begin{equation} -u_{0}^{T}+\beta u_{1}^{T}\big(1+r^{*}-2\Gamma _{s}b_{1}^{sp}\big)+\beta \int _{\underline {\phi }}^{\phi ^{c}}(\!-u_{1}^{T}+\beta u_{2}^{T}(1+r_{2}))\frac {db_{2}}{dw_{1}}(1+r^{*}-2\Gamma _{s}b_{1}^{sp})=0 \end{equation}

(20) \begin{equation} -u_{0}^{T}+\beta u_{1}^{T}(1+\overline {r})+\beta \int _{\underline {\phi }}^{\phi ^{c}}(\!-u_{1}^{T}+\beta u_{2}^{T}(1+r_{2}))\frac {db_{2}}{dw_{1}}\left (1+\overline {r}\right )=0 \end{equation}

where $w_{1}=b_{1}\left (1+r_{1}\right )+R$ and $b_{2}$ is characterized in Equations (10) and (11). It is straightforward to solve for $b_{1}^{sp}$ assuming an interior solution for both $b_{1}^{sp}$ and $R$ . Equations (19) and (20) give us

(21) \begin{align} b_{1}^{sp} & =\frac {r^{*}-\overline {r}}{2\Gamma _{s}} \end{align}

Equation (21) is an interior solution and $b_{1}^{sp}\gt 0$ . This implies that the government does not accumulate reserves if borrowing is the optimal choice. This is because capital control is a superior substitute for reserve accumulation when the optimal decision is to borrow abroad.Footnote ⁴⁴

Even when the government chooses to save, if the saving is less than $\frac {r^{*}-\overline {r}}{2\Gamma _{s}}$ , the government does not accumulate reserves as reserve accumulation is still an inferior saving technology than debt instruments. However, if the required saving exceeds $\frac {r^{*}-\overline {r}}{2\Gamma _{s}}$ , then the government does not expand its debt instrument holdings beyond that level. Instead, the government relies on reserve accumulation. This is because the marginal return to debt instruments, after accounting for intermediation costs, decreases with investment. These are summarized below.Footnote ⁴⁵

We can formulate this proposition differently with a corollary. It restates that capital control on debt flows always dominates reserve accumulation for the case of borrowing, while reserve accumulation can be more efficient for saving (See Corollary A.1 in Online Appendix B).Footnote ⁴⁶

An important observation is that the threshold, $\frac {r^{*}-\overline {r}}{2\Gamma _{s}}$ , is inversely related to the outflow friction measure, $\Gamma _{s}$ . If $\Gamma _{s}$ is large, the marginal benefit of overseas investment falls rapidly and it is more likely that the government accumulates reserves. Another significant observation is that if saving by decentralized households is larger than the threshold, then the optimal policy is a mix of taxation (outflow restriction) and reserve accumulation. We make it clear with the following corollary.

This analytical result corresponds well with our empirical findings. Proposition 3 and Corollary 1 imply that reserve management policy has a unique role, which capital controls cannot substitute. This contrasts with earlier studies on reserve accumulation such as Arce et al. (Reference Arce, Bengui and Bianchi2019) and Davis et al. (Reference Davis, Fujiwara, Huang and Wang2021) in which the prudential role of reserves can be fully replaced by capital controls. As IMF (2012) documents, however, reserve accumulation is often used with capital controls in many EMEs.Footnote ⁴⁷ Our theoretical findings suggest that EMEs receiving large direct investment flows driven by global factors may choose to accumulate reserves while restricting private outflows, especially when policymakers are concerned about their low financial development.Footnote ⁴⁸ Proposition 3 and Corollary 1 show that this policy combination can be optimal when direct investment inflows are large or when outflow frictions are more severe.Footnote ⁴⁹