Attracting private capital for development: Are poorer countries less efficient?

According to common measures of private capital mobilization, such as the shares of foreign direct and portfolio investment in GDP, many low-income countries perform poorly in attracting private capital flows. However, these indicators do not account for differences in economic characteristics across countries, and thus cannot provide insights on countries’ performance relative to their potential levels of private capital flows as determined by their domestic economic structure and constraints. This paper addresses this gap by using nonparametric data envelopment analysis (DEA) to empirically calculate the efficient frontier for private capital mobilization as a function of countries’ domestic enabling environment, and then assess each country’s performance relative to that of other countries featuring similar domestic conditions. Our results reveal that many low-income countries, particularly in Africa and South Asia, which do not rank high according to achieved levels of private capital flows, are in fact performing on or very close to the efficient frontier. This indicates that these countries are good performers given the limited resources available to them. Tracking the performance of countries and regions over time, we furthermore find that sub-Saharan Africa experienced the strongest increases in DEA efficiency scores between 2007 and 2018, indicating that various countries in this region were catching up with the frontier.


Introduction
Mobilizing private capital is increasingly being recognized as a key factor for achieving international development goals. While technological solutions to many challenges faced by developing countries are often readily available, estimates of the United Nations suggest that there is a gap of USD 2-3 trillion per year between the amount of capital needed to achieve the Sustainable Development Goals (SDGs) by 2030 and the financial resources currently available from government and development aid (UNCTAD 2014). 1 In response to this need, development banks and organizations are increasingly using their funds to mobilize and leverage private capital (AfDB et al. 2019;World Bank 2020).
Despite the prominence of such efforts on the international development agenda, the empirical evidence that allows policymakers to quantify and compare countries' achievements in mobilizing private capital, map achieved progress against stated goals, and guide decision making, is currently very limited. Specifically, indicators commonly used to capture differences in countries' performance in attracting private capital are often based exclusively on achieved outcomes (e.g., attracted foreign direct and portfolio investment relative to GDP) which do not account for the different economic conditions and constraints faced by different countries. Given that poorer countries often feature less-favorable infrastructure and economic conditions for generating private capital flows, it is not surprising that many low-income countries are found to perform poorly in attracting private capital according to these indicators (see the results presented in Sect. 4, Fig. 1). It is important to note, however, that the results obtained based on these indicators provide little insights on how efficient countries are in mobilizing private capital, i.e., how well they are performing relative to their potential levels of private capital flows as determined by their domestic economic structure and constraints.
This paper addresses this gap by using a non-parametric frontier analysis approach based on data envelopment analysis (DEA) to estimate countries' performance in mobilizing private capital relative to their enabling domestic environment. Our results reveal that many low-income countries, particularly in Africa and South Asia, which do not rank high according to achieved levels of private capital flows relative to GDP are in fact performing on or very close to the efficient frontier, indicating that these countries are good performers given the resources available to them. These results thus complement the insights of existing studies by providing a different perspective on countries' achievements than those obtained from indicators which only capture achieved outcomes. In addition, the frontier analysis allows us to derive quantitative estimates of the untapped mobilization potential in each country, i.e., the magnitude by which countries should in principle be able to increase their private capital flows given their currently available economic resources and conditions. Tracking the performance of countries and regions over time, we find that sub-Saharan Africa experienced the strongest increases in DEA efficiency scores among all regions between 2007 and 2018, indicating that various countries in this region were catching up with the frontier.
DEA is a widely used, non-parametric method for estimating production possibility frontiers based on linear programming (some methodological background is provided below; for more details, see Charnes et al. 1978 andCoelli et al. 2005). Our application of DEA is tailored to the context of private capital mobilization and involves three steps. First, we quantify achieved levels of aggregate private capital flows for 135 countries covering all income groups and geographical regions, focusing on foreign direct investment (FDI), portfolio equity investment, and private sector borrowing. Second, we use DEA to estimate the empirical production possibility frontier for aggregate private capital flows as a function of countries' domestic economic enabling environment, which is proxied by a composite index capturing various economic factors and constraints. The selection of the variables included in this index is based on a structured literature review on the factors that are commonly identified as being correlated with countries' achieved private capital flows. Third, we calculate countries' performance in attracting private capital relative to the estimated frontier. This allows us to identify those countries that generate relatively high levels of private capital compared to other countries facing similar economic conditions and constraints, and those countries that apparently fall short of their potential. This paper is mainly linked to two bodies of literature. First, our analysis both builds on and expands existing approaches to assess countries' performance in mobilizing private capital flows. Most studies in this literature use regression-based methods to identify factors that are correlated with indicators of countries' achieved magnitudes of private capital flows, and estimate the effects of changes in these factors on achieved outcomes (a structured review of this literature is presented in Appendix A). We build on the findings of these studies to inform our selection of variables included as input factors in the DEA. At the same time, we make several contributions to this literature. In particular, by using a non-parametric frontier approach to estimate countries' relative performance in attracting private capital, we add to the range of methods that has been used in this literature (to the best of our knowledge, this is the first paper that applies DEA in the context of private capital mobilization). We argue that the approach proposed in this paper can complement the insights obtained from existing studies in the following ways. First, DEA has the feature that it involves fewer assumptions about the structure of the data than parametric methods such as regression-based analyses. Consequently, the results generated using DEA tend to be easier to interpret and are not subject to the same econometric challenges that studies based on regression analysis typically face. 2 Another important feature of DEA is that the estimated efficiency scores for a given unit (e.g., country) are based on the performance of a subset of efficient units in the sample with similar enabling factors as the considered unit. In contrast, regressionbased approaches rely on comparisons relative to the average performance across all units in the sample. If the considered units are very heterogeneous (as is the case when analyzing countries from different parts of the world with different economic structures and stages of development), then DEA has the advantage that the estimates for any given country are not determined by other countries with fundamentally different characteristics and prospects, but only by those countries that feature comparable values of the included enabling factors.
Second, we add to the growing number of empirical studies in macroeconomics applying non-parametric frontier analysis. Existing studies in this literature focus on estimating efficiency of public spending (Gupta and Verhoeven 2001;Clements 2002;Afonso et al. 2005;Herrera and Pang 2005), national transportation and commerce systems (Rashidi and Cullinane 2019; Wang et al. 2020), regional economic integration (Naeher 2015;Naeher and Narayanan 2020), domestic revenues (Bogetić et al. 2021), and energy efficiency (Li et al. 2021).
By expanding the application of DEA to the context of private capital mobilization, our analysis generates new results that are useful for guiding policymaking in the international investment and development context. Specifically, the efficiency scores for individual countries that we obtain through DEA can help to inform decisions about how to allocate limited development funds to best leverage private capital by targeting those countries or regions with the largest untapped potential for generating additional private capital flows. These results should be seen as complementing the insights obtained from existing cross-country comparisons of achieved levels of private capital flows which do not account for differences in enabling economic factors across countries.
The remainder of the paper is structured as follows. Section 2 provides a brief introduction to data envelopment analysis and explains how the method is used to estimate countries' performance in attracting private capital flows relative to their domestic enabling environment. Section 3 describes the variables and data sources used in the empirical analysis. Section 4 presents the results. Section 5 discusses the robustness of the results to alternative specifications. Section 6 concludes.

Data envelopment analysis
DEA is a non-parametric method for estimating efficiency relative to an empirically determined production possibility frontier, which has been applied in a wide range of fields in economics. 3 In its standard form applied here, DEA assumes the existence of a convex production possibility set and estimates the frontier as the maximum attainable level of output for a given level of input. Efficiency is measured as the distance between an observed input-output combination and the corresponding point on the estimated frontier. Intuitively, units that produce more output with the same amount of input (or units that need less input for the same amount of output) are considered more efficient than others. The efficiency scores obtained from DEA are normalized to range between 0 and 1, where units located on the frontier are assigned the maximum value of 1.
In the context of private capital mobilization, DEA can be used to assess countries' achievements in attracting private capital relative to the quality of their domestic enabling environment (i.e., the economic conditions and constraints identified in the literature that determine each country's potential capital flows). For this purpose, we apply DEA to calculate the empirical production possibility frontier for private capital flows, and then rate the performance of each country relative to the frontier. Overall, this provides an estimate of the capital flows that each country should potentially be able to achieve based on what countries with similar characteristics and enabling factors are achieving. The obtained efficiency scores can be interpreted as follows. Scores close to one indicate that a country is attracting relatively large amounts of private capital given its domestic environment, i.e., the country is "efficient" in attracting private capital. DEA scores well below one indicate inefficiency or "untapped potential." For example, an efficiency score of 0.5 indicates that a country is currently only generating half of the capital flows that it should theoretically be able to, based on its performance relative to the estimated frontier. In line with the obtained efficiency scores, untapped capital mobilization potential is defined as the distance between a country's current level of private capital flows and the theoretically possible level as captured by the estimated frontier. 4 It should be noted that the estimates obtained from DEA are based exclusively on currently available resources and conditions, not on potential future developments. Our analysis thus does not seek to forecast capital flows under possible scenarios of future changes in political or economic conditions. Instead, the analysis compares levels of private capital flows across countries at a given point in time and identifies those countries that, relative to others with similar domestic conditions, are currently performing below the level which they should potentially be able to. Furthermore, it should be noted that the obtained estimates relate only to the considered measure of aggregate private capital flows and, as such, do not provide direct implications for potential welfare gains or growth effects associated with attracting more private capital.

Aggregate private capital flows and enabling environment
In the economic literature, the factors determining private capital flows across countries are usually divided into external "push" factors and domestic "pull" factors (Calvo et al. 1993;Fernandez-Arias 1996;Hannan 2018). 5 Push factors are supplyside factors that affect the supply of global liquidity and investors' willingness to increase exposure to higher-risk investments. For example, push factors include variables like global risk aversion, global commodity prices, and interest rates in the USA or other advanced economies (IMF 2016;Reinhart et al. 2016). Pull factors are domestic characteristics that attract foreign investors to a particular country, such as local macroeconomic conditions, regulations, governance, and market imperfections (Fernandez-Arias and Montiel 1996;Ghosh et al. 2014).
Since our analysis is concerned with estimating differences across countries rather than explaining developments in the overall size of global capital flows, we focus on domestic (pull) factors. There are various empirical indicators that have been identified in the literature as being important in this context. While we seek to account for all relevant factors, it would go beyond the scope of this study to analyze each of the factors separately. We therefore construct a composite measure of pull factors which we use to approximate the overall investment climate and enabling environment for private capital mobilization in each country. In aggregating the information from different indicators into a single composite measure we apply standard normalization and weighting methods which are also used in the construction of other well-known composite indices, such as the Doing Business Index and the Unit Nation's Human Development Index, and which are in line with the guidelines of constructing composite indices laid out by the OECD (2008). The following provides a description of the methodology underlying the construction of our composite measure. Alternative specifications and aggregation schemes are discussed as part of the robustness tests in Sect. 5.
The selection of variables included in our composite measure of the enabling environment is based on a structured literature review (the exact procedure is described in Appendix A). According to the results of this literature review, we construct our measure to capture seven aspects (dimensions) of countries' domestic enabling environment 6 : (i) market-related factors such as capital return and growth potential, (ii) institutional and regulatory quality, (iii) openness to trade, (iv) economic and political stability, (v) infrastructure development, (vi) financial development, and (vii) natural and human resources. Each of these seven dimensions comprises two empirical indicators. For example, dimension II (institutional and regulatory quality) is composed of subindicators II.a (political regime type) and II.b (business regulation environment). There are, of course, many other factors potentially affecting private capital flows than the 14 variables considered here. 7 The constructed composite measure should be thought of as a proxy variable capturing the broader enabling environment for private capital mobilization in each country.
To facilitate aggregation into a single composite measure, all indicators are normalized such that higher values indicate more favorable conditions, and all indicators feature comparable ranges of values. There are several possible methods for rescaling, each featuring its own set of advantages. We apply standard min-max rescaling, which ensures that all normalized variables range between 0 and 1. 8 For country i in the overall sample N , indicator I is normalized using the formula: Since this normalization method is very sensitive to outliers, we winsorize all variables at the 98% level before applying min-max rescaling. This effectively caps the two or three most extreme values in each variable and ensures that the aggregated values are not driven by a few outliers.
The construction of the composite measure involves two steps of aggregation. First, within each dimension, two indicators are combined into one measure for that dimension. Second, the seven dimensions are aggregated into the final measure. At both levels of aggregation, an equal weighting scheme is applied to combine the respective subindicators (alternative weighting schemes, including principal component analysis, are explored as part of the robustness tests in Section 5). The use of equal weights facilitates the interpretation of the results and is in line with many other studies that construct composite indices, including studies with the particular purpose of using these indices in data envelopment analysis (Afonso et al. 2005;Herrera and Pang 2005). Since each dimension enters the composite measure with equal weight, the resulting scores can be interpreted as the average performance of a given country along the considered dimensions of the domestic environment (the same applies to each of the seven dimensions individually across the two respective subindicators).
In the DEA, the composite measure of countries' domestic enabling environment represents the input variable (we therefore also refer to this measure as the DEA input index). Accordingly, the DEA output variable captures countries' aggregate private capital flows. Throughout the analysis, we focus on three types of capital flows, namely FDI, portfolio equity investment, and private sector borrowing (all (1) For example, health-related aspects of human capital (e.g., general health of the labor force) might also constitute a relevant pull factor of private capital flows. However, health indicators are not widely used in the studies found in our structured literature review (see Table 3 in the Appendix). One reason for this may be limited data availability for relevant population health outcomes, especially in low-income settings where vital registration (i.e., systems that record births, deaths, and causes of death) are often weak. 8 The same method is used in the construction of other well-known composite indices, such as the Doing Business Index and the Unit Nation's Human Development Index. expressed relative to a country's GDP). To make the analysis more tractable, we aggregate the information on these three variables into a single composite measure using the same methodology as for the DEA input index (i.e., normalization via min-max rescaling and aggregation using equal weights). The resulting aggregate measure of private capital flows greatly facilitates the computation and interpretation of DEA as it reduces the number of output variables to one and thus allows us to plot the frontier in two-dimensional space. One should think of this aggregate measure of private capital flows as a normalized proxy of the magnitudes of private capital flows relative to GDP in each country.  Table 1 lists the 14 variables used to construct the composite measure of the domestic enabling environment (DEA input index). Each of the seven dimensions of the enabling environment is based on two empirical indicators which were selected based on the structured literature review described in Appendix A. In line with other studies (Edwards 1990;Asiedu 2002), we use the inverse of per-capita GDP as a proxy for capital return. This approach is based on the idea that the return on capital is equal to the marginal product of capital, which implies that, all other factors being equal, investments in countries with higher per capita incomes will tend to yield a lower return, and therefore real GDP per capita should be inversely related to foreign investment. In addition, the inverse relationship may also reflect a perception that investment risk rises as per capita GDP declines, and thus investors tend to require higher returns to offset the perceived greater risk. Since discussing the intuition behind all the indicators included in the construction of the DEA input index it would go beyond the scope of this study, we refer the reader to the detailed reviews provided in Chakrabarti (2001) and Asiedu (2002), as well as to the other studies listed in Table 3 (in the Appendix).

Data and variables
The sample consists of all countries for which sufficient data on the variables listed in Table 1 are available. This results in a total of 135 countries, comprising 26  According to the results in A, countries with lower income levels tend to mobilize less private capital relative to GDP than richer countries. Considering the disaggregated values for the three included types of capital flows furthermore shows that these differences are mainly driven by differences in private sector borrowing and (to a lesser extent) portfolio equity. 9 Figure 1B shows that private capital flows also vary widely by geographical region. Especially the countries in South Asia and sub-Saharan Africa (which together comprise 23 of the 26 LICs in our sample) are found to generate less private capital than countries in other regions, on average. At the same time, countries with lower income levels also tend to feature less favorable economic conditions for generating private capital flows. This can be seen in Fig. 2 The finding that poorer countries tend to feature less-favorable economic conditions for generating private capital flows also holds for individual dimensions of the domestic enabling environment. In particular, Fig. 2 shows that except for Dimension I (market-related factors, i.e., capital return and growth potential) of the DEA input index there is a clear positive relationship between income levels and enabling factors, with HICs featuring the most favorable conditions across all dimensions except Dimension I. Based on the normalized values shown in Fig. 2, institutions (Dimension II) and economic and political stability (Dimensions IV) play the largest roles in determining the quality of countries' domestic enabling environment.
The fact that countries with lower levels of private capital mobilization also tend to feature less favorable economic conditions for generating private capital suggests    Table 1 that these countries are not necessarily less efficient in mobilizing private capital given the limited resources available to them. In order to examine whether (and to what extent) this is indeed the case, we now turn to the results of the frontier analysis.

Frontier Analysis
Based on the input and output variables described in Sect. 2, the frontier estimated through DEA captures the potential level of private capital flows as a function of the quality of a country's domestic enabling environment. Importantly, the point on the frontier that is used to assess the performance of a given country is determined by a subset of countries in the sample with similar enabling factors as the considered unit (recall the discussion in Sect. 1). DEA thus allows us to identify those countries that, relative to other countries facing similar domestic economic conditions, are achieving relatively high capital flows, and those countries that are apparently falling short of their potential. Figure 3 plots aggregate private capital flows over the composite measure of countries' domestic enabling environment for the periods 2007-2011 and 2015-2018, and shows the respective production possibility frontier (dotted line) for private capital mobilization. For the considered sample of 135 countries, the frontier in 2015-2018 turns out to be determined by three countries. At the lower end of the DEA input index, the frontier is defined by Yemen, which during this time period featured the weakest domestic environment among all included countries. In the middle of the sample, the frontier is defined by South Africa, which outperforms many countries with comparable domestic environments. At the upper end, the frontier is defined by the Netherlands, which features both the highest level of private capital flows and one of the strongest domestic environments in the sample. The efficiency scores associated with the estimated frontier in 2015-2018 range from 0.39 (Mongolia) to 1 (the three countries located on the frontier), with an average score of 0.62. This suggests that the countries in our sample achieved about 62% of their  Table 1 potential levels of private capital flows in the period 2015-2018, on average (recall that efficiency scores close to one indicate that a country is generating relatively large amounts of private capital as a percentage of GDP given its domestic environment, whereas smaller scores indicate inefficiencies in private capital mobilization). Most countries feature efficiency scores between 0.5 and 0.8, suggesting that these countries achieved between 50 and 80% of their potential levels of private capital flows in the period 2015-2018.
Notice from Fig. 3 Figure 4 shows box plots of the DEA efficiency scores obtained across income groups (Fig. 4A) and regions (Fig. 4B). Interestingly, these results indicate that countries with low or high performance are not concentrated in a particular income group or region. Rather, the different groupings feature strongly overlapping ranges of scores, and the median scores are relatively similar across income groups and regions (except for EAP, which features a somewhat higher median score than other regions). In addition, these results imply that when differences in economic conditions across countries are taken into account, many LICs are, in fact, more efficient in generating revenues than countries from higher income groups. This shows that accounting for differences in economic conditions via DEA leads to additional insights about countries' performance in mobilizing private capital. In particular, a simple comparison of mobilized capital flows relative to GDP suggests that LICs perform worse than countries in higher income groups (recall the results in Fig. 1).  Table 1 In contrast, the DEA results reveal that there are many LICs that, in fact, perform better than countries from higher income groups given the economic resources and conditions available to them. An example is Ethiopia, a LIC, which generates much less private capital relative to GDP (captured by a normalized private capital measure of 0.37 in 2015-2018) than, for example, Montenegro (an UMIC with normalized private capital flows of 0.50). Despite its lower level of achieved private capital flows, Ethiopia is achieving 81% of its potential capital flows according to the estimated frontier, more than Montenegro (66%). The underlying reason is that Montenegro features a much more favorable domestic environment for generating private capital than Ethiopia, as captured by the large gap in the DEA input index across these two countries (0.55 in Montenegro and 0.33 in Ethiopia). From a policy perspective, the finding that countries with large untapped potential for private capital mobilization are spread across all income groups and geographical regions also suggests that targeting development efforts towards countries with low (or high) performance in generating private capital flows would need to take into account underlying economic structures and not merely countries' broad income group or geographic region. 11 Importantly, our analysis also generates a rich set of results on the relative performance of individual countries on each of the seven dimensions of the enabling environment. For example, the results indicate that Mongolia (the country with the largest untapped potential in 2015-2018) performed well on stability (0.84), institutional and regulatory quality (0.81), and natural and human resources (0.79). At the same time, Mongolia performed less well on market-related factors (0.48) and economic and political stability (0.52), and relatively poorly on Infrastructure (0.21) and financial development (0.11). While a comprehensive discussion of the results for all countries would go beyond the scope of this paper, this example demonstrates that the analysis can be helpful in identifying the dimensions in which each country features the strongest deficits compared to other countries, and thus where policy action might be most critical.
Trends over time Our data also allow us to track countries' relative performance in attracting private capital flows over time, by calculating the frontier separately for each of the three 4-year periods between 2007 and 2018 (the frontier for 2007-2010 is shown in the left graph in Fig. 3). Table 2 reports the results by income group and region. As shown in the last column, LICs achieved significantly higher DEA scores in the period 2015-2018 than in 2007-2010, on average, whereas the DEA scores for all other income groups increased only marginally. Consistent with this finding, 11 One may also be interested in the factors explaining the variation in DEA efficiency scores across countries, i.e., why some countries attract higher private capital flows than other countries with comparable economic conditions. When we estimate cross-country panel regressions (including country fixed effects) for the same three 4-year periods as considered in the DEA, we find that the level of corruption is robustly correlated with higher DEA efficiency scores, while there are no significant results for tax rates, technological readiness, and foreign aid inflows. However, given the observational nature of our data, we stress that more research is needed to obtain reliable conclusions regarding the driving forces behind differences in countries' relative performance in attracting private capital flows.  the region with the largest increase in DEA scores is sub-Saharan Africa, which suggests that many (low-income) countries in this region managed to catch up with the frontier. When looking at changes in relative performance of individual countries, then Yemen (+ 0.46), Angola (+ 0.45), and Mozambique (+ 0.36) feature the strongest increases in DEA scores between 2007-2010 and 2015-2018. In contrast, the countries with the largest declines in DEA scores are Mongolia (− 0.51), Montenegro (− 0.34), and the Seychelles (− 0.33). More generally, this shows that it is not the case that all countries tend to move in the same direction with little changes in their relative positions to each other. Rather, some countries appear to catch up to the frontier over time while others fall behind. Note that there are three possible factors behind an increase in the DEA score of any given country: an increase in the country's private capital flows, a worsening of the country's domestic enabling environment (corresponding to a decline in the DEA input index), and changes in the frontier itself due to changes in the performance of other countries. A good example of the second case is Yemen, which increased its DEA score from 0. Together, this suggest that despite a significant deterioration in its domestic environment Yemen managed to keep capital flows at a similar level, and consequently the DEA scores of Yemen increased. However, the case of Yemen seems to be an exception. For all other LICs with increases in DEA scores, these increases appear to be due to improvements in private capital flows or changes in the frontier rather than declines in the quality of the domestic environment. 12 As can also be seen in Table 2, EAP and ECA are the only regions with a negative trend in DEA scores over time, despite increases in their measure of private capital flows. The declines in the DEA scores for these two regions are thus either driven by the improvements in their domestic environment between 2007 and 2018 or by changes in the frontier (or a combination of both). For all other regions, both the DEA scores and the normalized measure of private capital flows as well as the proxy of the domestic environment show positive trends over time.
It should be noted that the frontier analysis is designed to track countries' relative performance within the sample (i.e., in comparison to other countries during the same time period) rather than countries' absolute performance over time. This means that the DEA scores (as well as the values of the input index) cannot be directly compared across time. Instead, similar scores in two periods indicate that the relative performance of a country within the sample remained about the same. 13

Robustness
The construction of the composite measures of private capital flows and domestic enabling environment involve several decisions about the applied aggregation methodology which may affect our results. This section explores the robustness of our findings to alternative specifications and different weighting schemes.
Our measure of private capital flows (DEA output variable) aggregates information on three types of capital flows (FDI, portfolio equity, and private sector borrowing). For the baseline measure used in the analysis above each of these variables carries an equal weight. We test the robustness of our results to three alternative weighting schemes, where each scheme assigns double weight to one particular type of capital flow (this approach mirrors the robustness checks with respect to weighting in Afonso et al. 2005). For example, one alternative specification assigns a weight of 1/2 to FDI, while the indicators for the other two capital flows are assigned a weight of 1/4 each. The other two alternative specifications assign a weight of 1/2 to portfolio equity and to private sector borrowing, and 1/4 to the other two types of capital, respectively. To assess the similarity of the resulting outcomes with our baseline specification, we calculate two sets of correlation coefficients. The first set consists of standard Pearson correlation coefficients for continuous variables. These are used to test the similarity between the resulting values under alternative weighting schemes with those of the baseline measure. Second, we calculate Spearman correlation coefficients which measure the similarity between discrete rankings. The Spearman correlation coefficient ranges inside the interval [− 1,1] and takes the value 1 if the two rankings are identical whereas values smaller than 1 indicate less agreement (a value of 0 indicates that the rankings are completely independent and a value of -1 indicates that one ranking is the reverse of the other). These are used to assess the similarity between the resulting rankings of countries rather than the associated absolute values. In total, we calculate 18 correlation coefficients: two coefficients for each of the three weighting specifications in each of the three time periods. In all these cases, the correlation between our baseline measure and a given alternative specification is at least 90% and is always significant at the 1% significance level. This suggests that our main results are robust against moderate changes in the underlying weighting scheme for our measure of private capital flows.
The measure of the domestic enabling environment (DEA input variable) aggregates information on 14 indicators spanning seven dimensions (see Table 1). With so many variables involved, it is unlikely that alternative weighting schemes that assign double weights on one particular indicator or dimension will have a relevant effect on the final outcome. Instead, we test the robustness of the results to alternative specifications that drop one of the dimensions entirely. For this purpose, we construct seven alternative composite indices for each of the three time periods, in each case dropping one of the seven dimensions included in the baseline measure. In addition, we construct another alternative measure based on principal component analysis (PCA), where the weights for each dimension are based on the results of the PCA. In total, we construct 24 alternative specifications across the three time periods, leading to 48 correlation coefficients. Similar to above, the Pearson correlation coefficients between our baseline measure of the domestic environment and any given alternative specification is never below 90% and is always significant at the 1% significance level. The same holds for the Spearman correlation coefficients when comparing the rankings of countries resulting from the alternative specifications with the ranking associated with our baseline measure. In particular, this suggests that our results are not driven by a single factor or dimension in the composite measure of the domestic enabling environment.
Despite the apparent robustness of the results to moderate changes in the specifications and procedures used to construct the variables included in the DEA, we stress that all our quantitative results should be interpreted with caution, as data quality for the used indicators is limited. In particular, it should be noted that the variables used in the DEA provide only rough approximations of the aggregate private capital flows and domestic enabling environment in each country, and thus the precision of the efficiency score estimates is limited. We therefore suggest that the reported estimates should be seen as suggestive evidence of the relative performance and magnitudes of untapped potential in attracting private capital flows, and stress that more empirical research to investigate possibilities for scaling up private capital mobilization and guide policy decisions in this context is warranted.

Conclusion
Allocating scarce development funds in optimal ways to leverage private capital requires policymakers to know not only the achieved levels of private capital flows in each country but also which countries are already performing close to their limit, and which countries still feature large untapped potential for further increasing private capital flows. This paper proposes the use of non-parametric data envelopment analysis to estimate the empirical production possibility frontier for private capital mobilization as a function of countries' domestic enabling environment, and quantify each country's performance relative to its estimated potential.
Our analysis confirms the findings of previous studies (e.g., those listed in Table 3) that richer countries tend to feature more favorable conditions for attracting private capital flows. Many of these countries also perform well relative to their good conditions, e.g., the Netherlands (a HIC) and South Africa (an UMIC) are both estimated to operate on the efficiency frontier for private capital mobilization. At the same time, our results also reveal that many low-income countries, particularly in Africa and South Asia, which do not rank high according to achieved levels of private capital flows relative to GDP, are in fact performing on or very close to the frontier, which indicates that these countries are good performers given the resources available to them. This suggests that commonly used measures of achieved levels of private capital mobilization, such as the shares of foreign direct and portfolio investment in GDP, are poor indicators of the degree of efficiency with which countries manage to attract private capital flows given their domestic conditions and constraints.
The results of our DEA suggest that the levels of private capital flows in the 135 countries in our sample were at 62% of the estimated potential, on average, in the period 2015-2018. When tracking the performance of countries and regions over time, we find that most regions show positive trends in attracting private capital relative to their enabling environment. Sub-Saharan Africa experienced the strongest increase in efficiency scores between 2007 and 2018, indicating that various countries in this region are catching up with the frontier. At the same time, this also implies that it will become more difficult for these countries to further increase private capital flows unless there are significant improvements in their domestic enabling conditions. From a policy perspective, the finding that countries with large untapped potential for private capital mobilization are spread across all income groups and geographical regions suggests that targeting development efforts towards countries with low (or high) performance in generating private capital flows would need to take into account underlying economic structures and not merely countries' broad income group or geographic region. The proposed DEA approach also generates a rich set of results for individual countries, including the relative performance of countries on each of the seven dimensions of the enabling environment. For example, these results may be helpful in guiding reform priorities aimed at increasing countries' private capital flows through improvements in their enabling environments, by identifying the dimensions in which each country features the strongest deficits compared to other countries. At the same time, we stress that more research is needed to obtain reliable conclusions regarding the performance (and determinants) of countries' private capital mobilization efforts, and guide policy decisions. The non-parametric frontier approach proposed in this paper may provide a useful point of departure for future work in this direction. included in this composite measure is based on a structured literature review using the following procedure: 1. Two independent keyword searches are performed using Google Scholar (GS) and Web of Science (WoS) with the following parameters: • Keywords: "determinants capital flows developing countries" • Timespan: since 2000 • Additional settings: only articles (no patents, etc.); only economics database (WoS) • Sorting of results: by relevance (GS); by times cited (WoS) 2. The first 20 articles from each search are reviewed in detail and further considered if they provide information about (i) FDI, portfolio flows, or private sector borrowing (e.g., excluding articles focused on remittances), (ii) empirical determinants (not purely theoretical), and (iii) domestic pull factors in the host country (not focused exclusively on foreign push factors). There are 16 articles which meet these criteria. Table 3 provides a list of these articles and shows which factors are considered in each study to explain private capital flows. The roman numerals in Table 3 indicate the corresponding dimension of each factor in the DEA input index (see Table 1) and the signs in parentheses indicate the estimated direction of the relationship between each factor and private capital flows, where ( +) indicates a positive relationship, ( −) indicates a negative relationship, and (0) indicates a statistically insignificant relationship. 3. Finally, the variables used in the construction of the DEA input index are selected to match the factors that are found to be significantly related to private capital flows in a majority of the articles listed in Table 3, conditional on data availability for our sample and covered time period.   Authors (