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---

### Data Definitions and Sources
- Dependent variable: external liabilities and their subcomponents drawn from the “External Wealth of Nations” database by Lane and Milesi-Ferretti (2018), covering 212 economies for the period 1970-2015.
- Total equity: defined as the sum of FDI and portfolio equity relative to total international liabilities.
- Potential explanatory variables:
  - Size of the economy: total GDP in trillions of USD at constant 2010 prices.
  - Level of economic development: GDP per capita in thousands of USD at constant 2010 prices.
  - Trade openness: sum of imports and exports over GDP.
  - Importance of natural resources: share of exports of fuels, metals, and ores as a ratio of GDP.
  - Human capital: an index based on years of schooling and returns to education.
  - Financial development: the overall index from Svirydzenka (2016).
  - Institutional quality: the simple average of six institutional indicators drawn from Kaufmann, Kraay, and Mastruzzi (2010).
- Measures of income inequality:
  - Gini coefficient of disposable income from the Standardized World Income Inequality Database (SWIID) by Solt (2016).
  - Top 10 percent income share and Bottom 20 percent income share from the World Inequality Database.

### Sample construction and exclusions
- Baseline sample: 119 countries (25 advanced and 94 emerging or developing) with all key explanatory variables available for at least one year between 1996 and 2015 for each country.
- Non-high income country sample: 94 observations (developing and emerging economies).
- Offshore financial centers removed: 28 countries excluded due to prevalence of Phantom FDI and tax-minimization driven FDI composition.
- Rationale: final sample countries unlikely hosts to a large share of Phantom FDI since their ratio of total FDI to GDP is not very large and none of the usual suspects of Phantom FDI destinations identified in the literature are part of the sample.

### Empirical specification and identification
- Regression strategy: regress time-series mean of the dependent variable on time-series means of explanatory variables (between estimator).
- Nature of analysis: correlational; no causal claim.
- Robustness checks:
  - Results unchanged if GDP converted to international dollars using purchasing power parity rates.
  - Results robust to alternative measures/proxies of financial development such as private credit to GDP.
  - Robust regressions in Stata produce unchanged results, suggesting absence of influential outliers.

### Key descriptive statistics (averages 1996-2015)
- Sample sizes:
  - Whole sample: 119 observations.
  - Non-high income countries: 94 observations.
- Whole sample (Minimum, Maximum, Mean, Median, Standard deviation):
  - Total equity (equity share in ext. liabilities): 0.07, 0.69, 0.38, 0.37, 0.14
  - Institutional quality index: -1.56, 1.86, -0.06, -0.28, 0.84
  - GDP (constant US$ trillions): 0.001, 4.000, 0.44, 0.04, 1.49
  - GDP p.c. (constant US$ thousands): 0.23, 85.47, 11.43, 3.84, 16.65
  - Financial development index: 0.05, 0.87, 0.30, 0.22, 0.23
  - Natural resources: 0.00, 0.98, 0.26, 0.14, 0.28
  - Openness: 0.10, 1.82, 0.77, 0.69, 0.33
  - Human capital: 1.12, 3.63, 2.39, 2.34, 0.70
  - Net Gini: 23.88, 57.85, 39.39, 39.38, 7.95
  - Top10 Income Share: 28.04, 69.56, 45.98, 47.93, 9.04
  - Bottom20 Income Share: 0.35, 3.88, 1.86, 1.82, 0.73
- Non-high income countries (Minimum, Maximum, Mean, Median, Standard deviation):
  - Total equity (equity share in ext. liabilities): 0.07, 0.69, 0.38, 0.38, 0.15
  - Institutional quality index: -1.56, 1.17, -0.40, -0.42, 0.55
  - GDP (constant US$ trillions): 0.00, 4.43, 0.19, 0.03, 0.54
  - GDP p.c. (constant US$ thousands): 0.23, 65.95, 5.23, 2.56, 9.52
  - Financial development index: 0.05, 0.61, 0.22, 0.18, 0.14
  - Natural resources: 0.00, 0.98, 0.29, 0.17, 0.29
  - Openness: 0.10, 1.82, 0.76, 0.68, 0.34
  - Human capital: 1.12, 3.21, 2.16, 2.16, 0.59
  - Net Gini: 27.06, 57.85, 41.92, 41.77, 6.70
  - Top10 Income Share: 31.78, 69.56, 48.95, 50.06, 7.39
  - Bottom20 Income Share: 0.35, 3.46, 1.64, 1.62, 0.59

---

### Set-up and Equilibrium (model summary)
- Preferences and consumption:
  - Consumption aggregator: C = (C_T)^γ (C_N)^{1−γ}.
  - Traded good price normalized to one; non-traded goods are a CES aggregate C_N = [∫_0^μ c_N(i)^{ε−1} di]^{ε/(ε−1)} with ε > 1, μ endogenous.
  - Demand for variety i: c_N(i) = (1−γ) P C (p_N(i))^{−ε} (P_N)^{ε−1}.
- Production and pricing:
  - Traded and non-traded goods linear in labor with productivities a_T and a_N; wage w = a_T.
  - Non-traded firms monopolistic competition; marginal cost MC_N(i) = a_T / a_N.
  - Price by non-traded firm: p_N(i) = (1/α) a_T / a_N with α ≡ (ε−1)/ε < 1; markup 1/α > 1.
  - Demand simplifies to c_N(i) = (1−γ) PC α a_N / (μ a_T).
- Entry, fixed costs, and ownership:
  - Domestic setup cost κ; MNC setup cost κ_F > κ.
  - Continuum of individuals mass one with wealth endowment v(j) ~ F(v) on [v_min, v_max] and v_max < κ.
  - Agents can rent endowment at world interest rate r or enter as entrepreneurs if v(j) ≥ v_crit.
  - Entrepreneurial profit: π_N(j) = (1−γ)(1−α) PC / μ − [κ − v(j)] r.
- Foreign entry and equilibrium mass of firms:
  - Free-entry for MNCs: (1−α)(1−γ) PC / μ = r κ_F → μ = (1−α)(1−γ) PC / (r κ_F).
  - Labor market: L_T + L_N = L, with L = F(v_crit).
  - Labor demand per non-traded firm: L_N(i) = c_N(i) / a_N = α/(1−α) κ_F / r · a_T.
- Mass of foreign non-traded firms λ:
  - λ = μ − [1 − F(v_crit)] = (1−α)(1−γ) PC / (κ_F r) − [1 − F(v_crit)].
  - Raising v_crit reduces domestic entrepreneurs but the open-slot effect dominates, increasing λ.
- Individual and aggregate incomes:
  - Worker income for v(j) < v_crit: I_w(j) = a_T + r v(j).
  - Entrepreneur income for v(j) ≥ v_crit: I_e(j) = r(κ_F − κ) + r v(j).
  - Entrepreneurship preferred when (κ_F − κ) r > a_T (assumed satisfied).
  - Aggregate income I with PC = I: I = r v̄ + a_T F(v_crit) + r(κ_F − κ) [1 − F(v_crit)].
- Inequality amplification:
  - Ex-ante wealth inequality v(j) becomes ex-post income inequality because richer individuals earn higher r v(j); entrepreneurial rent magnifies inequality.
- Comparative-static results (selected equations):
  - Top x% income share S_H_x increases in v_crit (see equation (16)).
  - Bottom y% income share S_L_y decreases in v_crit (see equation (17)).
  - Closed-form mass of MNCs λ given by equation (18); effect of v_crit on λ is positive.
  - Equity share ρ in external liabilities: ρ = λ κ_F / [ λ κ_F + ∫_{v_crit}^{v_max} (κ − v) f(v) dv ] and ρ increases in v_crit (equation (19)).
- Mechanism summary:
  - Entry barriers ↑ → Number of entrepreneurs ↓ → (i) MNCs ↑, (ii) Inequality ↑, (iii) Borrowing ↓ → Equity share ↑.
  - Income inequality and equity share in external liabilities positively linked because both driven by entry barriers affecting entrepreneurial activity.

---

### Empirical findings: Inequality, Entry Barriers, and Equity Share (summary of Sections 3.2 and 5.2)
- Baseline replication (updated Faria and Mauro (2009) results):
  - Institutional quality, abundance of natural resources, and openness are positively and significantly associated with the share of total equity in external liabilities.
  - Size of the economy, human capital, and financial development are positively associated with total equity, though not always significantly.
  - GDP p.c. is significantly negatively related to the equity share in total liabilities.
- Inclusion of inequality measures:
  - Net Gini and Top 10 income share: positive relationships with the equity share.
  - Bottom 20 income share: negative relationship with the equity share.
  - Inclusion of inequality variables increases explanatory power by up to ten percentage points in R-squared.
  - Economic magnitude example: a country at the 75th percentile of the Gini index would ceteris paribus exhibit an equity share 7.5 pp larger than a country at the 25th percentile; this corresponds to about one quarter of the mean equity share in the sample.
- Non-high income country sample:
  - Economic size significantly positively associated with total equity.
  - Signs and magnitudes of coefficients largely unchanged compared to whole sample.
  - Inequality measures remain statistically significant except Top10 income share in one specification.
- Robustness:
  - Robust regressions yield unchanged results, indicating no contamination by outliers.

### Empirical approach testing entry barriers (Section 5.2)
- Added variable: World Bank “Starting a Business” score (Doing Business).
- Time-series country-means used for years 2011-2015; Benin, Cˆote d’Ivoire, and Togo excluded for implausible 2015 scores.
- Robustness: relationship also checked for year 2015 cross-section.

### Main empirical results (averages 2011-2015; Table 4)
- Sample size: Observations = 111.
- Adjusted R-squared values reported for columns (1)–(8): 0.316, 0.334, 0.400, 0.416, 0.263, 0.292, 0.384, 0.406.
- Starting a Business Score:
  - Coefficient = -0.003* or -0.003** across specifications with standard error (0.001).
- Top10 Income Share:
  - Coefficients = 0.006***, 0.005***, 0.003**, 0.003* with standard errors (0.002) where reported.
- Bottom20 Income Share:
  - Coefficients = -0.044*, -0.036, -0.027, -0.020 with standard errors (0.023), (0.023), (0.022), (0.022).
- GDP p.c.:
  - Coefficients = -0.006***, -0.006***, -0.005***, -0.005***, -0.006***, -0.007***, -0.005***, -0.006*** with standard errors (0.002) or (0.001).
- Natural Resources:
  - Coefficients = 0.179***, 0.182***, 0.211***, 0.214***, 0.200***, 0.204***, 0.221***, 0.224*** (standard errors ~ (0.064) to (0.055)).
- Openness:
  - Coefficients = 0.116***, 0.113***, 0.144***, 0.140***, 0.122***, 0.117***, 0.147***, 0.142*** (standard errors ~ (0.040) to (0.039)).
- Financial development and Institutional Quality: mixed significance across specifications.

### Main empirical results (year 2015; Table 5)
- Sample size: Observations = 96.
- R-squared values for columns (1)–(8): 0.209, 0.235, 0.294, 0.313, 0.161, 0.199, 0.285, 0.308.
- Starting a Business Score:
  - Coefficients = -0.003**, -0.003*, -0.003**, -0.003** with standard errors (0.001) — negative and statistically significant.
- Top10 Income Share:
  - Coefficients = 0.005**, 0.005**, 0.003, 0.002 with standard errors (0.002).
- Bottom20 Income Share:
  - Coefficients = -0.032, -0.025, -0.022, -0.016 with standard errors (0.026), (0.025), (0.025), (0.025).
- GDP p.c.:
  - Coefficients = -0.004***, -0.005***, -0.004***, -0.004***, -0.005***, -0.005***, -0.004***, -0.004*** with standard errors (0.002) or (0.001).
- Natural Resources:
  - Coefficients = 0.145*, 0.145**, 0.208***, 0.208***, 0.166**, 0.163**, 0.216***, 0.214*** (standard errors ~ (0.076) to (0.064)).
- Human Capital:
  - Coefficients include 0.084**, 0.097***, 0.067*, 0.079** (standard errors ~ (0.035)) in different specifications.

### Interpretation and theoretical link
- Starting a Business score has a negative effect on the equity share in foreign liabilities: higher (more favorable) score → lower equity share.
- Inclusion of Starting a Business score weakens the estimated effect of Top10 and Bottom20 income shares on equity share, consistent with model prediction that entry barriers drive both inequality and equity share.
- Model rationale: lower domestic entrepreneurial entry (higher barriers) increases residual market available to MNCs, attracting foreign equity and raising the equity share.

### Policy implications and normative trade-off
- Higher equity share in total external liabilities associated with lower crisis susceptibility and potential for technology diffusion via FDI.
- Mechanism generating higher equity shares—higher domestic entry barriers—is socially undesirable because it suppresses domestic entrepreneurial activity and may lower aggregate income.
- Policy trade-off:
  - Improving business environment (reducing entry barriers) is socially desirable but may mechanically reduce the equity share in external liabilities.
  - Enhancing equity share by preserving or increasing entry barriers is not recommended.
- The analysis highlights a nontrivial trade-off complicating straightforward policy recommendations.

### Methodological and data notes
- Dependent variables: total external liabilities and components (FDI, portfolio equity, debt) from Lane and Milesi-Ferretti (2018); variables in millions of U.S. dollars; dependent variables expressed as ratios to total liabilities.
- Baseline regressions use time-series means between 1996 and 2015 when available.
- Starting a Business indicator source: Doing Business Indicators, World Bank.
- Estimation: Ordinary least squares with robust standard errors. Significance notation: ***Significant at 1%; **significant at 5%; *significant at 10%.

*Source: wpiea2022138-print-pdf*

### 3.1    Data Definitions and Sources

### 3.1    Data Definitions and Sources

### Data sources and variable definitions
- Dependent variable: external liabilities and their subcomponents drawn from the “External Wealth of Nations” database by Lane and Milesi-Ferretti (2018), covering 212 economies for the period 1970-2015.
- Total equity: defined as the sum of FDI and portfolio equity relative to total international liabilities.
- Potential explanatory variables (following Faria and Mauro (2004) and Faria and Mauro (2009)):
  - Size of the economy: total GDP in trillions of USD at constant 2010 prices.
  - Level of economic development: GDP per capita in thousands of USD at constant 2010 prices.
  - Trade openness: sum of imports and exports over GDP.
  - Importance of natural resources: share of exports of fuels, metals, and ores as a ratio of GDP.
  - Human capital: an index based on years of schooling and returns to education.
  - Financial development: the overall index from Svirydzenka (2016).
  - Institutional quality: the simple average of six institutional indicators drawn from Kaufmann, Kraay, and Mastruzzi (2010).
- Measures of income inequality (novel augmentation):
  - Gini coefficient of disposable income from the Standardized World Income Inequality Database (SWIID) by Solt (2016).
  - Top 10 percent income share and Bottom 20 percent income share from the World Inequality Database.

### Sample construction and exclusions
- Baseline sample: 119 countries (25 advanced and 94 emerging or developing) for which all key explanatory variables are available (at least for one year between 1996 and 2015 for each country).
- Non-high income country sample: 94 observations (developing and emerging economies).
- Offshore financial centers eliminated from the sample (28 countries) because much of the increase in FDI starting in the mid-1990s reflects claims on offshore financial centers driven by tax minimization strategies (see Lane and Milesi-Ferretti (2018)); Damgaard, Elkjaer, and Johannesen (2019) decomposition of FDI into real FDI and Phantom FDI cited as motivation.
- Rationale: final sample countries are unlikely hosts to a large share of Phantom FDI since their ratio of total FDI to GDP is not very large and none of the usual suspects of Phantom FDI destinations identified in the literature (Casella (2019)) are part of the sample.

### Empirical specification and identification
- Regression strategy: regress the time-series mean of the dependent variable for the available years on the time-series means of the explanatory variables (equivalent to a between estimator regression).
- Justification: consistent with focus on composition of liability stocks and fundamental, slow-moving determinants of cross-country differences (see Faria and Mauro (2009)).
- No causal claim at this stage; the analysis is correlational. The literature contains mixed evidence on causality and on the effect of FDI on inequality (Feenstra and Hanson (1997); Choi (2006); Tsai (1995); Wu and Hsu (2012); Bogliaccini and Egan (2017); Milanovic (2005); Sylwester (2005)).
- Robustness: results remain unchanged if GDP is converted to international dollars using purchasing power parity rates; results robust to alternative measures/proxies of financial development such as private credit to GDP (Levine, Loayza, and Beck (2000)); robust regressions in Stata produce unchanged results, suggesting absence of influential outliers.

### Key descriptive statistics (averages 1996-2015)
- Sample sizes:
  - The whole sample consists of 119 observations.
  - The non-high income countries sample consists of 94 observations.
- Whole sample (Minimum, Maximum, Mean, Median, Standard deviation):
  - Total equity (equity share in ext. liabilities): 0.07, 0.69, 0.38, 0.37, 0.14
  - Institutional quality index: -1.56, 1.86, -0.06, -0.28, 0.84
  - GDP (constant US$ trillions): 0.001, 4.000, 0.44, 0.04, 1.49
  - GDP p.c. (constant US$ thousands): 0.23, 85.47, 11.43, 3.84, 16.65
  - Financial development index: 0.05, 0.87, 0.30, 0.22, 0.23
  - Natural resources: 0.00, 0.98, 0.26, 0.14, 0.28
  - Openness: 0.10, 1.82, 0.77, 0.69, 0.33
  - Human capital: 1.12, 3.63, 2.39, 2.34, 0.70
  - Net Gini: 23.88, 57.85, 39.39, 39.38, 7.95
  - Top10 Income Share: 28.04, 69.56, 45.98, 47.93, 9.04
  - Bottom20 Income Share: 0.35, 3.88, 1.86, 1.82, 0.73
- Non-high income countries:
  - Total equity (equity share in ext. liabilities): 0.07, 0.69, 0.38, 0.38, 0.15
  - Institutional quality index: -1.56, 1.17, -0.40, -0.42, 0.55
  - GDP (constant US$ trillions): 0.00, 4.43, 0.19, 0.03, 0.54
  - GDP p.c. (constant US$ thousands): 0.23, 65.95, 5.23, 2.56, 9.52
  - Financial development index: 0.05, 0.61, 0.22, 0.18, 0.14
  - Natural resources: 0.00, 0.98, 0.29, 0.17, 0.29
  - Openness: 0.10, 1.82, 0.76, 0.68, 0.34
  - Human capital: 1.12, 3.21, 2.16, 2.16, 0.59
  - Net Gini: 27.06, 57.85, 41.92, 41.77, 6.70
  - Top10 Income Share: 31.78, 69.56, 48.95, 50.06, 7.39
  - Bottom20 Income Share: 0.35, 3.46, 1.64, 1.62, 0.59

### Empirical findings (summary of Section 3.2)
- Baseline replication:
  - Column (1) replicates Faria and Mauro (2009) for the updated sample: institutional quality, abundance of natural resources, and openness are positively and significantly associated with the share of total equity in external liabilities.
  - Size of the economy, human capital, and level of financial development are also positively associated with total equity, though not always significantly.
  - GDP p.c. is significantly negatively related to the equity share in total liabilities.
- Inclusion of inequality measures (starting in column (2)):
  - All inequality variables are significantly correlated with the equity share or FDI in total external liabilities:
    - Net Gini and Top 10 income share: positive relationships with the equity share.
    - Bottom 20 income share: negative relationship with the equity share.
  - Inclusion of inequality variables substantially increases explanatory power of the model, with increases in R-squared of up to ten percentage points.
  - Economic magnitude example: a country at the 75th percentile of the Gini index (say Thailand) would ceteris paribus exhibit an equity share that is 7.5 pp larger than a country at the 25th percentile (e.g. Estonia). Such an increase corresponds to about one quarter of the mean equity share in the sample (see Table 1).
- Non-high income country sample (Table 3):
  - Economic size is significantly positively associated with total equity.
  - Signs and magnitudes of estimated coefficients remain largely unchanged compared to the whole sample.
  - Inequality measures remain statistically significantly different from zero, except Top10 income share which fails to meet standard levels of significance in column (6).
  - Coefficients of other regressors barely change once inequality is accounted for.
- Robustness:
  - Alternative estimation (robust regressions in Stata) yields unchanged results, suggesting no contamination by outliers or influential observations.

*Italic: Source: wpiea2022138-print-pdf - 3.1    Data Definitions and Sources*

### 4.2    Set-up and Equilibrium

### 4.2    Set-up and Equilibrium

### Preferences and consumption structure
- Consumption aggregator:
  - C = (C_T)^γ (C_N)^{1−γ}. (1)
- Traded good:
  - C_T denotes consumption of the traded good; price normalized to one (numéraire).
- Non-traded goods:
  - CES aggregate: C_N = [∫_0^μ c_N(i)^{ε−1} di]^{ε/(ε−1)}. (2)
  - c_N(i) is consumption of variety i, ε > 1 is elasticity of substitution across varieties, μ is mass of non-traded goods (endogenous).
- Demand for variety i (from preferences and prices):
  - c_N(i) = (1−γ) P C (p_N(i))^{−ε} (P_N)^{ε−1}. (3)
  - PC denotes value of total consumption = domestic residents’ total income I; p_N(i) is price of variety i; P and P_N are price indices of total and non-traded bundles.

### Supply, production technologies, and pricing
- Production:
  - Traded and non-traded goods firms: linear in labor with productivities a_T and a_N, respectively.
  - Economy-wide wage w = a_T.
- Non-traded sector market structure:
  - Perfect competition in traded sector; monopolistic competition in non-traded sector.
  - Marginal cost for non-traded variety i: MC_N(i) = a_T / a_N.
- Price setting by monopolistic non-traded firm:
  - p_N(i) = (1/α) MC_N(i) = (1/α) a_T / a_N with α ≡ (ε−1)/ε < 1. (4)
  - 1/α > 1 is the markup, decreasing in ε.
- Given identical marginal costs and prices across varieties, demand simplifies to:
  - c_N(i) = (1−γ) PC α a_N / (μ a_T). (5)
  - For given PC, demand for an individual non-traded good decreases in μ.

### Entry, fixed costs, and firm ownership
- Firm setup costs:
  - Domestic entrepreneur investment κ (independent of scale).
  - Multinational corporations (MNCs) face larger setup cost κ_F > κ.
  - κ_F > κ justified by additional resources foreign firms require to explore domestic environment.
- Domestic agents:
  - Continuum of individuals mass one, each endowed with wealth v(j) distributed F(v) with density f(v), support [v_min, v_max] and v_max < κ.
  - Agents can rent endowment at world interest rate r or become entrepreneurs if v(j) ≥ v_crit.
  - Interpretation: v(j) may reflect wealth or prerequisites correlated with wealth; v_crit represents entry barrier.
- Entrepreneurial profits for individual j:
  - π_N(j) = (1−γ)(1−α) PC / μ − [κ − v(j)] r. (6)

### Foreign entry, free entry condition, and equilibrium mass of firms
- MNCs:
  - Can borrow at world interest rate r; enter if profits non-negative.
  - Free-entry condition for MNCs:
    - (1−α)(1−γ) PC / μ = r κ_F. (7)
  - Implies mass of firms μ = (1−α)(1−γ) PC / (r κ_F). (8)
- Labor market equilibrium:
  - L_T + L_N = L. (9)
  - L is total domestic labor supply, implicitly determined by v_crit with L = F(v_crit).
  - Symmetry implies L_N = μ L_N(i).
- Labor demand of representative non-traded firm:
  - L_N(i) = c_N(i) / a_N = α/(1−α) κ_F / r · a_T. (10)
  - Second equality follows from Eqs. (4), (5), (7).

### Mass of foreign firms and decomposition
- Mass of foreign non-traded firms λ:
  - λ = μ − [1 − F(v_crit)] = (1−α)(1−γ) PC / (κ_F r) − [1 − F(v_crit)]. (11)
  - Interpretation:
    - Domestic economy attracts MNCs when market size PC is large and domestic firm mass is small.
    - Raising v_crit reduces domestic entrepreneurs but also reduces aggregate income PC; the model shows the first effect dominates, increasing λ.

### Individual incomes and aggregate income
- Worker income for v(j) < v_crit:
  - I_w(j) = w + r v(j) = a_T + r v(j). (12)
- Entrepreneur income for v(j) ≥ v_crit:
  - I_e(j) = π_N(j) = (1−γ)(1−α) PC / μ − [κ − v(j)] r = r(κ_F − κ) + r v(j). (13)
  - Third equality uses Eq. (7).
- Condition for entrepreneurship to be preferable for those passing entry barrier:
  - (κ_F − κ) r > a_T. (14)
  - Assumed satisfied (positive entrepreneurial rent).
- Aggregate income I (with PC = I):
  - I = r v̄ + a_T F(v_crit) + r(κ_F − κ) [1 − F(v_crit)]. (15)
  - v̄ denotes average wealth endowment.

### Inequality amplification by entrepreneurship
- Model implication:
  - Ex-ante wealth inequality (v(j)) becomes ex-post income inequality because richer individuals earn higher r v(j).
  - Entrepreneurial rent magnifies inequality when positive.
  - If v(j) interpreted as entrepreneurial skill endowment, entrepreneurial rent is sole source of income inequality.

### Comparative-statics intuition (introductory results included here)
- Entry barriers (higher v_crit) reduce domestic entrepreneurial activity, affecting inequality, MNC presence, borrowing, and equity share in external liabilities.
- Top and bottom income shares:
  - Top x% income share S_H_x (assuming v_H_x ≥ v_crit and 1 − F(v_H_x) = x/100):
    - S_H_x = [1 − F(v_H_x)] r(κ_F − κ) + r ∫_{v_H_x}^{v_max} v dF(v)  /  [ r v̄ + r(κ_F − κ) − F(v_crit) [ r(κ_F − κ) − a_T ] ]. (16)
    - S_H_x increases in v_crit (driven by decrease in aggregate income).
  - Bottom y% income share S_L_y (assuming v_L_y ≥ v_crit and F(v_L_y) = y/100):
    - S_L_y = F(v_L_y) r(κ_F − κ) + r ∫_{v_min}^{v_L_y} v dF(v) − F(v_crit) [ r(κ_F − κ) − a_T ]  /  [ r v̄ + r(κ_F − κ) − F(v_crit) [ r(κ_F − κ) − a_T ] ]. (17)
    - S_L_y decreases in v_crit (income of bottom y% declines by more than total income).
- Mass of MNCs in closed form:
  - λ = F(v_crit) { 1 − (1−γ)(1−α) / (κ_F r) [ r(κ_F − κ) − a_T ] } + (1−γ)(1−α)/κ_F v̄ + (1−γ)(1−α)(κ_F − κ)/κ_F. (18)
  - The term in curly brackets is > 0; overall effect of v_crit on λ is positive (open-slot effect dominates market-size effect).
- Equity share ρ in external liabilities:
  - ρ = λ κ_F / [ λ κ_F + ∫_{v_crit}^{v_max} (κ − v) f(v) dv ]. (19)
  - ρ increases in v_crit via two channels:
    - Higher v_crit → more MNCs → higher FDI (λ κ_F).
    - Higher v_crit → reduced domestic borrowing ∫_{v_crit}^{v_max} (κ − v) f(v) dv.
- Mechanism summary (illustrated in Figure 2 in source):
  - Entry barriers ↑ → Number of entrepreneurs ↓ → (i) MNCs ↑, (ii) Inequality ↑, (iii) Borrowing ↓ → Equity share ↑.
  - Thus, income inequality and equity share in external liabilities are positively linked because both are driven by entry barriers that affect entrepreneurial activity.

*Source: 4.2 Set-up and Equilibrium (extracted from provided content).*

### 5.2    Entry Barriers and the Equity Share in External Liabilities

### 5.2    Entry Barriers and the Equity Share in External Liabilities

### Empirical approach
- Re-run regressions from Section 3 adding the World Bank “Starting a Business” score (Doing Business).
- Use time-series country-means for available years from 2011-2015; eliminate Benin, Cˆote d’Ivoire, and Togo because their 2015 “Starting a Business” score deviates implausibly from the 2011-2015 average.
- As a robustness check, the relationship is also considered for the year 2015.
- Expectation from the model: a negative effect of the “Starting a Business” score on the equity share; inclusion of the score should weaken or render insignificant the effect of inequality measures.

### Main empirical findings (averages 2011-2015; Table 4)
- Sample size: Observations = 111.
- Adjusted R-squared values reported: 0.316, 0.334, 0.400, 0.416, 0.263, 0.292, 0.384, 0.406 (for columns (1)–(8) respectively).
- Starting a Business Score:
  - Coefficient = -0.003* (columns where reported) with standard error (0.001). Appears as -0.003*, -0.003*, -0.003**, -0.003** across specifications.
- Top10 Income Share:
  - Coefficients = 0.006***, 0.005***, 0.003**, 0.003* (standard errors (0.002) where reported).
- Bottom20 Income Share:
  - Coefficients = -0.044*, -0.036, -0.027, -0.020 (standard errors (0.023), (0.023), (0.022), (0.022)).
- GDP per capita (GDP p.c.):
  - Coefficients = -0.006***, -0.006***, -0.005***, -0.005***, -0.006***, -0.007***, -0.005***, -0.006*** (standard errors (0.002) or (0.001) as reported).
- Natural Resources:
  - Coefficients = 0.179***, 0.182***, 0.211***, 0.214***, 0.200***, 0.204***, 0.221***, 0.224*** (standard errors ~ (0.064) to (0.055) as reported).
- Openness:
  - Coefficients = 0.116***, 0.113***, 0.144***, 0.140***, 0.122***, 0.117***, 0.147***, 0.142*** (standard errors ~ (0.040) to (0.039)).
- Financial development (FinDevIndexIMF) and Institutional Quality show mixed significance across specifications.

### Main empirical findings (year 2015; Table 5)
- Sample size: Observations = 96.
- R-squared values reported: 0.209, 0.235, 0.294, 0.313, 0.161, 0.199, 0.285, 0.308 (for columns (1)–(8) respectively).
- Starting a Business Score:
  - Coefficients = -0.003**, -0.003*, -0.003**, -0.003** (standard errors (0.001)) — negative and statistically significant across specifications.
- Top10 Income Share:
  - Coefficients = 0.005**, 0.005**, 0.003, 0.002 (standard errors (0.002)).
- Bottom20 Income Share:
  - Coefficients = -0.032, -0.025, -0.022, -0.016 (standard errors (0.026), (0.025), (0.025), (0.025)).
- GDP per capita (GDP p.c.):
  - Coefficients = -0.004***, -0.005***, -0.004***, -0.004***, -0.005***, -0.005***, -0.004***, -0.004*** (standard errors (0.002) or (0.001)).
- Natural Resources:
  - Coefficients = 0.145*, 0.145**, 0.208***, 0.208***, 0.166**, 0.163**, 0.216***, 0.214*** (standard errors ~ (0.076) to (0.064)).
- Human Capital:
  - Coefficients include 0.084**, 0.097***, 0.067*, 0.079**, etc. (standard errors ~ (0.035)).

### Interpretation and theoretical link
- Evidence supports the hypothesis that less (more) severe barriers to entrepreneurial activity (higher Starting a Business score means more favorable environment) have a negative (positive) effect on the equity share in foreign liabilities.
- Including the “Starting a Business” score weakens the estimated effect of top10 and bottom20 income shares on the equity share, consistent with the model’s claim that both inequality and the equity share are driven by entry barriers.
- The result implies a counterintuitive empirical pattern: a more favorable business environment reduces the equity share in foreign liabilities.
  - Model rationale: domestic and foreign firms compete in the domestic market; lower domestic entrepreneurial entry (higher barriers) can raise the residual market size available to multinational companies, attracting foreign equity and increasing the equity share.

### Policy implications and normative trade-off
- A higher equity share in total external liabilities is associated with lower crisis susceptibility and may aid technology diffusion (via FDI).
- However, the mechanism through which higher equity shares arise (i.e., higher domestic entry barriers) is socially undesirable because it suppresses domestic entrepreneurial activity and may lower aggregate income.
- Policy trade-off: improving the business environment (reducing entry barriers) is socially desirable but may mechanically reduce the equity share in external liabilities; enhancing the equity share by preserving or increasing entry barriers is not a recommended policy objective.
- The analysis highlights a nontrivial trade-off that complicates straightforward policy recommendations.

### Additional methodological and data notes
- Dependent variables: total external liabilities and components (FDI, portfolio equity, debt) from Lane and Milesi-Ferretti (2018); variables in millions of U.S. dollars; dependent variables expressed as ratios to total liabilities; baseline regressions use time-series means between 1996 and 2015 when available.
- Starting a Business indicator source: Doing Business Indicators, World Bank.
- Robust standard errors in parentheses; Ordinary least squares regressions. Significance notation: ***Significant at 1%; **significant at 5%; *significant at 10%.

*Source: wpiea2022138-print-pdf — 5.2 Entry Barriers and the Equity Share in External Liabilities*

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*Inequality and the Structure of Countries’ External Liabilities Working Paper No. WP/2022/138*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022138-print-pdf.pdf_