## _wp09276

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---

### Introduction and research objective
- Large current account imbalances, especially large deficits (e.g., U.S. since 2002), motivate analysis of causes and adjustment needs.
- Alternative interpretation: large imbalances can reflect financial integration (savings glut view by Bernanke (2006)).
- Rising global dispersion of current accounts may be consistent with increasing financial and trade integration.
- Research objective: quantitatively investigate the distribution of current accounts and other external balances in a stochastic multi-country model where countries adjust consumption and external assets in response to idiosyncratic income shocks, subject to trade and financial frictions.
- Model summary:
  - Open-economy extension of the incomplete insurance model (Bewley (1986), Aiyagari (1994), Huggett (1995)).
  - Continuum of countries, each with a representative household facing stochastic endowment xt with transition law πx(x′|x).
  - Goods trade with iceberg cost τ and access to an incomplete world capital market with frictions (interest rate spread and borrowing constraint).
- Calibration and empirical matching:
  - Model calibrated to match observed pattern of international trade and finance for year 2000 using stochastic relative income shocks estimated from de-trended GDP data of 80 countries over 40 years.
  - Calibrated model accounts for about two-thirds of the global dispersion of current accounts.

### Model setup and key mechanisms
- Preferences and consumption aggregator:
  - Expected utility: E0 ∑t=0∞ βt (c1−γt −1)/(1−γ)
  - Composite consumption: c t = [φ cdt1−1/η + (1−φ) cft1−1/η]η/(η−1)
- Budget / law of motion:
  - at+1 = xt − cdt − (1 + τ) cft + (1 + r) at
  - Domestic consumption constraint: cdt ≤ xt
- Interest rate spread and borrowing constraint:
  - Spread ψ = rB − rL, with rL < rB; r = rL when at > 0 and r = rB otherwise.
  - Exogenously imposed borrowing constraint ̄a (set above natural limit −x/r).
- Trade and external balances:
  - Import/iceberg cost τ (relative price of foreign goods = 1 + τ).
  - Trade balance: tbt = xt − cdt − (1 + τ) cft.
  - Current account: cat = at+1 − at = tbt + { rB + (rL − rB) 1{at > 0} } at.
- Competitive equilibrium conditions:
  1. Individual optimization given rB and rL.
  2. World goods market clears: ∫ {x − cd(a,x)} dμ = (1 + τ) ∫ cf(a,x) dμ.
  3. World capital market clears: ∫ a′(a,x) dμ = 0.
  4. Invariant distribution μ(a,x) is time invariant.

### Calibration parameters (benchmark)
- Time unit: year.
- Income process: lnx′ = ρx lnx + εx, εx ∼ N(0, σx2); empirical estimates from de-trended log per capita GDP (80 countries, 1961-2003, PWTv6): ˆyt = 0.863 ˆyt−1 + et, ˆσe = 0.0493, ̄R2 = 0.81 → set ρx = 0.863 and σx = 0.0493.
- Preference and technology parameters:
  - γ = 2
  - β = 0.96
  - η = 6
  - τ = 0.5
  - φ = 0.475 (matches domestic-to-foreign expenditures ratio 4.2 and average import-GDP ratio of 19% in steady state)
- Financial frictions:
  - ψ = rB − rL = 1.5% (benchmark spread)
  - ̄a = −1.5 (borrowing limit, i.e., borrow up to 150% of average GDP)
- Benchmark market-clearing interest rate ˜r = 4.06% → lending rate rL = 3.3% and borrowing rate rB = 4.8%.

### Benchmark equilibrium and distributional findings
- Stationary distributions:
  - Current accounts and trade balances mostly within the range of 20 percent of GDP on both sides (most between −10% and 10% of GDP).
  - Net foreign assets distributed from −200% to 200%, bulk between −100% and 100%; NFA < −150% corresponds to income below average relative to the borrowing limit.
- Role of interest rate spread:
  - Spread reduces spike on left-to-center of current account distribution and fat right tail of NFA distribution by making borrowing more costly and lending less profitable; promotes asset accumulation for self-insurance.
  - Without spread, NFA extremely skewed with concentration on borrowing side and current account spike on borrowing side.
- Fit to 2000 data:
  - Standard deviation of NFA-to-GDP in benchmark model = 55 percent (equal to 2000 data).
  - Standard deviation of current account = 5 percent (slightly more than two-thirds of actual 2000 value).
  - Standard deviation of trade balance ≈ 1/2 of actual 2000 value.
- Primary source of dispersion: heterogeneity in income (relative to trend) combined with insurance motives and frictions.

### Comparative statics: trade vs financial frictions
- Goods market friction experiment:
  - Increase τ from 0.5 to 0.7 → average import-GDP ratio falls from 19% to 10%.
  - Little change in dispersion of external balances (standard deviations of current accounts, NFA, TB) because trade costs affect exports and imports symmetrically.
- Capital market friction experiments:
  1. Tighten borrowing limit ̄a from −1.5 to −0.5:
     - Dispersion of NFA-to-GDP decreases from 55.4% to 34.4% (a 38% decrease).
     - Dispersion of current account decreases from 5% to 4% (a 20% decrease).
  2. Increase spread ψ from 1.5% to 3%:
     - Dispersion of NFA-to-GDP decreases from 55.4% to 25% (a 55% decrease).
     - Dispersion of current account decreases from 5% to 3.3% (a 37% decrease).
- Implication: easing financial frictions (lower spreads, laxer borrowing limits) has a greater effect on increasing dispersion of current accounts and NFA than easing trade frictions.

### Quantitative comparisons with data (selected statistics)
- Data distributions (1970 vs 2000; Table 1 highlights):
  - CA/GDP:
    - Mean −2.4 (1970), −1.0 (2000)
    - Median −2.1 (1970), −2.5 (2000)
    - Max 11.6 (1970), 19.6 (2000)
    - Min −30.2 (1970), −18.3 (2000)
    - SD 4.9 (1970), 6.9 (2000)
  - NFA/GDP:
    - Mean −16.7 (1970), −40.2 (2000)
    - Median −13.4 (1970), −36.9 (2000)
    - Max 77.6 (1970), 156.6 (2000)
    - Min −136.2 (1970), −236.1 (2000)
    - SD 29.3 (1970), 55.4 (2000)
  - TB/GDP:
    - Mean −1.7 (1970), −1.9 (2000)
    - Median −1.5 (1970), −2.9 (2000)
    - Max 54.0 (1970), 36.2 (2000)
    - Min −31.6 (1970), −45.1 (2000)
    - SD 9.8 (1970), 11.6 (2000)
- Standard deviations: Data vs model (Table 3):
  - CA/GDP SD:
    - Data 1970: 4.9
    - Data 2000: 6.8
    - Benchmark model: 5.0
    - Trade friction (τ= 0.7): 4.9
    - Borrowing constraint (̄a=−0.5): 4.0
    - Spread (ψ= 3%): 3.3
  - NFA/GDP SD:
    - Data 1970: 29.3
    - Data 2000: 55.4
    - Benchmark model: 55.4
    - Trade friction (τ= 0.7): 55.4
    - Borrowing constraint (̄a=−0.5): 55.2
    - Spread (ψ= 3%): 34.4
    - Additional model value: 25.0
  - TB/GDP SD:
    - Data 1970: 9.8
    - Data 2000: 11.6
    - Benchmark model: 5.6
    - Trade friction (τ= 0.7): 5.5
    - Borrowing constraint (̄a=−0.5): 4.3
    - Spread (ψ= 3%): 3.5
- Distributional percentiles for CA/GDP (Table 5; selected):
  - 5% percentile:
    - Data 1970: −10.0
    - Data 2000: −10.3
    - Benchmark: −8.5
    - Constraint (̄a=−0.5): −6.9
    - Spread (ψ= 3%): −5.5
  - 50% percentile (median):
    - Data 1970: −1.9
    - Data 2000: −2.5
    - Benchmark: 0.0
    - Constraint (̄a=−0.5): 0.1
    - Spread (ψ= 3%): 0.0
  - 95% percentile:
    - Data 1970: 2.7
    - Data 2000: 13.1
    - Benchmark: 7.9
    - Constraint (̄a=−0.5): 6.3
    - Spread (ψ= 3%): 5.4

### Persistence, stationarity, and risk sharing
- Persistence (AR(1) coefficients; Table 4):
  - CA/GDP:
    - Advanced: 0.64
    - All countries: 0.84
    - Benchmark model: 0.81
    - Constraint (̄a=−0.5): 0.78
    - Spread (ψ= 3%): 0.75
  - NFA/GDP:
    - Advanced: 0.85
    - All countries: 0.92
    - Benchmark model: 0.99
    - Constraint (̄a=−0.5): 0.99
    - Spread (ψ= 3%): 0.99
  - TB/GDP:
    - Advanced: 0.70
    - All countries: 0.89
    - Benchmark model: 0.83
    - Constraint (̄a=−0.5): 0.80
    - Spread (ψ= 3%): 0.77
- Dickey–Fuller test results on thirty-year simulated samples:
  - Unit root rejected at 5% significance in 78 out of 500 cases (15.6%) in benchmark.
  - Rejection rates: 27.2% in model with a larger spread, 19.8% in model with a smaller (tighter) borrowing limit.
  - Implication: weak power of unit root tests in finite samples and under slowly evolving structural change; exercise caution inferring stationarity from three- or four-decade samples.
- Risk sharing:
  - Complete consumption risk sharing would equalize consumption across countries; model leaves a very large distance to first-best.
  - Consumption dispersion in benchmark is lower than income dispersion but far from degenerate.
  - Bilateral correlations of consumption growth (30-year simulated data):
    - Mean correlation: 0.031
    - Standard deviation: 0.495
    - Alternative model values: mean correlation 0.028 (larger spread) and 0.030 (smaller borrowing limit)
  - Conclusion: model produces partial risk sharing (positive correlations) but far from full risk sharing.

### Historical interpretation, limitations, and policy-relevant messages
- Historical interpretation:
  - Rising dispersion of current account imbalances is consistent with increased financial integration observed historically (e.g., pre–First World War and late 1990s/2000s).
  - Empirical data show fatter deficit tails than model economies in 1970 and 2000, suggesting some countries may have run excessive deficits leading to crises or sharp reversals; surplus side also shows deviations.
- Limitations and possible extensions:
  - Model excludes reversal-of-imports channel by construction; cannot generate trade-cost driven interest-rate spreads as in Obstfeld and Rogoff (2000).
  - Heterogeneity only in income; excludes demographics, terms-of-trade fluctuations, alternative financial instruments, and investment dynamics.
- Policy-relevant messages:
  - International financial integration is a key driver of increasing dispersion of current accounts.
  - Financial market frictions materially affect cross-country current account dispersion; policies that reduce such frictions are likely to increase dispersion and raise persistence of imbalances.
  - Caution advised in using standard unit-root tests on finite samples for policy assessment of sustainability of current account imbalances.

*Source: _wp09276*

### References..................................................................................................19

### _wp09276 - References..................................................................................................19

### Introduction
- Large current account imbalances often become a source of concern, especially when they are large deficits. The large current account deficit of the U.S. since 2002 has generated much debate on its causes and the need for eventual adjustment.
- Alternative view: large current account imbalances can be a sign of progress, interpreted as an outgrowth of an integrated financial market (e.g., savings glut view by Bernanke (2006)).
- Rising global dispersion of current accounts is potentially consistent with increasing financial and trade integration: as integration progresses, countries find it easier to lend and borrow, thereby generating a larger dispersion of current accounts.
- Existing literature: empirical work documents rising dispersion but theoretical analysis of the global distribution of current accounts is sparse (Clarida (1990) is cited as the most recent analysis).

### Research objective and approach
- Investigate quantitatively the distribution of current accounts and other external balances in a stochastic multi-country model where each country adjusts its consumption and external assets in response to idiosyncratic shocks to its income, subject to frictions in trade and financial accounts.
- Model features:
  - Open-economy version of the incomplete insurance model of Bewley (1986), Aiyagari (1994) and Huggett (1995).
  - Captures precautionary and self-insurance considerations arising from liquidity constraints.
  - World economy comprises a continuum of countries, each with a representative household endowed with a stochastic income.
  - Countries engage in goods trade subject to an iceberg cost of trade, and have access to the world capital market that is incomplete and subject to several frictions.
- Calibration and empirical matching:
  - Calibrated with conventional parameter values, the model accounts for about two-thirds of the global dispersion of current accounts.
  - Model is calibrated to match observed pattern of international trade and finance (e.g., average import-GDP ratio and net foreign asset distribution) for year 2000, using stochastic relative income shocks estimated from the de-trended GDP data of 80 countries over 40 years.

### Empirical facts documented (Global dispersion of current accounts)
- Time horizon and measure:
  - Figure 1 shows, for each year from 1960 to 2004, the 80-percent range that comprises the current account in percent of GDP except for the top and bottom deciles (thus from 10 to 90 percent, when ranked numerically).
- Key findings on dispersion:
  - The 80-percent range of current account balances nearly doubled over the sample.
  - Between 1970 and 2004 the cross-sectional standard deviation of current account balance to GDP ratio increased from 4.9% to 6.9% (Table 1).
  - Sample size evolution:
    - The top-panel sample rose from 70 countries in 1970 to about 120 countries in 2004 (after having started with 50 countries in 1960).
    - Advanced-country sample started with 18 countries in 1960 and 1970, adding three countries to comprise 21 countries in 2004.
  - Net foreign assets:
    - Dispersion of net foreign assets increased more than the dispersion in both current accounts and trade balances.
    - Between 1970 and 2000, the cross-sectional standard deviation of net foreign asset to GDP ratio increased from 29.3% to 55.4% (Table 1).
  - Trade balances:
    - Dispersion in trade balances increased somewhat less than net foreign assets or current accounts.
    - Between 1970 and 2000, the cross-sectional standard deviation of trade balance to GDP ratio increased from 9.8% to 11.6%.
- Literature links:
  - Blanchard and Giavazzi (2002) documented rising dispersion of current accounts in European countries and associated it with improving financial integration, including the launch of the euro area.
  - Faruqee and Lee (2008) examined nearly 100 countries and found an underlying trend-increase in the dispersion of current accounts; they found evidence supporting financial integration as the main contributing factor and little support for trade openness as a contributing factor.
  - Obstfeld and Taylor (2004) report the evolution in dispersion since the late-1800s and attribute centurial movements to underlying financial integration; they note the standard deviation among 15 sample countries was highest in the early 1900s (prior to the First World War), a period they view as highly integrated world capital markets comparable to the 2000s.

### Theoretical framework (Motivation)
- Need for multi-country distribution theory:
  - A theory of distribution requires going beyond a typical two-country framework to a multi-country model.
  - The incomplete insurance model with multiple (infinitely many) agents (originating with Bewley (1980) and developed by Clarida (1990), Aiyagari (1994), Huggett (1995)) is adopted.
- Mechanisms captured:
  - Incomplete insurance and limits to borrowing lead agents to accumulate assets as self-insurance against idiosyncratic income shocks.
  - In equilibrium, a stationary distribution emerges for endogenous variables including current accounts.
  - Precautionary and self-insurance motives behind lending, borrowing, and consumption decisions arise in the presence of liquidity constraints; the liquidity constraint itself is not derived from first principles (consistent with cited literature).
  - Precautionary motive does not require convexity of marginal utility as in small open-economy models (Obstfeld and Rogoff (1995) and references therein).
- Model innovation:
  - The model extends the conventional incomplete insurance framework to an international setting with trade and financial frictions, enabling analysis of how easing of frictions affects the world distribution of current accounts.

### Quantitative findings and comparative frictions
- Calibration result:
  - Calibrated model accounts for about two-thirds of the global dispersion of current accounts.
- Comparative effect of frictions:
  - Easing of financial frictions has a greater effect on the dispersion of current accounts than the easing of trade frictions.
- Additional analyses:
  - Examine implications on several stylized facts, including the persistence of current accounts and international risk sharing.

*Source: _wp09276 - References..................................................................................................19*

### introduction of the spread between the lending and borrowing interest rates which we interpret to

### _wp09276 - introduction of the spread between the lending and borrowing interest rates which we interpret to

### Model setup and key mechanisms
- World of a continuum (measure one) of countries, each with a representative household facing stochastic endowment xt with transition law πx(x′|x) over support [x, ̄x].
- Countries trade one-period consumption loans on a world capital market and face an exogenously imposed borrowing constraint ̄a (set above the natural limit −x/r).
- Net foreign asset holdings: at.
- Interest rate spread: there is a spread between the lending rate rL and borrowing rate rB so that rL < rB; r = rL when at > 0 and r = rB otherwise. The spread (rB − rL) reflects the cost of financial intermediation and discourages frequent borrowing, reinforcing asset accumulation for self-insurance.
- Preferences (per-country utility):
  - Expected utility: E0 ∑t=0∞ βt (c1−γt −1)/(1−γ)
  - Composite consumption aggregator: c t = [φ cdt1−1/η + (1−φ) cft1−1/η]η/(η−1)
- Budget / law of motion for assets:
  - at+1 = xt − cdt − (1 + τ) cft + (1 + r) at
- Domestic consumption constrained: cdt ≤ xt.
- Import/iceberg cost for foreign goods: τ (relative price of foreign goods in domestic market is 1 + τ).
- Trade balance: tbt = xt − cdt − (1 + τ) cft.
- Current account: cat = at+1 − at = tbt + { rB + (rL − rB) 1{at > 0} } at.
- Recursive problem (value function) V(a, x; rL, rB) with constraints and decision rules cd(a,x), cf(a,x), a′(a,x).
- Competitive equilibrium conditions:
  1. Individual optimization given rB and rL.
  2. World goods market clears: ∫ {x − cd(a,x)} dμ = (1 + τ) ∫ cf(a,x) dμ.
  3. World capital market clears: ∫ a′(a,x) dμ = 0.
  4. Invariant distribution μ(a,x) is time invariant (stationary distribution of net foreign assets and incomes).

### Calibration
- Time unit: year.
- Endowment (log) follows AR(1): lnx′ = ρx lnx + εx, εx ∼ N(0, σx2).
- Empirical AR(1) estimate from de-trended log per capita GDP (80 countries, 1961-2003, PWTv6): ˆyt = 0.863 ˆyt−1 + et, ˆσe = 0.0493, ̄R2 = 0.81. Set ρx = 0.863 and σx = 0.0493.
- Relative risk aversion γ = 2.
- Discount factor β = 0.96.
- Elasticity of substitution between domestic and foreign consumption η = 6.
- Trade cost τ set to 0.5 (consistent with survey estimate 48-63%).
- CES weight φ = 0.475 to match domestic-to-foreign expenditures ratio 4.2 (Obstfeld and Rogoff (2000)); generates average import-GDP ratio of 19% in steady state.
- Benchmark interest rate spread ψ = rB − rL = 1.5% (motivated by historical U.S. spread range 1–3%).
- Borrowing limit ̄a = −1.5 (implying a country can borrow up to 150% of its average GDP), positioned at the lower bound of NFA-to-GDP ratios of advanced economies in 2000.

### Benchmark economy equilibrium and quantitative findings
- Market-clearing interest rate ˜r = 4.06%, implying:
  - lending rate rL = 3.3%
  - borrowing rate rB = 4.8%
- Distributional outcomes (stationary distribution μ(a,x)):
  - Current accounts and trade balances mostly within the range of 20 percent of GDP on both sides (most between −10% and 10% of GDP).
  - Net foreign assets distributed from −200% to 200%, bulk between −100% and 100%; NFA < −150% corresponds to income below the average level relative to the borrowing limit.
- Role of interest rate spread:
  - The spread reduces the spike on the left-to-center of the current account distribution and the fat right tail of the net foreign asset distribution.
  - Without the spread, net foreign assets are extremely skewed with concentration on the borrowing side and current account exhibits a spike on the borrowing side.
  - With the spread, borrowing is more costly and lending less profitable; countries borrow less frequently and accumulate assets for self-insurance, producing distributions closer to observed shapes.
- Fit to data circa 2000:
  - Standard deviation of NFA-to-GDP in benchmark model = 55 percent (equal to 2000 data).
  - Standard deviation of current account = 5 percent (slightly more than 2/3 of actual 2000 value).
  - Standard deviation of trade balance ≈ 1/2 of actual 2000 value.
- Interpretation: Heterogeneity in income (relative to trend) is the primary source of dispersion; insurance motives combined with frictions in goods and finance can account for a large part of observed dispersion.

### Experiments with greater frictions (comparative statics)
- Goods market friction experiment:
  - Increase τ from 0.5 to 0.7 → average import-GDP ratio falls from 19% to 10%.
  - Little change in dispersion of external balances (standard deviations of current accounts, net foreign assets, and trade balances) because trade costs affect exports and imports.
- Capital market friction experiments:
  1. Tighten borrowing limit from ̄a = −1.5 to ̄a = −0.5:
     - Dispersion of NFA-to-GDP decreases from 55.4% to 34.4% (a 38% decrease).
     - Dispersion of current account decreases from 5% to 4% (a 20% decrease).
  2. Increase spread ψ from 1.5% to 3%:
     - Dispersion of NFA-to-GDP decreases from 55.4% to 25% (a 55% decrease).
     - Dispersion of current account decreases from 5% to 3.3% (a 37% decrease).
- Comparison with data between 1970 and 2000:
  - Data: dispersion of NFA in 1970 = 29.3% (≈ 53% of 2000 value 55.4%); dispersion of current accounts in 1970 = 4.9% (≈ 70% of 2000 value 6.8%).
  - Model results show changes in capital market frictions produce declines in dispersion comparable to the observed reversal between 1970 and 2000; changes in trade frictions have much smaller effects on cross-country dispersion of external balances.
- Mechanism summary:
  - Changes in borrowing cost and availability directly affect intertemporal consumption-savings choices and hence dispersion of external balances.
  - Trade frictions primarily affect intra-temporal choice between domestic and foreign goods, with secondary effects on intertemporal saving.

*Source: _wp09276 - introduction of the spread between the lending and borrowing interest rates which we interpret to*

### Section II), in that the international financial integration has likely been the leitmotif behind the

### _wp09276 - Section II), in that the international financial integration has likely been the leitmotif behind the

### Role of international financial integration and frictions
- International financial integration is identified as a key driver of the increase in the dispersion of current accounts.
- Financial frictions have a substantial effect on current account dispersion, greater than trade frictions.
- Trade costs play a limited role in the model relative to financial frictions; the model precludes the “reversal” of imports channel emphasized by Obstfeld and Rogoff (2000).
- The spread between lending and borrowing rates has a powerful effect on international flows of finance even if the import-reversal channel is precluded.

### Model construction, calibration, and benchmark parameters
- Simulated panel data: 500 countries for 1000 years generated from equilibrium distributions under alternative financial-market-friction specifications.
- Benchmark model parameters (Table 2):
  - β = 0.96 Discount factor
  - γ = 2 Relative risk aversion
  - η = 6 Substitution elast b/w domestic and foreign consumption
  - φ = 0.475 Weight on domestic goods in CES utility function
  - τ = 0.5 Trade friction
  - ψ = r_B − r_L = 1.5% Interest rate spread
  - ̄a = −1.5 Borrowing constraint
  - ρ_x = 0.863 Persistence of relative income shock
  - σ_x = 0.0495 Standard deviation of innovation to relative income

### Key quantitative results: distributions and moments
- Data distributions (Table 1; 1970 and 2000):
  - CA/GDP:
    - Mean -2.4 (1970), -1.0 (2000)
    - Median -2.1 (1970), -2.5 (2000)
    - Max 11.6 (1970), 19.6 (2000)
    - Min -30.2 (1970), -18.3 (2000)
    - SD 4.9 (1970), 6.9 (2000)
  - NFA/GDP:
    - Mean -16.7 (1970), -40.2 (2000)
    - Median -13.4 (1970), -36.9 (2000)
    - Max 77.6 (1970), 156.6 (2000)
    - Min -136.2 (1970), -236.1 (2000)
    - SD 29.3 (1970), 55.4 (2000)
  - TB/GDP:
    - Mean -1.7 (1970), -1.9 (2000)
    - Median -1.5 (1970), -2.9 (2000)
    - Max 54.0 (1970), 36.2 (2000)
    - Min -31.6 (1970), -45.1 (2000)
    - SD 9.8 (1970), 11.6 (2000)

- Standard deviations: Data vs model economies (Table 3)
  - CA/GDP:
    - Data 1970: 4.9
    - Data 2000: 6.8
    - Benchmark model: 5.0
    - Trade friction (τ= 0.7): 4.9
    - Borrowing constraint (̄a=−0.5): 4.0
    - Spread (ψ= 3%): 3.3
  - NFA/GDP:
    - Data 1970: 29.3
    - Data 2000: 55.4
    - Benchmark model: 55.4
    - Trade friction (τ= 0.7): 55.4
    - Borrowing constraint (̄a=−0.5): 55.2
    - Spread (ψ= 3%): 34.4
    - Additional model value: 25.0
  - TB/GDP:
    - Data 1970: 9.8
    - Data 2000: 11.6
    - Benchmark model: 5.6
    - Trade friction (τ= 0.7): 5.5
    - Borrowing constraint (̄a=−0.5): 4.3
    - Spread (ψ= 3%): 3.5

- Persistence (AR(1)) of current account and related series (Table 4)
  - CA/GDP:
    - Advanced: 0.64
    - All countries: 0.84
    - Benchmark model: 0.81
    - Constraint (̄a=−0.5): 0.78
    - Spread (ψ= 3%): 0.75
  - NFA/GDP:
    - Advanced: 0.85
    - All countries: 0.92
    - Benchmark model: 0.99
    - Constraint (̄a=−0.5): 0.99
    - Spread (ψ= 3%): 0.99
  - TB/GDP:
    - Advanced: 0.70
    - All countries: 0.89
    - Benchmark model: 0.83
    - Constraint (̄a=−0.5): 0.80
    - Spread (ψ= 3%): 0.77

- Distributional percentiles for CA/GDP (Table 5)
  - 5% percentile:
    - Data 1970: -10.0
    - Data 2000: -10.3
    - Benchmark: -8.5
    - Constraint (̄a=−0.5): -6.9
    - Spread (ψ= 3%): -5.5
  - 10% percentile:
    - Data 1970: -6.8
    - Data 2000: -7.6
    - Benchmark: -6.4
    - Constraint (̄a=−0.5): -5.2
    - Spread (ψ= 3%): -3.9
  - 50% percentile (median):
    - Data 1970: -1.9
    - Data 2000: -2.5
    - Benchmark: 0.0
    - Constraint (̄a=−0.5): 0.1
    - Spread (ψ= 3%): 0.0
  - 90% percentile:
    - Data 1970: 1.0
    - Data 2000: 9.9
    - Benchmark: 6.1
    - Constraint (̄a=−0.5): 4.9
    - Spread (ψ= 3%): 4.0
  - 95% percentile:
    - Data 1970: 2.7
    - Data 2000: 13.1
    - Benchmark: 7.9
    - Constraint (̄a=−0.5): 6.3
    - Spread (ψ= 3%): 5.4

### Stationarity, persistence, and implications for empirical practice
- Persistence of current accounts increases with the degree of financial integration.
- Dickey–Fuller tests applied to thirty-year simulated samples:
  - Unit root rejected at 5% significance in 78 out of 500 cases (15.6% of the sample) in the benchmark setting.
  - Rejection rates higher with tighter constraints: 27.2% in the model with a larger spread and 19.8% in the model with a smaller (tighter) borrowing limit.
- Implication: Weak power of unit root tests in finite samples and under slowly evolving structural change (rising financial and trade integration); exercise caution when inferring stationarity of current accounts from three- or four-decade samples.
- Higher AR(1) coefficients in more financially integrated economies imply longer durations for current account imbalances.

### Risk sharing and distance to first-best
- Under complete consumption risk sharing (first-best) each country would consume an equal share of world income; model leaves a very large distance to that outcome.
- Consumption distribution in the benchmark is less dispersed than income distribution but far from degenerate.
- Financial integration improves risk sharing: consumption dispersion is lower in economies with higher financial integration.
- Bilateral correlations of consumption growth (30-year simulated data):
  - Mean correlation: 0.031
  - Standard deviation: 0.495
  - Alternative model values: mean correlation 0.028 (larger spread) and 0.030 (smaller borrowing limit)
- Conclusion: model produces positive consumption correlations—evidence of partial risk sharing—but far from full risk sharing (correlation of one).

### Comparison with observed data and historical interpretation
- Model economies show rising dispersion of current account imbalances consistent with the view that financial integration leads to larger (sustainable) imbalances.
- Empirical data show fatter deficit tails than model economies in 1970 and 2000, suggesting some countries may have run excessive deficits (consistent with subsequent crises or sharp reversals).
- On the surplus side, 1970 data show smaller surpluses than in model economies while 2000 data show larger surpluses than model economies, suggesting some countries may be running excessively large surpluses relative to global equilibrium.
- Historical studies cited indicate high current-account dispersion during periods of high international financial integration (e.g., pre–First World War).

### Limitations, extensions, and policy-relevant messages
- Model excludes reversal-of-imports channel by construction; therefore trade-cost driven interest-rate spreads as in Obstfeld and Rogoff (2000) are not generated here.
- Results are obtained with heterogeneity in income only; other heterogeneities (demographics, terms-of-trade fluctuations, alternative financial instruments, investment dynamics) are not modeled and are left for future work.
- Practical policy inference:
  - Financial market frictions materially affect cross-country current account dispersion; policies that reduce such frictions are likely to increase dispersion and prolong adjustments (higher persistence).
  - Caution in using standard unit-root tests on finite samples for policy assessment of sustainability of current account imbalances.

*Source: _wp09276 - Section II), in that the international financial integration has likely been the leitmotif behind the*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09276.pdf_