## _wp1050 ## Source details **Canonical URL:** [_wp1050](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1050.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1050.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1050.pdf.json) --- ### I. Key questions and analytical approach - Central questions: - Are global imbalances sustainable, i.e., consistent with external solvency conditions (the intertemporal budget constraint, IBC)? - Do differences in sustainability across country groups depend on characteristics (income levels, creditor/debtor status)? - Analytical approach: - Apply Bohn (2007) Proposition 3 (PB3): if NX and NFA satisfy an error-correction specification NX_t + ρ NFA_{t-1} = z_t with ρ < 0 and |ρ| ∈ (0, 1 + r], then the IBC holds. - Estimate panel error-correction relationship between NX-GDP ratio (nx) and NFA-GDP ratio (nfa) for a dataset covering 51 countries during 1970-2004. - Use Pesaran et al. (1999) Pooled Mean Group (PMG) and Mean Group (MG) estimators; choose between them using a Hausman test for long-run slope homogeneity. ### II. Data and sample - Sample period: 1970-2004. - Country coverage: 51 countries (21 industrial countries (IC) and 29 emerging markets (EM) noted; sample selection based on data starting on or before 1990). - Observations: 1742 total observations; 733 observations correspond to IC group and 1009 observations to EM group. - NFA data source: Lane and Milesi-Ferretti (2006). - NX and GDP data source: IMF International Financial Statistics. ### III. Main estimation results (PMG preferred where homogeneity cannot be rejected) - Full sample (Block 1, baseline): - Long-run response coefficient (ρ): 0:07. - Error-correction coefficient (phi): 0:31. - Implied average half-life of adjustment of nx to a change in nfa: just over 1.85 years (also reported as just over 1.75 years in another calculation using log formula; half-life formula used: log(0:5)/log(1 - |EC|)). - Interpretation: PB3 and external solvency conditions hold for the full sample. - Industrial vs Emerging markets (Block 1): - Long-run response coefficients: IC: 0:053; EM: 0:085. - Relative responsiveness: EM response coefficient is about 1.6 times larger than IC. - Half-lives: - IC average half-life: about 2:8 years. - EM average half-life: 1 1/2 years. - Implication: nx is more responsive to nfa in EMs; industrial countries converge to lower long-run averages of nfa consistent with external solvency. - World-GDP normalization (Block 2 robustness): - Full sample PMG response coefficient: 0:08; average half-life: 1 3/4 years. - IC (world GDP ratios): PMG 0:057; half-life: 2.6 years. - EM (world GDP ratios): MG preferred; MG estimate 0:225; half-life: 1.2 years. - Creditor vs Debtor split (Panel 1, Table 4): - Creditor (High NFA) PMG: 0:095; average half-life: 1.94 years. - Debtor (Low NFA) PMG: 0:061; average half-life: 1.8 years. - Conclusion: No significant behavioral difference for sustainability; creditors converge to higher nfa in the long run. - Trade openness split (Panel 2, Table 4): - More open economies PMG: 0:070; half-life: 2.8 years. - Less open economies PMG: 0:065; half-life: 1.4 years. - Conclusion: No significant difference between more and less open economies in long-run response. - Institutional quality, financial development, capital account openness (Panels 3–5, Table 4): - In all cases the Hausman test cannot reject long-run homogeneity and PMG preferred. - Countries with weaker fundamentals display more negative long-run coefficients (stronger nx response to nfa), consistent with more limited access to financial markets or greater financial frictions. - Baseline conclusion on sustainability preserved. ### IV. Long-run NFA convergences and heterogeneity - Long-run average formula when nfa is stationary under estimated parameters: - E[nfa_i] = mu_i / (phi_i (rho_i + r)) - Under PMG, rho_i = rho (common), but mu_i and phi_i may be country-specific → heterogeneity in predicted E[nfa_i]. - Table 3 exercise: selected countries with significant phi and mu show marked variation in long-run nfa driven by differences in phi and mu even when rho is common. - Impulse response analysis (Figures 2a-b using PMG estimates) with a one-standard-deviation noise shock: - nx can converge back faster, but nfa (the stock imbalance) can persist much longer. - Convergence of nfa to long-run values takes from about 10 years up to 50 years across countries. - Framework preserves heterogeneity across countries in responses to similar shocks. ### V. Integration and stationarity evidence (PB1-based tests) - PB1: If NFA is integrated of finite order m, then the IBC holds; testing for solvency via integration order is an alternative approach. - Tests applied: - Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests on nfa levels and first differences. - KPSS stationarity tests (null of stationarity) as robustness. - Findings: - ADF and PP cannot reject unit root in nfa levels at common significance levels for all countries. - For first differences, ADF and PP reject the unit root null in favor of stationarity for almost all countries → most countries’ nfa are I(1). - KPSS results corroborate that nfa is integrated of finite order for most countries. - Exceptions and caveats: - Very few countries (e.g., Belgium, Norway) where first-difference stationarity could not be rejected. - Transition economies (Lithuania, Poland, Russia, Slovenia): tests inconclusive, largely due to shorter samples (data starting in early 1990s). - U.S. robustness: long-run U.S. nfa series (1790-2004) and valuation-corrected series preserve main finding: nfa nonstationary in levels but stationary in first differences. - Overall implication: observed NFA positions are consistent with external solvency per PB1 and PB3. ### VI. Interpretation, general-equilibrium considerations, and economic intuition - PB3 implication: a statistically significant negative error-correction relationship between NX and lagged NFA is a sufficient condition for transversality condition (TC) and IBC. - Economic intuition: - Negative rho implies NX reacts in the long run to changes in NFA so that NFA grows slower than a Ponzi scheme implies. - Larger |rho| implies stronger NX response to NFA changes; typically associated with countries facing greater financial frictions or less access to international financial markets. - General equilibrium extension: - In small open-economy general equilibrium with complete contingent-claims markets, the IBC involves stochastic discount factors (equilibrium pricing kernel). - PB3’s sufficiency for solvency holds even when discount rates vary across time and states, although the appropriate discounting in the IBC becomes the equilibrium asset pricing kernel rather than a constant risk-free rate. - Covariances between stochastic discount factors and NX enter the IBC; countries with lower covariances (for given expected PDV of NX) should display lower initial NFA. - Policy-relevant implication: - Stronger NX responsiveness (more negative rho) can be interpreted as evidence of limited financial market access or binding financial frictions, which shapes the long-run NFA outcomes and adjustment dynamics. ### VII. Robustness and limitations - Robustness checks performed: - Alternative normalizations (world GDP ratios), creditor/debtor splits, trade openness, institutional quality, financial development, capital account openness. - Alternative estimators (MG vs PMG) with Hausman tests guiding estimator choice. - ADF, PP, KPSS stationarity/integration tests; allowance for structural breaks, intercepts, and trends. - Longer U.S. series and valuation-corrected series for the U.S. confirm main results. - Limitations noted: - Data availability limits (best NFA dataset covers 1970-2004). - Inference caveats from short samples: ADF and PP tests have limited power to distinguish unit roots from near unit roots or drifting processes. - Some country-specific results inconclusive due to short samples (transition economies). ### VIII. Summary of salient numerical findings - Sample and observations: - 51 countries; period 1970-2004. - 1742 observations total; 733 IC; 1009 EM. - Estimated coefficients and implied dynamics (baseline PMG, full sample): - Long-run response coefficient (rho): 0:07. - Error-correction coefficient (phi): 0:31. - Implied half-life of nx adjustment: just over 1.85 years (reported also as just over 1.75 years). - Subsample coefficients and half-lives: - IC long-run response: 0:053; half-life ≈ 2:8 years. - EM long-run response: 0:085; half-life ≈ 1 1/2 years. - EM response ≈ 1.6 times IC response. - World-GDP normalization: - Full sample PMG: 0:08; half-life 1 3/4 years. - EM MG (world-GDP ratios): 0:225; half-life 1.2 years. - Creditor vs Debtor: - Creditors PMG: 0:095; half-life 1.94 years. - Debtors PMG: 0:061; half-life 1.8 years. - Trade openness: - More open PMG: 0:070; half-life 2.8 years. - Less open PMG: 0:065; half-life 1.4 years. - Integration tests: - ADF and PP: nfa nonstationary in levels for most countries; first differences stationary for almost all → nfa ≈ I(1) in most cases. - Unit-root testing reported coefficient range and errors: - Reported estimated coefficients lie in the range 0.59 to 1.06, and their standard errors are relatively large (ranging from 0.065 to 0.146). ### IX. Conclusion (main messages) - The paper finds a statistically significant error-correction relationship linking NX and NFA, consistent with Bohn (2007) proposition that solvency holds if NX and NFA are linked by an error-correction reaction function. - There is a systematic, negative long-run response of nx to changes in nfa. - Emerging economies exhibit a larger response coefficient than industrial countries and converge to higher long-run averages of nfa. - Testing for error-correction dynamics and estimating adjustment speeds provides richer information about sustainability than stationarity tests alone, given the low power of unit-root tests and the economic irrelevance of simple difference-stationarity in the presence of debt bounds. _Italic: Content derived from the supplied excerpt of the IMF working paper._ ### References ............................................................................................................. ### _wp1050 - References ............................................................................................................. ### Appendices - Appendix I: Derivation of the PMG equation ..........................................................................28 - Appendix II: Sample of Countries ...........................................................................................30 ### Tables - 1. Sample Statistics ..........................................................................................................31 - 2. Dynamic Panel Estimates of Net Exports on Net Foreign Assets ...............................32 - 3. Long-run NFA .............................................................................................................33 - 4. Dynamic Panel Estimates of Net Exports on Net Foreign Assets ...............................34 ### Figures - 1a. Current Account Balances ...........................................................................................35 - 1b. Net Foreign Assets .......................................................................................................36 - 2. The Order of Integration of Net Foreign Assets Positions ..........................................37 - Lag = 1 .........................................................................................................................38 *Source: _wp1050 - References .............................................................................................................* ### 3. The Estimated AR(1) Coefficients -Net Foreign Assets..............................................39 ### 3. The Estimated AR(1) Coefficients -Net Foreign Assets..............................................39 ### I. Key questions and analytical approach - Central questions: - Are global imbalances sustainable, i.e., consistent with external solvency conditions (the intertemporal budget constraint, IBC)? - Do differences in sustainability across country groups depend on characteristics (income levels, creditor/debtor status)? - Analytical approach: - Apply Bohn (2007) Proposition 3 (PB3): if NX and NFA satisfy an error-correction specification NX_t + ρ NFA_{t-1} = z_t with ρ < 0 and |ρ| ∈ (0, 1 + r], then the IBC holds. - Estimate panel error-correction relationship between NX-GDP ratio (nx) and NFA-GDP ratio (nfa) for a dataset covering 51 countries during 1970-2004. - Use Pesaran et al. (1999) Pooled Mean Group (PMG) and Mean Group (MG) estimators; choose between them using a Hausman test for long-run slope homogeneity. ### II. Data and sample - Sample period: 1970-2004. - Country coverage: 51 countries (21 industrial countries (IC) and 29 emerging markets (EM) noted; sample selection based on data starting on or before 1990). - Observations: 1742 total observations; 733 observations correspond to IC group and 1009 observations to EM group. - NFA data source: Lane and Milesi-Ferretti (2006). - NX and GDP data source: IMF International Financial Statistics. ### III. Main estimation results (PMG preferred where homogeneity cannot be rejected) - Full sample (Block 1, baseline): - Long-run response coefficient (ρ): 0:07 (i.e., a one percentage point drop in nfa leads to a 0.07 percentage points increase in nx in the long run). - Error-correction coefficient (phi): 0:31. - Implied average half-life of adjustment of nx to a change in nfa: just over 1.85 years (also reported as just over 1.75 years in another calculation using log formula; half-life formula used: log(0:5)/log(1 - |EC|)). - Interpretation: PB3 and external solvency conditions hold for the full sample. - Industrial vs Emerging markets (Block 1): - Long-run response coefficients: IC: 0:053; EM: 0:085. - Relative responsiveness: EM response coefficient is about 1.6 times larger than IC. - Half-lives: - IC average half-life: about 2:8 years. - EM average half-life: 1 1/2 years. - Implication: nx is more responsive to nfa in EMs; industrial countries converge to lower long-run averages of nfa consistent with external solvency. - World-GDP normalization (Block 2 robustness): - Full sample PMG response coefficient: 0:08; average half-life: 1 3/4 years. - IC (world GDP ratios): PMG 0:057; half-life: 2.6 years. - EM (world GDP ratios): MG preferred; MG estimate 0:225 (almost 3 times larger than earlier EM estimate); half-life: 1.2 years. - Creditor vs Debtor split (Panel 1, Table 4): - Creditor (High NFA) PMG: 0:095; average half-life: 1.94 years. - Debtor (Low NFA) PMG: 0:061; average half-life: 1.8 years. - Conclusion: No significant behavioral difference for sustainability; creditors converge to higher nfa in the long run. - Trade openness split (Panel 2, Table 4): - More open economies PMG: 0:070; half-life: 2.8 years. - Less open economies PMG: 0:065; half-life: 1.4 years. - Conclusion: No significant difference between more and less open economies in long-run response. - Institutional quality, financial development, capital account openness (Panels 3–5, Table 4): - In all cases the Hausman test cannot reject long-run homogeneity and PMG preferred. - Countries with weaker fundamentals display more negative long-run coefficients (stronger nx response to nfa), consistent with more limited access to financial markets or greater financial frictions. - Baseline conclusion on sustainability preserved. ### IV. Long-run NFA convergences and heterogeneity - If nfa is stationary under estimated parameters, long-run average E[nfa_i] is given by: - E[nfa_i] = mu_i / (phi_i (rho_i + r)) - Under PMG, rho_i = rho (common across countries), but mu_i and phi_i can be country-specific, producing heterogeneity in predicted E[nfa_i]. - Table 3 exercise (selected countries with significant phi and mu) shows marked variation in long-run nfa driven by differences in phi and mu even when rho is common. - Impulse response analysis (Figures 2a-b using PMG estimates) with a one-standard-deviation noise shock: - nx can converge back faster, but nfa (the stock imbalance) can persist much longer. - Convergence of nfa to long-run values takes from about 10 years up to 50 years across countries. - Framework preserves heterogeneity across countries in responses to similar shocks. ### V. Integration and stationarity evidence (PB1-based tests) - PB1: If NFA is integrated of finite order m, then the IBC holds; testing for solvency via integration order is an alternative approach. - Tests applied: - Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests on nfa levels and first differences. - KPSS stationarity tests (null of stationarity) as robustness. - Findings: - ADF and PP cannot reject unit root in nfa levels at common significance levels for all countries. - For first differences, ADF and PP reject the unit root null in favor of stationarity for almost all countries → most countries’ nfa are I(1). - KPSS results corroborate that nfa is integrated of finite order for most countries. - Exceptions and caveats: - Very few countries (e.g., Belgium, Norway) where first-difference stationarity could not be rejected. - Transition economies (Lithuania, Poland, Russia, Slovenia): tests inconclusive, largely due to shorter samples (data starting in early 1990s). - Us robustness: long-run U.S. nfa series (1790-2004) and valuation-corrected series preserve main finding: nfa nonstationary in levels but stationary in first differences. - Overall implication: observed NFA positions are consistent with external solvency per PB1 and PB3. ### VI. Interpretation, general-equilibrium considerations, and economic intuition - PB3 implication: a statistically significant negative error-correction relationship between NX and lagged NFA is a sufficient condition for transversality condition (TC) and IBC. - Economic intuition: - Negative rho implies NX reacts in the long run to changes in NFA so that NFA grows slower than a Ponzi scheme implies. - Larger |rho| implies stronger NX response to NFA changes; typically associated with countries facing greater financial frictions or less access to international financial markets. - General equilibrium extension: - In small open-economy general equilibrium with complete contingent-claims markets, the IBC involves stochastic discount factors (equilibrium pricing kernel). - PB3’s sufficiency for solvency holds even when discount rates vary across time and states, although the appropriate discounting in the IBC becomes the equilibrium asset pricing kernel rather than a constant risk-free rate. - Covariances between stochastic discount factors and NX enter the IBC; countries with lower covariances (for given expected PDV of NX) should display lower initial NFA. - Policy-relevant implication: - Stronger NX responsiveness (more negative rho) can be interpreted as evidence of limited financial market access or binding financial frictions, which shapes the long-run NFA outcomes and adjustment dynamics. ### VII. Robustness and limitations - Robustness checks performed: - Alternative normalizations (world GDP ratios), creditor/debtor splits, trade openness, institutional quality, financial development, capital account openness. - Alternative estimators (MG vs PMG) with Hausman tests guiding estimator choice. - ADF, PP, KPSS stationarity/integration tests; allowance for structural breaks, intercepts, and trends. - Longer U.S. series and valuation-corrected series for the U.S. confirm main results. - Limitations noted: - Data availability limits (best NFA dataset covers 1970-2004). - Inference caveats from short samples: ADF and PP tests have limited power to distinguish unit roots from near unit roots or drifting processes. - Some country-specific results inconclusive due to short samples (transition economies). ### VIII. Summary of salient numerical findings - Sample and observations: - 51 countries; period 1970-2004. - 1742 observations total; 733 IC; 1009 EM. - Estimated coefficients and implied dynamics (baseline PMG, full sample): - Long-run response coefficient (rho): 0:07. - Error-correction coefficient (phi): 0:31. - Implied half-life of nx adjustment: just over 1.85 years (reported also as just over 1.75 years). - Subsample coefficients and half-lives: - IC long-run response: 0:053; half-life ≈ 2:8 years. - EM long-run response: 0:085; half-life ≈ 1 1/2 years. - EM response ≈ 1.6 times IC response. - World-GDP normalization: - Full sample PMG: 0:08; half-life 1 3/4 years. - EM MG (world-GDP ratios): 0:225; half-life 1.2 years. - Creditor vs Debtor: - Creditors PMG: 0:095; half-life 1.94 years. - Debtors PMG: 0:061; half-life 1.8 years. - Trade openness: - More open PMG: 0:070; half-life 2.8 years. - Less open PMG: 0:065; half-life 1.4 years. - Integration tests: - ADF and PP: nfa nonstationary in levels for most countries; first differences stationary for almost all → nfa ≈ I(1) in most cases. *Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1050.pdf* ### 0.59 to 1.06, and that their standard errors are relatively large (ranging from 0.065 to ### IV. Conclusion ### Main findings - The paper finds a statistically significant error-correction relationship linking NX and NFA in the data, consistent with Bohn (2007) proposition that solvency holds if NX and NFA are linked by an error-correction reaction function. - There is a systematic, negative long-run response of nx to changes in nfa. - Comparing country groups: - The response coefficient for emerging countries is higher than for industrial countries. - As a result, emerging economies converge to higher long-run averages of nfa than industrial countries. - Sample and period: - Panel of 21 industrial and 30 emerging market countries. - Period covered: 1970-2004. ### Tests, estimation, and numerical evidence - Unit-root testing results: - The hypothesis of unit roots in nfa could not be rejected. - Reported estimated coefficients lie in the range 0.59 to 1.06, with standard errors ranging from 0.065 to 0.146. - The authors note that due to the low power of the tests, the true data generating process might be stationary in levels; stationarity in levels would still be consistent with PB1 and would not affect the finding that the data support the hypothesis that the solvency condition holds. - Estimation approach: - Main solvency test based on Bohn (2007). - Dynamic panel estimation methods used to detect the error-correction relationship between NX and NFA. - Analytical framework: - The ARDL/PMG representation is used to highlight the long-run equilibrium relationship, where the long-run coefficient ζ_i (denoted as _i in the derivation) equals -ϵ_i^{-1} ' _i and ϵ_i denotes the speed at which NX adjust toward their long-run equilibrium following a change in NFA. ### Caveats and interpretation - Bohn (2007) caveat reiterated: - It is hard to imagine a macroeconomic time series that is not integrated of low order. - If bounds on debt or nfa exist, testing the null hypothesis of difference-stationarity seems economically uninteresting because, with debt limits, m = 1 is not sufficient for sustainability. - Implication: - Shedding light on the characteristics of the adjustment process that sustains solvency is more important than relying solely on stationarity tests; this motivates testing for error-correction relationships. _Italic: Content derived from the supplied excerpt of the IMF working paper._ --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1050.pdf_