## wpiea2019193-print-pdf

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---

### Data sources and measurement
- Foreign and domestic value added embedded in gross exports destined to final demand are from the OECD TiVA database; the latest OECD TiVA edition spans 2005-2015 and is spliced with 1995-2005 from the previous edition.
- Data include trade in services as well as goods.
- Deflators: baseline uses export deflators; alternative GDP deflators were considered. All deflator data are from the World Economic Outlook database.
- For foreign value added embedded in country i’s exports to final demand, the deflator is a weighted average of country i’s partners’ deflators; weights account for direct and indirect input requirements using input-output methods (W = (I − X)−1) and re-normalizing non-diagonal elements to add up to one.
- Trade-based weights use 3-year rolling windows (with 1995 and 1996 handled via one- and two-year windows).
- Intermediate-input trade data are from the OECD Inter-Country Input-Output Tables.
- Real effective exchange rates (REER) are from the IMF INS database; the weighted REER of trading partners is used with weights based on direct and indirect input requirements.
- Foreign demand is measured as an export-weighted average of partners’ real GDPs (weights based on final-goods exports). Real GDP and commodity price indices are from the World Economic Outlook database.
- Variables (except domestic and foreign value added shares) are measured in natural logarithms. REERs and interaction terms are measured with a one-period lag to mitigate endogeneity.

### Sample coverage and composition
- Sample excludes four large oil exporters available in TiVA (Bahrain, Norway, Russia and Saudi Arabia) for some calculations; leaves a sample of 59 economies: Argentina, Australia, Austria, Belgium, Bulgaria, Brazil, Canada, Switzerland, Chile, China, Colombia, Costa Rica, Cyprus, Czech Republic, Germany, Denmark, Spain, Estonia, Finland, France, the UK, Greece, Hong Kong SAR, Croatia, Hungary, Indonesia, India, Ireland, Iceland, Israel, Italy, Japan, Cambodia, Korea, Lithuania, Luxembourg, Latvia, Morocco, Mexico, Malta, Malaysia, the Netherlands, New Zealand, Peru, Philippines, Poland, Portugal, Romania, Singapore, Slovakia, Slovenia, Sweden, Thailand, Tunisia, Turkey, Taiwan P.O.C., the U.S., Vietnam and South Africa.
- The dataset covers over 90 percent of global output.

### Evolution of trade and supply chains (summary statistics)
- For the 63 economies in the dataset:
  - Gross trade rose from 16½ percent of GDP in 1995 to peak at 23½ percent in 2008, then fell to 21½ percent in 2015.
  - Trade in domestic value added rose from 14 percent of GDP in 1995 to a peak of 18 percent in 2008, then fell to 17 percent in 2015.
- Interpretation: major deepening of supply chains up to 2008, followed by a modest decline; China’s shift to relying on domestic demand after 2008 contributed to the post-2008 decline.
- Excluding China, trade openness (gross trade or domestic value added) flat-lined after the global crisis, suggesting offsetting forces (e.g., rising protectionism).
- Regional patterns (examples):
  - Central and eastern European supply chain (centered on Germany) value added (gross) exports: from 16½ (19½) percent of GDP in 1995 to 25½ (35) percent in 2008, and to 28 (38) percent in 2015.
  - Asian supply chain excluding China continued to deepen after 2008.
  - Initial 12 Euro area members (excluding Germany) accelerated export openness after 2008.
  - North American region and several remaining European countries stagnated.
  - Rest of the world group saw significant reversal: value added (gross) export openness rose from 13 (14½) percent of GDP in 1995 to 18 (21½) percent by 2008, then lost much of those gains by 2015.
- Country positions in 2015 by roles in value chains:
  - Final-assembly specialists (low domestic value added, high final goods): Slovakia, Mexico, Vietnam.
  - Middle-of-supply-chain (high foreign goods, not final assembly): Korea, Taiwan Province of China, Malaysia, Thailand, Hungary, Czech Republic, Bulgaria, Estonia.
  - Hubs (high domestic value added, middling final goods): Germany, China, Japan, United States, Brazil, Israel, India.
  - Commodity producers (high domestic value added, low final goods): Saudi Arabia, Bahrain, Chile, Peru, Russia, Canada, South Africa.

### Empirical strategy and controls
- Error-correction model specification is used; an error correction term is estimated.
- Controls included in all regressions: foreign demand (export-weighted partners’ real GDP), an index of oil prices, and an index of non-fuel commodity prices.
- Short-run dynamics and long-run coefficients are reported separately.

### Main empirical results
- Error correction and adjustment:
  - The estimated error correction term is highly significant in both foreign and domestic value-added equations, indicating a cointegrating relationship.
  - Estimated speed of adjustment implies a half-life for deviations from the long-run relationships of about 3 years for the foreign value-added equation, and 4 years for domestic value added.
  - Closing three-quarters of any short-run deviation requires between 8 and 9 years.
  - Short-run coefficients remain relevant even for horizons of 5 years.
- Controls:
  - Foreign demand increases exports of foreign and domestic value added, in both short and long run.
  - Higher commodity prices mostly act as a negative supply shock in exports of domestic value added (negative sign in baseline results for DVA), with some exceptions for non-fuel commodity prices in the long-run equation.
  - Commodity-price variables positively affect exports of foreign value added in the baseline, possibly reflecting deflator issues and a larger share of commodities in FVA series.
- Supply-chain flexibility vs. inflexibility:
  - The hypothesis that global supply chains are flexible is overwhelmingly rejected in both short and long run.
  - Interaction terms in the foreign value-added equation are highly significant in the short run; domestic value-added estimates are less precise.
  - A rough estimate of the degree of inflexibility (short term, foreign value added) is between ¾ and 1, more precisely from 0.477/0.64 to 0.677/0.64 (a formal test that trade is fully inflexible is rejected).
  - Equivalent coefficients in the domestic value added equation are above 1 but less well estimated; in that case a formal test does not reject that the supply chain is fully inflexible.
  - Overall, using the entire sample, supply chains are estimated to be not far from the extreme case of a Leontief (fully inflexible) structure.

### Appendix B — Short-run inflexibility and core finding
- Appendix B corollary: if one thinks of a world with a mixture of one fully flexible and one fully inflexible good, the estimates imply that the contribution of the inflexible good to global supply chains in the short run is of at least 60 percent.
- Short-run production structure is described as "very inflexible" in the paper’s estimates.
- Short-run results: estimated coefficients tend to be smaller in absolute value than long-run ones, but interaction terms indicate production complementarities and short-run inflexibility persist.

### Long-run complementarities and inflexibility
- Long-run elasticities are larger in absolute value, but complementarities in production persist.
- Estimated coefficient of inflexibility:
  - foreign valued equation: ¼ to ½
  - domestic value-added equation: 2/3 to 1
- Conclusion: expenditure decisions at the production stage remain less flexible to price changes than final-demand expenditure decisions even in the long run.

### Evolution over time and structural break
- The growth of supply chains accelerated since the early 2000s; if this reflects more complex intermediates traded, overall degree of flexibility should fall.
- Short-run responses of supply chains have become increasingly inflexible over time as supply chains deepened.
- Subsample re-estimation (removing either the last or first five years) suggests that production linkages might have become fully inflexible in the short run more recently:
  - Hypothesis that supply chain is completely inflexible in the short-term (훼훼=훽훽=−훾훾) is rejected in the 1995-2010 sample with Wald test p-values of 0.0001 and 0.0152 in the FVA and the DVA equations, respectively.
  - The same hypothesis cannot be rejected in either equation over the 2000-2015 sample (Wald-test p-values of 0.87 and 0.13, respectively).
- Interpretation: the rising share of foreign inputs in international trade is associated with increasingly complex production chains involving more specialized inputs.

### Dominant Currency Paradigm (DCP) robustness
- DCP effective exchange rate for country i (non-U.S.) is defined as:
  - RER_i^DCP ≡ ν_i RER_{i,US} + (1−ν_i) RER_{i,−US}
  - where ν_i is the share of trade invoiced in U.S. dollars, RER_{i,US} is bilateral real exchange rate vis-à-vis the U.S., and RER_{i,−US} is the real effective exchange rate recalculated to exclude the U.S.
- Country-level shares of trade invoiced in U.S. dollars are taken from Gopinath (2016); ν_i is the simple average of export and import dollar invoicing for own EER; partner ν_i for import-weighted partner EERs is set equal to partner’s share of exports invoiced in dollars.
- Results using the DCP measure (smaller sample due to invoicing data availability):
  - All estimates remain significant in the foreign value-added (FVA) equation.
  - Significance of interaction terms increases in the domestic value-added (DVA) equation.
  - In the smaller sample, estimated speed of adjustment in the FVA equation is substantially lower and foreign demand enters with the wrong sign.
- Overall conclusion: evidence of supply-chain inflexibility is robust to using an effective exchange rate that accounts for the U.S. dollar’s role in trade invoicing.

### Country-level evidence of production complementarities
- The pooled-mean-group estimator is used to compute, for each country and each value-added component, a test statistic for the null hypothesis of no production complementarities (훽훽=훾훾=0).
- Complementarities are strong enough in many countries to overcome sample imprecision despite a short time span (21 years).
- Countries showing strong evidence include supply-chain hubs and major participants:
  - Asian chain examples: Thailand, Taiwan POC, China, Japan
  - North American chain: Mexico, Canada, United States
  - Some European countries: France, Germany
- Using the DCP-based effective exchange rate leads to the same overarching conclusion.

### Implications for trade and economic activity (quantitative mapping)
- System of equations (3)-(4) is used to trace effects of REER movements on components of a country’s gross exports.
- For intermediates exports, short-run response of i’s intermediates exports to a change in i’s REER of magnitude ∆REER_i is:
  - ∆REER_i × Σ_{j≠i} ω_{ij} (α_i + γ_i dvat_{ij})
  - where ω_{ij} is share of j’s imports of intermediates originating from i, and coefficients α_i and γ_i correspond to equation (3).
- Average-sample numerical example (average country in sample):
  - average domestic value-added share dvat_bar = 0.75
  - in the cross-section, exports of intermediates represent 58 percent of total exports
  - Short-run estimated response of the average country’s value-added exports to a one percentage point depreciation:
    - Calculated aggregate response = 0.12
    - Breakdown implied by point estimates:
      - domestic value-added exports destined to final demand increase by 0.11 percent in response to a one percentage point REER depreciation
      - domestic value added exported as intermediates increase by 0.13 percent in response to a one percentage point REER depreciation
- Interpretation: complementarities in production temper the effect of depreciations. While openness has been rising (even measured as domestic value-added content), the impact of exchange rate changes on output has been rising even as supply-chain development has tempered the impact on gross trade.

### Concluding remarks and policy implications
- Core finding restated: global supply chains are largely inflexible in the short term and relatively inflexible in the long run.
- Business-cycle implications:
  - International production structure is crucial to understand how shocks reverberate globally.
  - Under supply-chain inflexibility, temporary disruptions are harder to resolve (example: natural-disaster effects on supply chains).
  - Insensitivity of producers to price changes increases the importance of countries with large final consumption in competitiveness calculations.
  - Exchange-rate changes vis-à-vis countries that consume final goods become more important; partners within the same regional value chain become relatively less important.
- Robustness: finding is robust to alternative price measures, including those accounting for the U.S. dollar’s outsized role in trade invoicing.
- Suggested future work: examine results excluding commodity trade to focus on supply chains incorporating manufacturing components and complementary services.

### Appendix B — Formal derivation and numerical bound (selected expressions and solution)
- Parameter estimates and implied values (from expression (6) and equation (5) as referenced in the source):
  - α [1 − (I_IF_DVA / I_DVA) × (I_DVA_dom / I) ] = −2/3
  - α (I_IF_DVA / I_DVA) × (I_DVA_dom / I) = −1/2
- Solution for the two unknowns (source):
  - α = −7/6
  - (I_IF_DVA / I_DVA) × (I_DVA_dom / I) = 3/7  (equation (7))
- Numerical bound using cross-country average:
  - The 2015 cross-country average domestic value added share of exports in the dataset is 0.75.
  - Using that upper bound, the foreign-value added coefficient estimates suggest that:
    - I_IF_DVA / I_DVA ≥ 3/7 0.75 ≅ 0.6.
  - Short-run implication stated in the source: "in the short run global supply chains can be thought of as being at least 60 percent fully inflexible."
- Supporting example note: Timmer et al. (2015, Table 1) show that, as of 2008, German value added represents only 66 percent of the total value of Germany’s automotive output, illustrating a case where domestic value added share is below 0.75.

### Table A1 (selected estimation results — export deflators baseline v. GDP deflators)
- Panel: LONG RUN (selected coefficients and t statistics)
  - Importing partners' EER: -2.252  (t statistic: -5.45) ***
  - Own EER x DVA share: -0.607  (t statistic: -4.60) ***
  - Importing partners' EER: 1.295  (t statistic: 5.07) ***
  - Own EER: -0.750  (t statistic: -6.34) ***
  - Importing partners' EER: -0.435  (t statistic: -0.75)
  - Own EER x FVA share: 1.381  (t statistic: 2.31) **
  - Foreign demand: 0.170  (t statistic: 1.51)
  - Oil price: 0.156  (t statistic: 3.89) ***
  - Non-fuel commodity: 0.262  (t statistic: 4.28) ***
- Panel: SHORT RUN (selected coefficients and t statistics)
  - Error-correction term: -0.202  (t statistic: -7.10) ***
  - Importing partners' EER: -0.640  (t statistic: -2.94) ***
  - Own EER x DVA share: -0.477  (t statistic: -4.43) ***
  - Importing partners' EER: 0.677  (t statistic: 5.56) ***
  - Own EER: -0.297  (t statistic: -1.54)
  - Importing partners' EER: -0.719  (t statistic: -1.01)
  - Own EER x FVA share: 0.757  (t statistic: 1.05)
  - Foreign demand: 3.227  (t statistic: 12.23) ***
  - Oil price: 0.0090  (t statistic: 0.43)
  - Non-fuel commodity: 0.124  (t statistic: 2.58) ***
  - Constant: 1.899  (t statistic: 7.03) ***
- Additional reporting:
  - N = 1,116, 1,117, 1,116, 1,117 (as reported in the table)
  - t statistics in parentheses
  - Significance codes: * p<0.1   ** p<0.05   *** p<0.01

*Source: wpiea2019193-print-pdf (excerpt provided).*

### conclusions for the average economy in the world. Second, the shocks associated with these

### wpiea2019193-print-pdf - conclusions for the average economy in the world. Second, the shocks associated with these

### Data sources and measurement
- Foreign and domestic value added embedded in gross exports destined to final demand are from the OECD TiVA database; the latest OECD TiVA edition spans 2005-2015 and is spliced with 1995-2005 from the previous edition.
- Data include trade in services as well as goods.
- Deflators: baseline uses export deflators; alternative GDP deflators were considered. All deflator data are from the World Economic Outlook database.
- For foreign value added embedded in country i’s exports to final demand, the deflator is a weighted average of country i’s partners’ deflators; weights account for direct and indirect input requirements using input-output methods (W = (I − X)−1) and re-normalizing non-diagonal elements to add up to one.
- Trade-based weights use 3-year rolling windows (with 1995 and 1996 handled via one- and two-year windows).
- Intermediate-input trade data are from the OECD Inter-Country Input-Output Tables.
- Real effective exchange rates (REER) are from the IMF INS database; the weighted REER of trading partners is used with weights based on direct and indirect input requirements.
- Foreign demand is measured as an export-weighted average of partners’ real GDPs (weights based on final-goods exports). Real GDP and commodity price indices are from the World Economic Outlook database.
- Variables (except domestic and foreign value added shares) are measured in natural logarithms. REERs and interaction terms are measured with a one-period lag to mitigate endogeneity.

### Sample coverage and composition
- Sample excludes four large oil exporters available in TiVA (Bahrain, Norway, Russia and Saudi Arabia) for some calculations; leaves a sample of 59 economies: Argentina, Australia, Austria, Belgium, Bulgaria, Brazil, Canada, Switzerland, Chile, China, Colombia, Costa Rica, Cyprus, Czech Republic, Germany, Denmark, Spain, Estonia, Finland, France, the UK, Greece, Hong Kong SAR, Croatia, Hungary, Indonesia, India, Ireland, Iceland, Israel, Italy, Japan, Cambodia, Korea, Lithuania, Luxembourg, Latvia, Morocco, Mexico, Malta, Malaysia, the Netherlands, New Zealand, Peru, Philippines, Poland, Portugal, Romania, Singapore, Slovakia, Slovenia, Sweden, Thailand, Tunisia, Turkey, Taiwan P.O.C., the U.S., Vietnam and South Africa.
- The dataset covers over 90 percent of global output.

### Evolution of trade and supply chains (summary statistics)
- For the 63 economies in the dataset:
  - Gross trade rose from 16½ percent of GDP in 1995 to peak at 23½ percent in 2008, then fell to 21½ percent in 2015.
  - Trade in domestic value added rose from 14 percent of GDP in 1995 to a peak of 18 percent in 2008, then fell to 17 percent in 2015.
- Interpretation: major deepening of supply chains up to 2008, followed by a modest decline; China’s shift to relying on domestic demand after 2008 contributed to the post-2008 decline.
- Excluding China, trade openness (gross trade or domestic value added) flat-lined after the global crisis, suggesting offsetting forces (e.g., rising protectionism).
- Regional patterns (examples):
  - Central and eastern European supply chain (centered on Germany) value added (gross) exports: from 16½ (19½) percent of GDP in 1995 to 25½ (35) percent in 2008, and to 28 (38) percent in 2015.
  - Asian supply chain excluding China continued to deepen after 2008.
  - Initial 12 Euro area members (excluding Germany) accelerated export openness after 2008.
  - North American region and several remaining European countries stagnated.
  - Rest of the world group saw significant reversal: value added (gross) export openness rose from 13 (14½) percent of GDP in 1995 to 18 (21½) percent by 2008, then lost much of those gains by 2015.
- Country positions in 2015 by roles in value chains:
  - Final-assembly specialists (low domestic value added, high final goods): Slovakia, Mexico, Vietnam.
  - Middle-of-supply-chain (high foreign goods, not final assembly): Korea, Taiwan Province of China, Malaysia, Thailand, Hungary, Czech Republic, Bulgaria, Estonia.
  - Hubs (high domestic value added, middling final goods): Germany, China, Japan, United States, Brazil, Israel, India.
  - Commodity producers (high domestic value added, low final goods): Saudi Arabia, Bahrain, Chile, Peru, Russia, Canada, South Africa.

### Empirical strategy and controls
- Error-correction model specification is used; an error correction term is estimated.
- Controls included in all regressions: foreign demand (export-weighted partners’ real GDP), an index of oil prices, and an index of non-fuel commodity prices.
- Short-run dynamics and long-run coefficients are reported separately.

### Main empirical results
- Error correction and adjustment:
  - The estimated error correction term is highly significant in both foreign and domestic value-added equations, indicating a cointegrating relationship.
  - Estimated speed of adjustment implies a half-life for deviations from the long-run relationships of about 3 years for the foreign value-added equation, and 4 years for domestic value added.
  - Closing three-quarters of any short-run deviation requires between 8 and 9 years.
  - Short-run coefficients remain relevant even for horizons of 5 years.
- Controls:
  - Foreign demand increases exports of foreign and domestic value added, in both short and long run.
  - Higher commodity prices mostly act as a negative supply shock in exports of domestic value added (negative sign in baseline results for DVA), with some exceptions for non-fuel commodity prices in the long-run equation.
  - Commodity-price variables positively affect exports of foreign value added in the baseline, possibly reflecting deflator issues and a larger share of commodities in FVA series.
- Supply-chain flexibility vs. inflexibility:
  - The hypothesis that global supply chains are flexible is overwhelmingly rejected in both short and long run.
  - Interaction terms in the foreign value-added equation are highly significant in the short run; domestic value-added estimates are less precise.
  - A rough estimate of the degree of inflexibility (short term, foreign value added) is between ¾ and 1, more precisely from 0.477/0.64 to 0.677/0.64 (a formal test that trade is fully inflexible is rejected).
  - Equivalent coefficients in the domestic value added equation are above 1 but less well estimated; in that case a formal test does not reject that the supply chain is fully inflexible.
  - Overall, using the entire sample, supply chains are estimated to be not far from the extreme case of a Leontief (fully inflexible) structure.

*Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019193-print-pdf.pdf*

### Appendix B includes a formal derivation based on our estimates. The corollary is that, if one were to think of

### wpiea2019193-print-pdf - Appendix B includes a formal derivation based on our estimates. The corollary is that, if one were to think of

### Short-run inflexibility and core finding
- Appendix B corollary: if one thinks of a world with a mixture of one fully flexible and one fully inflexible good, the estimates imply that the contribution of the inflexible good to global supply chains in the short run is of at least 60 percent.
- Short-run production structure is described as "very inflexible" in the paper’s estimates.
- Short-run results: estimated coefficients tend to be smaller in absolute value than long-run ones, but interaction terms indicate production complementarities and short-run inflexibility persist.

### Long-run complementarities and inflexibility
- Long-run elasticities are larger in absolute value, but complementarities in production persist.
- Estimated coefficient of inflexibility:
  - foreign valued equation: ¼ to ½
  - domestic value-added equation: 2/3 to 1
- Conclusion: expenditure decisions at the production stage remain less flexible to price changes than final-demand expenditure decisions even in the long run.

### Evolution over time and structural break
- The growth of supply chains accelerated since the early 2000s; if this reflects more complex intermediates traded, overall degree of flexibility should fall.
- Short-run responses of supply chains have become increasingly inflexible over time as supply chains deepened.
- Subsample re-estimation (removing either the last or first five years) suggests that production linkages might have become fully inflexible in the short run more recently:
  - Hypothesis that supply chain is completely inflexible in the short-term (훼훼=훽훽=−훾훾) is rejected in the 1995-2010 sample with Wald test p-values of 0.0001 and 0.0152 in the FVA and the DVA equations, respectively.
  - The same hypothesis cannot be rejected in either equation over the 2000-2015 sample (Wald-test p-values of 0.87 and 0.13, respectively).
- Interpretation: the rising share of foreign inputs in international trade is associated with increasingly complex production chains involving more specialized inputs.

### Dominant Currency Paradigm (DCP) robustness
- The paper re-estimates the baseline specification using a DCP-derived effective exchange rate that accounts for U.S. dollar invoicing.
- DCP effective exchange rate for country i (non-U.S.) is defined as:
  - RER_i^DCP ≡ ν_i RER_{i,US} + (1−ν_i) RER_{i,−US}
  - where ν_i is the share of trade invoiced in U.S. dollars, RER_{i,US} is bilateral real exchange rate vis-à-vis the U.S., and RER_{i,−US} is the real effective exchange rate recalculated to exclude the U.S.
- Country-level shares of trade invoiced in U.S. dollars are taken from Gopinath (2016); ν_i is the simple average of export and import dollar invoicing for own EER; partner ν_i for import-weighted partner EERs is set equal to partner’s share of exports invoiced in dollars.
- Results using the DCP measure (smaller sample due to invoicing data availability):
  - All estimates remain significant in the foreign value-added (FVA) equation.
  - Significance of interaction terms increases in the domestic value-added (DVA) equation.
  - In the smaller sample, estimated speed of adjustment in the FVA equation is substantially lower and foreign demand enters with the wrong sign.
- Overall conclusion: evidence of supply-chain inflexibility is robust to using an effective exchange rate that accounts for the U.S. dollar’s role in trade invoicing.

### Country-level evidence of production complementarities
- The pooled-mean-group estimator is used to compute, for each country and each value-added component, a test statistic for the null hypothesis of no production complementarities (훽훽=훾훾=0).
- Figure 6 (baseline) plots:
  - horizontal axis: statistic for the foreign value-added equation
  - vertical axis: statistic for the domestic value-added equation
  - black dotted line: 0.05 significance level
  - red dotted line: 0.10 significance level
- Complementarities are strong enough in many countries to overcome sample imprecision despite a short time span (21 years).
- Countries showing strong evidence include supply-chain hubs and major participants:
  - Asian chain examples: Thailand, Taiwan POC, China, Japan
  - North American chain: Mexico, Canada, United States
  - Some European countries: France, Germany
- Using the DCP-based effective exchange rate leads to the same overarching conclusion.

### Implications for trade and economic activity (quantitative mapping)
- The system of equations (3)-(4) is used to trace effects of REER (real effective exchange rate) movements on components of a country’s gross exports.
- For intermediates exports, short-run response of i’s intermediates exports to a change in i’s REER of magnitude ∆REER_i is:
  - ∆REER_i × Σ_{j≠i} ω_{ij} (α_i + γ_i dvat_{ij})
  - where ω_{ij} is share of j’s imports of intermediates originating from i, and coefficients α_i and γ_i correspond to equation (3).
- Average-sample numerical example (average country in sample):
  - average domestic value-added share dvat_bar = 0.75
  - in the cross-section, exports of intermediates represent 58 percent of total exports
  - Short-run estimated response of the average country’s value-added exports to a one percentage point depreciation:
    - Calculated aggregate response = 0.12
    - Breakdown implied by point estimates:
      - domestic value-added exports destined to final demand increase by 0.11 percent in response to a one percentage point REER depreciation
      - domestic value added exported as intermediates increase by 0.13 percent in response to a one percentage point REER depreciation
- Interpretation: complementarities in production temper the effect of depreciations. While openness has been rising (even measured as domestic value-added content), the impact of exchange rate changes on output has been rising even as supply-chain development has tempered the impact on gross trade.

### Concluding remarks and policy implications
- Core finding restated: global supply chains are largely inflexible in the short term and relatively inflexible in the long run.
- Business-cycle implications:
  - International production structure is crucial to understand how shocks reverberate globally.
  - Under supply-chain inflexibility, temporary disruptions are harder to resolve (example: natural-disaster effects on supply chains).
  - Insensitivity of producers to price changes increases the importance of countries with large final consumption in competitiveness calculations.
  - Exchange-rate changes vis-à-vis countries that consume final goods become more important; partners within the same regional value chain become relatively less important.
- Robustness: finding is robust to alternative price measures, including those accounting for the U.S. dollar’s outsized role in trade invoicing.
- Suggested future work: examine results excluding commodity trade to focus on supply chains incorporating manufacturing components and complementary services.

*Source: wpiea2019193-print-pdf (excerpt provided).*

### References

### References

### Bibliographic citations (selection)
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- Atalay, E. 2017. “How Important Are Sectoral Shocks?” American Economic Journal: Macroeconomics, Vol. 9 (4), pp. 254-80.
- Armington, P.A. 1969a. “A Theory of Demand for Products Distinguished by Place of Production,” IMF Staff Papers, Vol. 16, pp. 159-76.
- Armington, P.A. 1969b. “The Geographic Pattern of Trade and the Effects of Price Changes," IMF, Staff Papers, Vol. 16, pp. 179-201.
- Baldwin, R. 2016. The Great Convergence: Information Technology and the New Globalization, Harvard University Press.
- Baldwin, R. and A.J. Venables. 2013. “Spiders and snakes: Offshoring and agglomeration in the global economy,” Journal of International Economics, Vol. 90 (2), pp. 245-254.
- Bayoumi, T., M. Saito and J. Turunen. 2013. “Measuring Competitiveness: Trade in Goods or Tasks?” IMF Working Paper 13/100.
- Bayoumi, T., M. Appendino, J. Barkema and D.A. Cerdeiro. 2018. “Measuring Competitiveness in a World of Global Value Chains,” IMF Working Paper 18/229.
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### Appendix A — Charts and figures (captions)
- Figures A1–A18: Regional depictions of "Ratio of Domestic Value Added to Gross Exports" and "Ratio of Final Goods to Gross Exports" for multiple regions and years (Asian Supply Chain, European Supply Chain, Euro Area, Non-Euro Area, North-American Supply Chain, RoW) in 2015, 2008, and 1995. (Charts labeled A1–A18 correspond to regions listed in the source.)

### Appendix B — Gauging the degree of inflexibility in the full sample (1995–2015)
- Framework:
  - Trade of final goods is assumed to comprise two types: fully flexible value chains (F) and completely inflexible ones (I).
  - Flexible case: F_F = α RER* (notation in source).
  - Inflexible case: I_F = α [ (I_F_DVA / I) × RER* + (I_DVA_dom / I) × RER ] where I = I_F + I_DF (notation retained as in source).
- Aggregate elasticity expression (equation (6) as in source) is shown and manipulated in the source text.
- Parameter estimates and implied values (from expression (6) and equation (5) as referenced in the source):
  - α [1 − (I_IF_DVA / I_DVA) × (I_DVA_dom / I) ] = −2/3
  - α (I_IF_DVA / I_DVA) × (I_DVA_dom / I) = −1/2
- Solution for the two unknowns (source):
  - α = −7/6
  - (I_IF_DVA / I_DVA) × (I_DVA_dom / I) = 3/7  (equation (7))
- Interpretation and numerical bound:
  - The product in equation (7) pins down the product of: (share of foreign value added produced under Leontief supply chains) and (share of domestic value added in such Leontief supply chains).
  - Interest focuses on the ratio I_IF_DVA / I_DVA, i.e., how much of foreign value added could be seen as part of fully-inflexible supply chains.
  - The domestic value added share over the total (flexible and inflexible) value added exports is conjectured to provide an upper bound for I_DVA_dom / I.
  - The 2015 cross-country average domestic value added share of exports in the dataset is 0.75.
  - Using that upper bound, the foreign-value added coefficient estimates suggest that:
    - I_IF_DVA / I_DVA ≥ 3/7 0.75 ≅ 0.6.
  - Short-run implication stated in the source: "in the short run global supply chains can be thought of as being at least 60 percent fully inflexible."

- Supporting example note (footnote 21 in source):
  - Timmer et al. (2015, Table 1) show that, as of 2008, German value added represents only 66 percent of the total value of Germany’s automotive output, illustrating a case where domestic value added share is below 0.75 and supporting the use of 0.75 as an upper bound.

### Table A1 (estimation results — selected coefficients and statistics)
- Table caption: "Table A1. Export deflators (baseline) v. GDP deflators"
- Panel: LONG RUN (columns labeled (1) Baseline (export deflator), (2) GDP deflator, (3) Baseline (export deflator), (4) GDP deflator)
  - Importing partners' EER: -2.252  (t statistic: -5.45) ***
  - Own EER x DVA share: -0.607  (t statistic: -4.60) ***
  - Importing partners' EER: 1.295  (t statistic: 5.07) ***
  - Own EER: -0.750  (t statistic: -6.34) ***
  - Importing partners' EER: -0.435  (t statistic: -0.75)
  - Own EER x FVA share: 1.381  (t statistic: 2.31) **
  - Foreign demand: 0.170  (t statistic: 1.51)
  - Oil price: 0.156  (t statistic: 3.89) ***
  - Non-fuel commodity: 0.262  (t statistic: 4.28) ***
- Panel: SHORT RUN
  - Error-correction term: -0.202  (t statistic: -7.10) ***
  - Importing partners' EER: -0.640  (t statistic: -2.94) ***
  - Own EER x DVA share: -0.477  (t statistic: -4.43) ***
  - Importing partners' EER: 0.677  (t statistic: 5.56) ***
  - Own EER: -0.297  (t statistic: -1.54)
  - Importing partners' EER: -0.719  (t statistic: -1.01)
  - Own EER x FVA share: 0.757  (t statistic: 1.05)
  - Foreign demand: 3.227  (t statistic: 12.23) ***
  - Oil price: 0.0090  (t statistic: 0.43)
  - Non-fuel commodity: 0.124  (t statistic: 2.58) ***
  - Constant: 1.899  (t statistic: 7.03) ***
- Additional reporting:
  - N = 1,116, 1,117, 1,116, 1,117 (as reported in the table)
  - t statistics in parentheses
  - Significance codes: * p<0.1   ** p<0.05   *** p<0.01

*Italic: Source: wpiea2019193-print-pdf - References (canonical PDF content provided).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019193-print-pdf.pdf_