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### Main Findings
- A hypothetical drop of China’s imports by 10 percent below the baseline in 2016 and 2017 would lead to:
  - a loss of about 1.2 percent GDP of export revenue in 2016 for all countries;
  - network effects may increase the loss to 2.0 percent of GDP in 2017;
  - the effect would abate gradually to about 0.2 percent of GDP in 2020.
- Quantified network amplification (baseline results):
  - the spillover of 0.4 percent of world’s GDP in 2016 and 2017 from the original import demand shock in China might be augmented by spillins from the rest of the network in the amount of 0.4 and 1 percent of the world’s GDP;
  - the spillback effect on China would amount to 0.5 and 1.1 percent of its GDP in 2016 and 2017, respectively.
- Regional exposure and magnitude:
  - Asia and Pacific affected most, followed by Middle East and Central Asia; sub-Saharan Africa impact noticeable because of small economic size and growing trade with China; spillovers on Europe moderate; spillovers on Western Hemisphere marginal.
- Sectoral exposure:
  - commodity exporters hit most; metal exporters most affected; non-fuel primary commodity exporters may experience substantial losses; impact on fuel exporters most likely marginal.
- Country-level strongest negative spillovers: Hong Kong SAR, Singapore, Mauritania, Republic of Congo, Mongolia, Solomon Islands.
- Robustness and sensitivity:
  - classification of countries as shock amplifiers, absorbers and blockers can materially impact higher-round effects, particularly in early years; baseline model may on average underestimate higher-round effects.
- Research gaps: need to differentiate between price and volume effects in nominal spillovers and to account for China’s position in the global value chain.

### Introduction: motivation and objectives
- Context and forecasting assumption:
  - China’s growth expected to continue declining from unprecedentedly high rates; transition to a new consumption-led model with less reliance on import-intensive investment could increase risks of an import shock.
  - Assumes policy action consistent with reducing vulnerabilities and not fully offsetting moderation in activity.
- Purpose and contribution:
  - Assess impact of potential slowdown in China’s imports on rest of world, including network effects.
  - Uses method from Kireyev-Leonidov (2015) for quantifying network effects via sequential transformation of inflow-outflow bilateral trade matrices.
  - Develops a computable network model of international spillovers; proposes pass-through coefficient to quantify percolation through individual countries.

### Policy Setting and Recent Trends
- China’s growth path and policy targets:
  - growth stayed in the range of 10 percent a year through 2010; declined to an average of 8 percent in 2011-14.
  - leadership targeted growth for 2015-16 of 6-7 percent; IMF staff view for 2015: GDP growth of 6½-7 percent.
- Evidence of larger-than-expected spillovers:
  - WTO revised Asia import-side forecast for 2015 from 5.1% to 2.6%;
  - China’s imports were down 2.2% year-on-year in Q2 (non-seasonally adjusted);
  - customs statistics: machinery -9%, iron and steel -10%, copper -6% year-on-year quantity drops.
- Risk scenarios referenced:
  - without reforms growth could gradually fall to around 5 percent in 2020 with steeply increasing debt;
  - alternate scenario: four consecutive years of lower growth yields permanent cumulative loss of 12 percent on level of real GDP after four years.
- Channels for larger import drop:
  - rebalancing from import-intensive investment to less import-intensive consumption; lower demand for exports of final goods assembled in China reduces demand for intermediate imports.

### Trade Network Economics: modeling approach (overview)
- Network model captures:
  - initial nominal demand shock spillovers; spillin effects among other countries; spillback effects on China;
  - method works by sequential transformation of bilateral inflow-outflow trade matrices.
- Empirical positioning:
  - complements FSGM and GIMF by focusing on bilateral trade-network propagation mechanisms that can amplify shocks beyond direct bilateral exposures.

### Network representation and mechanics
- Network characteristics:
  - directed, weighted, incomplete, and asymmetric graph; exports revenue and import payments as directed weighted links; not all countries connected; out-links differ from in-links.
- Elementary bilateral link configurations and implications for shock propagation:
  - No links: no direct impact; indirect spillins still possible.
  - One-way A → C: import-demand shock in A does not directly affect C; spillins possible.
  - One-way D → A: A imports from D; A’s import-demand shock directly reduces D’s export revenue.
  - Two-way A ↔ E: immediate effect and immediate spillback.
- Cascade round mechanics:
  - initial import demand shock ΔM distributed proportionally among exporters to epicenter producing export revenue shocks;
  - export shocks generate secondary import shocks for exporters’ partners; model uses matrix multiplication and column-normalized forms for transformations.
- Pass-through coefficients K_i:
  - estimated from import demand functions in real and nominal specifications;
  - real specification: changes in real imports depend on changes in real export revenue, real domestic income, relative prices, and country-specific error.
  - nominal specification: changes in nominal imports driven by changes in export revenue and domestic income; captures price and volume effects together.
  - interpretation: K > 1 amplifiers; 0 < K < 1 absorbers; K = 0 or insignificant blockers.
- Dynamic quarterly cascade:
  - vector of import drops applied each quarter; direct and network-generated import shocks produce cascade sequence.

### Empirical classification of countries by pass-through (aggregate)
- Out of 185 countries, 148 capable of passing through shocks:
  - 51 (28 percent) potential shock-amplifiers.
    - Examples: United States, India, Brazil, Italy, Switzerland (insignificant amplifications of 5–10 percent); small subgroup of strong amplifiers: Argentina, Thailand, Korea, Hong Kong SAR, Denmark, Indonesia, India (can expand original shock by 30 percent and more).
  - 97 (52 percent) shock-absorbers.
    - Examples: Italy, Japan, Germany pass-through coefficients very close to unity; China, Canada, UK reduce shock strength for second neighbors.
  - 37 (20 percent) shock-blockers.
    - Examples: Bhutan, Chad, Central African Republic, Djibouti, Azerbaijan, Qatar, Iran, Iraq, Oman, Venezuela.
- Classification depends on each country’s economic structure only; not on network location.

### Data, shock calibration, and simulation setup
- Dataset and calibration:
  - bilateral flows for 1993–2014; October 2015 WEO projections for 2015-2020; sample includes 170 countries with bilateral trade data.
  - Of 28,730 possible bidirectional trade flows, 9,029 (about 31 percent) absent.
  - Annual flows split into four equal quarterly flows.
- Shock specification:
  - a drop by 10 percent relative to baseline projections applied each quarter in 2016-17 (i.e., China’s imports 10 percent lower relative to baseline WEO projections in 2016 and 2017).
  - Under assumption, growth in China would be by 1 percentage lower than baseline and lead to drop in its nominal imports by about 2.5 percent of projected GDP in 2016 and 2017.
  - The 10 percent import reduction is illustrative; not an IMF assessment.

### Empirical findings: first-round export shocks and regional heterogeneity
- Initial average impact:
  - loss of about 1.2 percent of GDP in export revenue in 2016 by all countries, rising with network effects to 2.0 percent of GDP in 2017, abating to about 0.2 percent of GDP in 2020.
- Regional specifics:
  - Asia and Pacific: about 2.3 percent of GDP in 2016 and 3.5 percent of GDP in 2017; accumulated average shock during 2016-20 might exceed 8 percent of their GDP. Most affected: Hong Kong SAR, Singapore, Solomon Islands, Malaysia, Mongolia, Vietnam.
  - Middle East and Central Asia: cumulative shock might exceed 5 percent of GDP; largest reductions in Oman, Mauritania, Qatar, Saudi Arabia.
  - Major advanced economies: 2016 shock not exceed 0.6 percent of GDP and might double in 2017; average accumulated five-year shock about 3 percent of GDP. Germany, Canada, Japan more exposed among advanced economies.
  - Emerging and developing economies:
    - Fuel exporters: might lose 2.3 percent of GDP in export revenue in 2016 and additional 3.6 percent of GDP in 2017; cumulative five-year impact might reach 9 percent of GDP (most affected: Equatorial Guinea, Oman, Brunei Darussalam, Angola).
    - Metal exporters: 2.1 percent of GDP in 2016 and 2.9 percent of GDP in 2017; cumulative five-year loss might reach 7 percent of GDP (most affected: Mauritania, Mongolia, Zambia, Chile).
    - Non-fuel commodity exporters: loss in 2016-20 might exceed 5 percent of GDP (most affected: Mauritania, Solomon Islands, Sierra Leone, Mongolia).
  - If oil-exporters try to maintain global sales by reducing prices, spillin effects could be much larger.

### Higher-round effects: secondary import shocks
- Average translation:
  - 2016 loss of export revenue by all countries would translate to about 0.4 percent of GDP reduction in imports financed with this revenue.
  - With network effects, drop in imports would increase to 1 percent of GDP in 2017, then decline to virtually zero by 2020.
  - Average import shock during 2016-20 might amount to at most a half of the export shock.
- Regional distribution of second-round import effects:
  - Asia and Pacific: pass-through to rest of world about 1.4 percent of GDP in 2016 and 2.8 percent of GDP in 2017; total secondary shock from region might reach almost 7 percent of GDP in 2016-20. Major pass-through countries: Hong Kong SAR, Singapore, Malaysia, Mongolia.
  - Europe: secondary shock persistent and increasing until 2018; cumulative average secondary import shock from Europe might reach about 3.5 percent of GDP in 2016-20. Small European pass-through/amplifiers include Malta, Estonia, Slovak Republic, Ukraine, Ireland, Czech Republic.
  - Advanced economies: most pass through less than 0.05 percent of GDP; overall accumulated secondary import shock passed through by advanced economies should not exceed 0.1 percent of GDP. Largest secondary import reductions from advanced economies expected in Canada, Italy, Germany; U.S. and U.K. spillovers likely negligible.
  - Emerging/developing: metal exporters pass through largest share: 0.8 percent of GDP in 2016 and 1.5 percent in 2017; cumulative average drop in import demand almost 4 percent by 2020. Non-fuel commodity exporters: total secondary import reduction about 2 percent of GDP (driven by Mauritania and Solomon Islands). Oil producers pass through shock at margin; most maintain imports via alternative financing.

### Network effects and spillback on China
- Aggregate and regional network-effect magnitudes:
  - Initial shock uniformly equals 0.4 percent of each region’s GDP.
  - Network effects may add around 1 percent of GDP by 2017 via higher-round effects.
  - Regional network effects by end-2017 (in addition to initial 0.4 percent):
    - Middle East and Central Asia: might exceed 2.3 percent of GDP;
    - Sub-Saharan Africa: about 1.8 percent of GDP;
    - Asia and Pacific: about 1.6 percent of GDP;
    - Europe: about 0.2 percent of GDP in 2016, expanding to about 1 percent of GDP in 2017;
    - Western Hemisphere: very small in first year; expands to about 0.4 percent of GDP in 2017.
- Spillback on China:
  - If China’s imports drop by more than 2 percent of its GDP in 2016 and 2017, spillback on China’s own exports could reach 0.5 percent of GDP in 2016 and exceed 1 percent of GDP in 2017.
  - Spillback would further reduce China’s GDP growth and persist into 2018-20 before fading.

### Spillin effect: definition, measurement, and results
- Definition and measurement:
  - Spillin effect = total spillovers − initial shock − spillback to China.
  - Total spillover period: 20 quarters (2016-20); initial shock persists for 8 quarters (2016-17).
  - Measured as relative size (difference in percent of GDP) and relative strength (ratio of total spillin to initial shock).
- Key results:
  - On average, relative size of spillin effect exceeds 6 percent of individual countries’ GDP (distribution skewed).
  - Only 9 countries (mainly immediate Asian partners: Hong Kong SAR, Singapore, Thailand, Malaysia, Mongolia, Vietnam, Korea) generate spillins substantially exceeding world average; over 80 countries generate relatively low spillins.
  - Average ratio of total spillover to initial shock is 7.6.
  - Only 14 countries radiate strong spillins substantially exceeding average; most are small open European economies (e.g., Bosnia and Herzegovina, Slovak Republic, Croatia, Slovenia, Latvia).
  - Spillback on China from rest of network would amount to only 1.5 percent of its GDP; strength of spillback effect very low in this measure.
- Projected aggregates (2016–20) under assumption China growth 1 percentage point below baseline in 2016-17, reducing import demand about 10 percent each:
  - initial nominal shock about 0.4 percent of world’s GDP in 2016 and 1.1 percent in 2017;
  - induced spillover and spillin effects can more than double initial shock;
  - spillback on China would be 0.5 and 1.1 percent of its GDP in 2016 and 2017.

### Sensitivity analysis, robustness checks, and counterfactuals
- Model specifications:
  - Nine specifications in real (1–5) and nominal (6–9) terms considered.
  - Nominal-term models especially sensitive to country classification as amplifiers/absorbers/blockers.
  - β coefficients across specifications do not significantly change magnitude or profile of spillovers in most models.
- Counterfactuals on country classification:
  - Extreme amplifiers scenario (103 amplifiers, 48 absorbers): 2017 spillovers can quadruple relative to baseline.
  - Opposite extreme (23 amplifiers, 97 absorbers): network spillover ~half of 2017 baseline level.
  - Average classification (56 amplifiers, 63 absorbers): 2017 spillover about 40 percent higher than baseline.
- Model advantages:
  - Captures higher-round feedback processes starting from second round; strength of network effects depends on network structure, epicenter centrality, trading partners’ positions, domestic economic structure, and compounding/offsetting signals.
  - Adds value to GE/DSGE approaches by quantifying higher-round effects via observable directional flows.
- Limitations:
  - Partial equilibrium analysis; abstracts from endogenous responses of exchange rates, policy, financial market channels, commodity prices.
  - Uses nominal trade flows and does not separate price vs. volume effects.
  - Not based on trade in value added; does not capture processing trade/value-added chain implications.
  - Assumes trade matrix, pass-through coefficients, and commodity structure unchanged across spillover rounds; proportional distribution of initial shock across partners.

### Policy implications and recommendations
- For China:
  - Avoid a sharp growth slowdown; reduce vulnerabilities from excess leverage after credit and investment boom; strengthen market forces and continue structural reforms to allow private consumption to pick up slack.
- For China’s trading partners:
  - Modest policy support may be needed for those most exposed to trade with China.
  - Compensatory policy measures can shift countries from shock amplifiers to absorbers or blockers, helping arrest proliferation of negative spillovers.
  - If no policy measures taken, capacity to pass-through shocks remains unchanged and baseline higher-round spillovers persist.

### Annex 2: Import Shock by Region (Percent of GDP)
- Sub-Saharan Africa: 2016 0.07, 2017 0.16, 2018 0.12, 2019 0.04, 2020 0.02, Average 0.08
- Europe: 2016 0.29, 2017 1.09, 2018 1.22, 2019 0.61, 2020 0.26, Average 0.69
- Western Hemisphere: 2016 0.17, 2017 0.46, 2018 0.40, 2019 0.16, 2020 0.06, Average 0.25
- Asia and Pacific: 2016 1.43, 2017 2.76, 2018 1.79, 2019 0.60, 2020 0.24, Average 1.36
- Middle East and Central Asia: 2016 0.23, 2017 0.51, 2018 0.38, 2019 0.15, 2020 0.06, Average 0.27

- Selected high-impact country figures (Percent of GDP, 2016–2020 and Average):
  - Hong Kong SAR: 2016 15.68, 2017 25.59, 2018 13.20, 2019 4.02, 2020 1.60, Average 12.02
  - Singapore: 2016 3.53, 2017 8.68, 2018 6.78, 2019 2.40, 2020 0.97, Average 4.47
  - Mongolia: 2016 4.06, 2017 6.02, 2018 2.63, 2019 0.69, 2020 0.26, Average 2.73
  - Thailand: 2016 2.06, 2017 5.09, 2018 4.03, 2019 1.50, 2020 0.62, Average 2.66
  - Korea: 2016 2.03, 2017 3.98, 2018 2.58, 2019 0.89, 2020 0.36, Average 1.97
  - China: 2016 0.77, 2017 0.66, 2018 0.62, 2019 0.24, 2020 0.09, Average 0.48
  - India: 2016 0.37, 2017 1.08, 2018 0.98, 2019 0.39, 2020 0.16, Average 0.59

### Annex 3: Pass-Through Coefficients — estimation and limitations
- Model specifications:
  - Real import-demand specification variables: DLM, DLX, DLR (total real income minus real income from exports), relative prices (DLP/DLE), nominal effective exchange rate, country-specific error.
  - Nominal specification uses nominal imports, export revenue, and domestic income; does not separate price and volume effects.
- Pooled OLS results (no-lag pooled models):
  - R-squared ~0.25 in real terms, ~0.45 in nominal terms.
  - Pooled pass-through estimates: real DLX ≈ 0.45; nominal DLX ≈ 0.76.
- Country-specific estimation approach:
  - 20 specifications per country (10 real, 10 nominal) including contemporary and lagged versions; backward selection used to retain significant variables.
  - No-lag, real terms averages: R2 = 0.5568; no-lag, nominal terms averages: R2 = 0.6385.
  - With lags, real terms averages: R2 = 0.5340; with lags, nominal terms averages: R2 = 0.3254.
- Key empirical takeaways:
  - Nominal models generally perform better and cover 185 countries; real models cover 167 countries.
  - Pass-through coefficients in nominal terms about 30 percent higher than in real terms.
  - Model 9 (reduced nominal contemporaneous model) chosen for spillover estimation:
    - 51 countries amplify shock with average pass-through 1.15;
    - 97 countries absorb with average pass-through 0.71;
    - 37 countries block the incoming shock.
  - Average margin of error in estimation of spillovers: +/- 15 percent.
- Methodological cautions:
  - Real specification separates price/volume but relies on small-country assumption and may understate spillovers.
  - Nominal specification broader coverage but does not separate price vs. volume effects.
  - Annual data and assumption of slow exchange rate/price adjustment may bias pass-through estimates.
  - Economies’ amplifier/absorber/blocker status may depend on participation in global supply chains; country-level research required for robust elasticities.

*Italic source attribution: Source: IMF Working Paper chapter "1. China: Growth Projections Revisions, 2016-20" (excerpted content).*

### 1. China: Growth Projections Revisions, 2016-20.....................................................................6

### 1. China: Growth Projections Revisions, 2016-20

### Main Findings
- A hypothetical drop of China’s imports by 10 percent below the baseline in 2016 and 2017 would lead to:
  - a loss of about 1.2 percent GDP of export revenue in 2016 for all countries;
  - network effects may increase the loss to 2.0 percent of GDP in 2017;
  - the effect would abate gradually to about 0.2 percent of GDP in 2020.
- Definition of network effects:
  - higher-round effects generated by the network structure of trade;
  - consist of spillovers of the nominal shock in China to its trading partners; spillin effects among all countries other than China, propagating secondary shocks to each other; and spillback effects from all countries on China itself.
- Quantified network amplification (baseline results):
  - the spillover of 0.4 percent of world’s GDP in 2016 and 2017 from the original import demand shock in China might be augmented by spillins from the rest of the network in the amount of 0.4 and 1 percent of the world’s GDP;
  - the spillback effect on China would amount to 0.5 and 1.1 percent of its GDP in 2016 and 2017, respectively.
- Robustness and sensitivity:
  - classification of countries as shock amplifiers, absorbers and blockers can impact higher round effects, particularly in early years of shock proliferation;
  - on average, the presented baseline model may underestimate the magnitude of higher round effects.
- Regional exposure and magnitude:
  - Asia and Pacific will be affected the most because of high exposure to trade with China, followed by the Middle East and Central Asia;
  - sub-Saharan Africa impact would be noticeable because of small economic size and growing trade with China;
  - spillovers on Europe, including the euro area, will be moderate relative to its economic size;
  - spillovers on the Western Hemisphere, including the United States, would be marginal.
- Sectoral exposure:
  - commodity exporters would be hit the most by the import demand shock in China;
  - metal exporters might be most affected as China is the largest metal importer in the world;
  - non-fuel primary commodity exporters may experience substantial losses;
  - impact on fuel exporters most likely will be marginal.
- Country-level strongest negative spillovers (in terms of impact on GDP): Hong Kong SAR, Singapore, Mauritania, Republic of Congo, Mongolia, and Solomon Islands.
- Research gaps: need to differentiate between price and volume effects in nominal spillovers and to account for China’s position in the global value chain.

### Introduction: motivation and objectives
- Context:
  - Growth in China is expected to continue declining in the medium term from unprecedentedly high rates in the first decade of the 2000s.
  - Transition to a new consumption-led growth model with less reliance on import-intensive investment could increase risks of an import shock.
  - Excesses in real estate, credit, and investment continue to unwind, with further moderation in growth rates of investment, especially in residential real estate.
- Forecasting assumption:
  - Assumes policy action will be consistent with reducing vulnerabilities from recent rapid credit and investment growth and hence not aim at fully offsetting the underlying moderation in activity.
- Purpose of the paper:
  - Assess the impact of a potential slowdown in China’s imports on the rest of the world, including through network effects.
  - Use the method proposed in Kireyev-Leonidov (2015) for quantifying network effects via sequential transformation of inflow-outflow matrices of bilateral trade flows.
- Contribution to literature:
  - develops a computable network model of international spillovers applicable to any bilateral balance of payments flows;
  - allows identification and estimation of network effects that can significantly amplify initial shocks;
  - proposes a pass-through coefficient to quantify percolation of shocks through individual countries (amplify, absorb, block);
  - applies model to assess potential spillovers from China’s import slowdown.

### Policy Setting and Recent Trends
- China’s recent growth path:
  - growth stayed in the range of 10 percent a year through 2010, driven mainly by domestic investment and exports;
  - growth gradually declined to an average of 8 percent in 2011-14.
- Policy shift and targets:
  - leadership announced a new growth model to rebalance in favor of domestic consumption, including services, with less reliance on import-intensive investment;
  - targeted growth for 2015-16 of 6-7 percent;
  - IMF staff view for 2015: GDP growth of 6½-7 percent as striking the right balance between addressing vulnerabilities and minimizing the risk of too sharp a slowdown/disorderly adjustment.
- Evidence of larger-than-expected spillovers:
  - WTO revised its previous trade forecast for 2015, with the downward revision to Asia on the import side from 5.1% to 2.6%;
  - China’s imports were down 2.2% year-on-year in Q2 (non-seasonally adjusted data);
  - large year-on-year drops in quantities of imported machinery (-9%) and metals (iron and steel -10%, copper ‑6%) recorded in customs statistics (WTO, 2015).
- Risk scenarios discussed in other IMF work:
  - without reforms growth could gradually fall to around 5 percent in 2020, with steeply increasing debt (IMF, 2015b);
  - alternate scenario: four consecutive years of lower growth for a permanent cumulative loss of 12 percent on the level of real GDP after four years (Anderson et al., 2015);
  - simulations based on FSGM and GIMF find impacts depending on how slowdown is perceived and the degree of anticipation/misperception, with potential medium- to long-term negative spillovers.
- Channels of a larger-than-baseline import drop:
  - domestic rebalancing shift from import-intensive investment to less import-intensive consumption reduces demand for imports by Chinese companies and government;
  - lower demand for exports of final goods assembled in China reduces demand for intermediate imports.

### Trade Network Economics: modeling approach (overview)
- Network model approach:
  - adapts earlier developed network model of economic spillovers to quantify higher-round trade network effects for China’s case;
  - captures: initial nominal demand shock spillovers, spillin effects among other countries, and spillback effects on China;
  - model works by sequential transformation of bilateral inflow-outflow trade matrices.
- Empirical positioning:
  - complements existing general equilibrium and multi-country model exercises (FSGM, GIMF) by focusing on bilateral trade-network propagation mechanisms that can amplify shocks beyond direct bilateral exposures.

*Italic source attribution: Source: IMF Working Paper chapter "1. China: Growth Projections Revisions, 2016-20" (excerpted content).*

### 13. International trade can be presented in a network form. Each country would be

### _wp1651 - 13. International trade can be presented in a network form. Each country would be

### Network representation of international trade
- Trade network described as a directed, weighted, incomplete, and asymmetric graph:
  - Directed: links denote flow direction (exports revenue and import payments).
  - Weighted: links reflect payment values differing by country and flow.
  - Incomplete: not all countries are connected through trade.
  - Asymmetric: number of export partners (out-links) typically differs from import partners (in-links).

### Elementary types of bilateral connections and immediate implications
- Four possible link configurations from epicenter country A:
  - No links in any direction: no direct impact from A on B; indirect spillins still possible.
  - One-way link in "wrong" direction (A → C): A exports to C; an import-demand shock in A does not directly affect C; spillins remain possible.
  - One-way link in "right" direction (D → A): A imports from D; an import-demand shock in A directly reduces D’s export revenue; no direct spillback but indirect spillbacks possible.
  - Two-way links (A ↔ E): import-demand shock in A affects E immediately and triggers an immediate spillback from E to A via E’s reduced export revenue and lower imports.

### Types of shocks and the spillover cascade
- Two shock types:
  - Import shock: drop in epicenter country’s import demand.
  - Export revenue shock: drop in export revenue of trading partners caused by epicenter’s import demand shock.
- Directionality:
  - Import shock = exit shock: signal from epicenter to first neighbors, then onward to further neighbors.
  - Export shock = entrance shock: affects first and other neighbors following import shock at epicenter.
- Key dynamic:
  - An export shock for a country will always be nonzero.
  - An import shock is nonzero only where imports depend on export revenue; otherwise it is zero.

### Network modeling mechanics (matrices and cascades)
- Trade data represented by export-import matrices: element X_ij stands for exports from country i to j.
- Cascade round consists of two schematic steps:
  - Initial import demand shock in epicenter country is proportionally distributed among its exporters and creates a vector of export shocks to their export revenue.
  - These export shocks generate secondary import shocks for the exporters’ trading partners; additional exogenous shocks can be added to secondary shocks.
- Export shock generation:
  - If epicenter’s total imports drop by ΔM, each component negative import demand shock Δm_j translates into losses in export revenue for exporters to the epicenter proportionally to their shares in those exports.
  - Transformation corresponds to modifying the import-export matrix and producing a drop in the export revenue vector.
- Equivalent matrix forms:
  - Matrix multiplication form adjusting relative import weights.
  - Column-normalized matrix form where each column is normalized by its sum.

### Pass-through coefficients, estimation, and interpretation
- Pass-through coefficients K_i estimated from import demand functions:
  - Real-term specification: changes in real imports depend on changes in real export revenue, real domestic income (total real income minus real income from exports), relative prices (index of import prices over domestic prices converted into dollars by exchange rate), and country-specific error.
  - Nominal-term specification: changes in nominal imports driven by changes in export revenue and domestic income; captures price and volume effects.
  - Assumption: export shock transmits to imports (contemporaneously or with lag) but does not directly affect domestic income in this specification.
- Pass-through interpretation:
  - Secondary import shock generated on average by linear relation between export revenue shock and ensuing imports; newly generated import demand shock becomes export revenue shock for next round.
- Dynamic quarterly cascade:
  - Vector of import drops by fixed amount each quarter; direct import shocks for quarter t and network-generated import shocks at end of each quarter produce the cascade sequence.

### Categories of countries by estimated pass-through and implications
- Three cases for shock diffusion based on estimated pass-through K:
  - Spillover amplifying: K > 1 — change in export revenue leads to proportionally larger change in imports; shock expands through such countries.
  - Spillover absorbing: 0 < K < 1 — change in export revenue leads to proportionally smaller change in imports; shock weakens.
  - Spillover blocking: K = 0 or statistically insignificant — export revenue not a constraint for imports; shock does not transmit through these countries.
- Aggregate network property:
  - On aggregate, the network is shock absorbing as spillovers die down after several rounds.

### Empirical classification summary (Box 2)
- Of 185 countries, 148 countries are capable of passing through shocks (Annex 3).
  - 51 (28 percent) are potential shock-amplifiers.
    - Examples: United States, India, Brazil, Italy, Switzerland pass through shocks with insignificant amplifications of 5–10 percent.
    - Small subgroup of strong amplifiers (can expand original shock by 30 percent and more): Argentina, Thailand, Korea, Hong Kong SAR, Denmark, Indonesia, India.
    - Policy implication: shock-offsetting policies in these countries are particularly important.
  - 97 (52 percent) are shock-absorbers.
    - Examples: Italy, Japan, Germany have pass-through coefficients very close to unity; China, Canada, UK in principle reduce shock strength for second neighbors.
  - 37 (20 percent) are shock-blockers (pass-through coefficients statistically insignificant).
    - Examples include small developing countries (Bhutan, Chad, Central African Republic, Djibouti) and some oil producers (Azerbaijan, Qatar, Iran, Iraq, Oman, Venezuela).
    - Characteristics: imports financed mainly by public/private capital flows or accumulated wealth; shock dies out naturally when reaching these countries.
- Note: classification depends only on each country’s economic structure, not on network structure or location.  

### Model assumptions and limitations (specific to China application)
- Model assumes partial equilibrium effects from import slowdowns; excludes general equilibrium effects beyond trade and GDP.
- Assumes trade matrix, pass-through coefficients, and commodity structure remain unchanged in each spillover round.
- Does not differentiate between consumption and investment goods in China’s imports; proportional distribution of initial import shock across partners assumed.
- Abstracts from output gaps, potential growth rates, and some self-equilibrating dynamics (simulations run 5 years ahead).
- Presented in nominal terms; does not directly separate price and volume effects.
- Does not account for China’s role in the value-added chain and processing trade implications.

### Empirical findings: China in the world trade network
- China central position:
  - China’s in/out degree: 168/166 out of the maximum of 170.
  - Visualization (Fruchterman-Reingold layout) places China in the middle; largest trade flows pass through China.
- China’s main import partners:
  - Almost 90 percent of China’s imports are sourced from 30 countries.
  - Main partners include large spillover amplifiers (United States, Hong Kong SAR, Korea, Italy, India) and spillover absorbers (Japan, Germany, United Kingdom, Netherlands).
  - Shock dynamics: the shock most likely would amplify at each iteration because China’s main partners are large spillover amplifiers; shock blockers (Argentina, Kuwait, Oman, Saudi Arabia, Vietnam) are peripheral and unlikely to impede shock propagation.

*Source: Excerpt from the provided IMF chapter/section content.*

### 31. The network structure of China’s main export partners suggests that it differs

### 31. The network structure of China’s main export partners suggests that it differs substantially from the import structure

### Network structure and immediate implications
- Of top 20 China’s trading partners, about 30 percent are not same on the export and import side.
- China exports virtually to every country of the world, but the top 30 countries absorb about 85 percent of China’s exports.
- China is surrounded by large shock amplifiers: United States, Hong Kong, Korea, India.
- Important shock absorbers for China’s exports (but with lower importance) include: Japan, Germany, the Netherlands, Great Britain.
- Shock blockers are clearly very peripheral in China’s export network: Belarus, Panama, Saudi Arabia, Vietnam.
- Note: node areas in Figure 7 are proportional to the share of a partner in China’s imports; link weights are proportional to the value of trade in each direction.

### Asymmetries between export and import partner networks
- The value of China’s trade in most directions is unbalanced, with large trade surpluses with many important countries.
- Geographically, at least half of China’s main export and import partners are not the same.
- Dominant on both export and import lists: United States, Hong Kong SAR, Japan, Korea.
- Important export destinations not among key import sources: Singapore, Australia, Malaysia, Brazil.
- Important import sources not among key export destinations: Saudi Arabia, Russia, Angola, Iran, Oman, Kuwait, and some other countries.

### Spillover-blockers among China’s import partners
- Among China’s most important import partners, only five are spillover-blockers: Saudi Arabia, Kuwait, Angola, Oman, Venezuela.
- Rationale: oil producing countries can finance imports by accumulated savings regardless of the drop in current export revenue.

### Data and shock calibration
- Dataset derived from bilateral flows for 1993–2014 and October 2015 WEO projections for 2015-2020.
- Sample includes 170 countries with bilateral trade flow data.
- Of 28,730 possible bidirectional trade flows, 9,029 (about 31 percent) are absent (no trade in either direction or trade only in one direction).
- Model estimated using world trade data for 1993–2014; 2013-14 weights used for 2015-20 projections.
- The import demand shock is applied on top of the projected slowdown of China’s imports for 2015-20 already included in the baseline.
- Data source: UN Comtrade database; TiVA database not used due to limited country coverage and periodicity.
- Annual trade flows split into four equal quarterly flows for modeling intrayear transmission.
- Shock specification: a drop by 10 percent relative to the baseline projections applied each quarter in 2016-17 (i.e., China’s imports would be 10 percent lower relative to the baseline WEO projections in 2016 and 2017).
- Under this assumption, growth in China would be by 1 percentage lower than the baseline and would lead to a drop in its nominal imports by about 2.5 percent of the projected GDP in 2016 and 2017.
- The assumed 10 percent import reduction in China for 2016-17 is illustrative and was not discussed in the October 2015 WEO; it does not represent an IMF assessment.

### Export shock to China’s trading partners (first-round effects)
- Initial average impact: a loss of about 1.2 percent of GDP in export revenue in 2016 by all countries, rising with network effects to 2.0 percent of GDP in 2017, abating to about 0.2 percent of GDP in 2020.
- Regional heterogeneity:
  - Asia and Pacific: about 2.3 percent of GDP in 2016 and 3.5 percent of GDP in 2017; accumulated average shock during 2016-20 might exceed 8 percent of their GDP.
    - Most affected Asian economies include: Hong Kong SAR, Singapore, Solomon Islands, Malaysia, Mongolia, Vietnam.
  - Middle East and Central Asia: cumulative shock might exceed 5 percent of their GDP; largest reductions in export revenue in Oman, Mauritania, Qatar, Saudi Arabia.
  - Other regions: impact most likely below the average.
- Major advanced economies:
  - In 2016, shock to export revenue would not exceed 0.6 percent of GDP and might double in 2017.
  - Average accumulated shock during next five years: about 3 percent of their GDP (below world average).
  - Germany, Canada, and Japan more exposed and likely affected most among advanced economies.
- Emerging and developing economies:
  - Fuel exporters: might lose 2.3 percent of their GDP in export revenue in 2016 and an additional 3.6 percent of GDP in 2017; cumulative impact during next five years might reach 9 percent of their GDP.
    - Poorly diversified oil-exporting countries most affected: Equatorial Guinea, Oman, Brunei Darussalam, Angola.
  - Metal exporters: 2.1 percent of GDP in 2016 and 2.9 percent of GDP in 2017; cumulative five-year loss might reach 7 percent of GDP.
    - Most affected metal exporters: Mauritania, Mongolia, Zambia, Chile.
  - Non-fuel commodity exporters: loss of export revenue in 2016-20 might exceed 5 percent of GDP.
    - Most affected: Mauritania, Solomon Islands, Sierra Leone, Mongolia.
  - If oil-exporters try to maintain global sales by reducing prices, spillin effects could be much larger.

### Higher-round effects of the import shock in China (secondary import shocks)
- The profile of the import shock differs from the export shock due to asymmetries and presence of shock-blockers.
- On average, the 2016 loss of export revenue by all countries would translate to about 0.4 percent of GDP reduction in the imports financed with this revenue.
- With network effects, the drop in imports would increase to 1 percent of GDP in 2017, then decline to virtually zero by 2020.
- The average import shock during 2016-20 might amount to at most a half of the export shock.
- Regional distribution of second-round import effects:
  - Asia and Pacific: pass-through to the rest of the world of about 1.4 percent of GDP in 2016 and 2.8 percent of GDP in 2017; total secondary shock from this region might reach almost 7 percent of GDP in 2016-20. Major pass-through countries: Hong Kong SAR, Singapore, Malaysia, Mongolia (some may amplify the shock).
  - Europe: secondary shock might be persistent and increase until 2018; cumulative average secondary import shock from Europe might reach about 3.5 percent of its GDP in 2016-20. Small European countries able to pass through or augment the shock include: Malta, Estonia, Slovak Republic, Ukraine, Ireland, Czech Republic.
  - Other regions: most likely below the average.
- Advanced economies:
  - Most advanced economies pass through a shock amounting to less than 0.05 percent of their GDP.
  - The overall accumulated secondary import shock passed through by advanced economies should not exceed 0.1 percent of their GDP.
  - Largest secondary import reductions emanating from advanced economies could be expected in Canada, Italy, and Germany; spillovers from the United States and the United Kingdom most likely negligible.
- Emerging and developing economies:
  - Metal exporters pass through the largest share of the export revenue shock to their imports: 0.8 percent of GDP in 2016 and 1.5 percent in 2017; cumulative average drop in import demand almost 4 percent by 2020. Mongolia is the largest source of the secondary import shock among metal exporters.
  - Non-fuel commodity exporters: total secondary import reduction of about 2 percent of GDP (driven by Mauritania and Solomon Islands).
  - Oil producers: will pass through the shock to their export revenue at the margin; most can maintain imports at roughly unchanged levels owing to alternative import financing (sovereign funds, capital inflows).

### Network effects and spillback on China
- Total shock (initial plus network effects) measured as a share of region GDP:
  - Initial shock uniformly equals 0.4 percent of each region’s GDP.
  - Network effects would differ substantially across regions and might add around 1 percent of GDP by 2017 via multiple higher-round effects.
- Regional network-effect magnitudes by end-2017 (in addition to initial 0.4 percent shock):
  - Middle East and Central Asia: network effect might exceed 2.3 percent of GDP by end-2017.
  - Sub-Saharan Africa: network effect about 1.8 percent of GDP.
  - Asia and Pacific: network effect about 1.6 percent of GDP.
  - Europe: network effect about 0.2 percent of GDP in 2016, expanding to about 1 percent of GDP in 2017.
  - Western Hemisphere: network effect very small in first year; expands to about 0.4 percent of GDP in 2017.
- Vulnerability drivers: strong network effects in Middle East and Central Asia, Sub-Saharan Africa, and Asia and Pacific reflect high connectivity to affected countries and small individual GDPs relative to potential export revenue losses.
- Spillback effect on China’s own exports:
  - If China’s imports drop by more than 2 percent of its GDP in 2016 and 2017, the spillback on China’s own exports could reach 0.5 percent of GDP in 2016 and exceed 1 percent of GDP in 2017.
  - Spillback would further reduce China’s GDP growth; negative spillback effects persist into 2018-20 before fading toward the end of the period.

*Italic: Source: Authors' calculations and analysis in the provided content.*

### 50. The spillin effect can be calculated as the difference between total spillovers, the

### 50. The spillin effect can be calculated as the difference between total spillovers, the

### Definition and measurement of the spillin effect
- The spillin effect is calculated as the difference between total spillovers, the initial shock, and the spillback to China.
- For a shock to China:
  - The total spillover period stretches to 20 quarters, that is, 2016-20.
  - The initial shock is assumed to persist for 8 quarters, that is, 2016-17.
- The spillin effect is generated by the import shock.
- Measurement approaches:
  - Relative size: the difference between the overall and the initial shock in percent of GDP of each country.
  - Relative strength: the ratio of the total spillin to the initial shock.

### Results for a shock radiating from China
- Distribution and magnitude:
  - On average, the relative size of spillin effect exceeds 6 percent of individual countries’ GDP (with a much skewed distribution).
  - Only 9 countries (mainly China’s immediate Asian trading partners, such as Honk Kong SAR, Singapore, Thailand, Malaysia, Mongolia, Vietnam, and Korea) generate spillins substantially exceeding the average for the world; over 80 remaining countries generate relatively low spillins.
  - On average the ratio of the total spillover to the initial shock is 7.6.
  - Only 14 countries radiate strong spillins, substantially exceeding the average; virtually all of them are small open economies in Europe (examples given: Bosnia and Herzegovina, Slovak Republic, Croatia, Slovenia, Latvia).
  - The spillback effect on China itself from the rest of the network would amount to only 1.5 percent of its GDP.
  - The strength of the spillback effect would be very low.

### Projected aggregate impacts (2016–20)
- Assumptions and headline projections:
  - China’s growth at a bound 1 percentage point below the baseline in 2016-17, leading to a drop of in demand for imports by about 10 percent each.
  - This would lead to a loss of about 1.2 percent GDP of export revenue in 2016 for all countries.
  - With network effects this may increase to 2.0 percent of GDP in 2017 before abating gradually by 2020 to about 0.2 percent of GDP in 2020.
- Nominal shock size and induced effects:
  - The assumed nominal shock amounts to about 0.4 percent of the world’s GDP in 2016 and 1.1 percent of GDP in 2017.
  - The induced spillover and spillin effects can more than double the magnitude of the initial shock.
  - The spillback effect on China would amount to 0.5 and 1.1 percent of its GDP in each of these years.

### Regional, sectoral, and country heterogeneity
- Regional impacts:
  - Asia and Pacific would be affected the most.
  - Middle East and Central Asia would be affected next because of relatively higher exposure to trade with China.
  - Sub-Saharan Africa would be less visible because of still relatively low trade with China.
  - Europe’s impact would be moderate because of its substantial economic size.
  - Western Hemisphere impact would be marginal.
- Sectoral impacts:
  - Metal exporters might be hit the hardest (China is the largest metal importer in the world).
  - Non-fuel primary commodity exporters would be next most affected.
  - Fuel exporters most likely would be marginally impacted.
- Individual countries with strongest negative spillovers (in terms of GDP impact) include:
  - Hong Kong SAR, Singapore, Mauritania, Republic of Congo, Mongolia, and Solomon Islands.

### Sensitivity analysis and robustness checks
- Model specifications and sensitivity:
  - Nine model specifications were considered in real (1-5) and nominal (6-9) terms.
  - Models in nominal terms were found especially sensitive to the classification of countries as shock amplifiers, absorbers, and blockers.
  - The values of β coefficients across all model specifications do not seem to have any significant impact on the magnitude of shock spillovers or their profile (most models depict a shock very close to the baseline).
  - Different assumptions regarding the numbers of countries capable to amplify, absorb and block shocks can change the magnitude of spillovers and their time profile.
- Counterfactual experiments on country classification:
  - Extreme amplifiers/absorbers scenario:
    - If a total of 103 countries are capable to augment the shock (as in models 7 and 8) and only 48 countries would absorb at least part of the shock (as in model 1), with all remaining countries assumed shock blockers, and assuming no policy actions to prevent pass-through:
      - The spillovers in 2017 can quadruple relative to the baseline.
  - Opposite extreme:
    - If the model with the minimum number of shock amplifiers (23 as in model 5) and the maximum number of shock absorbers (97 as in model 9) is true:
      - The network spillover effect would be roughly half of the 2017 baseline level.
  - Average classification:
    - If the number of shock amplifiers and absorbers is set at the average level across all nine models, i.e. at 56 and 63 respectively:
      - The 2017 spillover would still be about 40 percent higher relative to the baseline.

### Model advantages and limitations
- Advantages of the network model:
  - Captures higher-round network effects originating from feedback processes starting from the second round of shock propagation.
  - Strength of network effects depends on network structure, initial shock magnitude, epicenter centrality, positions of trading partners, domestic economic structure, compounding strength of aligned spillover signals, and offsetting strength of opposing signals.
  - Network effects can become comparable to and often exceed the initial shock at the epicenter when compounded through rounds.
  - Adds value relative to other models (e.g., GVARs, FSGM, GE/DSGE) by directly quantifying higher-round effects using observable directional flows and capturing direction of causality from data.
- Limitations and cautions:
  - The analysis is partial equilibrium and abstracts from endogenous responses of exchange rates and policy variables; it does not incorporate financial market channels, exchange rates, commodity prices, etc.
  - The model is not based on trade in value added and therefore does not capture direct and indirect linkages in global supply chains; it uses a comprehensive Comtrade database of bilateral trade flows.
  - Applied to data in nominal terms, so it does not distinguish explicitly between price and volume effects in spillovers; findings may differ if reduced nominal exports arise from volume vs. price changes.
  - The network model does not capture potentially different impacts of processing imports versus non-processing imports.

### Policy implications and recommendations
- For China:
  - Avoid a sharp growth slowdown.
  - Reduce vulnerabilities from excess leverage after a credit and investment boom.
  - Strengthen the role of market forces in the economy.
  - Further progress in implementing structural reforms to allow private consumption to pick up slack from slowing investment growth; core reforms include giving market mechanisms a broader role, eliminating distortions, and strengthening institutions.
- For China’s trading partners:
  - Modest policy support may be needed, particularly for those most exposed to trade with China.
  - Compensatory policy measures can shift countries from shock amplifiers to shock absorbers or shock blockers, helping arrest proliferation of negative spillovers through the trade network.
  - If trading partners take no policy measures, their capacity to pass-through shocks would remain unchanged relative to previous years, leaving baseline higher-round spillovers intact.

*Source: Excerpt from IMF working paper content provided in the supplied document.*

### Annex 2. Import Shock by Region

### Annex 2. Import Shock by Region

### Regional and aggregate statistics (Percent of GDP)
- Sub-Saharan Africa: 2016 0.07, 2017 0.16, 2018 0.12, 2019 0.04, 2020 0.02, Average 0.08
- Europe: 2016 0.29, 2017 1.09, 2018 1.22, 2019 0.61, 2020 0.26, Average 0.69
- Western Hemisphere: 2016 0.17, 2017 0.46, 2018 0.40, 2019 0.16, 2020 0.06, Average 0.25
- Asia and Pacific: 2016 1.43, 2017 2.76, 2018 1.79, 2019 0.60, 2020 0.24, Average 1.36
- Middle East and Central Asia: 2016 0.23, 2017 0.51, 2018 0.38, 2019 0.15, 2020 0.06, Average 0.27

- Many individual economies report zeros across 2016–2020 (e.g., São Tomé and Príncipe, Burundi, Cape Verde, Ethiopia, Niger, Comoros, Mali, Burkina Faso, CAR, Benin, Cameroon, Malawi, Mauritius, Togo, Guinea-Bissau, Nigeria, Côte d'Ivoire, Mozambique, Zimbabwe, Chad, DRC, Guinea, The Gambia, Liberia, Angola, Equatorial Guinea, Republic of Congo, Cyprus, Moldova, Luxembourg, Belarus, Belgium, and several Middle East countries).

### Selected high-impact country figures (Percent of GDP, 2016–2020 and Average)
- Hong Kong SAR: 2016 15.68, 2017 25.59, 2018 13.20, 2019 4.02, 2020 1.60, Average 12.02
- Singapore: 2016 3.53, 2017 8.68, 2018 6.78, 2019 2.40, 2020 0.97, Average 4.47
- Mongolia: 2016 4.06, 2017 6.02, 2018 2.63, 2019 0.69, 2020 0.26, Average 2.73
- Thailand: 2016 2.06, 2017 5.09, 2018 4.03, 2019 1.50, 2020 0.62, Average 2.66
- Korea: 2016 2.03, 2017 3.98, 2018 2.58, 2019 0.89, 2020 0.36, Average 1.97
- China: 2016 0.77, 2017 0.66, 2018 0.62, 2019 0.24, 2020 0.09, Average 0.48
- India: 2016 0.37, 2017 1.08, 2018 0.98, 2019 0.39, 2020 0.16, Average 0.59

### Observations from country-level table
- Regional averages and country averages vary substantially, with Asia and Pacific showing the highest regional average (1.36 percent of GDP) driven by large shocks in several economies (Hong Kong SAR, Singapore, Mongolia, Thailand).
- Europe’s average (0.69 percent of GDP) is driven by heterogeneity across countries (e.g., Malta average 1.48, Estonia average 1.41).
- Substantial portions of the sample report zero import-shock values over 2016–2020, reflecting data or shock-profile heterogeneity across many low-income and resource-exporting countries.

---

### Annex 3. Pass-Through Coefficients: Estimation and Limitations

### Model specifications and identification
- Real import-demand specification variables:
  - Changes in real imports (DLM)
  - Changes in exports revenue in real terms (DLX)
  - Real domestic income (DLR) defined as total real income minus real income from exports
  - Relative prices: ratio of index of import prices (DLP) to domestic prices (DLE)
  - Nominal effective exchange rate (noted in text)
  - Country-specific error term
- Nominal specification uses nominal imports, export revenue, and domestic income; it does not separate price and volume effects but does not require the small country assumption.
- Both specifications follow Tokarick (2010), Morin and Schwellnus (2014), and IMF (2015a).
- Coefficient interpretation: coefficient on DLX is a pass-through coefficient indicating percent change in imports when export revenue changes by one percent.

### Pooled OLS estimation results (model selection and fit)
- Twelve pooled specifications were estimated: six in real terms (models 1–6) and six in nominal terms (models 7–12). Variations included inclusion/exclusion of trend, relative prices, and lags.
- Pooled models with no lags of dependent variables outperform models with lags.
  - Coefficient of determination (R-squared): ~0.25 in real terms, ~0.45 in nominal terms for no-lag pooled models.
  - R-squared drops to ~0.05 when lags are included in pooled models.
  - Akaike and Schwarz information criteria select no-lag models over lagged models in both real and nominal specifications.
- Pass-through coefficient estimates (pooled):
  - Real terms: DLX ≈ 0.45
  - Nominal terms: DLX ≈ 0.76
  - Interpretation: a 10 percent decline in export volume would translate into about a 4.5 percent decline in imports volume; a comparable 10 percent decline in export value would lead to a 7.6 percent decline in value of imports.

### Country-specific estimations and preferred specification
- Individual-country approach: 20 specifications per country were estimated (10 real, 10 nominal); each set included contemporary and lagged-variable versions.
- Average diagnostics across individual OLS estimations (Figure 15 summary):
  - For dependent variable DLM, sample-average estimates reported (selected reported coefficients in figure): C ≈ 0.0269–0.0648 across specifications; DLX ≈ 0.4903–0.7746; DLX(-1) reported in some specifications ≈ 0.0489–0.2203; DLR ≈ 0.0024–0.3721 where reported; DLP ≈ -0.1459 to -0.1338 (negative coefficients on relative prices); D1 (a dummy) ≈ -0.0184 to -0.0979 in various specifications.
  - Aggregate fit and statistics across specifications (selected):
    - R-squared ranges reported in table: e.g., 0.2584, 0.2420, 0.0491, 0.4427, 0.4566, 0.0535, 0.0839 (varies by specification).
    - Periods included, cross-sections included, and total panel observations differ by specification (examples: periods included 21 or 20; cross-sections included 167 or 185; total observations e.g., 3,507; 3,340; 3,885; 700).
- Model performance conclusion:
  - Models in nominal terms and with no lags generally superior to other specifications.
  - Overall average fit: nominal models average R-squared 0.64; real models average R-squared 0.56 (per-country averages).
  - Introduction of lags reduces explanatory power: average R-squared drops to 0.53 in real terms and 0.33 in nominal terms when lags of dependent variables are included.
  - Model 6 (contemporaneous export revenue and lagged other variables) suggests pass-through is on average contemporaneous.
  - Coverage: nominal specification estimated for 185 countries; real specification for 167 countries (data limitations noted).

### Key methodological takeaways and limitations
- Real-specification allows separating price and volume effects but relies on the small country assumption (international prices treated as given for all countries other than China).
- Nominal-specification is more parsimonious, does not separate price and volume effects, and does not require the small country assumption.
- Estimating country-specific import-demand elasticities robustly requires substantial country-level research beyond the scope of this analysis.
- Estimated pass-through coefficients indicate a materially contemporaneous link from export revenue shocks to import contractions, with larger estimated magnitudes in nominal terms than in real terms.

*Source: Annex 2 and Annex 3 (selected tables and text) from the provided content unit.*

### 67. As the next step, import demand equations were estimates for each country with

### _wp1651 - 67. As the next step, import demand equations were estimates for each country with

### Methodology: model selection and estimation
- Import demand equations were estimated for each country with available data, both in real and nominal terms.
- The model building approach was based on a backward selection:
  - A model was fitted with all the variables of interest following the initial screen.
  - The least significant variable is dropped so long as it is not significant at the 95 percent critical level.
  - Successive re-fitting of the reduced models continues until all remaining variables are statistically significant.
- The process has been applied to the data with no lags of dependent variables and with lag specifications (results reported separately).
- Models 1 and 6 are the broadest models in real and nominal terms, respectively, with all independent variables included.
- Models 5 and 9 are the narrowest possible models with only one independent variable left, exports revenue in real and nominal terms.

### Model fit statistics (selected aggregates and counts)
- No lags, real terms averages: R2 = 0.5568, AIC = -2.3031.
- No lags, nominal terms averages: R2 = 0.6385, AIC = -2.1204.
- With lags, real terms averages: R2 = 0.5340, AIC = -2.0684.
- With lags, nominal terms averages: R2 = 0.3254, AIC = -1.2074.
- Max/min reported examples: Max/min real = 0.6608 / -2.3719; Max/min nominal = 0.6828 / -2.1925.
- Number of countries: real terms 167; nominal terms 185.

### Classification of countries by pass-through behavior
- The models classify countries as:
  - Shock amplifiers (pass-through > 1),
  - Shock absorbers (pass-through < 1),
  - Shock blockers (pass-through statistically insignificant or equal to 0 as per the model).
- On average across all countries:
  - Real-model average pass-through for shock amplifiers = 1.22.
  - Nominal-model average pass-through for shock amplifiers = 1.24.
  - Real-model average pass-through for shock absorbers = 0.75.
  - Nominal-model average pass-through for shock absorbers = 0.79.
- The pass-through coefficients are relatively robust to model specifications for China’s key trading partners.
  - Example: United States pass-through coefficients:
    - Real terms: very robust and stay within the 0.64-0.67 range for most models.
    - Nominal terms: stay at 2.5-2.7 for most models.
- On average, pass-through coefficients in nominal terms are about 30 percent higher than in real terms (difference reflecting price effects).

### Selection of coefficients for spillover estimation
- Considerations for selecting pass-through coefficient set:
  - Real-term pass-throughs available for 167 countries; nominal-term for 185 countries — this argues for using nominal models for broader coverage.
  - Nominal models do not distinguish price vs. volume effects, which can be important (e.g., for large countries like China).
  - Real models capture only volume effects and may understate spillovers by imposing a small-country assumption and producing more shock blockers.
  - Nominal models may overstate spillovers by capturing unspecified price effects that increase pass-through for some countries.
- Given these trade-offs, the paper selected pass-through coefficients from a nominal model for calculations.
  - Specifically, a reduced model 9 was selected, in which imports depend contemporaneously on exports revenue and all other factors are captured by α.

### Spillover classification and quantitative results using reduced nominal model 9
- Using reduced nominal model 9:
  - 51 countries would amplify the shock with an average pass-through coefficient of 1.15.
  - 97 countries would absorb part of the shock with an average pass-through coefficient of 0.71.
  - 37 countries would block the incoming shock altogether.
- The average margin of error in the estimation of the magnitude of spillovers by this approach would be +/- 15 percent.

### Cautions and limitations (as stated in source)
- In estimating pass-through coefficients from exports to imports, only trade data is included and an assumption is made that exchange rates and prices do not adjust quickly.
  - Given that annual data are used in the estimation, such assumption may lead to biases in the pass-through coefficients.
- An economy’s status as shock amplifier, absorber, or blocker may depend on its participation in the global supply chain.
- Real-model assumptions (small country, volume-only effects) may be too restrictive and underestimate price effects; nominal models may capture price effects but cannot separate them from volume effects.

_Authors’ estimates._

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1651.pdf_