## wp17266 — Sections 1–3

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### Introduction
- Nonviable “zombie” firms are a key government priority for addressing corporate debt vulnerabilities and improving resource allocation in China.
- Firm-level industrial survey data document the central role of zombies and their strong linkages with state-owned enterprises (SOEs) in contributing to debt vulnerabilities and low productivity.
- Resolving weak firms can generate significant gains of 0.7–1.2 percentage points in long-term growth per year.
- Deleveraging, reducing government subsidies, and operational restructuring through divestment and reducing redundancy have significant benefits in restoring corporate performance for zombie firms.

### Corporate debt vulnerabilities and misallocation of resources
- China’s nonfinancial private sector debt reached 176 percent of GDP as of the end of March 2017.
- Corporate debt stood at about 135 percent of GDP and contributed most of the rising debt.
- SOEs account for 57 percent of total corporate debt or 72 percent of GDP in 2016.
- SOEs contributed to almost 60 percent of the rise in total corporate debt during 2008–16.
- SOEs’ share of output and employment declined from over 40 percent in the late 1990s to about 15–20 percent in 2015.
- The share of nonviable zombie firms in total corporate debt rose quickly to 6 percent by 2016 (or 15 percent of total industrial liabilities), the highest level since 2009.
- Zombie debt concentration and geography:
  - Despite declining employment, profitability, and fixed asset investment, the debt share of zombie firms remained high, suggesting rising vulnerability due to a debt overhang.
  - Zombies overlap considerably with overcapacity sectors and SOEs, which account for half of total debt and about one-third of employment in zombie firms.
  - 40 percent of zombie debt is in the North and Northeast regions (Heilongjiang, Jilin, Liaoning, Hebei, Shanxi, and Shaanxi provinces, and Inner Mongolia autonomous region).

### Definition of zombies and related classification
- State Council (SC) definition: firms that incur three years of losses, cannot meet environmental and technological standards, do not align with national industrial policies, and rely heavily on government or bank support to survive.
- Fukuda and Nakamura (FN) definition: firms that face persistent losses and receive subsidized credit (actual interest cost less than market prime interest rates), or debt-to-asset ratio higher than 50 percent and increasing, and EBIT smaller than interest payment at market interest rate.
- Nie, Jiang, Zhang, and Fang (NJZF) definition: firms that fit the FN definition for two successive years.
- Baseline definition (used in this paper): modified from Fukuda and Nakamura (2011) — firms that fit the FN definition but considering only one-fourth of short-term debt due less than a year when applying the criteria (i.e., assuming half of short-term debt of six-month maturity).

### Why zombie firms matter
- Zombies have higher leverage, lower returns, slower growth, and lower productivity than non-zombie firms.
- About 30 percent of zombie firms remain zombies after 5 years.
- Zombies formed during 2008–13 are more entrenched than those formed in the early 2000s.
- Duration analysis: an SOE zombie is 30 percent more likely to stay a zombie in the next year than a non-SOE zombie.
- Empirical studies find zombies crowd out non-zombie investment by 2–8 percent (Tan and others 2017).
- Sustaining nonviable companies suppresses competition and can amplify financial stability risks via nonperforming loans.

### Data and empirical methodology
- Data:
  - Firm-level annual industrial survey data from the National Bureau of Statistics covering industrial firms in China between 1998 and 2013, about one million companies each year.
  - Annual sales thresholds: RMB5 million or above (1998–2009) and RMB20 million or above (2011–13). For consistency, the paper uses firm-level observations with annual sales of 20 million or above.
- Data cleaning and outlier elimination follow Feenstra, Li, and Yu (2014) and Cai and Liu (2009); observations deleted if key financial variables are missing or negative, balance sheet values violate accounting principles, employment is 10 people or less, firm identification code is missing or non-unique, or inception date is missing or invalid.
- Overcapacity sectors classified using four-digit industry codes; sectors include coal, steel, cement, plated glass, aluminum, paper, solar power, chemicals, ship building, coal-fueled power.

### Determinants of zombie firms (empirical findings)
- Probit model: Pr(zombieit = 1) = Φ(Xi,t−1 β + DInd + Dyear + Dreg + εit), where Xi,t−1 includes lagged explanatory variables; industry (two-digit), year, and province/region dummies included.
- Key findings:
  - Higher leverage and lower profitability significantly increase likelihood of being a zombie.
  - A one-percentage-point increase in the liabilities-to-assets ratio raises the likelihood of being a zombie firm by about 0.15 percent on average.
  - A reduction of aggregate demand (proxied by average growth of revenue in the industrial sector) contributes to an increase in zombie companies.
  - Zombies are more common among SOEs, concentrated in overcapacity industries, and in the North and Northeast regions, holding other factors constant.
- Role of government and banks:
  - Local government support: an index of government direct intervention (average share of working hours firm managers spend with provincial government officials) is a decisive positive determinant of zombie formation (statistically significant at the 5 percent level).
  - A one percentage-point increase in government subsidies to total sales raises the likelihood of becoming a zombie by 0.15 percent, holding other factors constant.
  - Local banks: the share of deposits held by major state-owned banks (proxy for close bank-government ties) is positively and statistically significantly associated with zombie prevalence.
- Robustness: findings are robust across different zombie definitions.

### Restructuring options and determinants of recovery
- Probit setup for recovery:
  - Sample: firms classified as zombies in period t-1.
  - Dependent variable: equals one if firm in period t moves to non-zombie category; zero otherwise.
  - Explanatory variables: one-period lagged restructuring options, controlling for industry and year fixed-effects.
- Restructuring-option variables:
  - Deleveraging: dummy = 1 when debt-to-asset ratio is reduced by more than 5 percentage points over a year.
  - Ownership change:
    - SOE to private (state- or collectively owned to privately owned).
    - Corporatization (incorporation of the zombie firm).
  - Reduction in the labor force: proxied by wage-payment-to-asset ratio.
  - Asset sale or injection:
    - “Asset injection” dummy when fixed asset growth > +10 percentage points.
    - “Asset sale” dummy when fixed asset growth < −10 percentage points.
- Empirical correlations (no causality implied):
  - Deleveraging is correlated with higher likelihood of turning into viable firms.
  - Privatization/corporatization shows a strong statistically significant positive coefficient for transition to viability.
  - Reducing labor costs has a significant marginal effect in some specifications but is less robust; debt burden is more determinant than labor redundancy.
  - Both asset injection and asset sale dummies have statistically significant positive effects on transition to viable status.

### Duration analysis methodology and findings
- Methodology:
  - Kaplan-Meier estimator and Cox-proportional hazard model used to analyze zombie duration and recovery hazards.
  - Left-censoring: firms classified as zombies in the first year of the dataset are excluded.
  - Some zombies with multiple transitions are treated as independent observations.
- Key duration findings:
  - SOE zombies are more difficult to recover due to soft budget constraints and implicit support.
  - Higher debt burden reduces likelihood of recovery.
  - Zombies in overcapacity industries and/or in the North and Northeast regions are more entrenched.

### Productivity gains from resolving resource misallocation (TFPR/TFP framework and magnitudes)
- Framework: follows Hsieh and Klenow (2009); measures efficiency via revenue total factor productivity (TFPR) equalization within industry and within groups (zombie vs non-zombie, SOE vs non-SOE).
- Historical and potential gains:
  - During 1998–2000, resolving debt vulnerabilities would respectively boost aggregate industrial TFP by 5–8 percent for zombie firms and SOEs.
  - As debt vulnerabilities have risen in recent years, potential gains appear to have risen to about 7 percent between SOEs and non-SOEs.
- Cross-country counterfactuals:
  - Narrowing China’s revenue-productivity gap to the 75th-percentile of a 57-country sample would boost output by about 16 percent or raise long-term growth potential by 0.7 percentage points per year.
  - Converging to the 90th percentile would raise output by 28 percent or about 1.2 percentage points in long-term growth.
- Aggregate implications:
  - Resolving weak firms contributes to large potential gains (0.7–1.2 percentage points) in output per year.
  - Scaling TFPR efficiency gains to total output suggests roughly half of total potential gains in output arise from resolving weak firms.
  - SOE reforms can account for over 0.4 percentage points of long-term output increase.
  - Substantial overlap among weak firms implies complementarity of reforms to maximize gains.

### Government measures, assessment, and progress on SOE/zombie resolution
- Government strategy and institutional actions:
  - Aim to build market and legal framework for debt restructuring while guarding against systemic/regional risks.
  - Multipronged firm-by-firm options: merger and consolidation, liquidation, debt-equity swaps, corporate asset sales (State Council 2016).
  - Inter-ministerial group led by the National Development and Reform Commission to facilitate deleveraging; financial regulators renewed focus on controlling financial risks (CBRC 2016, 2017).
- Recent SOE measures (highlights):
  - Consolidating some central SOEs.
  - Phasing out SOE social functions.
  - Transferring about ½ percent of state-owned equity to social security funds.
  - Cutting central SOE losses.
  - Individually incorporating the subsidiaries of central SOEs by 2017.
  - Implementing pilot employee stock-ownership programs.
  - Bringing in other investors under mixed-ownership pilot reforms and opening up sectors (travel, medical care, electricity, power and utilities) to private and foreign investment.
- Zombies specifically:
  - About 2,000 central SOEs (with total assets of about 4 percent of GDP) and over 7,000 local SOEs have officially been identified as zombie firms.
  - Reportedly, about 20 percent of the identified central SOE zombies have already been resolved (no resolution-method details provided).
  - Regulatory amendments relevant to nonperforming loans have been made to expedite liquidation of zombies.
- Assessment and implementation gaps:
  - Deleveraging guidelines lack details on loss recognition and operational restructuring time frames.
  - Some debt-equity swaps appear to be equity in name but effectively debt.
  - Risk of superficial financial restructuring if credit growth is not slowed.
  - Transfer of SOE profits to the government budget is well below the target 30 percent.
  - Central SOEs still bear the cost of over 7,000 social entities, amounting to 0.2 percent of GDP per year.
  - Preliminary classification: less than 60 percent of SOEs were considered commercially competitive.
    - In a sample of 10–15 city or provincial State-Owned Asset and Supervision Commissions, about 56 percent of SOEs were classified as commercial competitive, 36 percent as commercial strategic, and 8 percent as social function SOEs.
  - Lack of resolution details complicates assessment of progress; zombies remain difficult to resolve without firmer measures.

### Policy implications and recommended actions
- Overarching principle:
  - Resolving weak firms requires a holistic, coordinated, time-bound, government-led process that allows market forces to operate and follows up with operational restructuring.
- Financial sector and regulatory actions:
  - Banks should initiate a targeted asset quality review to assess firm viability.
  - Reinforce accounting and audit rules to provide timely and accurate financial information.
  - Raise standards of appraisers for asset valuation.
  - Develop efficient credit registers.
  - Regulators should strengthen reviews of loan classification, bank capital, collateral valuation, and prudential reporting to foster proactive NPL resolution.
  - Newly-established creditor committees should align with international best practices (for example, INSOLs principles) to allow sufficient standstill period and information sharing.
- Operational restructuring:
  - Quickly develop operational restructuring plans for weak firms.
  - Empirical results support corporate governance reforms (divestment, management change), deleveraging, and tighter budget constraints to restore viability.
  - The state should not “window-dress” by merging zombies with sound SOEs nor encourage refinancing without addressing underlying problems—even if that implies immediate loss recognition and a mild growth slowdown.
- Hardening budget constraints and exit:
  - Suspend implicit support on credit access and allow greater corporate defaults.
  - Publicly identify nonviable zombies and subject them to greater use of liquidation.
  - Complement with a clear timetable to resolve all identified zombies within 1–2 years.
- SOE reform priorities:
  - Reduce entry barriers and phase out restrictions that give SOEs privileged roles to level the playing field and enhance contestability.
  - Implement commitments to open protected services markets (logistics, finance, telecommunications) and break up administrative monopolies.
- Social and institutional mitigation:
  - Targeted social policies via the budget should complement local social security to mitigate welfare costs of layoffs, estimated at about 2.5–2.8 million workers.
  - Ensure sufficient resources for bankruptcy courts and professionals on valuation; address remaining hurdles in the insolvency framework.

### Conclusions
- Zombie firms and SOEs have contributed significantly to China’s high and rising corporate debt and low productivity, accounting for an outsized share of corporate debt and much of its rise.
- Implicit guarantees and government support encourage excessive investment by these firms, raising leverage and weakening profitability and debt service capacity.
- Firm-level analysis shows strong linkages between zombies and SOEs in creating debt vulnerabilities and low productivity.
- Measures addressing redundant workers, reducing debt burden, scaling down state subsidies, and divesting noncore activities have the largest positive impact on restoring viability.
- Estimated gains from resolving weak firms are around 0.7–1.2 percentage points per year in long-term growth potential.
- Accelerating progress requires a holistic, coordinated strategy: debt restructuring to recognize losses, fostering operational restructuring, reducing implicit support, and liquidating zombies.

*Source: WP/17/266 — Resolving China’s Zombies: Tackling Debt and Raising Productivity (Sections 1–3).*

### Section 1

### wp17266 - Section 1

### Introduction
- Nonviable “zombie” firms are a key government priority for addressing corporate debt vulnerabilities and improving resource allocation in China.
- Using firm-level industrial survey data, the study documents the central role of zombies and their strong linkages with state-owned enterprises (SOEs) in contributing to debt vulnerabilities and low productivity.
- Resolving weak firms can generate significant gains of 0.7–1.2 percentage points in long-term growth per year.
- The paper evaluates effects of different restructuring options, finding that deleveraging, reducing government subsidies, and operational restructuring through divestment and reducing redundancy have significant benefits in restoring corporate performance for zombie firms.

### Background: corporate debt vulnerabilities and misallocation of resources
- China’s nonfinancial private sector debt reached 176 percent of GDP as of the end of March 2017.
- Corporate debt stood at about 135 percent of GDP and contributed most of the rising debt.
- SOEs account for 57 percent of total corporate debt or 72 percent of GDP in 2016.
- SOEs contributed to almost 60 percent of the rise in total corporate debt during 2008–16.
- SOEs’ share of output and employment has declined from over 40 percent in the late 1990s to about 15–20 percent in 2015.
- The share of nonviable zombie firms in total corporate debt rose quickly to 6 percent by 2016 (or 15 percent of total industrial liabilities), the highest level since 2009.
- The debt share of zombie firms remained high despite declining employment, profitability, and fixed asset investment, suggesting rising vulnerability due to a debt overhang.
- Zombie firms overlap considerably with overcapacity sectors and SOEs, which account for half of total debt and about one-third of employment in zombie firms.
- Zombie firms have high regional exposure, with 40 percent of zombie debt in the North and Northeast regions (Heilongjiang, Jilin, Liaoning, Hebei, Shanxi, and Shaanxi provinces, and Inner Mongolia autonomous region).

### Definition of zombies and related classification
- State Council (SC) definition: firms that incur three years of losses, cannot meet environmental and technological standards, do not align with national industrial policies, and rely heavily on government or bank support to survive.
- Fukuda and Nakamura (FN) definition: firms that face persistent losses and receive subsidized credit (actual interest cost less than market prime interest rates), or debt-to-asset ratio higher than 50 percent and increasing, and EBIT smaller than interest payment at market interest rate.
- Nie, Jiang, Zhang, and Fang (NJZF) definition: firms that fit the FN definition for two successive years.
- Baseline definition (used in this paper): modified from Fukuda and Nakamura (2011) — firms that fit the FN definition but considering only one-fourth of short-term debt due less than a year when applying the criteria (i.e., assuming half of short-term debt of six-month maturity).

### Why zombie firms matter
- Zombies have higher leverage, lower returns, slower growth, and lower productivity than non-zombie firms.
- Zombies continue to survive despite weak fundamentals and losses; about 30 percent of zombie firms remain zombies after 5 years.
- Zombies formed during 2008–13 are more entrenched than those formed in the early 2000s.
- Duration analysis: an SOE zombie is 30 percent more likely to stay a zombie in the next year than a non-SOE zombie.
- Empirical studies find zombies crowd out non-zombie investment by 2–8 percent (Tan and others 2017).
- Sustaining nonviable companies suppresses competition and can amplify financial stability risks via nonperforming loans.
- Addressing misallocation by resolving zombie firms can lift productivity; related studies (Hsieh and Klenow 2009) show misallocation reduces TFP and that correcting it can produce gains.

### Empirical analysis — data
- Firm-level annual industrial survey data from the National Bureau of Statistics covering industrial firms in China between 1998 and 2013, about one million companies each year.
- Annual sales thresholds: RMB5 million or above (1998–2009) and RMB20 million or above (2011–13). For consistency, the paper uses firm-level observations with annual sales of 20 million or above.
- Data cleaning and outlier elimination follow Feenstra, Li, and Yu (2014) and Cai and Liu (2009); observations deleted if:
  - key financial variables are missing or negative (total assets, sales revenue, gross value of industrial output, employment, net fixed assets);
  - balance sheet values violate accounting principles (liquid assets, total fixed assets, net fixed assets exceed total assets);
  - employment is 10 people or less;
  - firm identification code is missing or non-unique;
  - inception date is missing or invalid.
- Overcapacity sectors classified using four-digit industry codes; sectors include coal, steel, cement, plated glass, aluminum, paper, solar power, chemicals, ship building, coal-fueled power.

### Empirical analysis — determinants of zombie firms
- Probit model specification: Pr(zombieit = 1) = Φ(Xi,t−1 β + DInd + Dyear + Dreg + εit), where Xi,t−1 includes lagged explanatory variables to reduce endogeneity; industry (two-digit), year, and province/region dummies included.
- Key empirical findings:
  - Higher leverage and lower profitability significantly increase likelihood of being a zombie.
  - A one-percentage-point increase in the liabilities-to-assets ratio raises the likelihood of being a zombie firm by about 0.15 percent on average.
  - A reduction of aggregate demand (proxied by average growth of revenue in the industrial sector) contributes to an increase in zombie companies.
  - Zombies are more common among SOEs and concentrated in overcapacity industries and the North and Northeast regions, holding other factors constant.
- Role of government and banks:
  - Local government support: an index of government direct intervention (average share of working hours firm managers spend with provincial government officials) is a decisive positive determinant of zombie formation (statistically significant at the 5 percent level).
  - A one percentage-point increase in government subsidies to total sales raises the likelihood of becoming a zombie by 0.15 percent, holding other factors constant.
  - Local banks: using the share of deposits held by major state-owned banks as a proxy for close bank-government ties, zombies are more likely in provinces where ties between banks and local governments are close (positive and statistically significant coefficients).
- Findings are robust across different zombie definitions.

*Source: WP/17/266 — Resolving China’s Zombies: Tackling Debt and Raising Productivity (Section I).*

### Section 2

### wp17266 - Section 2

### Key empirical findings on zombie firms and SOEs
- Zombie firms contribute to corporate debt vulnerability, have weaker corporate performance on profitability and leverage ratios, and overlap with overcapacity firms and SOEs.
- Except for two definitions, all provincial indicators capturing the dominance of the government or public entities in directing activity are significant at the 10 percent level.
- The varying results across definitions may reflect the lesser extent to which the State Council and NJZF definitions capture interest cost relative to market rates.
- Nearly half of zombie firms’ debt is related to SOEs.
- Zombie firms that are also SOEs remain zombies for a longer period and are about 30 percent more likely to remain zombies if they are state-owned.

### Factors associated with resolving zombies (probit specification and restructuring options)
- Probit regression setup:
  - Sample: firms classified as zombies in period t-1.
  - Dependent variable: equals one if firm in period t moves to non-zombie category; zero otherwise.
  - Explanatory variables: one-period lagged common restructuring options, controlling for industry and year fixed-effects.
- Restructuring-option variables (all expected to increase likelihood of transition to non-zombie):
  - Deleveraging: dummy = 1 when debt-to-asset ratio is reduced by more than 5 percentage points over a year.
  - Ownership change:
    - SOE to private (state- or collectively owned to privately owned).
    - Corporatization (incorporation of the zombie firm).
  - Reduction in the labor force: proxied by wage-payment-to-asset ratio.
  - Asset sale or injection:
    - “Asset injection” dummy when fixed asset growth > +10 percentage points.
    - “Asset sale” dummy when fixed asset growth < −10 percentage points.

### Empirical results on restructuring measures
- General note: empirical results illustrate correlations and do not imply causality.
- Deleveraging:
  - Debt restructuring that reduces leverage is correlated with higher likelihood of turning into viable firms; creditors may obtain ownership stakes and incentives to improve performance.
- Ownership change:
  - Privatization/corporatization (as in past SOE reforms) shows a strong statistically significant positive coefficient for transition to viability.
- Reduction in labor costs:
  - Marginal effect of reducing labor cost is significant in some specifications but less robust across specifications; zombies in the sample are more determined by debt burden than labor redundancy.
- Asset injection and sale:
  - Both asset “injection” and “sale” dummies have statistically significant positive effects, suggesting unloading noncore assets or injections from parents helps transition to viable status.

### Productivity gains from resolving resource misallocation
- Framework: follows Hsieh and Klenow (2009); measures efficiency via revenue total factor productivity (TFPR) equalization within industry and within groups (zombie vs non-zombie, SOE vs non-SOE).
- Historical example:
  - During 1998–2000, resolving debt vulnerabilities would respectively boost aggregate industrial TFP by 5–8 percent for zombie firms and SOEs.
- Recent/potential magnitudes:
  - As debt vulnerabilities have risen in recent years, potential gains appear to have risen to about 7 percent between SOEs and non-SOEs.
- International comparison:
  - Narrowing China’s revenue-productivity gap to the 75th-percentile of a 57-country sample would boost output by about 16 percent or raise long-term growth potential by 0.7 percentage points per year.
  - Converging to the 90th percentile would raise output by 28 percent or about 1.2 percentage points in long-term growth.
- Aggregate implications:
  - Resolving weak firms contributes to large potential gains (0.7–1.2 percentage points) in output per year.
  - Scaling TFPR efficiency gains to total output suggests roughly half of total potential gains in output arise from resolving weak firms.
  - SOE reforms can account for over 0.4 percentage points of long-term output increase.
  - Substantial overlap among weak firms implies complementarity of reforms to maximize gains.

### Government measures and assessment
- Government strategy (corporate debt vulnerabilities and SOE efficiency):
  - Aim: market and legal framework for debt restructuring; guard against systemic/regional risks.
  - Approach: multipronged firm-by-firm options (merger and consolidation, liquidation, debt-equity swaps, corporate asset sales) (State Council 2016).
  - Institutional action: inter-ministerial group led by the National Development and Reform Commission to facilitate deleveraging; financial regulators renewed focus on controlling financial risks (CBRC 2016, 2017).
- Recent SOE measures (listed):
  - Consolidating some central SOEs.
  - Phasing out SOE social functions.
  - Transferring about ½ percent of state-owned equity to social security funds.
  - Cutting central SOE losses.
  - Individually incorporating the subsidiaries of central SOEs by 2017.
  - Implementing pilot employee stock-ownership programs.
  - Bringing in other investors under mixed-ownership pilot reforms and opening up sectors (travel, medical care, electricity, power and utilities) to private and foreign investment.
- Zombies specifically:
  - About 2,000 central SOEs (with total assets of about 4 percent of GDP) and over 7,000 local SOEs have officially been identified as zombie firms.
  - Reportedly, about 20 percent of the identified central SOE zombies have already been resolved (no resolution-method details provided).
  - Regulatory amendments relevant to nonperforming loans have been made to expedite liquidation of zombies.
- Assessment of measures:
  - Deleveraging guidelines are positive initial steps but lack details on loss recognition and operational restructuring time frames.
  - Some debt-equity swaps appear to be equity in name but effectively debt.
  - Risk of superficial financial restructuring if credit growth is not slowed—e.g., meeting deleveraging “targets” without tackling structural problems.
  - Broader SOE reform implementation has lagged and has not yet raised growth potential.
    - Transfer of SOE profits to the government budget is well below the target 30 percent.
    - Central SOEs still bear the cost of over 7,000 social entities, amounting to 0.2 percent of GDP per year.
    - Preliminary classification: only less than 60 percent of SOEs were considered commercially competitive.
      - In a sample of 10–15 city or provincial State-Owned Asset and Supervision Commissions, about 56 percent of SOEs were classified as commercial competitive, 36 percent as commercial strategic, and 8 percent as social function SOEs.
  - Lack of resolution details complicates assessment of progress; zombies remain difficult to resolve without firmer measures.

### Policy implications and recommended actions
- Overarching principle:
  - Resolving weak firms is a first step to addressing debt vulnerabilities and raising productivity; requires a holistic, coordinated, time-bound, government-led process that allows market forces to operate and follows up with operational restructuring.
- Financial sector and regulatory actions:
  - Banks should initiate a targeted asset quality review to assess firm viability.
  - Reinforce accounting and audit rules to provide timely and accurate financial information.
  - Raise standards of appraisers for asset valuation.
  - Develop efficient credit registers.
  - Regulators should strengthen reviews of loan classification, bank capital, collateral valuation, and prudential reporting to foster proactive NPL resolution.
  - Newly-established creditor committees should align with international best practices (for example, INSOLs principles) to allow sufficient standstill period and information sharing.
- Operational restructuring:
  - Quickly develop operational restructuring plans for weak firms.
  - Empirical results support corporate governance reforms (divestment, management change), deleveraging, and tighter budget constraints to restore viability.
  - The state should not “window-dress” by merging zombies with sound SOEs nor encourage refinancing without addressing underlying problems—even if that implies immediate loss recognition and a mild growth slowdown.
- Hardening budget constraints and exit:
  - Suspend implicit support on credit access and allow greater corporate defaults.
  - Publicly identify nonviable zombies and subject them to greater use of liquidation.
  - Complement with a clear timetable to resolve all identified zombies within 1–2 years.
- SOE reform priorities:
  - Reduce entry barriers and phase out restrictions that give SOEs privileged roles to level the playing field and enhance contestability.
  - Implement commitments to open protected services markets (logistics, finance, telecommunications) and break up administrative monopolies.
- Social and institutional mitigation:
  - Targeted social policies via the budget should complement local social security to mitigate welfare costs of layoffs, estimated at about 2.5–2.8 million workers.
  - Ensure sufficient resources for bankruptcy courts and professionals on valuation; address remaining hurdles in the insolvency framework.

### Conclusions (summary)
- Zombie firms and SOEs have contributed significantly to China’s high and rising corporate debt and low productivity, accounting for an outsized share of corporate debt and much of its rise.
- Implicit guarantees and government support encourage excessive investment by these firms, raising leverage and weakening profitability and debt service capacity.
- Firm-level analysis shows strong linkages between zombies and SOEs in creating debt vulnerabilities and low productivity.
- Measures addressing redundant workers, reducing debt burden, scaling down state subsidies, and divesting noncore activities have the largest positive impact on restoring viability.
- Estimated gains from resolving weak firms are around 0.7–1.2 percentage points per year in long-term growth potential.
- Accelerating progress requires a holistic, coordinated strategy: debt restructuring to recognize losses, fostering operational restructuring, reducing implicit support, and liquidating zombies.

*Source: wp17266 - Section 2*

### Section 3

### wp17266 - Section 3

### Duration analysis of zombie firms: methodology
- Survival and hazard functions assume n independent observations denoted (t_j, C_j), where j = 1, 2, ..., n, where t_j is the “survival” time (zombie duration) and C_j is the event indicator variable C of observation j. C_j takes on a value of 1 if “failure event” (zombies recover into non-zombies) occurred and 0 otherwise.
- Assume there are 푚≤푛 recorded times of zombie recovery. Denote the rank-ordered zombie duration times as 푡1<푡2<⋯<푡푚. Let n_j denote the number of subjects at t_j and let d_j denote the number of observed zombie recovery.
- Kaplan-Meier estimator at time t (nonparametric estimate of the survivor function):
  - 푆̂(푡) = ∏( (푛_푗 − 푑_푗) / 푛_푗 )_{푗|푡_푗 ≤ 푡}
  - Interpretation: shows the probability of not turning into a non-zombie in time period t, and is robust to data censoring.
- Cox-proportional hazard model specification used:
  - h_j(t) = h_0(t) exp(x_j,)
  - Log-linear form: ln h_j(t) = ln h_0(t) + x_j 
  - Interpretation: h_j(t) is the probability of a zombie firm turning into a non-zombie firm, conditional on observation j that has been a zombie for t years; h_0(t) denotes the underlying baseline hazard function not specified for parameter estimation; x_j includes all independent explanatory variables.
- Left-censoring treatment: excludes firms that are classified as zombies in the first year of the dataset to avoid estimation bias.
- Some zombies may experience multiple transitions; these are treated as independent observations.

### Key empirical duration findings (baseline)
- Zombies that are SOEs are more difficult to recover because of soft budget constraints and implicit support.
- Zombies that have higher debt burden are less likely to recover.
- Zombies in overcapacity industries and/or in the North and Northeast regions are more entrenched.

### Empirical results (appendices overview)
- Appendix Table 1: Baseline Results on the Duration Analysis of Nonviable Zombie Firms (Kaplan-Meier estimates based on Cox-proportional hazard with multivariate regression).
- Appendix Table 2.1: Determinants of Nonviable Zombie Firms—Different Specifications under Baseline Definition.
- Appendix Table 2.2: Determinants of Zombie Firms Based on Alternative Definitions.
- Appendix Table 2.3: Baseline Results on the Effects of Restructuring on Zombie Recovery.
- Appendix Table 2.4: Restructuring Effects across Alternative Definitions of Zombie Firms.

### Theoretical framework for estimating gains from resolving weak firms
- Context: Resource misallocation leads to dispersion of revenue productivity across firms and contributes to cross-country differences in total factor productivity (TFP). Reallocating resources from low-productivity to high-productivity firms increases aggregate output.
- Aggregate production structure (industry and final output):
  - 1
    s
    S
    s
    s
    Y
    
    =
    =
    ∏
  with
  - 1
    1
    S
    s
    s
    
    =
    =
    ∑
  - Industry output Y_s is a CES aggregate of M_s differentiated products:
    - 1
      1
      1
      (
      )
      s
      M
      s
      si
      i
      Y
      
      
      −
      −
      =
      =
      ∑
    - Y_s,i denotes firm i’s output, and  denotes the elasticity of substitution between output variety i.
- Firm production function (Cobb-Douglas):
  - 1
    s s
    si
    si
    si
    Y
    A  K   L
    
    −
    =
- Profit function with distortions:
  - (1)
    (1)
    YK
    si
    si
    si   si
    si
    si
    si
    P Y
    L
    RK
    
    
    
    
    =
     −
     −    −  +
- First-order conditions (marginal products):
  - 1
    si
    Y
    si
    MRPL
    
    
    =
    −
    and
  - (1)
    1
    K
    si
    si
    Y
    si
    R
    MRPK
    
    
    
    =
    −
- Definitions distinguishing revenue and physical productivity:
  - 1
    ss
    si   si
    si
    si
    si
    si
    si
    PY
    TFPR
    P A
    LK
    
    −
    =
    ==
  - 1
    ss
    si
    si
    si
    si
    si
    Y
    TFPQ
    A
    LK
    
    −
    =
    ==
- Firm-specific distortions reflected in revenue productivity:
  - 1
    (1)
    (
    )
    (
    )
    1
    1
    1
    s
    ss
    K
    si
    si
    Y
    s
    s
    si
    R
    TFPR
    
    
    
    
       
    
    
    −
    
    =
    −
    −
    −
- Aggregation to industry TFP:
  - 1
    1
    1
    1
    (A)
    s
    M
    s
    s
    si
    i
    si
    TFPR
    TFP
    TFPR
    
    
    −
    −
    =
    =
    [
    =
    ]
    ∑
- Interpretation: sTFPR is a geometric mean of the average marginal revenue product of capital and labor. Equalizing marginal products across firms raises TFP relative to the distorted case.
- Output gain and resource reallocation measure (concept):
  - For each industry, calculate the ratio of actual TFP to the efficient level of TFP. Aggregating up yields the measure of resource reallocation gain.
  - Resolving debt vulnerabilities from SOE reforms, cutting overcapacity, and cleaning up zombies is equivalent to equalizing TFPR across firms. Output gains are expressed as total gain when equalizing TFPR within industries and net of the gain when equalizing TFPR only within ownership (SOE and non-SOE) or firm status (zombie and non-zombie).
  - Reducing overcapacity implies resources would also be redistributed across industries.
- Representative expression linking output gains, TFP gains from reallocation, and gains from inputs redistribution (as presented):
  - *
    *
    *
    (1)
    (1)
    **
    (1)
    **
    *
    1
    11
    (1)
    (1)
    1
    s
    s
    ss
    s
    ss
    s
    s
    s
    ss
    ss
    S
    s
    ss
    SS
    ss
    s
    efficient
    s
    ss
    S
    s
    s
    ss
    ss
    s
    A K
    L
    KL
    Y
    A
    Y
    A
    KL
    A K
    L
    
    
    
    
    
    
    
    
    
    
    −
    −
    =
    =
    =
    −
    −
    =
    =
    =
    =
    
    ∏
    ∏
    ∏
    ∏

*Source: wp17266 - Section 3 (IMF working paper, Section 3, Appendices 1–3).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17266.pdf_