## Credit Misallocation and Economic Growth in Vietnam

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---

### Abstract and framing
- Paper examines legacy non-performing loans (NPLs), high opportunity cost of government financing of bank recapitalization, and effects on financial intermediation efficiency, economic growth, and welfare in Vietnam.
- Methodology: combined empirical analysis using corporate panel data and a micro-founded banking model embedded in a political economy setting.
- Key theoretical insight: recapitalization depends on factors including the tightness of the government budget and the decision maker’s concern for the favored sector.
- JEL Classification Numbers: E61, G21, H81

### International context and motivation
- Empirical evidence from other transition economies suggests credit misallocation between SOEs and non-SOEs can substantially suppress aggregate productivity and growth.
- Examples cited:
  - China: SOEs’ share in urban employment dropped from 60 percent in 1994 to about a third in 2000 after restructuring.
  - Hsieh and Klenow result: improvement in resource allocation raised Chinese TFP by 2 percent per year during1998-2005.
- Cross-country evidence: undercapitalized banks tend to under-provision and engage in forbearance lending, worsening credit misallocation.

### Dataset and variable definitions
- Data source: annual unbalanced panel from Worldscope covering listed firms during 2005-2015.
- Variable definitions:
  - dum_soe = 1 if the state share is more than 10 percent, and dum_soe = 0 otherwise.
  - roa = EBIT/total asset
  - roa_soe = dum_soe*roa
  - intr = interest expenses/total debt
  - d_debt = Year-on-year growth rate of total debt
  - d_ta = Year-on-year growth rate of total asset
- Sample exclusions and cleaning:
  - Industries dropped: Telecommunications, Utilities, and Financials (ICB: 6000-9000).
  - Outlier removal criteria: roa outside 1–99 percentile (then roa in [-0.17, 0.38]); intr negative or more than 40 percent; d_debt more than 100 percent; d_ta more than 50 percent.
- Note: only listed firms included; fully state owned enterprises are not included; actual credit misallocation may be more pervasive.

### Empirical findings — interest payments and credit pricing
- Regression (controls include roa_t, roa_t-1, and log total assets) result:
  - β5 = −0.0044 (t: −2.30), suggesting SOEs obtain credit at lower rates on average even after controlling for profitability and firm size.
- Interest rate sensitivity:
  - On average, ex-ante profitability is negatively associated with interest payments (β1 < 0).
  - Ex-post profitability is positively associated with interest payments (β3 > 0), interpreted as banks charging less ex-post to temporarily unprofitable firms (interest payment forgiveness).
- For unprofitable SOEs:
  - Coefficient for SOE interaction in bad-firm sample: β5 = 0.183, indicating typical negative relationship between loan rates and profitability is biased toward zero for SOEs.
  - Conclusion: underperforming SOEs obtain loans at lower loan rates compared with non-SOEs; lending rates for SOEs are almost unrelated to ex-ante profitability.

### Empirical findings — loan growth and profitability
- Regression: debt growth (d_debt) on lagged profitability and controls (total asset, year dummies), firm fixed effects.
- Key coefficients reported:
  - For all firms: 0.731*** (roa_t-1)
  - Subsamples (good / bad firms): 0.693 and 1.768***
  - SOE interactions (all / good / bad): −0.800**, −1.421*, −1.252**
- Interpretation:
  - On average, debt growth is positively correlated with prior profitability (β1 > 0): profitable firms expand debt to grow.
  - For SOEs—particularly SOEs in the bad-firm sample—the sensitivity of debt growth to profitability is biased downward (β2 < 0), and net relationship for SOEs is close to zero, implying some underperforming SOEs continue to obtain credit (forbearance lending).
- Empirical summary:
  - (i) SOEs obtain bank credit at lower costs on average, even after controlling for profitability and size.
  - (ii) While lending rates and loan growth are positively correlated with ex-ante profitability on average, for underperforming SOEs these relationships are almost unrelated to ex-ante profitability.
  - Combined implication: commercial banks continue lending to unprofitable SOEs at unreasonably low rates, creating credit misallocation.

### Theoretical model overview
- Model type: two-sector extension of the Monti-Klein framework with a representative bank having monopolistic power in lending and deposit markets.
- Production sectors: high-productivity (H) and low-productivity (L) requiring working capital financed by bank credit; emphasis on bank capital buffers' role in resolving NPLs and reallocating credit.
- Analytical steps:
  - Establish bank profit-maximizing behavior and banking-sector equilibrium.
  - Study policy effects of bank recapitalization on NPL resolution, credit allocation, productivity, output, and welfare.
  - Embed banking equilibrium into a political economy model where government optimally selects recapitalization size balancing fiscal constraints and favoritism toward the favored sector.

### Model setup and sectoral technologies
- Two sectors:
  - H sector production: y_H = z_H k_H^α with decreasing returns to scale (α < 1).
  - L sector production: y_L = z_L k_L (linear).
- Productivity ordering: z_H ≥ z_L.
- Economic interpretation:
  - H sector: high-return projects with diminishing returns as firm size grows.
  - L sector: abundant low-return projects; represents inefficient SOEs and stock of legacy NPLs.

### Bank optimization problem and constraints
- Bank choices: lending to H and L sectors, invest in riskless bonds B, fund through deposits d and equity e.
- Riskless bond return: r_f (exogenous).
- Initial L-sector credit (legacy NPLs): k̄_L. Bank chooses fraction x of NPLs resolved this period with k_L = (1 − x) k̄_L.
- NPL resolution incurs loan impairment costs: e = ē − x · LGD · k̄_L with LGD parameter ϕ where 0 ≤ ϕ ≤ 1.
- Initial equity: ē = e_a + e_g (accumulated equity e_a and government capital injection e_g); bank treats ē as given when optimizing.
- Deposit supply: d = d̄ · (r_d)^η, where r_d is deposit rate and 0 < η is elasticity of deposit supply.
- Capital requirement: e / d ≥ κ (later κ = 0.1).
- Bank chooses r_L, r_H, r_d, B, and x to maximize profit subject to budget constraint, law of motion for k_L and e, deposit supply, loan demand functions, and capital requirement.

### Optimal deposit rate, lending rates, and NPL resolution
- Optimal deposit rate:
  - r_d^* = (η / (1 + η)) r_f.
- Optimal lending rates (qualitative):
  - r_H^* = r_f + ζ κ + (θ term present); when capital constraint binds (ζ > 0), r_H^* is higher.
  - r_L^* depends on z_L and model parameters.
- Implication: Undercapitalization (binding capital constraint, ζ > 0) raises the H-sector lending rate, reducing credit to H sector and creating misallocation toward L sector.
- Equilibrium NPL resolution x^*:
  - x^* is an increasing function of government capital injection e_g; greater recapitalization raises equilibrium NPL resolution because banks need sufficient capital buffers e_a + e_g to absorb losses from NPL resolution.

### Policy effects of recapitalization — calibration and key quantitative inputs
- Calibration choices used for comparative statics:
  - κ = 0.1
  - ϕ = 0.3
  - Initial NPL ratio = 12 percent
  - r_f = 1.06
  - z_H = 1.06
  - z_L = 0.7
  - deposit rate target = 5 percent
  - lending rate target = 9 percent
  - initial x (with e_g = 0) = 20 percent
- Notes on calibration:
  - η and α chosen to match deposit and lending rate targets.
  - Initial equity ē set so that NPL resolution x = 20 percent when e_g = 0.

### Macroeconomic aggregates and profitability metrics
- Aggregate output and productivity:
  - Y = y_H + y_L = z_H k_H^α + z_L k_L
  - A = Y / (k_H + k_L)
- Bank profitability (NIM):
  - NIM = (r_H k_H + r_L k_L + r_f B − r_d d) / (k_H + k_L)
- Credit misallocation lowers aggregate productivity A and aggregate output Y.

### Comparative-statics: partial NPL resolution (0 < x < 1)
- As government recapitalization e_g increases:
  - Equilibrium x^* (NPL resolution) increases.
  - Credit allocated to L sector decreases proportionally as x rises.
  - Credit to H sector remains unchanged while 0 < x < 1 because Lagrange multiplier ζ on capital constraint stays constant; hence r_H^* and k_H are constant in this range.
- Aggregate output Y:
  - Slightly decreasing during 0 < x < 1 because total credit falls as reduction in L-sector credit is not offset by H-sector credit increases until full resolution.
- Bank profitability (NIM):
  - NIM increases during partial-resolution phase: deposit rates constant while average asset return rises due to reallocating loans from L to H, boosting profitability.

### Comparative-statics: full NPL resolution (x = 1)
- Full NPL resolution achieved at some e_g as recapitalization increases.
- Two subcases when x = 1:
  - (a) Capital constraint still binds (x = 1, ζ > 0): "full capitalization case" — realistic for policy discussion.
  - (b) Capital constraint slack (x = 1, ζ = 0): unrealistic large-scale recapitalization; excluded from political-economy analysis.
- After x = 1:
  - L sector credit shuts down completely (k_L = 0).
  - ζ decreases with e_g; since r_H^* decreases with ζ, r_H^* falls as e_g rises.
  - Credit to H sector k_H increases with e_g after x = 1.
  - Aggregate output Y begins to increase with further recapitalization after the kink at x = 1, producing a V-shaped response of Y to e_g (Y decreases slightly during partial resolution, then increases after full resolution).
  - Bank NIM starts to decline after x = 1 because r_H^* falls; NIM may be inflated when banks are undercapitalized because they squeeze corporate loans.
- At very large e_g where capital constraint becomes slack (ζ = 0), all variables become constant with respect to e_g and further capital injection is ineffective.

### Political equilibrium for recapitalization (government decision)
- Government budget constraint: e_g = T − q, where T is fixed tax revenue and q denotes other government expenditures.
- Government maximizes social welfare:
  - W = α y_L + Y + S(q), with S'(·) > 0, S''(·) < 0, and parameters capturing government weights.
- Optimal recapitalization choices:
  - Corner solution: e_g = 0 if fiscal cost exceeds benefits (characterizes status quo in Vietnam per text).
  - Interior solution: e_g > 0 when first-order condition holds:
    - ∂W/∂e_g ≡ ∂Y/∂e_g + α ∂y_L/∂e_g + S'(T − e_g) · (−1) = 0.
  - Solve for e_g* satisfying the FoC; if no interior e_g with ∂W/∂e_g = 0 exists for e_g ≥ 0, optimal policy is e_g = 0.

### Government first-order condition and bank response
- If recapitalization parameter ݁ீ satisfies the FoC (݁ீ∗), then the bank will resolve all NPLs (ݔ∗ = 1) under ݁ீ = ݁ீ∗ in the second stage.
- Intuition: halfway recapitalization is never optimal for the government in the static model because the marginal benefit of recapitalization is always negative in that range due to the V-shaped response of output.
- Footnote caveats:
  - There must exist ݁ீ such that ߲݁ ܷ߲ீ⁄ ൏0 at large values because ݂ᇱܩ(൫) = ∞ at some ܩ൐0, ruling out corner solution where government injects capital until capital constraint becomes slack.
  - With dynamic optimization, halfway recapitalization could be justified as an interim stage.

### Welfare comparison and determinants of optimal recapitalization
- Define social welfare under zero recapitalization as ܷ଴ and under optimal recapitalization ݁ீ = ݁ீ∗ as ܷ∗.
- Aggregate outputs under the two policies are ܻ଴ and ܻ∗ respectively; under ݁ீ = ݁ீ∗ (with NPLs fully resolved and ݔ = 1), ݕ௟∗ = 0.
- Government chooses zero recapitalization (݁ீ = 0) if ܷ଴ ܷੇ∗ = ( (ܻ଴ ܻੇ∗) ݕߙ + ௟଴ ߚ + ሺ݂(ܶ) ሻ ݂େ(݁െܶீ∗) ) ൐0, and chooses ݁ீ = ݁ீ∗ if ܷ଴ ܷੇ∗ ൏0.
- Political-economy determinants:
  - High ߙ and/or high ߚ reduce government incentive to recapitalize with public funds.
    - High ߙ: government favors L sector (SOEs).
    - High ߚ: government values other expenditures more than bank recapitalization.
  - Large fiscal space (high ܶ) increases tendency to conduct recapitalization using public funds due to concavity of S(·).

### Conclusion and policy implications
- Empirical and theoretical summary:
  - Paper documents empirical evidence of credit misallocation between SOEs and non-SOEs in Vietnam.
  - Theoretical analysis frames bank recapitalization and its effects within a political economy trade-off determined by government favoritism toward the low-productivity sector, relative value assigned to fiscal expenditures, and tightness of fiscal space.
- First-best vs second-best:
  - First-best: fast NPL resolution and full recapitalization by public funds improves credit allocation and growth relative to second-best (no public funds, only banks’ retained earnings).
  - First-best requires government budget not too tight (marginal cost of funds below a threshold), underscoring the importance of fiscal space for financial stability.
- Important caveat:
  - Recapitalization is necessary but not sufficient to resolve credit misallocation. Model assumes sufficient capital buffers lead banks to shut down underperforming SOEs immediately.
  - In reality, additional constraints hinder resolution, including political connections of SOEs and weak law enforcement for NPL resolution; those constraints must be addressed alongside recapitalization.

*Source: IMF Working Paper WP/19/189 — Sections 1–3*

### Section 1

### Credit Misallocation and Economic Growth in Vietnam

### Abstract and framing
- The paper examines legacy non-performing loans (NPLs), high opportunity cost of government financing of bank recapitalization, and their effects on the efficiency of financial intermediation, economic growth, and welfare in Vietnam.
- Methodology: combined empirical analysis using corporate panel data and a micro-founded banking model embedded in a political economy setting.
- Key theoretical insight: recapitalization depends on factors including the tightness of the government budget and the decision maker’s concern for the favored sector.
- JEL Classification Numbers: E61, G21, H81

### International context and motivation
- Empirical evidence from other transition economies suggests credit misallocation between SOEs and non-SOEs can substantially suppress aggregate productivity and growth.
- Examples and empirical numbers cited:
  - China: SOEs’ share in urban employment dropped from 60 percent in 1994 to about a third in 2000 after restructuring.
  - Hsieh and Klenow result: improvement in resource allocation raised Chinese TFP by 2 percent per year during1998-2005.
- Bank-capital buffer importance supported by cross-country studies: undercapitalized banks tend to under-provision and engage in forbearance lending, worsening credit misallocation.

### Dataset and variable definitions
- Data source: annual unbalanced panel from Worldscope covering listed firms during 2005-2015.
- Variable definitions:
  - dum_soe = 1 if the state share is more than 10 percent, and dum_soe = 0 otherwise.
  - roa = EBIT/total asset
  - roa_soe = dum_soe*roa
  - intr = interest expenses/total debt
  - d_debt = Year-on-year growth rate of total debt
  - d_ta = Year-on-year growth rate of total asset
- Sample exclusions:
  - Industries dropped: Telecommunications, Utilities, and Financials (ICB: 6000-9000).
  - Outlier removal criteria: roa outside 1–99 percentile (then roa in [-0.17, 0.38]); intr negative or more than 40 percent; d_debt more than 100 percent; d_ta more than 50 percent.
- Note: because only listed firms are included, fully state owned enterprises are not included; actual credit misallocation may be more pervasive.

### Empirical findings — interest payments and credit pricing
- Regression (controls include roa_t, roa_t-1, and log total assets) result:
  - β5 = −0.0044 (t: −2.30), suggesting SOEs obtain credit at lower rates on average even after controlling for profitability and firm size.
- Interest rate sensitivity:
  - On average, ex-ante profitability is negatively associated with interest payments (β1 < 0).
  - Ex-post profitability is positively associated with interest payments (β3 > 0), interpreted as banks charging less ex-post to temporarily unprofitable firms (interest payment forgiveness).
- For unprofitable SOEs:
  - The coefficient for the SOE interaction in the bad-firm sample is β5 = 0.183, indicating that the typical negative relationship between loan rates and profitability is biased toward zero for SOEs.
  - Conclusion: underperforming SOEs obtain loans at lower loan rates compared with non-SOEs; lending rates for SOEs are almost unrelated to ex-ante profitability.

### Empirical findings — loan growth and profitability
- Regression setup: debt growth (d_debt) on lagged profitability and controls (total asset, year dummies), firm fixed effects.
- Key coefficients reported in Table 2 (as presented):
  - For all firms: 0.731*** (roa_t-1)
  - Subsamples (good / bad firms): 0.693 and 1.768***
  - SOE interactions (all / good / bad): −0.800**, −1.421*, −1.252**
- Interpretation:
  - On average, debt growth is positively correlated with prior profitability (β1 > 0): profitable firms expand debt to grow.
  - For SOEs—particularly SOEs in the bad-firm sample—the sensitivity of debt growth to profitability is biased downward (β2 < 0), and the net relationship for SOEs is close to zero, implying some underperforming SOEs continue to obtain credit (forbearance lending).
- Summary of empirical results:
  - (i) SOEs obtain bank credit at lower costs on average, even after controlling for profitability and size.
  - (ii) While lending rates and loan growth are positively correlated with ex-ante profitability on average, for underperforming SOEs these relationships are almost unrelated to ex-ante profitability.
  - Combined implication: commercial banks continue lending to unprofitable SOEs at unreasonably low rates, creating credit misallocation.

### Theoretical model overview (setup and purpose)
- Model type: a simple two-sector extension of the Monti-Klein framework where a representative bank has monopolistic power in lending and deposit markets.
- Focus: two production sectors — high-productivity (H) and low-productivity (L) — that require working capital financed by bank credit; emphasis on bank capital buffers' role in resolving NPLs and reallocating credit.
- Analytical steps:
  - Establish bank profit-maximizing behavior and equilibrium in the banking sector.
  - Study policy effects of bank recapitalization on NPL resolution, credit allocation, productivity, output, and welfare.
  - Embed the banking equilibrium into a political economy model where the government optimally selects the size of recapitalization, balancing fiscal constraints and favoritism toward the favored sector.

*Source: IMF Working Paper WP/19/189 — Section 1*

### Section 2

### wpiea2019189-print-pdf - Section 2

### Model setup and sectoral technologies
- Two sectors: H (high-return) and L (low-return).  
- Firm production functions:
  - H sector: y_H = z_H k_H^α with decreasing returns to scale (α < 1).
  - L sector: y_L = z_L k_L (linear).
- Productivity ordering: z_H ≥ z_L.  
- Economic interpretation:
  - H sector: firms have high-return projects but diminishing returns as firm size grows (scarcity of high-return projects).
  - L sector: firms perform abundant low-return projects; represents inefficient, lower-productivity SOEs and a stock of legacy NPLs on the loan book.

### Bank optimization problem and constraints
- Representative bank lends to firms in H and L sectors and invests in riskless bonds (B), funds through deposits (d) and equity (e).
- Riskless bond return: r_f (exogenous).  
- Initial amount of credit to L sector (legacy NPLs): k̄_L. Bank chooses fraction x of NPLs resolved this period. Law of motion for L-sector credit:
  - k_L = (1 - x) k̄_L.
- NPL resolution incurs loan impairment costs that erode equity: e = ē - x · LGD · k̄_L (text expresses impairment with LGD parameter ϕ where 0 ≤ ϕ ≤ 1).
- Initial equity ē consists of accumulated equity e_a and government capital injection e_g: ē = e_a + e_g. Bank treats ē as given when optimizing.
- Deposit supply: d = d̄ · (r_d)^η, where r_d is deposit rate and 0 < η is elasticity of deposit supply (notation in text: r_d and θ where θ∈(0,1) is mark-down parameter).
- Capital requirement (equity-to-debt ratio) constraint: e / d ≥ κ (notation: κ is required minimum ratio; later κ = 0.1).

- Bank chooses r_L, r_H (lending rates to L and H sectors), r_d (deposit rate), B (bonds), and x (NPL resolution) to maximize profit subject to:
  - budget constraint (net interest profit from loans and bonds minus deposit cost),
  - law of motion for k_L and e given k̄_L and ē,
  - deposit supply function,
  - loan demand functions in each sector,
  - capital requirement e / d ≥ κ.

### Optimal deposit rate, lending rates, and NPL resolution
- Optimal deposit rate:
  - r_d^* = (η / (1 + η)) r_f. (deposit mark-down: η/(1+η) < 1)
- Optimal lending rates:
  - r_H^* = r_f + ζ κ + (θ term present in model) (text: r_H^* = r_f + ζ κ + θ/...; ζ is Lagrange multiplier for capital constraint). Key qualitative point: when capital constraint binds (ζ > 0), r_H^* is higher.
  - r_L^* = (expression depends on z_L and parameters; text indicates r_L^* is a function of z_L).
- Implication: Undercapitalization (binding capital constraint, ζ > 0) raises the H-sector lending rate, reducing credit supply to the H sector and creating credit misallocation toward the L sector.

- Equilibrium NPL resolution x^* (text formula):
  - x^* = e_g / (e_a + e_g + e_a ???) · (κ − ϕ) · k̄_L · (κ − ϕ^ν) · k̄_L^(something) ... (text presents a formal expression and then explains qualitative properties).
  - Noteworthy: x^* is an increasing function of government capital injection e_g. Greater recapitalization raises equilibrium NPL resolution because banks need sufficient capital buffers e_a + e_g to absorb losses from NPL resolution.

### Policy effects of recapitalization — calibration and key quantitative inputs
Calibration choices used for comparative statics:
- Minimum capital ratio: 9 percent → κ = 0.1.
- Loss given default (LGD): 30 percent → ϕ = 0.3.
- Initial NPL ratio: set so that NPL in initial period k̄_L implies NPL ratio = 12 percent.
- Market return and H-sector productivity: r_f = 1.06 and z_H = 1.06 (i.e., 6 percent).
- Deposit and lending rates targets: deposit rate = 5 percent, lending rate = 9 percent (η and α chosen to match these).
- L-sector (bad sector) productivity: z_L = 0.7 (for illustration; qualitative results robust to different z_L).
- Initial equity ē chosen so that NPL resolution x = 20 percent when e_g = 0.

Key calibrated numeric values (preserved exactly):
- κ = 0.1
- ϕ = 0.3
- Initial NPL ratio = 12 percent
- r_f = 1.06
- z_H = 1.06
- z_L = 0.7
- deposit rate target = 5 percent
- lending rate target = 9 percent
- initial x (with e_g = 0) = 20 percent

### Macroeconomic aggregates and profitability metrics
- Aggregate output Y and aggregate productivity A defined as:
  - Y = y_H + y_L = z_H k_H^α + z_L k_L
  - A = Y / (k_H + k_L) (aggregate productivity rises if credit allocated more to H sector because z_H ≥ z_L).
- Bank profitability measured by net interest margin (NIM):
  - NIM = (r_H k_H + r_L k_L + r_f B − r_d d) / (k_H + k_L).
- Credit misallocation lowers aggregate productivity A and thus aggregate output Y.

### Comparative-statics results: partial NPL resolution (second-best, 0 < x < 1)
- As government recapitalization e_g increases:
  - Equilibrium x^* (NPL resolution) increases.
  - Credit allocated to L sector decreases proportionally as x rises (bank reduces L-sector lending by resolving NPLs).
  - Credit to H sector remains unchanged while 0 < x < 1 because the Lagrange multiplier ζ on capital constraint stays constant; hence r_H^* and k_H are constant with respect to e_g in this range.
- Aggregate output Y:
  - Slightly decreasing in the process of recapitalization when 0 < x < 1. Explanation: total credit in the economy falls because reduction in L-sector credit is not offset by an increase in H-sector credit until full resolution is achieved → temporary economic downturn during adjustment before long-term gains.
- Bank profitability (NIM):
  - NIM increases as recapitalization proceeds in the partial-resolution phase. Reason: deposit rates constant while asset return rises on average due to improved credit allocation (reallocating loans from L to H increases average asset return), boosting profitability and potentially attracting outside equity investors.

### Comparative-statics results: full NPL resolution (first-best, x = 1)
- Full NPL resolution is achieved at some e_g as government recapitalization increases.
- Two subcases when x = 1:
  - (a) Capital constraint still binds (x = 1, ζ > 0): "full capitalization case" in political-economy analysis — considered realistic for policy discussion.
  - (b) Capital constraint slack (x = 1, ζ = 0): unrealistic large-scale recapitalization; excluded from political-economy analysis.
- After full NPL resolution (x = 1):
  - L sector credit shuts down completely (k_L = 0).
  - Lagrange multiplier ζ becomes a decreasing function of e_g; since r_H^* decreases with respect to ζ, r_H^* falls as e_g rises.
  - Credit to H sector k_H increases with e_g after x = 1 because the bank no longer needs to hold capital buffer for NPL losses and can extend new loans to productive H-sector firms.
  - Aggregate output Y begins to increase with further recapitalization after the kink at x = 1, producing a V-shaped response of Y to e_g (Y decreases slightly during partial resolution, then increases after full resolution).
  - Bank NIM starts to decline after x = 1 because lending rate r_H^* falls; implication: NIM may be slightly inflated when banks are undercapitalized because they squeeze corporate loans.
- At very large e_g where capital constraint becomes slack (ζ = 0), all variables (lending rates, credit amounts, output, profitability) become constant with respect to e_g and further capital injection is ineffective.

### Political equilibrium for recapitalization (government decision)
- Government budget constraint: e_g = T − q, where T is fixed tax revenue and q denotes other government expenditures (text: e_g = T − q).
- Government maximizes social welfare:
  - W = α y_L + Y + S(q), where S(q) is social welfare from other government expenditures (S' > 0, S'' < 0, S(0) = ∞ when q ≥ 0 in text notation). Parameters α and β represent relative weights:
    - High α: government favors supporting L-sector firms (SOEs and other favored enterprises).
    - High β: government places more value on other government expenditures.
- Optimal recapitalization choices:
  - Corner solution: e_g = 0 if fiscal cost exceeds benefits (characterizes status quo in Vietnam per text).
  - Interior solution: e_g > 0 when first-order condition holds:
    - ∂W/∂e_g ≡ ∂Y/∂e_g + α ∂y_L/∂e_g + S'(T − e_g) · (−1) = 0.
  - Procedural computation: solve for e_g* satisfying the FoC; if no interior e_g with ∂W/∂e_g = 0 exists for e_g ≥ 0, optimal policy is corner solution e_g = 0.

*Source: wpiea2019189-print-pdf - Section 2*

### Section 3

### wpiea2019189-print-pdf - Section 3

### Government first-order condition and bank response
- The first-order condition (FoC) is evaluated for recapitalization parameter ݁ீ; if ݁ீ satisfies the FoC (denoted ݁ீ∗), then the claim holds that the bank will resolve all NPLs (i.e., ݔ∗ = 1) under ݁ீ = ݁ீ∗ in the second stage of the game.
- Intuition: when ݁ = 1ݔ, the marginal benefit of recapitalization, ߲݁ ܷ߲ீ⁄, is always negative because all terms in the FoC are negative due to the V-shape response of output (Figure 1-3). Thus any halfway recapitalization is never optimal for the government because it does not induce credit reallocation from the L sector to the H sector.
- Footnotes in the source note:
  - There must exist ݁ீ such that ߲݁ ܷ߲ீ⁄ ൏0 at large values because ݂ᇱܩ(൫) = ∞ at some ܩ൐0, ruling out a corner solution where the government injects capital until the capital constraint becomes slack (the Lagrange multiplier ߣ reaches zero).
  - The result that halfway recapitalization is not optimal may depend on the static model structure; with dynamic optimization, halfway recapitalization could be justified as an interim stage.

### Welfare comparison and determinants of optimal recapitalization
- Define social welfare under zero recapitalization as ܷ଴ and under optimal recapitalization ݁ீ = ݁ீ∗ as ܷ∗.
- Aggregate outputs in the second stage under the two policies are ܻ଴ and ܻ∗ respectively; L-sector output under zero recapitalization is ݕ௟௢௪଴. Under ݁ீ = ݁ீ∗ (and with NPLs fully resolved and ݔ = 1), ݕ௟∗ = 0.
- Government chooses zero recapitalization (݁ீ = 0) if ܷ଴ ܷੇ∗ = ( (ܻ଴ ܻੇ∗) ݕߙ + ௟଴ ߚ + ሺ݂(ܶ) ሻ ݂ੇ(݁െܶీ∗) ) ൐0, and chooses ݁ீ = ݁ீ∗ if ܷ଴ ܷੇ∗ ൏0.
- Political economy implications — optimal recapitalization depends on key parameters:
  - High ߙ and/or high ߚ reduce government incentive to recapitalize with public funds.
    - High ߙ: government has special interests to help the L sector (SOEs).
    - High ߚ: government values other expenditures (infrastructure, social security) more than bank recapitalization.
  - Large fiscal space (high ܶ) increases tendency to conduct recapitalization using public funds.
    - This follows from ܷ(߲଴ ܷੇ∗)′݂ = ߲ܶ/ሻ(ܶ)′݂ੇ(݁െܶీ∗) due to concavity of ݂(ܩ) (i.e., ݂ᇱᇱ(ܩ) ൏0); hence sufficient fiscal space is key for recapitalization using public funds.

### Conclusion and policy implications
- Empirical and theoretical summary:
  - The paper documents empirical evidence of credit misallocation between SOEs and non-SOEs in Vietnam.
  - Theoretical analysis frames bank recapitalization and its effects on credit misallocation within a political economy trade-off determined by:
    - the government's special-interest concern for the low-productivity sector (SOEs),
    - the relative importance assigned to fiscal expenditures (infrastructure, education, social benefits, etc.) versus bank recapitalization,
    - the tightness of fiscal space.
- First-best vs second-best:
  - First-best: fast NPL resolution and full recapitalization by public funds improves credit allocation and growth relative to the second-best (no public funds, only banks’ retained earnings).
  - The first-best requires government budget not too tight (marginal cost of funds below a threshold), underscoring the importance of fiscal space for financial stability.
- Important caveat:
  - Recapitalization is necessary but not sufficient to resolve credit misallocation. The model assumes that with enough capital buffers, banks will shut down underperforming SOEs immediately.
  - In reality, additional constraints hinder resolution, including political connections of SOEs and weak law enforcement for NPL resolution. Those constraints must be addressed alongside recapitalization to resolve credit misallocation.

*Source: wpiea2019189-print-pdf - Section 3*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019189-print-pdf.pdf_