## _wp05169

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---

### Introduction and paper objective
- Since the early summer of 2003, Japan started to recover from its long recession; non-performing loan problems of the major banks appears to be abating.
- Major banks were helped by large injections of equity from the government and a recovering economy that boosted profits, allowing major banks to increase loan-loss reserves and capital-asset ratios.
- Difficulties persist with regional banks, which have been slow to write-off non-performing loans.
- Paper objective: consider possibility that public policy toward the financial system is the root cause of the Japanese banking and growth crisis.
- Method: present a simple endogenous growth model with a bank-centered financial system, solved for equilibrium in closed-form, incorporating three stylized facts of the Japanese financial system.

### Three characteristics of the Japanese financial system (model assumptions)
- Predominance of commercial bank intermediation of corporate finance (informational advantage of banks).
- Prospect of government-provided deposit insurance or public sector bailouts.
- Supervisory forbearance and absence of effective prudential regulation.
- Stylized factual support (quoted as in source):
  - Small- and medium-sized business loans to total loans increased from 73 percent over 1977-86 to 78 percent over 1987-1990 (Ogawa and Kitasaka [2000]).
  - Between 1987-1990: bank loans to manufacturing sector increased by 1 percent; to service, construction, and real estate sectors rose by 14 percent, 7 percent, and 18 percent, respectively (Ogawa and Kitasaka [2000]).
  - Prior to 1991 official policy: “no failures of financial institutions.” From 1991 to 1995, eleven small banks were formally declared insolvent, but no depositor lost funds due to guarantees.
- Institutional responses:
  - Financial supervision moved from Ministry of Finance to the Financial Supervisory Agency in 1996.
  - Prompt Corrective Action system introduced in 1998, with required interventions (e.g., close a bank if capital-asset ratio falls below zero).
  - Initial enforcement led to closures of five smaller banks; subsequent redefinition and delays weakened enforcement.

### Model structure and key equations
- Production and bank lending
  - Output per firm: y_jt = α_jt k_jt.
  - Aggregate output: y_t = α/2 k_t (uniform distribution of α_t over 0≤α_t≤α and continuum of firms implies no aggregate uncertainty).
  - Expected net return for one-period bank loan (equation (1) in source):  
    1/α ∫_{α̂r}^{α} (1+r′_t) dα_t + 1/α ∫_{0}^{r̂} (1+α_t−γ)k_jt dα_t − (1+r)ς_jt  (as given in source).
  - Equilibrium loan rate relation (equation (2)): r′ (1− 1/2 r′ α − γ/α) = r.
  - Interest that maximizes lender expected return equals α−γ (per unit of firm capital) under assumptions allowing rollovers.
  - Aggregate flow of net output on balanced growth path: (α/2 − γ r′/α) k_t.
  - Resource constraint: ̇k = (α/2 − γ r′/α) k_t − c_t.
  - Aggregate corporate sector flow profits: d_t = (α−r′)^2 / (2α) k_t (paid as dividends).
- Households and portfolios
  - Representative household utility: U_t = ∫_t^∞ c_s^{1−σ}/(1−σ) e^{−ρ(s−t)} ds.
  - Household budget: ̇a = r a_t + d_t + x_t − c_t; solvency constraint lim_{s→∞} e^{−r(s−t)} a_s ≥ 0.
  - Households hold deposits and equities; in equilibrium portfolios are fully diversified given continuum of firms and banks.
- Benchmark equilibrium with continuous loan-loss reserving
  - Bank profits zero; value of bank equity is zero; government accumulates no deposit-insurance liabilities.
  - Under perfect foresight, equilibrium consumption: c_t = (α/2 − γ r′/α − (r−ρ)/σ) k_t (equation (4)).
  - Equilibrium growth rate (consumption, capital, output): ̇c/c = ̇k/k = ̇y/y = (r−ρ)/σ (equation (5)).
  - Aggregate corporate equity value (equation (7)): V_f_t = (α−r′)^2 / (2α) k_t (r− (r−ρ)/σ)^{−1} (as in source).

### Growth with deposit guarantees and regulatory forbearance — mechanism and dynamics
- Regulatory forbearance assumption: government fails to enforce loan-loss reserve requirements; banks keep uncollected interest as performing assets and pay dividends from current loan income.
- Consequences
  - Banks accumulate non-performing assets while paying dividends; these unpaid obligations become deposit insurance claims against the government (public debt b_t).
  - Banking sector assets = corporate capital k_t + government debt b_t; total household interest-bearing assets a_t = k_t + b_t.
  - Bank dividends constrained by flows: x_t = (r′ − r − γ r′/α) k_t (until regulatory intervention halts accumulation).
  - Aggregate unpaid interest flow equal to (1/(2α) r′^2 − r r′/α) k_t (equation (8)).
- Policy timing and equilibrium under perfect foresight
  - Banks allowed to accumulate losses for 0≤t≤T; government intervenes at time T and halts further accumulation. Public liabilities b_T determined in equilibrium given T.
  - Government finances deposit insurance post-T by taxing interest income at constant proportionate rate τ; post-tax deposit rate = r̂ = (1−τ) r.
  - Government flow budget for t≥T: ̇b = r b_t − τ r (k_t + b_t) = r̂ b_t − τ r k_t (equation (13)).
  - Intertemporal budget constraint (equation (14)) links accrued dividends up to T, future tax revenue, and b_T.
- Household dynamics with perfect foresight
  - For 0≤t≤T, household resource: ̇k + ̇b = r(k_t + b_t) + x_t + d_t − c_t (equation (15)).
  - For t≥T: ̇k + ̇b = r̂ (k_t + b_t) + d_t − c_t (equation (16)).
  - Equilibrium consumption growth rates: ̇c/c = (r−ρ)/σ for 0≤t≤T (equation (17)); ̇c/c = (r̂ − ρ)/σ for t≥T (equation (18)).
  - Consumption as share of capital for 0≤t≤T (equation (19)):
    c_t = [ (1 − e^{−θ(T−t)})/(θ−1) + e^{−θ(T−t)} (θ + (r−r̂)/σ)^{−1} ]^{−1} k_t,
    where θ = α/2 − γ r′/α − (r−ρ)/σ.
  - Capital growth rate for 0≤t≤T (equation (21)): ̇k/k = (α/2 − γ r′/α) − [the bracketed expression in (19)]^{−1} ≡ φ(T−t, τ), decreasing in t for t≤T, equals r̂−ρ/σ at t=T, converges to (r−ρ)/σ as T−t → ∞.
- Asset value dynamics
  - Bank equity value under perfect foresight (equation (23)): V_b_t = ∫_t^T (r′ − r − γ r′/α) k_s e^{−r(s−t)} ds = (r′ − r − γ r′/α) k_t ∫_t^T e^{∫_s^t (φ(T−v,τ)−r) dv} ds.
  - Ratio V_b_t / k_t falls monotonically to zero up to time T.
  - Corporate equity V_f_t given by present value of dividends (equation (25)); up to T grows proportionately with k_t if σ = 1, faster than k_t if σ > 1.

### Banking crisis under perfect foresight — thresholds, collapse and collateral dynamics
- Longer regulatory forbearance (larger T) → larger b_T → larger τ required → lower post-tax deposit rate r̂ → lower long-run growth rate ̇y/y = (r̂ − ρ)/σ.
- If r̂−ρ ≤ 0 then growth can fall to zero before government intervenes; with irreversible investment, growth can reach zero at some time ̂T < T leading to net deposit withdrawals.
- Pre-tax maximal deposit rate when loan rate reaches α−γ is r^* = (α−γ)^2 / (2α) (as in source).
  - Corporate profits fall to d^* = α/2 − (α−γ)^2 / (2α) k, unpaid interest rises to (α−γ)^2 / (2α) k.
  - At time ̂T when pre-tax deposit rate equals r^* and post-tax equals household discount rate ρ (r^*(1−τ^*) = ρ), deposit insurance liability reaches b^*.
- Crisis dynamics and collateral market
  - When banks must meet withdrawals by foreclosing loans, market for collateral collapses: seized collateral has zero price because aggregate deposits have decreased by the amount of foreclosed loans and no new financing is available to purchase collateral (irreversible investment).
  - Prediction: collapse in market for collateral at moment of crisis; under continuous loan-loss reserving, collateral price q would remain equal to one.
- Convoy system interpretation
  - Government-forced mergers (convoy) transfer losses among banks; convoy leaders bear costs and may avoid being leaders by paying maximum dividends — reinforcing accumulation of deposit insurance claims.
- Fiscal policy notes
  - Model assumes deposit insurance liabilities not continuously priced and ultimately financed via proportional tax on interest; alternative fiscal responses (time-varying τ, delayed taxation) change dynamics (e.g., temporary sharp fall in growth followed by recovery if b declines relative to output).

### Empirical tests of asset prices and fundamentals
- Motivation: model imposes perfect foresight — asset prices reflect fundamentals and bubbles excluded; test whether data support fundamentals-driven prices.
- Unit root and cointegration tests (selected results exactly as reported)
  - Phillips-Perron unit root tests show log stock price changes are stationary for periods reported.
  - Log dividend-price ratio: for 1980Q2-2002Q2 and 1991Q1-2002Q2 the null of nonstationarity rejected at 10 percent; for 1980Q2-1990Q4 nonstationarity cannot be rejected.
  - Log price-earnings ratio nonstationarity not rejected for each period using Phillips-Perron tests.
  - Short-term interest rates (call rate) appear stationary until end of 1991 but not thereafter.
  - Overall: evidence for bubbles not compelling; fundamentals assumption reasonable though cannot be fully rejected for 1980Q2-1990Q4.
- Predictability of stock returns from fundamentals
  - Long-horizon regressions (horizons: 1 quarter, 4 quarters, 12 quarters) with fundamentals (log price-earnings ratio, log dividend-price ratio, short-term interest rate) show increasing forecast accuracy with horizon.
  - High current log price-earnings ratios predict low stock returns at medium-to-long horizons (negative coefficients).
  - High current log dividend-price ratios imply increasing stock returns.
  - High current short-term interest rates predict high stock returns at long horizons.
  - VAR analysis: dividend-price and price-earnings ratios have explanatory power beyond lagged stock returns; inclusion of first-differences of variables (including lagged credit-GDP first-difference) shows credit first-difference highly significant.
  - Conclusion: fundamentals have good forecasting power, especially at long horizons; bubbles likely small or superfluous for Japanese stock returns.

### Application of the model to Japan in the 1990s — empirical implications and fit
- Model predictions and Japanese data parallels (as stated in source)
  - GDP growth prediction: GDP growth declines leading up to a banking crisis.
    - Data: significant decline in GDP growth rate for Japan over the three years, 1990 through 1992.
    - Consumption growth begins to decline as GDP growth fell in 1990; consumption as share of GDP rises slightly in 1990.
    - Hayashi and Prescott [2002] estimate regulatory changes in the 1980s raised leisure consumption by about 20 percent.
  - Investment dynamics
    - Investment growth does not decline before 1990, but after 1990 the share of investment in GDP declines as predicted.
    - Share of investment in GDP rises in the late 1980s before the collapse — consistent with an agency-extended model.
  - Productivity and returns (reported statistics)
    - Total factor productivity (TFP) growth rates: 1.1 percent per annum (1970-80) to 0.2 percent per annum (1990-98).
    - Manufacturing TFP growth: 4.9 percent to 0.5 percent per annum.
    - Return on equity: fell from 12 percent in 1980 to 4 percent in 1998.
    - Return on invested capital: fell from 6 percent in 1980 to 4 percent in 1998.
    - U.S. 1998 comparisons: returns on equity and invested capital of 22 percent and 14 percent respectively.
  - Bank credit growth
    - Model identity: Total bank credit = firm capital stocks + deposit insurance claims accumulated by banks, k + b.
    - Empirical parallel: distinct reduction in the growth rate for the ratio of bank credit to GDP in 1991 in Japan — consistent with early-1990s beginning of the crisis and deepening in 1997-98.
  - Non-performing loans and land prices
    - NPLs were 2 percent of GDP between 1992 and 1994, rose sharply to about 5 percent of GDP in 1996 and were 7 percent of GDP in 2000.
    - Between 1980 and 1995, about 40 percent of all corporate borrowing was collateralized by real estate.
    - Average land prices in Japan declined by about 60 percent between 1992 and 2000.
    - Model predicts a sudden fall in the total value of collateral in a banking crisis; Japan’s land-price collapse in the 1990s parallels the predicted collapse in collateral value.
  - Stock valuations and banking sector value
    - Model implies stock market value of domestic banks should decline up to time T; ratio of bank equities to total stock market value should decline once private sector realizes banking-sector deterioration.
    - Empirical: ratio of bank stock value to total stock market value started to decline sharply in 1987, at least 3-4 years before the beginning of the crisis.

### VAR estimates and Granger causality results (selected reported statistics)
- VAR variables: BSTS (bank equity ratio: bank stock equity / total stock market equity), CRED (credit to GDP), INVEST (investment to GDP), LANDPRIC (land prices).
- VAR specification and fit
  - Optimal lag length of two chosen by the Akaike Information Criterion.
  - R-squared (Table 4): BSTS = 0.94; CRED = 0.98; INVEST = 0.98; LANDPRIC = 0.99.
- Granger causality (Chi-squared exclusion tests; Table 5)
  - BSTS temporally precedes (Granger causes) CRED and INVEST.
    - In CRED equation: Chi-sq = 5.94; Prob. = 0.05.
    - In INVEST equation: Chi-sq = 12.81; Prob. = 0.0016.
  - BSTS does not temporally precede LANDPRIC (Chi-sq = 3.65; Prob. = 0.16) — BSTS and LANDPRIC appear simultaneously determined.

### Major findings and key implications (concise bullets)
- As the banking system accumulates a deposit insurance claim in the form of non-performing corporate loans against which dividends were paid, the growth rate of output decreases steadily to its post-crisis level and consumption rises as a share of output under perfect foresight.
- The stockmarket value of the corporate sector can grow more rapidly than output before the crisis is realized for the empirically plausible case of inelastic intertemporal substitution (σ>1).
- The stockmarket value of the banking sector will decline before the crisis, implying a decrease in the value of bank stocks relative to the aggregate value of the stock market before the banking crisis.
- Accumulation of non-performing corporate loans that create a deposit insurance claim leads to a steady decline in output growth toward post-crisis levels under perfect foresight.
- Consumption as a share of output increases in the transition toward the post-crisis equilibrium when the deposit insurance claim accumulates.
- Behavioral and valuation differences across sectors: corporate sector valuations may outpace output growth pre-crisis under σ>1, while banking sector valuations fall, producing a relative decline in bank stock values ahead of a banking crisis.

### Policy implications and recommended interventions (as stated in source)
- Enforcement of individual loan-loss reserves or loan write-downs eliminates the ability of bank managers to finance transfers to shareholders or depositors at public expense.
- Prompt intervention (for example, implementation of Prompt Corrective Action) is supported; postponing regulatory intervention allows deposit insurance liabilities to rise and leads to larger declines in GDP growth.
- The economy cannot “grow out” of the problem in equilibrium if deposit insurance liabilities continue to rise against dividends paid to shareholders or depositors.
- Effective external monitoring of banks is difficult under relationship banking; bank regulatory authorities must fulfill the monitoring role to discipline banks.

*Source: _wp05169 - 5. Granger Casualty/Chi-Squared Exogeneity Test — extracted content from the supplied IMF PDF chapter/section*

### References..............................................................................................................

### _wp05169 - References

### Tables listed in this content unit
- 1. Phillips-Perron Unit Root Statistics .................................................................... 27
- 2. Long-Horizon Regressions of Stock Returns on Log Price-Earnings and Log Dividend-Price Ratios, and Short-Term Interest Rates ............................. 27
- 3. Fundamentals and Stock Returns Dependent Variable: Stock Returns .............. 28
- 4. VAR Estimates of the Model .............................................................................. 29

*Source: _wp05169 - References (PDF filename: _wp05169 - References..............................................................................................................).*

### 5. Granger Casualty/Chi-Squared Exogeneity Test ................................................ 30

### 5. Granger Casualty/Chi-Squared Exogeneity Test ................................................ 30

### Introduction
- Since the early summer of 2003, Japan started to recover from its long recession; non-performing loan problems of the major banks appears to be abating.
- Major banks were helped by large injections of equity from the government and a recovering economy that boosted profits, allowing major banks to increase loan-loss reserves and capital-asset ratios.
- Difficulties persist with regional banks, which have been slow to write-off non-performing loans.
- Paper objective: consider possibility that public policy toward the financial system is the root cause of the Japanese banking and growth crisis.
- Method: present a simple endogenous growth model with a bank-centered financial system, solved for equilibrium in closed-form, incorporating three stylized facts of the Japanese financial system.

### Three characteristicsof the financial system of Japan
- Assumptions incorporated into the model:
  - Predominance of commercial bank intermediation of corporate finance (informational advantage of banks).
  - Prospect of government-provided deposit insurance or public sector bailouts.
  - Supervisory forbearance and absence of effective prudential regulation.
- Stylized facts and supporting data excerpts:
  - Bank loans dominate Japanese corporate debt; small- and medium-sized business loans to total loans increased from 73 percent over 1977-86 to 78 percent over 1987-1990 (Ogawa and Kitasaka [2000]).
  - Between 1987-1990: bank loans to manufacturing sector increased by 1 percent; to service, construction, and real estate sectors rose by 14 percent, 7 percent, and 18 percent, respectively (Ogawa and Kitasaka [2000]).
  - Prior to 1991 official policy: “no failures of financial institutions.” From 1991 to 1995, eleven small banks were formally declared insolvent, but no depositor lost funds due to guarantees.
- Institutional responses noted:
  - Financial supervision moved from Ministry of Finance to the Financial Supervisory Agency in 1996.
  - Prompt Corrective Action system introduced in 1998, with required interventions (e.g., close a bank if capital-asset ratio falls below zero).
  - Initial enforcement led to closures of five smaller banks; subsequent redefinition and delays weakened enforcement.

### A model of growth and banking crises — structure and key equations
- Production and bank lending:
  - Output per firm: y_jt = α_jt k_jt.
  - Aggregate output: y_t = α/2 k_t (uniform distribution of α_t over 0≤α_t≤α and continuum of firms implies no aggregate uncertainty).
  - Expected net return for one-period bank loan (equation (1) in source):  
    1/α ∫_{α̂r}^{α} (1+r′_t) dα_t + 1/α ∫_{0}^{r̂} (1+α_t−γ)k_jt dα_t − (1+r)ς_jt  (as given in source).
  - Equilibrium loan rate relation (equation (2)): r′ (1− 1/2 r′ α − γ/α) = r.
  - Interest that maximizes lender expected return equals α−γ (per unit of firm capital) under assumptions allowing rollovers.
  - Aggregate flow of net output on balanced growth path: (α/2 − γ r′/α) k_t.
  - Resource constraint: ̇k = (α/2 − γ r′/α) k_t − c_t.
  - Aggregate corporate sector flow profits: d_t = (α−r′)^2 / (2α) k_t (paid as dividends).
- Households and portfolios:
  - Representative household utility: U_t = ∫_t^∞ c_s^{1−σ}/(1−σ) e^{−ρ(s−t)} ds.
  - Household budget: ̇a = r a_t + d_t + x_t − c_t; solvency constraint lim_{s→∞} e^{−r(s−t)} a_s ≥ 0.
  - Households hold deposits and equities; in equilibrium portfolios are fully diversified given continuum of firms and banks.
- Benchmark equilibrium with continuous loan-loss reserving:
  - Bank profits zero; value of bank equity is zero; government accumulates no deposit-insurance liabilities.
  - Under perfect foresight, equilibrium consumption: c_t = (α/2 − γ r′/α − (r−ρ)/σ) k_t (equation (4)).
  - Equilibrium growth rate (consumption, capital, output): ̇c/c = ̇k/k = ̇y/y = (r−ρ)/σ (equation (5)).
  - Aggregate corporate equity value (equation (7)): V_f_t = (α−r′)^2 / (2α) k_t (r− (r−ρ)/σ)^{−1} (as in source).

### Growth with deposit guarantees and regulatory forbearance — mechanism and dynamics
- Regulatory forbearance assumption: government fails to enforce loan-loss reserve requirements; banks keep uncollected interest as performing assets and pay dividends from current loan income.
- Consequences:
  - Banks accumulate non-performing assets while paying dividends; these unpaid obligations become deposit insurance claims against the government (public debt b_t).
  - Banking sector assets = corporate capital k_t + government debt b_t; total household interest-bearing assets a_t = k_t + b_t.
  - Bank dividends constrained by flows: x_t = (r′ − r − γ r′/α) k_t (until regulatory intervention halts accumulation).
- Institutional constraints introduced:
  - If a bank cannot meet net withdrawal demand at any time, it is illiquid and government intervenes.
  - Banks cannot accumulate non-performing assets faster than flow of unpaid interest obligations; aggregate unpaid interest flow equal to (1/(2α) r′^2 − r r′/α) k_t (equation (8)).
- Policy timing and equilibrium under perfect foresight:
  - Banks allowed to accumulate losses for 0≤t≤T; government intervenes at time T and halts further accumulation. Public liabilities b_T determined in equilibrium given T.
  - Government finances deposit insurance post-T by taxing interest income at constant proportionate rate τ; post-tax deposit rate = r̂ = (1−τ) r.
  - Government flow budget for t≥T: ̇b = r b_t − τ r (k_t + b_t) = r̂ b_t − τ r k_t (equation (13)).
  - Intertemporal budget constraint (equation (14)) links accrued dividends up to T, future tax revenue, and b_T.
- Household dynamics with perfect foresight:
  - For 0≤t≤T, household resource: ̇k + ̇b = r(k_t + b_t) + x_t + d_t − c_t (equation (15)).
  - For t≥T: ̇k + ̇b = r̂ (k_t + b_t) + d_t − c_t (equation (16)).
  - Equilibrium consumption growth rates: ̇c/c = (r−ρ)/σ for 0≤t≤T (equation (17)); ̇c/c = (r̂ − ρ)/σ for t≥T (equation (18)).
  - Consumption as share of capital for 0≤t≤T (equation (19)):
    c_t = [ (1 − e^{−θ(T−t)})/(θ−1) + e^{−θ(T−t)} (θ + (r−r̂)/σ)^{−1} ]^{−1} k_t,
    where θ = α/2 − γ r′/α − (r−ρ)/σ.
  - Capital growth rate for 0≤t≤T (equation (21)): ̇k/k = (α/2 − γ r′/α) − [the bracketed expression in (19)]^{−1} ≡ φ(T−t, τ), decreasing in t for t≤T, equals r̂−ρ/σ at t=T, converges to (r−ρ)/σ as T−t → ∞.
- Asset value dynamics:
  - Bank equity value under perfect foresight (equation (23)): V_b_t = ∫_t^T (r′ − r − γ r′/α) k_s e^{−r(s−t)} ds = (r′ − r − γ r′/α) k_t ∫_t^T e^{∫_s^t (φ(T−v,τ)−r) dv} ds.
  - Ratio V_b_t / k_t falls monotonically to zero up to time T.
  - Corporate equity V_f_t given by present value of dividends (equation (25)); up to T grows proportionately with k_t if σ = 1, faster than k_t if σ > 1.

### Banking crisis under perfect foresight — thresholds and collapse
- Mechanism:
  - Banks’ accumulation of deposit insurance claims b_t against government mirrors increase in public liabilities; government eventually must tax interest to service b_T.
  - Longer regulatory forbearance (larger T) → larger b_T → larger τ required → lower post-tax deposit rate r̂ → lower long-run growth rate ̇y/y = (r̂ − ρ)/σ.
- Critical conditions:
  - If r̂−ρ ≤ 0 then growth can fall to zero before government intervenes; with irreversible investment, growth can reach zero at some time ̂T < T leading to net deposit withdrawals.
  - Pre-tax maximal deposit rate when loan rate reaches α−γ is r^* = (α−γ)^2 / (2α) (as in source).
  - Corporate profits fall to d^* = α/2 − (α−γ)^2 / (2α) k, unpaid interest rises to (α−γ)^2 / (2α) k.
  - At time ̂T when pre-tax deposit rate equals r^* and post-tax equals household discount rate ρ (r^*(1−τ^*) = ρ), deposit insurance liability reaches b^*.
- Crisis dynamics and collateral market:
  - When banks must meet withdrawals by foreclosing loans, market for collateral collapses: seized collateral has zero price because aggregate deposits have decreased by the amount of foreclosed loans and no new financing is available to purchase collateral (irreversible investment).
  - Prediction: collapse in market for collateral at moment of crisis; under continuous loan-loss reserving, collateral price q would remain equal to one.
- Convoy system interpretation:
  - Government-forced mergers (convoy) transfer losses among banks; convoy leaders bear costs and may avoid being leaders by paying maximum dividends — reinforcing accumulation of deposit insurance claims.
- Fiscal policy notes:
  - Model assumes deposit insurance liabilities not continuously priced and ultimately financed via proportional tax on interest; alternative fiscal responses (time-varying τ, delayed taxation) change dynamics (e.g., temporary sharp fall in growth followed by recovery if b declines relative to output).

### Empirical tests of asset prices and fundamentals
- Motivation: model imposes perfect foresight — asset prices reflect fundamentals and bubbles excluded; test whether data support fundamentals-driven prices.
- Unit root and cointegration tests (summary from source):
  - Phillips-Perron unit root tests show log stock price changes are stationary for periods reported.
  - Log dividend-price ratio: for 1980Q2-2002Q2 and 1991Q1-2002Q2 the null of nonstationarity rejected at 10 percent; for 1980Q2-1990Q4 nonstationarity cannot be rejected.
  - Log price-earnings ratio nonstationarity not rejected for each period using Phillips-Perron tests.
  - Short-term interest rates (call rate) appear stationary until end of 1991 but not thereafter.
  - Overall: evidence for bubbles not compelling; fundamentals assumption reasonable though cannot be fully rejected for 1980Q2-1990Q4.
- Predictability of stock returns from fundamentals:
  - Long-horizon regressions (horizons: 1 quarter, 4 quarters, 12 quarters) with fundamentals (log price-earnings ratio, log dividend-price ratio, short-term interest rate) show increasing forecast accuracy with horizon.
  - High current log price-earnings ratios predict low stock returns at medium-to-long horizons (negative coefficients).
  - High current log dividend-price ratios imply increasing stock returns.
  - High current short-term interest rates predict high stock returns at long horizons.
  - VAR analysis: dividend-price and price-earnings ratios have explanatory power beyond lagged stock returns; inclusion of first-differences of variables (including lagged credit-GDP first-difference) shows credit first-difference highly significant.
  - Conclusion: fundamentals have good forecasting power, especially at long horizons; bubbles likely small or superfluous for Japanese stock returns.

### Application of the model to Japan in the 1990s — empirical implications and fit
- Model implications that can be compared to Japanese data (as stated in source immediately before cutoff):
  - Dynamics for investment, consumption, output, bank credit growth, asset prices, and value of collateral before and after crisis.
  - Prediction: ratio of value of bank equities to overall stock market declines before crisis and precedes movements in macro aggregates (e.g., investment-output ratio).
  - Prediction: relative value of bank stocks falls ahead of a banking crisis while corporate equity value may be rising; collapse in market for collateral at crisis.
- Empirical approach noted in source:
  - Test maintained hypothesis of perfect foresight and that asset prices reflect fundamentals.
  - Use structural vector autoregressions and causality tests to compare model predictions to Japanese experience.
  - Summary of finding reported earlier: causality tests are consistent with theory — the ratio of bank equity value to overall stock market precedes movements in other macro aggregates.

*Source: _wp05169 - 5. Granger Casualty/Chi-Squared Exogeneity Test — extracted content from the supplied IMF PDF chapter/section*

### 1. As the banking system accumulates a deposit insurance claim in the form of non-performing

### _wp05169 - 1. As the banking system accumulates a deposit insurance claim in the form of non-performing

### Major findings

- As the banking system accumulates a deposit insurance claim in the form of non-performing corporate loans against which dividends were paid, the growth rate of output decreases steadily to its post-crisis level and consumption rises as a share of output under perfect foresight.

- The stockmarket value of the corporate sector can grow more rapidly than output before the crisis is realized for the empirical plausible case of inelastic intertemporal substitution (σ>1).

- The stockmarket value of the banking sector will decline before the crisis, implying that we should observe a decrease in the value of bank stocks relative to the aggregate value of the stock market before the banking crisis.

### Key implications

- Accumulation of non-performing corporate loans that create a deposit insurance claim leads to a steady decline in output growth toward post-crisis levels under perfect foresight.

- Consumption as a share of output increases in the transition toward the post-crisis equilibrium when the deposit insurance claim accumulates.

- Behavioral and valuation differences across sectors: corporate sector valuations may outpace output growth pre-crisis under σ>1, while banking sector valuations fall, producing a relative decline in bank stock values ahead of a banking crisis.

*Source: _wp05169 - 1. As the banking system accumulates a deposit insurance claim in the form of non-performing; PDF: _wp05169 - 1. As the banking system accumulates a deposit insurance claim in the form of non-performing; canonical URL: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05169.pdf*

### 4. The value of collateral in the model equalsq

### 4. The value of collateral in the model equalsq_t k_t

### Model assumptions and interpretation
- Collateral value q_t k_t grows proportionately with output until output growth falls to zero in a banking crisis and the market for collateral collapses.
- Two simplifying assumptions highlighted for comparison with Japan:
  - Full information under perfect foresight:
    - Under perfect foresight, corporate stock values grow in proportion to gross domestic product after the crisis for a constant tax rate.
    - If the tax rate varies over time (for example, to eliminate the deposit insurance liability, b, in finite time), the growth rate of the value of the stock market will be different than the growth rate of output during the transition because equity is forward-looking.
    - Therefore, the model does not predict that the value of the stock market grows with output after time T regardless of policy choices or private sector expectations.
  - Investment irreversibility (used for analytical simplicity):
    - If smooth adjustment costs to disinvestment were introduced, a banking crisis would result in corporate bankruptcies and a falling price of capital, q_t.
    - Under more general adjustment costs the value of collateral should fall below the growth rate of output in a crisis.

### A. Output growth, consumption and investment
- Model prediction: GDP growth declines leading up to a banking crisis.
- Empirical parallels for Japan:
  - Data show a significant decline in the GDP growth rate for Japan over the three years, 1990 through 1992.
  - Consumption growth does not fall before the 1990s, but begins to decline as the GDP growth rate fell in 1990.
    - Model-consistent: consumption as a share of GDP rises slightly in 1990 (consumption growth falls by less than output growth).
    - Government increased transfer payments to households in the 1990s, which could contribute to a smaller contraction in household consumption as a share of GDP.
    - Hayashi and Prescott [2002] estimate regulatory changes in the 1980s raised leisure consumption by about 20 percent.
  - Investment growth does not decline before 1990 (contrary to savers anticipating the crisis), but after 1990 the share of investment in GDP declines as predicted by the model.
    - Share of investment in GDP rises in the late 1980s before the collapse — consistent with an agency-extended model that can generate a rise in investment share in advance of a crisis.
- Productivity and returns:
  - Total factor productivity (TFP) growth rates: 1.1 percent per annum (1970-80) to 0.2 percent per annum (1990-98).
  - Manufacturing TFP growth: 4.9 percent to 0.5 percent per annum.
  - Return on equity: fell from 12 percent in 1980 to 4 percent in 1998.
  - Return on invested capital: fell from 6 percent in 1980 to 4 percent in 1998.
  - U.S. 1998 comparisons: returns on equity and invested capital of 22 percent and 14 percent respectively.

### B. Bank credit growth
- Model identity: Total bank credit = firm capital stocks + deposit insurance claims accumulated by banks, k + b; equals total bank deposits held by households.
- Model prediction: Bank credit as a share of GDP grows up to the crisis, then stops rising at the crisis and should decline if deposit insurance liabilities are expected to be cleared in finite time.
- Empirical parallel: Distinct reduction in the growth rate for the ratio of bank credit to GDP in 1991 in Japan — consistent with an early-1990s beginning of the crisis and deepening in 1997-98.

### C. Non-performing bank loans and land prices
- Asset-price implications:
  - Model implies stock market value of domestic banks should decline up to time T.
  - Ratio of bank equities to total stock market value should decline once private sector realizes banking-sector deterioration.
  - Empirical: Ratio of bank stock value to total stock market value started to decline sharply in 1987, at least 3-4 years before the beginning of the crisis.
- Non-performing loans (NPLs):
  - NPLs were 2 percent of GDP between 1992 and 1994, rose sharply to about 5 percent of GDP in 1996 and were 7 percent of GDP in 2000.
- Land as collateral:
  - Between 1980 and 1995, about 40 percent of all corporate borrowing was collateralized by real estate.
  - Average land prices in Japan declined by about 60 percent between 1992 and 2000.
  - The model predicts a sudden fall in the total value of collateral in a banking crisis; Japan’s land-price collapse in the 1990s parallels the predicted collapse in collateral value.
  - Note: the model treats capital stock as the collateral analogue; land is not explicitly modeled but is empirically central in Japan.

### D. Vector Autoregression (VAR) estimates and Granger causality
- VAR variables: BSTS (bank equity ratio: bank stock equity / total stock market equity), CRED (credit to GDP), INVEST (investment to GDP), LANDPRIC (land prices).
- VAR specification and lag:
  - Optimal lag length of two chosen by the Akaike Information Criterion.
  - In the BSTS equation, besides its own lagged values, none of the other variables are significant.
  - In the CRED equation, besides its own lagged values, only LANDPRIC lagged once is significant.
  - In the INVEST equation, besides its own lagged values, LANDPRIC lagged once and twice are significant.
  - In the LANDPRIC equation, none of the other variables are significant.
- Granger causality (Chi-squared exclusion tests; Table 5):
  - BSTS temporally precedes (Granger causes) CRED and INVEST.
    - Example statistics from Table 5 for exclusion of BSTS:
      - In CRED equation: Chi-sq = 5.94; Prob. = 0.05.
      - In INVEST equation: Chi-sq = 12.81; Prob. = 0.0016.
  - BSTS does not temporally precede LANDPRIC (Chi-sq = 3.65; Prob. = 0.16) — BSTS and LANDPRIC appear simultaneously determined, consistent with both equity and land prices responding to correlated future fundamentals.
- VAR fit statistics (Table 4):
  - R-squared: BSTS = 0.94; CRED = 0.98; INVEST = 0.98; LANDPRIC = 0.99.
  - Adjusted R-squared reported for each equation in Table 4.

### Policy implications and conclusions
- Core mechanism: regulatory forbearance plus high corporate reliance on bank borrowing and implicit/explicit deposit insurance can lower long-run growth and yield an endogenous banking crisis.
- Accumulated unrealized deposit insurance liability of the government to the banking sector acts as public debt used to finance transfers to bank shareholders or depositors; banks accumulate this public debt as non-performing loans on their balance sheets.
- Two major policy implications from the model:
  - Enforcement of individual loan-loss reserves or loan write-downs eliminates the ability of bank managers to finance transfers to shareholders or depositors at public expense.
  - Prompt intervention (for example, implementation of Prompt Corrective Action) is supported; postponing regulatory intervention allows deposit insurance liabilities to rise and leads to larger declines in GDP growth.
- Additional points:
  - The economy cannot “grow out” of the problem in equilibrium if deposit insurance liabilities continue to rise against dividends paid to shareholders or depositors.
  - Effective external monitoring of banks is difficult under relationship banking; bank regulatory authorities must fulfill the monitoring role to discipline banks.

*Italic: IMF Working Paper excerpt — section 4 and accompanying empirical analysis and conclusions.*

### References

### _wp05169 - References

### Books and Monographs
- Campbell, John, Andrew Lo and A. Craig MacKinlay [1997], The Econometrics of Financial Markets (Princeton: Princeton University Press).
- Cargill, Thomas, Hutchison, Michael, and Takatoshi Ito [1997], The Political Economy of Japanese Monetary Policy (Cambridge, MA: MIT Press).
- Dekle, Robert and Kenneth Kletzer [2003], “The Japanese Banking Crisis and Economic Growth: Theoretical and Empirical Implications of Deposit Guarantees and Weak Financial Regulation,” Journal of the Japanese and International Economies, 17, pp. 305-335.
- Diamond, Douglas [1984], “Financial Intermediation and Delegated Monitoring,” Review of Economic Studies, 51, pp. 393-414.
- Diamond, Douglas and Phillip Dybvig [1983], “Bank Runs, Deposit Insurance and Liquidity,” Journal of Political Economy, 91, June, pp. 401-419.
- Freixas, Xavier and Jean-Charles Rochet [1997], Microeconomics of Banking (Cambridge, MA: MIT Press).
- Grimes, William [2001], Unmaking the Japanese Miracle (Ithaca: Cornell University Press).
- Hamilton, James [1994], Time Series Analysis (New Jersey: Princeton University Press).
- Hoshi, Takeo and Anil Kayshap [2001], Corporate Financing and Governance in Japan (Cambridge: MIT Press).

### Chapters, Edited Volumes, and Conference Proceedings
- Cargill, Thomas [2000], “What Caused Japan's Banking Crisis?,” in Takeo Hoshi and Hugh Patrick, eds., Crisis and Change in the Japanese Financial System (Norwell, MA: Kluwer Academic Publishers).
- Chinn, Menzie and Kenneth Kletzer [2000], “International Capital Inflows, Domestic Financial Intermediation and Financial Crises under Imperfect Information,” in Reuven Glick, Ramon Moreno and Mark Spiegel, eds., Emerging Market Crises (New York: Cambridge University Press, pp. 196-237).
- Dekle, Robert and Kenneth Kletzer [2002a], “Domestic Bank Regulation and Financial Crises: Theory and Empirical Evidence from East Asia,” in Jeffrey Frankel and Sebastian Edwards, eds., Preventing Currency Crises in Emerging Markets (Chicago: The University of Chicago Press).
- Dekle, Robert and Kenneth Kletzer [2002b], “Financial Intermediation, Agency and Collateral and the Dynamics of Banking Crises: Theory and Evidence for the Japanese Banking Crisis,” Federal Reserve Bank of San Francisco, Conference on “Financial Issues in the Pacific Basin Region,” September 26-27.
- Hoshi, Takeo and Anil Kashyap [1999], “The Japanese Banking Crisis: Where Did It Come from and How Will it End,” in Ben Bernanke and Jerome Rotemberg, eds., NBER Macroeconomics Annual, 1999 (Cambridge: MIT Press).
- Hoshi, Takeo and Hugh Patrick [2000], “The Japanese Financial System: An Introductory Overview,” in Takeo Hoshi and Hugh Patrick, eds., Crisis and Change in the Japanese Financial System (Norwell, MA: Kluwer Academic Publishers).
- Ito, Takatoshi [2000], “The Stagnant Japanese Economy in the 1990s: The Need for Financial Supervision to Restore Sustained Growth,” in Takeo Hoshi and Hugh Patrick, eds., Crisis and Change in the Japanese Financial System (Norwell, MA: Kluwer Academic Publishers).
- Ogawa, Kazuo and Shinichi Kitasaka [2000], “Bank Lending in Japan: Its Determinants and Macroeconomic Implications,” in Takeo Hoshi and Hugh Patrick, eds., Crisis and Change in the Japanese Financial System (Norwell, MA: Kluwer Academic Publishers).
- Ueda, Kazuo [2000], “Causes of Japan's Banking Problems in the 1990s,” in Takeo Hoshi and Hugh Patrick, eds., Crisis and Change in the Japanese Financial System (Norwell, MA: Kluwer Academic Publishers).

### Journal Articles, Working Papers, Manuscripts, and Miscellaneous
- Barseghyan, Levon [2002], “Non Performing Loans, Prospective Bailouts, and Japan's Slowdown,” manuscript, Northwestern University.
- Bayoumi, T. [2001], “The Morning After: Explaining the Slowdown in Japanese Growth in the 1990s,” Journal of International Economics, 53, April, pp. 241-59.
- Dekle, Robert and Kenneth Kletzer [2003], “The Japanese Banking Crisis and Economic Growth: Theoretical and Empirical Implications of Deposit Guarantees and Weak Financial Regulation,” Journal of the Japanese and International Economies, 17, pp. 305-335.
- Fukao, Kyoji, Inui, Tomohiko, Kawai, Hiroki, and Tsutomu Miyagawa [2002], “Sectoral Productivity and Economic Growth in Japan: 1970-98,” manuscript, Hitostubashi University.
- Horiuchi, Akiyoshi [2003], “A Bank Crisis in a Bank Centered Financial System-The Japanese Experience Since the 1990s,” mimeographed, Chuo University.
- Hutchison, Michael [1998], “Are all Banking Crisis Alike?” University of California, Santa Cruz, Working Paper.
- Kwon, E. [1998], “Monetary Policy, Land Prices, and the Collateral Effects on Economic Fluctuations: Evidence from Japan,” Journal of Japanese and International Economies, 12, pp. 175-203.
- Hayashi, Fumio and Edward Prescott [2002], “The 1990s in Japan: A Lost Decade,” manuscript, University of Minnesota.
- Townsend, Robert M. [1979], “Optimal Contracts and Competitive Markets with Costly State Verification,” Journal of Economic Theory, 21, no.2 (October), pp. 265-93.
- Bayoumi, T. [2001], “The Morning After: Explaining the Slowdown in Japanese Growth in the 1990s,” Journal of International Economics, 53, April, pp. 241-59.
- Hoshi, Takeo and Anil Kashyap [1999], “The Japanese Banking Crisis: Where Did It Come from and How Will it End,” in Ben Bernanke and Jerome Rotemberg, eds., NBER Macroeconomics Annual, 1999 (Cambridge: MIT Press).

*Source: _wp05169 - References.*

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