2016年-PIIE彼得森国际经济研究所_Benefits_and_Costs_of_Higher_Capital_Requirements_for_Banks_31页_344kb

Summary of "Benefits and Costs of Higher Capital Requirements for Banks" by William R. Cline

Core Content

This paper examines the benefits and costs of increasing bank capital requirements, aiming to determine the socially optimal level of capital. It integrates empirical evidence on the economic impact of banking crises with the Modigliani-Miller effect to assess the trade-offs between financial stability and economic growth.

Main Views

• Benefits of Higher Capital Requirements:

  • Increasing bank capital reduces the probability of banking crises.
  • The benefits are measured as the expected damage avoided by lowering the risk of crises.
  • The benefits curve is highly nonlinear, with diminishing returns as capital increases.
  • The optimal level of capital is where the slope of the benefits curve equals the slope of the cost curve.

• Costs of Higher Capital Requirements:

  • Higher capital requirements increase the cost of capital for the economy.
  • This leads to higher lending rates, reduced investment, and lower output.
  • The cost curve is an upward-sloping straight line, influenced by factors such as the Modigliani-Miller offset, spillovers to nonbank finance, capital share in output, and the elasticity of substitution between capital and labor.

• Socially Optimal Capital Ratio:

  • The central estimate for the optimal capital ratio is about 7% of total assets.
  • A more cautious estimate (75th percentile) is 8% of total assets.
  • These levels correspond to 12% and 14% of risk-weighted assets, respectively.
  • These ratios are one-fourth to one-half higher than the Basel III requirements for large global systemically important banks (G-SIBs).

Key Information

Banking Crisis Losses

• The paper uses historical data to estimate the economic losses from banking crises.

• Trend Output and Cumulative Initial-Years Loss:

  • Losses are calculated as the difference between expected and actual GDP over the first five years of a crisis.
  • Expected GDP is adjusted for the output gap in the year before the crisis.
  • The formula used is:
    $$
    L_{cum5} = \sum_{t=T}^{t=T+4} \hat{Q}_t - Q_t
    $$
    where $ \hat{Q}_t $ is expected GDP and $ Q_t $ is actual GDP.

• Long-Term Losses:

  • Output does not fully return to trend after five years, so the long-term loss is also considered.
  • The formula for long-term losses is:
    $$
    L_{LT} = L_5 \sum_{t=6}^{t=M+5} \left(1 - \frac{1}{M}(t - 5)\right) / (1 + \rho)^{t - 5}
    $$
    where $ M $ is the productive capacity lifetime and $ \rho $ is the discount rate.
  • The median total loss from a banking crisis is estimated at 64% of base-year GDP.

Control Group Analysis

• The paper also analyzes advanced economies that did not experience banking crises during the Great Recession.
• These economies show relatively high "losses" as well, due to external factors.
• The median total loss for the control group is 54% of GDP, compared to 64% for crisis countries.
• The difference between the two groups is used to estimate the marginal contribution of banking crises to overall economic losses.

Basel Committee Estimates

• The Basel Committee (BCBS) estimated the long-term economic impact (LEI) of banking crises at:
  • 19% of GDP (no permanent effects)
  • 158% of GDP (permanent effects with infinite horizon)
  • 63% of GDP (median cumulative effect)
• The paper's central estimate of 64% of GDP aligns closely with the BCBS median estimate.
• The annual expected loss from banking crises under BCBS estimates is 8.2% of GDP at the high end, but the paper argues that this may be exaggerated.
• Using the paper's estimates, the annual expected loss is 1.7% of GDP, which is considered more plausible.

Capital Requirements Benefits Curve

• The probability of a banking crisis is modeled as a function of the capital ratio:
  $$
  P_{crk} = A k^{\gamma}
  $$
  where $ \gamma < 0 $, indicating that higher capital reduces the probability of crisis.

• The benefits of increasing capital are calculated as the reduction in expected annualized crisis losses:
  $$
  B = - (P_{crk} - P_{cr0}) \lambda_0
  $$
  where $ \lambda_0 $ is the fraction of GDP lost in a crisis.

• The benefits curve is concave, meaning that the marginal benefit of increasing capital diminishes as capital increases.

• The curve levels off after a capital ratio of about 7%, reaching a plateau of 1.67% of output.

Calibration of the Benefits Curve

• The probability function is calibrated using data from the BCBS 2010a survey.
• The base capital ratio is 3.9% of total assets (or 7% of risk-weighted assets).
• The probability of a crisis at the base level is 4.6% (all models) or 3.3% (models considering liquidity).
• The paper adjusts the constant $ A $ to 2.6%, based on historical crisis frequency from 1977 to 2015.
• The benefits curve is then plotted against alternative capital ratios, showing the trade-off between financial stability and economic cost.

Conclusion

• The socially optimal level of capital is estimated to be 7% of total assets (or 12% of risk-weighted assets).
• The analysis highlights the nonlinear benefits of higher capital and the linear costs, leading to a concave benefits curve.
• The paper emphasizes that while increasing capital reduces the risk of banking crises, it also raises the cost of capital and reduces economic output.
• The wide range of potential damage estimates (from 10% to 450% of GDP) is acknowledged, but the central estimate remains 64% of GDP, with the optimal capital ratio being narrower than expected due to the sharp curvature of the benefits function.