## _wp12202 — 1. Monetary Policy ## Source details **Canonical URL:** [_wp12202 — 1. Monetary Policy](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12202.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12202.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12202.pdf.json) --- ### Overview and research objective - Embeds a calibrated U.S. monetary-DSGE model with an explicit banking sector to evaluate the Chicago Plan (100% reserve backing of deposits and separation of monetary and credit functions). - Tests Fisher’s four claims: (1) better control of credit cycles, (2) elimination of bank runs, (3) large reduction of (net) government debt, (4) dramatic reduction of private debt. - Main quantified preview findings: - Longer-term output gains approaching 10 percent. - Steady state inflation can drop to zero without liquidity-trap problems. - Replacement of private debt by debt-free government-issued money and large seigniorage windfalls. ### Model architecture and key mechanisms - Agents and sectors: two household types (unconstrained, constrained), manufacturers, capital investment funds, banks, government; nominal and real rigidities included. - Banks endogenously create deposit money when lending; deposits and loan stocks dominate transactions (aggregate financial-system transactions liabilities ≈ 200% of GDP). - Banking frictions and prudential regulation: - Minimum capital adequacy ratio parameter: γ_t with calibrated minimum γ = 8% of risk-weighted assets. - Banks’ average actual capital adequacy ratio in baseline steady state: 10.5%. - Penalty cost parameter implied: χ ≈ 0.7% of asset value (applies only to small fraction of violating banks); as fraction of total banking system assets penalty equals 0.02% per period in steady state. - Loan types and steady-state shares (flows and stocks used in calibration): - Working capital loans ℓ̄m t set equal to 20% of GDP. - Investment loans ℓ̄k t set to 60% of GDP (including 20% housing component of investment loans). - Mortgages ℓ̄a t around 60% of GDP. - Consumer loans ℓ̄c t = 20% of GDP. - Domestic intermediation of government bonds ≈ 20% of GDP. ### Fisher’s four claims and modeling strategy - Monetary policy under current system: interest-rate rule (forecast-based) where policy rate simultaneously affects money and credit but control over money is weak because banks largely determine deposit money. - Under Chicago Plan: - Deposits must equal government-issued reserves: \tilde d_t = \tilde m_t (equation (23)). - Banks cannot create deposits to fund lending; lending must be financed by equity and non-monetary liabilities (assumed provided by treasury credit \tilde f_t). - Government uses a money-growth rule for nominal money control and sets treasury credit rate for bank funding. - Modeling approach preserves: - Banks’ balance-sheet dynamics, loan-loss risks, Basel-style capital regulation, borrower default thresholds and monitoring costs, and extended-family equity payout mechanism. ### Transition mechanics and illustrative balance-sheet changes (percent of GDP) - Pre-implementation consolidated financial system (Figure 1 left column): - Total balance sheet: 200% of GDP. - Equity: 16% of GDP. - Deposits: 184% of GDP. - Assets composition: government bonds 20% of GDP, investment loans 80% of GDP, other loans (mortgage, consumer, working capital) 100% of GDP. - Transition stage 1 (banks borrow from treasury to procure reserves): - Treasury credit and reserves increase by 184% of GDP. - Transition stage 2 (cancellation and buy-back operations): - Cancellation of principal: bank loans to government 20% of GDP and bank loans to private sector except investment loans 100% of GDP cancelled against treasury credit. - Government transfers treasury credit balances to restricted private accounts to repay outstanding bank loans. - Banks pay out part of equity; government injects additional treasury credit of 7% of GDP to make up net worth difference. - Post-transition banking sector (summary after adjustments): - Money nearly unchanged in quantity but fully backed by reserves. - Credit consists only of investment loans financed by reduced equity 9% of GDP and remaining treasury credit 71% of GDP (after buy-backs and injection) — illustrative figures from transition narrative. - Government balance-sheet changes (Figure 2 summary): - Pre-Chicago Plan government debt: 80% of GDP. - Issuance of treasury credit: 184% of GDP (government asset). - Cancellation of private debts reduces both treasury credit and government equity by 100% of GDP. - Cancellation of bank-held government debt reduces both government debt and treasury credit by 20% of GDP. - Net outcomes emphasized: - Government attains a much lower, in fact negative, net debt burden in unadjusted terms and large net equity position via money issuance. - Private sector left with much lower debt burden while deposits remain essentially unchanged. - Bank runs impossible under the Chicago Plan since monetary liabilities are debt-free government money. ### Post-transition policy toolkit and rules (verbatim forms and calibration) - Monetary rule (Friedman-style money-growth rule, equation (30)): - \tilde d_t = π_m \tilde d_{t−1}^x π_t - In calibration πm set equal to real growth rate x to target zero inflation. - Deposit/reserve interest and dynamics: - Long-run deposit rate set to \bar i_d = 1 (government eventually pays zero nominal interest on money). - Short-run autoregressive path for deposit rate (equation (31)): i_{d,t} = (1 − ρ_d) \bar i_d + ρ_d i_{d,t−1}, with ρ_d = 0.25 in calibration. - Treasury credit (bank funding) rate policy: - Steady-state target \bar i_f chosen so wholesale bank lending rate \bar i_ℓ equals government bond rate \bar i. - Feedback rule (equation (32)): i_{f,t} = (\bar i_f)^{1−m_i} (i_{f,t−1})^{m_i} (π_{4,t+3}/(\bar π)_4)^{(1−m_i) m_{π}} with mi = 0.7 and m_π = 2.0 in calibration. - Immediate post-transition gradual path (equation (33)) uses ρ_f = 0.9 for slow reduction from pre-transition deposit rate to \bar i_f. - Treasury credit rate can be set negative in severe downturns (no zero lower bound constraint on treasury credit). - Prudential (countercyclical) rule (verbatim from source, equation (34)): - γ_t = γ (ˇI_t  I)_pℓ, - where p_ℓ > 0; raising γ_t in booms forces higher equity per unit of loans to limit lending expansions. ### Calibration highlights (steady state and key parameter values — preserved exactly) - Real economy: - Trend real growth rate x = 2% per annum. - Average inflation rate π = 3% per annum. - Historical average real interest rate on U.S. government debt = 3% per annum. - Population share of unconstrained households ω = 0.1. - Parameter ι set to obtain unconstrained:constrained per capita consumption ratio of 4:1. - r = 0.25 (share of monitoring and transactions costs that are real resource costs). - Labor income share calibrated at 61%. - Private investment to GDP ratio = 19% of GDP. - Depreciation rate close to 10% per annum. - Investment adjustment cost parameter φ_I = 2.5. - Price and wage markups A_p = A_w = 1.1. - Price and wage stickiness parameters φ_p = 200 and φ_w = 200 (average duration 5 quarters). - Government and fiscal calibration: - Government spending to GDP ratio = 18% of GDP. - Steady state tax rates: τ_L = 0.317, τ_k = 0.259, τ_c = 0.073. - Steady state lump-sum transfer τ_ls = 6.6% of GDP; constrained households receive f_cc = 0.95 of it. - Calibrated government debt-to-GDP ratio = 80%. - Elasticity of real interest rate w.r.t. government debt: 3 basis points per percentage point increase in debt-to-GDP ratio. - Degree of automatic stabilizers d_gdp = 0.34 (OECD estimate); transition illustrations sometimes use d_gdp = 0. - Banking and financial calibration: - Basel minimum capital adequacy ratio parameter γ = 8% of risk-weighted assets. - Banks’ average actual capital adequacy ratio = 10.5% (buffer of 2.5%). - Percentage of banks violating minimum capital adequacy ratio = 2.5% per quarter in steady state. - Steady state interest rate margin between policy rate i_t and banks’ deposit rate i_{d,t} = 1%. - Steady state margin between deposit rate and (riskless) private loan rate i_ℓ,t = 1.5% per annum. - Financial system overall size = 200% of GDP; liabilities = 184.25% of GDP; bank equity = 15.75% of GDP. - Chicago Plan post-transition calibration specifics: - πm set equal to x (zero steady-state inflation). - īd = 1 (net nominal interest rate on reserves). - īℓ (treasury credit steady-state rate) chosen so banks’ wholesale rate equals government bond rate in steady state. - Convergence rates: ρd = 0.25 and ρf = 0.9. - Gross government debt-to-GDP ratio reduced from 80% to 60% after permanent repayment of government debt held by banking system. - θ = 0.5 used in computing net government debt-to-GDP ratio. - Steady-state nominal (and real) interest rates in Chicago Plan calibration: - Government bonds: 1.07% - Treasury credit: 0.49% - Deposits: 0% - Prudential rule baseline p_ℓ = 0; alternative with p_ℓ = 8 analyzed. ### Transition dynamics: quantitative impacts and steady-state results - First-stage balance-sheet shock: - Banks borrow from treasury to back deposits: treasury credit and reserves increase by 184.25% of GDP on impact. - Immediate stock changes on impact: - Loans to private sector (except investment loans) drop by 100% of GDP on impact; bank-held government bonds drop by 20% of GDP on impact. - Bank net worth drops by around 7% of GDP on impact (reflecting equity payout and adjustments). - Reserves rise from near zero to around 180% of GDP. - Treasury credit initially rises to just over 70% of GDP on impact and later to around 90% of GDP in steady state. - Deposits drop very slightly long-run (~4% of GDP decline overall); household deposits fall while manufacturer deposits rise. - Share of banks violating MCAR falls from 2.5% to around 0.8% per period. - Monitoring costs as share of GDP fall from 2.0% to 0.7%. - Long-run macroeconomic steady-state gains (calibrated): - Output eventually approaches a 10% gain for GDP. - Investment increases by 27%. - Consumption eventually increases by almost 5% (short-run consumption initially drops due to investment crowding-out). - Interest-rate and fiscal steady-state effects: - Gross government debt drops from 80% to 60% of GDP. - Adjusted net government debt (with θ = 0.5) drops from 80% of GDP to eventually 16% of GDP. - Gradual reduction in real bond and deposit rates of 1.93% per annum. - Additional 3% per annum reduction in nominal rates due to elimination of steady-state inflation. - Real treasury credit rate drops by 1.51% per annum to 0.49% per annum. - Real wholesale lending rates drop by 2.43% per annum. - Retail real rates on investment loans drop by 1.64% per annum. - Fiscal and seigniorage effects: - Seigniorage from large reserve stock: 3.6% of GDP (reserves over 180% of GDP with zero nominal and real rate on reserves but positive growth). - Seigniorage used to finance reductions in distortionary taxes equal to 3.6% of GDP. - Debt service (net nominal interest charges) drops by 4.2% of GDP. - Government deficit ratio reduced by 2.8% of GDP. - Treasury credit requires ongoing budgetary expenditure of 1.3% of GDP (0.49% real rate below 2% economy growth). - Transfers held constant in real terms decline by 0.6 percentage points relative to GDP. ### Credit boom–bust experiments: pre-transition versus post-transition scenarios - Experiment design: “good news” shocks reduce borrower-risk standard deviations cumulatively by 60% by quarter 12; at quarter 13 borrower risk jumps to 125% of steady state, then reverts. - Pre-transition economy (baseline): - Bank loans grow strongly over the boom by over 50% of GDP; banks create corresponding deposits endogenously. - Boom end-of-quarter-12 outcomes: - Investment grows by 2.5% relative to trend. - Consumption grows by 1.5%. - GDP ends just under 2% higher. - Inflation exceeds target by over 3% per annum. - Real policy rate rises by 2% per annum. - Bust outcomes: output drops by over 5%, consumption around 3%, investment well over 10%; over 20% of banks violate MCAR at trough; wholesale real lending rate rises ≈ 2% per annum; average real retail lending rate rises ≈ 5% per annum. - Post-transition Chicago Plan with treasury-credit-rate-only policy: - Quantities of credit and money decoupled; credit increase much smaller as share of GDP. - Treasury credit rate swings deeply and can go negative in boom–bust cycle; investment volatility remains high; reversals produce larger valuation losses in capital and higher spikes in retail lending rates than pre-transition. - Post-transition with countercyclical MCAR (quantitative tool active): - Example response: raise capital adequacy ratio from 10.5% to 15% during boom. - Wholesale and retail lending rates remain higher during boom, reducing investment increase to one third of the interest-only scenario. - At reversal banks more resilient; spikes in lending rates milder and smaller than pre-transition. - Amplitude of GDP fluctuations roughly halved relative to pre-transition scenario. - Policy implication from experiments: - Under the Chicago Plan, price-based credit policy alone may be insufficient; combining treasury-credit interest-rate rule with flexible countercyclical quantitative lending targets (MCAR) is effective in stabilizing boom–bust dynamics. ### Key analytic conclusions and operational policy recommendations (verbatim and preserved implications) - Model validates Fisher’s main claims: - Chicago Plan can reduce bank-credit-driven business cycle volatility if accompanied by appropriate policy tools. - Bank runs are eliminated because monetary liabilities become government-issued, debt-free money. - Net government debt becomes much smaller; adjusted net government debt falls substantially (example calibration: from 80% to 16% of GDP using θ = 0.5). - Private debts can be dramatically reduced via one-off buy-backs financed by seigniorage and treasury-credit arrangements; in calibration buy-back excludes investment loans. - Additional advantages: - Large steady-state output gains approaching 10% due to lower real rates, lower distortionary taxes, lower monitoring costs. - Zero steady-state inflation feasible without liquidity-trap problems because government directly controls broad money. - Seigniorage provides a recurring fiscal revenue source (3.6% of GDP in calibration). - Operational policy recommendations under Chicago Plan: - Strict separation between monetary (government-issued, debt-free money) and credit (bank-provided investment loans) functions. - Adopt a monetary rule for nominal money growth (πm) — calibration suggests matching πm to real growth x to target zero inflation. - Set net nominal interest on reserves to zero in steady state and manage treasury-credit rates so wholesale lending and bond rates align. - Use countercyclical capital adequacy requirements (MCAR) as a quantitative tool to limit credit-driven investment booms and stabilize macroeconomic fluctuations. - Ensure treasury credit is strictly disbursed only to finance investment projects to prevent arbitrage and near-money creation outside regulated channels. *Source: _wp12202 - 1. Monetary Policy (IMF working paper excerpt).* ### 1. Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 ### 1. Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 ### Major sections and themes (by heading and page number) - 1. Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 - 2. Prudential Policy . . . . . . . . . . . . . . . . . . . . . . . . . 32 - 3. Fiscal Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 - 4. Government Budget Constraint . . . . . . . . . . . . . . . . . . . 33 - L. Market Clearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 ### The Model under the Chicago Plan (structure and subheadings) - IV. The Model under the Chicago Plan . . . . . . . . . . . . . . . . . . . 33 - A. Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 - B. Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 - C. Manufacturers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 - D. Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 ### Policy and constraints (post-Model headings and pages) - 1. Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 - 2. Prudential Policy . . . . . . . . . . . . . . . . . . . . . . . . . 39 - 3. Fiscal Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 - 4. Government Budget Constraint . . . . . . . . . . . . . . . . . . . 41 - 5. Controlling Boom-Bust Cycles - Additional Considerations . . . . 42 ### Calibration, transition, and empirical analysis - V. Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 - VI. Transition to the Chicago Plan . . . . . . . . . . . . . . . . . . . . . . . . . 49 - VII. Credit Booms and Busts Pre-Transition and Post-Transition . . . . . . 52 - VIII. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 ### Supplementary material - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 ### Figures (titles and page numbers) - 1. Changes in Bank Balance Sheet in Transition Period (percent of GDP) . . . 64 - 2. Changes in Government Balance Sheet in Transition Period (percent of GDP) 65 - 3. Changes in Bank Balance Sheet - Details (percent of GDP) . . . . . . . . 66 - 4. Transition to Chicago Plan - Bank Balance Sheets . . . . . . . . . . . . . . 67 - 5. Transition to Chicago Plan - Main Macroeconomic Variables . . . . . . . . 68 - 6. Transition to Chicago Plan - Fiscal Variables . . . . . . . . . . . . . . . 69 *Source: _wp12202 - 1. Monetary Policy . . . . . . . . . . . . . . . . . . . . . 32 (IMF PDF).* ### 7. Business Cycle Properties Pre-Transition versus Post-Transition . . . . . . . . 70 ### 7. Business Cycle Properties Pre-Transition versus Post-Transition . . . . . . . 70 ### I. Introduction: motivation and overview - The decade following the onset of the Great Depression triggered major developments in monetary economics, with focus on private bank behavior and central bank policies. - The Chicago Plan (championed by Henry Simons and summarized by Irving Fisher (1936)) proposed separation of monetary and credit functions of banking: - Require 100% backing of deposits by government-issued money. - Ensure financing of new bank credit only via retained earnings in government-issued money or borrowing existing government-issued money from non-banks, not by creating new deposits ex nihilo. - Fisher (1936) claimed four advantages of the Chicago Plan: - Better control of credit cycles and business cycle fluctuations. - Complete elimination of bank runs. - Reduction in interest burden on government finances and dramatic reduction of (net) government debt. - Dramatic reduction of private debt levels. - Empirical and theoretical support noted: - Reinhart and Rogoff (2009) document high costs of boom-bust credit cycles and bank runs. - Schularick and Taylor (2012) support that high debt levels predict major crises. - Kumhof and Rancière (2010) show very high debt levels can increase probability of financial and real crises. ### Fisher’s four claims and assessment strategy - The paper embeds a comprehensive calibrated model of the U.S. financial system in a monetary DSGE model to test Fisher’s claims. - Main findings previewed: - Strong support for Fisher’s claims: smoother business cycles (to be fully verified later), no bank runs, large reduction of debt levels, replacement of that debt by debt-free government-issued money. - Additional advantages highlighted: - In calibration, the Chicago Plan generates longer-term output gains approaching 10 percent. - Steady state inflation can drop to zero without posing problems for monetary policy; liquidity traps cannot exist under the reform. ### The four advantages explained (textual summary) - First advantage: control of credit cycles - Under current system broad monetary aggregates depend almost entirely on banks’ willingness to supply deposits. - Under Chicago Plan, quantity of money and quantity of credit become independent: money growth can be controlled via a money growth rule; credit growth controlled because banks must obtain outside funding before lending. - Second advantage: elimination of bank runs - Requires: (i) banking system’s monetary liabilities fully backed by government-issued money; (ii) banking system’s credit assets funded by non-monetary liabilities that are not subject to runs (policy must prevent such liabilities becoming near-monies). - Institutional arrangements discussed: - Banks fund credit assets with equity and treasury loans only (core element of the paper’s version of the Chicago Plan). - Debt-based investment trusts funded by savers’ deposits in exchange for trust debt instruments (risk of near-monies unless strictly regulated). - Investment trusts funded exclusively by net savers’ equity investments (eliminates near-money risk) — not part of formal analysis due to model homogeneity assumptions. - Third advantage: dramatic reduction of (net) government debt - Under Chicago Plan banks must borrow reserves from the treasury to back deposits: government acquires a very large asset vis-à-vis banks; government debt net of this asset becomes highly negative. - Government-issued money is not a debt of government (fiat money not redeemable); treated as government equity (Federal Accounting Standards Advisory Board (2012) cited). - Fourth advantage: reduction of private debts - Full reserve backing creates a highly negative net government debt position; government can use seigniorage windfall to buy back private debt from banks against cancellation of treasury credit. - Simulation assumption: buy-back covers all private bank debt except loans that finance investment in physical capital. ### Illustrative balance sheet changes (single transition period; quantities in percent of GDP) - Pre-implementation consolidated financial system (left column of Figure 1): - Total balance sheet: 200% of GDP. - Equity: 16% of GDP. - Deposits: 184% of GDP. - Assets: government bonds 20% of GDP, investment loans 80% of GDP, other loans (mortgage, consumer, working capital) 100% of GDP. - Transition stage 1 (middle column of Figure 1): - Banks borrow from treasury to procure reserves: treasury credit and reserves increase by 184% of GDP. - Transition stage 2 (right column of Figure 1): - Cancellation of principal of bank loans to government (20% of GDP) and of bank loans to private sector except investment loans (100% of GDP) against treasury credit. - For private debt cancellation the government transfers treasury credit balances to restricted private accounts for repaying outstanding bank loans. - Banks pay out part of equity; government injects additional treasury credit of 7% of GDP to make up net worth difference. - Post-transition financial system: - Money nearly unchanged but fully backed by reserves. - Credit consists only of investment loans financed by reduced equity 9% of GDP and remaining treasury credit 71% of GDP (after buy-backs and injection). - Solid line in balance sheet denotes strict separation between monetary and credit functions. - Government balance sheet changes (Figure 2 summary): - Pre-Chicago Plan government debt: 80% of GDP (with unspecified other assets as balancing item). - Issuance of treasury credit: 184% of GDP (government asset). - Issuance of reserves (money): equal amount (government equity). - Cancellation of private debts reduces both treasury credit and government equity by 100% of GDP. - Taxation of bank equity payout to households and reinjection as treasury credit increases both treasury credit and government equity by 7% of GDP. - Cancellation of bank-held government debt reduces both government debt and treasury credit by 20% of GDP. - Net outcome summary bullets: - Government left with much lower, in fact negative, net debt burden; gains large net equity position due to money issuance. - Government spends large share of one-off seigniorage gains on buy-back of private debts. - Private sector left with much lower debt burden; deposits unchanged. - Bank runs impossible under the Chicago Plan. ### Quantitative and welfare implications (model preview) - Longer-term output gains: - Calibration result: output gains approaching 10 percent. - Mechanisms: - Large reductions of real interest rates as lower net debt levels reduce required spreads. - Lower distortionary tax rates due to higher seigniorage income (despite lower inflation) improving government budget. - Lower credit monitoring costs as resources no longer spent monitoring loans created solely to create money. - Inflation and monetary policy: - Steady state inflation can drop to zero without problems. - Policy instruments under Chicago Plan: - Nominal money growth rule (regulates money supply). - Basel-III-style countercyclical bank capital adequacy rule (controls bank lending quantity). - Interest rate rule for price of government credit to banks (replaces conventional Taylor rule for interest on government debt); this rate can be negative so zero lower bound does not apply. - Liquidity traps cannot exist because: - Policymaker can directly increase aggregate quantity of broad money in private agents’ hands. - Interest rate on treasury credit is not an opportunity cost of money for asset investors; it is a borrowing rate for banks for funding physical investment and can become negative without practical problems. ### Modeling approach: key features and theoretical foundations - Central modeling insight: banks’ central function is creation and destruction of money, not merely financial intermediation. - Model captures endogenous money creation via: - Agents who borrow to generate deposits for transaction purposes (simultaneous borrowing from and depositing with banks). - Financially unconstrained agents whose savings include land, government bonds and deposits; sales of mortgageable assets to credit-constrained agents or of government bonds to banks generate new bank credit/deposits. - Transmission where bank lending creates purchasing power that makes actual investment (and thus saving) possible. - High marginal interest-rate sensitivity of deposit demand implies banks effectively control deposit money quantity through lending decisions. - Omissions: - Cash outside banks and bank reserves at the central bank are omitted because privately created deposit money plays central role; government-issued money quantitatively negligible in current U.S. system. - Rogoff (1998) estimate: currency outside banks ~5% of GDP for the United States in late 1990s, with 95% held by foreigners and/or underground economy implying currency circulating in formal U.S. economy ~0.25% of GDP; contrasted with transactions-related liabilities of U.S. financial system ~200% of GDP. - Model lineage and features: - Banking model elements based on Benes and Kumhof (2011): - Banks have balance sheets and net worth; profits and net worth exposed to non-diversifiable aggregate risk via optimal debt contracts. - Banks are lenders rather than holders of risky equity. - Bank lending modeled on Bernanke, Gertler and Gilchrist (1999) but with risky non-contingent lending interest rates (banks can make losses if defaults exceed expectations). - Bank capital subject to regulation replicating Basel features, with costs of violating minimum capital adequacy; capital buffers arise endogenously. - Banks raise lending rates after loan losses to rebuild net worth, affecting real economy. - Imperfections in acquiring fresh capital modeled via “extended family” approach of Gertler and Karadi (2010): bankers transfer part of equity to household budget at exogenously fixed rate. - The rest of the paper’s organization (as previewed): - Section II: literature survey on monetary history and thought leading to the Chicago Plan. - Section III: model under current monetary system. - Section IV: model under the Chicago Plan. - Section V: model calibration. - Section VI: impulse responses simulating dynamic transition (analyzing three of Fisher’s four claims). - Section VII: analysis of the claim on stabilization of bank-driven business cycles. - Section VIII: conclusion. ### II. The Chicago Plan in the history of monetary thought (selected highlights) - Origins and nature of money: - Critique of textbook barter-origin story; Graeber (2011) and others show earliest commercial transactions based on elaborate credit systems denominated in agricultural commodities, not barter. - Evidence supports state/institutional origin of money (needs of state, religious/temple institutions, social ceremony) rather than private trading origins. - Control of money issuance: - State/institutional theory supports government issuance and control of money under rule of law (interest-free notes/coins or electronic deposits) versus private issuance. - Precious-metals-backed money vs fiat money: - Debate largely a diversion: even commodity-based regimes derived monetary value from government fiat rather than intrinsic metal value (Zarlenga (2002)). - Historical examples of private money harms and debt crises: - Zarlenga (2002) and Del Mar (1895) document repeated societal problems from private money issuance and usury across history. - Two historical forms of usury identified: - Private appropriation of convenience yield of money: private creators of money appropriate liquidity service returns. - Manipulation of money supply: creating credit/money in expansions and contracting in downturns, causing borrower defaults and wealth concentration. - Ancient remedies and precedents: - Solon’s 599 BC reforms in Greece responded to severe debt crisis: debt cancellation, restitution of lands, monetization of agricultural commodities via official floor prices (turning debt finance closer to equity finance), and more plentiful government-issued debt-free coinage. - Solon’s reforms influenced Roman monetary practices; Aristotle and Plato articulated state/institutional theories (“Money exists not by nature but by law.”). - Historical pattern: - Many ancient systems used state-backed fiat currencies (examples: Spartan iron disks, Athenian copper, early Roman bronze tablets/coins whose material value was far below face value). - Historical episodes show private accumulation of precious metals and private issuance of bank money complemented state roles, but state fiat was central to money’s role. *Source: Excerpt from the supplied chapter text.* ### introduction of privately controlled silver money, and later gold money, at prices that far ### _wp12202 - introduction of privately controlled silver money, and later gold money, at prices that far ### Historical evolution of monetary control - Private issuance of silver and gold money emerged during emergencies (Punic wars), with prices that "far exceeded their earlier commodity value prices." - After the collapse of Rome much ancient monetary knowledge was lost in the West; Aristotle’s teachings influenced scholastics including St. Thomas Acquinas (1225-1274). - Until the Industrial Revolution monetary control in the West was generally in government or religious hands and "was inseparable from ultimate sovereignty in society." - Private banking beginnings traced to post-Byzantium (1204), with rulers increasingly relying on loans from private bankers to finance wars. - Key institutional milestones: - Bank of Amsterdam (1609-1820): government-owned, maintained a 100% reserve backing for deposits. - Mixt Moneys of Ireland (1601) legal case: confirmed sovereign right to issue intrinsically worthless base metal coinage as legal tender. - English Free Coinage Act of 1666: "placed control of the money supply into private hands." - Founding of the privately controlled Bank of England in 1694: major sovereign relinquishing monetary control to a central bank and private banking interests. ### Comparative historical evidence and lessons - United Kingdom: - Shaw (1896): monarchs used monetary prerogative responsibly, with one exception (Henry VIII), and "no major financial crises." - Del Mar (1895): Free Coinage Act inaugurated commercial panics and disasters; "between 1694 and 1890 twenty-five years never passed without a financial crisis in England." - United States: - Colonial paper monies issued by individual states were of "the greatest economic advantage" (Franklin (1729)); English suppression contributed to the revolution (Del Mar (1895)). - Continental Currency financed the revolutionary war; inflation later attributed to "massive British counterfeiting" (Franklin (1786), Schuckers (1874)). - Government issuance periods 1812-1817 and 1837-1857 managed conservatively (Zarlenga (2002)). - Greenbacks issued during the Civil War were "crucial" and "responsibly managed" with comparatively less inflation than World War I financing (Randall (1937); Studenski and Kroos (1952)). - Aldrich-Vreeland system (1907-1913): money issuance government controlled through the Comptroller of the Currency and "very effectively administered" (Friedman and Schwartz (1963), p. 150). - Van Buren presidency: insistence on 100% gold/silver backing triggered the 1837 depression by constraining money supply. - Private issuance record: - Private banks and the privately-owned First and especially Second Bank of the United States repeatedly triggered disastrous business cycles via initial monetary over-expansion followed by contraction and debt deflation. - Spurious private bank note issuance caused massive losses in 1810-1820; similar experiences continued throughout the century (Gouge (1833), Knox (1903)). - Large expansion of private credit before the Great Depression another example of bank-induced boom-bust, severity exacerbated by Federal Reserve mistakes (Friedman and Schwartz (1963)). - German hyperinflation of 1923: - Key causal factors described: in May 1922 Allies granted total private control over the Reichsbank; private Reichsbank allowed massive private currency issuance and facilitated speculation. - When Hjalmar Schacht was appointed in late 1923 he stopped converting private monies to Reichsmark on demand, stopped granting Reichsmark loans on demand, and made the new Rentenmark non-convertible against foreign currencies, which "crushed" speculators and stopped hyperinflation. - Conclusion: 1923 episode blamed on "excessive reparations claims and of massive money creation by private speculators, aided and abetted by a private central bank," not on excessive money printing by a government-run central bank. ### Summary judgment from historical evidence - Government-issued currencies have sometimes collapsed amid high inflation, but causes are typically: reckless individual managers (example: John Law 1717-1720) or wars (especially lost ones), not the mere fact of government monetary control. - The Great Depression suggests "privately controlled money creation has much more problematic consequences than government money creation." - Bank-based money creation problems identified: - High and potentially destabilizing debt levels become necessary to create sufficient money supply. - Banks and their optimism effectively control broad monetary aggregates. - These insights motivated formulation of the Chicago Plan. ### The Chicago Plan: objectives, history, and variants - Objective: transition from privately-issued debt-based money to government-issued debt-free money. - Intellectual lineage: - Originated with Frederick Soddy (Soddy (1926)); Frank Knight (Knight (1927), Knight (1933)) and Henry Simons (Simons et al. (1933)) at the University of Chicago were early proponents. - Irving Fisher supported the plan, with an additional focus on using monetary policy to affect debtor-creditor relations through reflation. - Many Chicago economists later known as founders of the Chicago School supported an exclusive government monopoly on money issuance. - Core prescriptions common to all versions: - 100% reserve backing for deposits, either immediately or over time. - Advocacy of monetary rules rather than discretion. - Credit-side variations: - Original plan: replace traditional banks with "investment trusts" funded by equity and private non-monetary interest-bearing securities. - Simons (1946) concern: private securities might become near-monies. Two alternatives to prevent this: 1. Simons’ "financial good society": private property in forms of government currency, government bonds, corporate stock, or real assets; investment trusts funded by equity and investing in corporate equity (corporate debt disappears). 2. Banks issue their debt instruments to the government rather than to the private sector (government funding of bank liabilities). Advantages of government-funded credit: - Enables immediate and full transition to the Chicago Plan when required reserves exceed outstanding government debt (Angell (1935)). - Maximizes fiscal benefits of the Chicago Plan, giving budgetary space to reduce tax distortions. - Keeps bank loan interest rates aligned with government borrowing costs by allowing government to set a lower funding interest rate. - Implementation favored in this paper: - Use of treasury-funded banks for the core financial system. - After government buy-back of non-investment loans, remaining credit function carried out by private institutions funding conventional investment loans with a combination of equity and treasury credit provided at a policy-determined rate. - Under calibration where private bank debtor classes have identical debt levels within each class, fair debt buy-back can cancel every agent’s debts exactly; Simons’ investment trusts needed mainly when debt heterogeneity is present. - Historical traction: - Strong banking-industry resistance prevented adoption as law, but Chicago Plan influenced the 1935 Banking Act. - Continued advocacy in academic literature: Whittlesey (1935), Douglas (1935), Angell (1935), Fisher (1936), Graham (1936), and later Allais (1947), Friedman (1960), Tobin (1985). - "Narrow banking" literature shares similar safety focus on deposit parts of banks. ### Chicago Plan motivations of key proponents - Simons and Fisher: main concern was instability of bank credit determining money supply; advocated eliminating private money creation and instituting government control over money creation plus fixed money growth rule. - Friedman: supported the Chicago Plan to create a government commitment to fixed rules to prevent discretionary interference with borrowing and lending relationships; favored fixed money growth rule to give policymakers control over monetary aggregates. - The implementation in this paper is "closer to Simons and Fisher than to Friedman" by mostly eliminating private debt funding (but not equity funding) of banks’ residual lending. ### Model under the current monetary system — architecture and banking sector - Economy components: - Two household sectors (financially unconstrained households; financially constrained households). - Productive sector. - Banking sector. - Government. - Rigidities: multiple nominal and real rigidities included to generate empirically realistic transition scenarios and to align with empirical DSGE literature. - Private agents interacting with banks (four types): - Financially unconstrained households: large unencumbered investments including bank deposits, land, government debt. - Financially constrained households: own bank deposits and land used as collateral for consumer loans and mortgages. - Manufacturers: own bank deposits used as collateral for working capital loans. - Capital investment funds: own physical capital used as collateral for investment loans. - Other agents: capital goods producers (investment adjustment costs); unions (nominal wage-setting rigidities). - Technology growth: constant positive technology growth rate g = T_t / T_{t-1}, where T_t is labor-augmenting technology. - Normalization and notation: - Real normalized variable: ˇx_t = X_t / (T_t P_t) = x_t / T_t, steady state denoted by ̄x. - Population shares: ω and 1−ω for unconstrained and constrained households respectively. - Banks: - Banks lend to constrained households via consumer loans secured on deposits (superscript c) and mortgages secured on land (superscript a); to manufacturers via working capital loans secured on deposits (superscript m); to capital investment funds via investment loans secured on fixed capital (superscript k); and hold government bonds. - Banks maintain deposits for unconstrained households (superscript u), constrained households and manufacturers. Deposits modelled as a single asset type with one-period maturity; in calibration this includes demand deposits and all other near-monies. - Banks’ net worth and minimum capital adequacy requirements (MCAR) modeled to resemble current Basel regime; banks pay penalties if they violate MCAR. - Banks maintain equity buffers above MCAR to avoid penalties and insolvency; probability of insolvency and calling on deposit insurance set to be vanishingly small in calibration. - Deposit insurance is assumed and coupled with capital adequacy regulation to protect taxpayers from systemic crises while limiting depositors’ monitoring costs. - Bank variables and notation (preserved exactly as in source): - Loan stocks between t and t+1: L^x_t(j) and ˇℓ^x_t(j). - Deposit stocks: D^x_t(j) and ˇd^x_t(j). - Holdings of government bonds: B^b_t(j) and ˇb^b_t(j). - Net worth: N^b_t(j) and ˇn^b_t(j). - Deposit rates: nominal i_{d,t} and ex-post real r_{d,t}, where r_{d,t} = i_{d,t−1} / π_t and π_t = P_t / P_{t−1}. - Wholesale cost of funding loans: i_{ℓ,t} and r_{ℓ,t} for all loans except mortgages; h_ℓ,t and h_ℓ,t for mortgage loans. - Retail nominal and real lending rates: i^x_{r,t} and x^r_t. - Interest rates on government debt: i_t and r_t. - Bank balance sheet in real normalized terms (equation preserved exactly): - (1−ω)(ˇℓ^c_t(j)+ˇℓ^a_t(j)) + ˇℓ^m_t(j)+ˇℓ^k_t(j)+ˇb^b_t(j) = ωˇd^u_t(j)+(1−ω)ˇd^c_t(j)+ˇd^m_t(j)+ˇn^b_t(j). (1) - Additional definitions (preserved): - ˇℓ_t(j) = (1−ω)ˇℓ^c_t(j)+ˇℓ^m_t(j)+ˇℓ^k_t(j). - ˇℓ^h_t(j) = (1−ω)ˇℓ^a_t(j). - ˇℓ^ℓ_t(j) = ˇℓ_t(j)+ˇℓ^h_t(j). - ˇd_t(j) = ωˇd^u_t(j)+(1−ω)ˇd^c_t(j)+ˇd^m_t(j). - Loan losses and bond holdings (preserved statements): - Banks’ losses on four loan categories: ˇΛ^b_t(j) = (1−ω)(ˇΛ^c_t(j)+ˇΛ^a_t(j)) + ˇΛ^m_t(j)+ˇΛ^k_t(j). - Stock of government bonds on banks’ balance sheets equals a fixed share of total balance sheet: ˇb^b_t(j) = s_b (ˇd_t(j) + ˇn^b_t(j)). - Modeling choices: - Cash constraint specification used (financial markets analogue of goods market rationale for cash constraints), rather than cash-in-advance, to simplify analysis without losing insights. - Model focuses on bank solvency considerations and ignores liquidity management problems (no incentive to maintain central bank cash reserves). - In this economy "there is no demand for government-provided real cash balances" because cash is dominated in return by bank deposits. *Source: Excerpt from working paper content unit _wp12202 (provided content).* ### introduction, such balances are vanishingly small relative to the size of bank deposits. ### _wp12202 - introduction, such balances are vanishingly small relative to the size of bank deposits. ### Banks and the regulatory framework - Banks face pecuniary costs of falling short of official minimum capital adequacy ratios (MCAR). - Regulatory framework introduces a discontinuity: in any period a bank either remains sufficiently well capitalized or falls short and pays a penalty; if the latter, net worth drops further. - To generate realistic partial incidence of penalties, the model assumes a continuum of heterogeneous banks exposed to idiosyncratic shocks so that a time-varying small fraction of banks pay penalties each period. - Risk-weights: non-mortgage loans = 100%, mortgage loans = ζ, government debt = zero. - Penalty: banks pay a real penalty of χ(ˇℓ/ℓ_t(j) + ˇb/b_t(j)) at time t+1 if a cutoff condition is breached. ### Bank heterogeneity and idiosyncratic loan-return shocks - Bank loan-book return shock: ω^b_{t+1} is lognormally distributed with E(ω^b_{t+1}) = 1 and Var(ln(ω^b_{t+1})) = (σ^b_{t+1})^2. - Density and cumulative density: f^b_t(ω^b_{t+1}) and F^b_t(ω^b_{t+1}). - Heterogeneity captures differing loan recovery rates, non-interest income, and non-interest expense differences (sum of last two categories sums to zero over banks). ### Penalty cutoff condition and cutoff shock (equations preserved) - Penalty cutoff condition (as given): (r_{ℓ,t+1} ˇℓ_t(j) + r^h_{ℓ,t+1} ˇℓ^h_t(j) + r_{t+1} ˇb b_t(j)) ω^b_{t+1} − r_{d,t+1} ˇd_t(j) − ˇΛ^b_{t+1}(j) (2) < γ_t (r_{ℓ,t+1} ˇℓ_t(j) + ζ r^h_{ℓ,t+1} ˇℓ^h_t(j)) ω^b_{t+1}. - Interpretation: left-hand side = pre-dividend (and pre-penalty) net worth in t+1; term multiplying γ_t = value of risk-weighted assets in t+1; γ_t represents the minimum capital adequacy ratio of the Basel framework. - Cutoff idiosyncratic shock ω̄^b_t defined by (3): ω̄^b_t ≡ r_{d,t} ˇd_{t−1} + x ˇΛ^b_t (1−γ_{t−1}) / (r_{ℓ,t} ˇℓ_{t−1} + (1−γ_{t−1} ζ) r^h_{ℓ,t} ˇℓ^h_{t−1} + r_t ˇb b_{t−1}). (preserve exact formatting of numerator/denominator as in source) ### Bank optimization, spreads, and maintained capital adequacy - Banks choose loan volumes ˇℓ_t(j), ˇℓ^h_t(j) to maximize pre-dividend net worth: Max ˇℓ_t(j), ˇℓ^h_t(j) E_t[ (r_{ℓ,t+1} ˇℓ_t(j) + r^h_{ℓ,t+1} ˇℓ^h_t(j) + r_{t+1} ˇb b_t(j)) ω^b_{t+1} − r_{d,t+1} ˇd_t(j) − ˇΛ^b_{t+1}(j) − χ(ˇℓ_t(j) + ˇℓ^h_t(j) + ˇb b_t(j)) F^b_t(ω̄^b_{t+1}) ]. - Optimality conditions (Technical Appendix) imply: - Wholesale lending rates i_{ℓ,t} and i^h_{ℓ,t} are at a premium over deposit rate i_{d,t} by magnitudes depending on γ_t, χ, and F^b_t(ω̄^b_{t+1}), f^b_t(ω̄^b_{t+1}) — reflecting expected riskiness σ^b_{t+1} and likelihood of breach. - Retail rates i^x_{r,t} are at another premium over i_{ℓ,t} and i^h_{ℓ,t} to compensate for borrower-type bankruptcy risks. - Policy rate i_t does not enter these optimality conditions as the marginal cost of funds; marginal cost of funds = i_{d,t} (rate at which banks can create their own funds). - Banks’ actually maintained Basel capital adequacy ratio γ^a_t is considerably above minimum γ_t (buffer choice); steady state notation γ̄^a used for calibration. ### Aggregate bank net worth and penalty costs - Aggregation (linearity of banks’ technology) allows dropping bank-specific indices. - Aggregate bank net worth ˇn^b_t is a state variable: ˇn^b_t = (1/x)(r_{ℓ,t} ˇℓ_{t−1} + r^h_{ℓ,t} ˇℓ^h_{t−1} + r_t ˇb b_{t−1} − r_{d,t} ˇd_{t−1}) − ˇΛ^b_t − ˇM^b_t − δ_b ˇn^b_t. (4) - Cost of penalties: ˇM^b_t = χ x (ˇℓ_{t−1} + ˇℓ^h_{t−1} + ˇb b_{t−1}) F^b_t(ω̄^b_t). - Dividends: δ_b ˇn^b_t. ### Lending technologies and borrower contracts - Borrower types x ∈ {c, a, m, k} (consumer, mortgage, manufacturers, capital investment funds). - Borrower loan-return shock ω^x_{t+1} is unit-mean lognormal; StdDev of ln(ω^x_{t+1}) = S^z_{t+1} σ^x_{t+1}, with S^z_{t+1} aggregate component and σ^x_{t+1} type-specific. - Density and CDF: f^x_t(ω^x_{t+1}), F^x_t(ω^x_{t+1}). - Debt contract: nominal loan L^x_t(j)/ℓ^x_t(j) and pre-committed gross nominal retail rate i^x_{r,t} (set in period t). - Borrowers with ω^x_{t+1} < ω̄^x_{t+1} default; bank recovers fraction (1−ξ_x) of asset value; ξ_x is monitoring cost fraction (part redistributed to households, remainder real resource cost). - Banks’ ex-ante zero profit condition for borrower group x (real terms) summarized and transformed into zero-profit condition (5): E_t{ r_{ℓ,t+1} ˇℓ^x_t − ˇx_t ret^x_{t+1} (Γ_{x,t+1} − ξ_x G_{x,t+1}) } = 0. (5) - Γ_{x,t+1} = ∫_0^{ω̄^x_{t+1}} ω^x_{t+1} f^x_t(ω^x_{t+1}) dω^x_{t+1} + ω̄^x_{t+1} ∫_{ω̄^x_{t+1}}^∞ f^x_t(ω^x_{t+1}) dω^x_{t+1}. - ξ_x G_{x,t+1} = ξ_x ∫_0^{ω̄^x_{t+1}} ω^x_{t+1} f^x_t(ω^x_{t+1}) dω^x_{t+1}. - Bank sets i^x_{r,t} so expected gross share Γ_{x,t+1} covers monitoring costs and opportunity cost; borrower retains 1−Γ_{x,t+1}. - Capital investment funds: optimal loan contract condition identical to Bernanke et al. (1999), equation (6): E_t{ (1−Γ_{k,t+1}) ret_{k,t+1} / r_{ℓ,t+1} + ˜λ^k_{t+1} [ ret_{k,t+1} / r_{ℓ,t+1} (Γ_{k,t+1} − ξ_k G_{k,t+1}) − 1 ] } = 0, (6) with ˜λ^k_{t+1} = Γ^ω_{k,t+1} / (Γ^ω_{k,t+1} − ξ_k G^ω_{k,t+1}), and Γ^ω, G^ω derivatives w.r.t. ω̄^k_{t+1}. - For mortgages, due to lower Basel risk-weighting, wholesale rate r^h_{ℓ,t+1} < r_{ℓ,t+1}. ### Default, net loan losses, and business cycle shock to borrower riskiness - Banks’ net loan losses are positive if wholesale interest expenses exceed banks’ net (of monitoring costs) share in borrowers’ gross earnings — occurs when unexpectedly many borrowers default. - Fisher (1936) hypothesis evaluated: banks’ optimism about business conditions drives business cycle volatility. - Standardized shock S^z_t multiplies each standard deviation σ^x_{t} for x ∈ {c, a, m, k}. - S^z_t = S^z1_t S^z2_t with: - ln S^z1_t = Σ_{j=0}^{12} ε^{news}_{t−j} (sum of news shocks over current and preceding 12 quarters), - ln S^z2_t = ρ_z ln S^z2_{t−1} + ε^z2_t (autoregressive). ### Transactions cost technologies - Transactions cost s^x_t = A_x v^x_t + B_x v^x_t^{-2} √(A_x B_x). (7) - Velocity definitions: - For households: v^x_t = c^x_t (1+τ_{c,t}) / d^x_t. (8) - For manufacturers: v^m_t = (w_t h_t + r_{k,t} k_{t−1}) / d^m_t. (9) - Consumption expenditures for households: c^x_t (1+τ_{c,t}) (1+s^x_t). - Manufacturers’ total expenditures on inputs equal (w_t h_t + r_{k,t} k_{t−1}) (1+s^m_t). ### Equity ownership, dividends, and the “extended family” structure - “Extended family” approach (Gertler and Karadi (2010)): bankers, manufacturers, entrepreneurs transfer part of accumulated equity to households at exogenous rate. - Representative household composed of workers, manufacturers, entrepreneurs, bankers — perfect consumption insurance within household. - Occupational flows: fractions (1−f) workers; f(1−b) manufacturers; f(1−b)(1−m) entrepreneurs; f b bankers. Occupational persistence probabilities p_m, p_k, p_b. - Net worth payouts to households (per period) summarized by δ_m n^m_t, δ_k n^k_t, δ_b n^b_t (dividend-policy parameters). - Start-up funds provided by households equal small fractions ι_m, ι_k, ι_b of existing aggregate net worth. ### Unconstrained households (preferences, assets, budget) - Utility: Max E_0 Σ_{t=0}^∞ β^t_u { (1−v_x) log(c^u_t(i) − ν c^u_{t−1}) − ψ h^u_t(i)^{1+1/η} / (1+1/η) + κ log(a^u_t(i)) }. (10) - Assets: land a^u_t (price ˇp^a_t), real government debt ˇb^u_t, real bank deposits ˇd^u_t. - Small transactions cost on acquiring financial assets: (ˇb^u_t + ˇd^u_t) φ_b (b_rat_t − b̄_rat), where b_rat_t = ˇb^g_t / (4 g ˇd p_t) and b̄_rat is initial steady state value. - Lump-sum transfer ˇΨ^u_t redistributes that cost back to unconstrained households. - Budget constraint (11) preserved exactly as in source: (ˇb^u_t + ˇd^u_t)(1+φ_b (b_rat_t − b̄_rat)) + ˇp^a_t a^u_t (11) = r^x_t ˇb^u_{t−1} + r_{d,t}^x ˇd^u_{t−1} + ˇp^a_t a^u_{t−1} + ˇΨ^u_t − ˇc^u_t (1+s^u_t) (1+τ_{c,t}) − ˇτ^{uu}_t + ˇw^h_t h^u_t (1−τ_{L,t}) + ˇΠ^k_t + ˇC_{I,t} + ˇC_{P,t} + (1−ι)/ω ˇo_t. ### Constrained households (preferences, borrowing, loan contracts) - Utility identical form but discount factor β_c may differ: Max E_0 Σ β^t_c { S^c_t (1−v_x) log(c^c_t(i) − ν c^c_{t−1}) − ψ h^c_t(i)^{1+1/η} / (1+1/η) + κ log(a^c_t(i)) }. (12) - Can invest in bank deposits ˇd^c_t and land a^c_t; borrow via consumer and mortgage loans ˇℓ^c_t and ˇℓ^a_t. - Budget constraint (constrained) preserved as in source (second-line terms include monitoring shares ξ_c G_{c,t}, ξ_a G_{a,t}; banks’ net losses ˇΛ^c_t, ˇΛ^a_t). - Period t+1 budget constraint replaces certain terms with (1−Γ_{c,t+1}) r_{d,t+1}^x ˇd^c_t + (1−Γ_{a,t+1}) ˇp^a_{t+1} a^c_t. - Optimal consumer loan contract conditions (13) and mortgage loan contract conditions (14) preserved: - (13): ˇλ^c_t (1+φ_b (b_rat_t − b̄_rat)) (1−s_c′_t(v^c_t)^2) = E_t β_c x ˇλ^c_{t+1} r_{d,t+1} [ (1−Γ_{c,t+1}) + ˜λ^c_{t+1} (Γ_{c,t+1} − ξ_c G_{c,t+1}) ], and ˇλ^c_t = E_t β_c x ˇλ^c_{t+1} ˜λ^c_{t+1} r_{ℓ,t+1}. - (14): ˇλ^c_t − κ ˇp^a_t a^c_t = E_t β_c ˇλ^c_{t+1} ˇp^a_{t+1} / ˇp^a_t [ (1−Γ_{a,t+1}) + ˜λ^a_{t+1} (Γ_{a,t+1} − ξ_a G_{a,t+1}) ], and ˇλ^c_t = E_t β_c x ˇλ^c_{t+1} ˜λ^a_{t+1} r^h_{ℓ,t+1}. - Monetary wedges appear in consumer loan condition (13); utility-related wedge appears in mortgage contract condition (14). ### Unions - Unions buy labor from households at nominal household wage W^h_t and sell labor variety i to manufacturers at producer wage W_t(i). - CES labor demand elasticity θ_w; gross markup A_w = θ_w/(θ_w − 1). - Wage adjustment costs: C_{W,t}(i) = (φ_w / 2) h_t^T_t (W_t(i)/W_{t−1}(i) / W_{t−1}/W_{t−2} − 1)^2. - Optimization yields New Keynesian Phillips curve for wages. - Unions owned by constrained households; dividends go to constrained households. ### Manufacturers - CES demand (elasticity θ), markup A = θ/(θ−1). - Price adjustment costs C_{P,t}(i) = (φ_p / 2) y_t (P_t(j)/P_{t−1}(j) / P_{t−1}/P_{t−2} − 1)^2. - Production y_t(j) = (T_t h_t(j))^{1−α} k_{t−1}(j)^α. - Balance sheet: ˇd^m_t = ˇℓ^m_t + ˇn^m_t. (15) - Timet optimization problem includes sales revenues, earnings on deposits (1−Γ_{m,t+1}) i_{d,t} D^m_t(j), input costs with transaction cost s^m_t(j), fixed cost F, price adjustment costs, and bank participation constraint. - Optimal working-capital loan contract condition (16): E_t{ [ (1−Γ_{m,t+1}) i_{d,t} + s_m′_t(v^m_t)^2 ] + ˜λ^m_{t+1} [ (Γ_{m,t+1} − S^x_{t+1} ξ_{m,t+1} G_{m,t+1}) i_{d,t} − i_{ℓ,t} ] } = 0. - Manufacturers’ net worth accumulation (17): ˇn^m_t = r_{d,t}^x ˇd^m_{t−1} (1−ξ_m G_{m,t}) + ˇΛ^m_t − r_{ℓ,t}^x ˇℓ^m_{t−1} + ˇy_t − (ˇw_t h_t + r_{k,t} ˇk_{t−1}^x)(1+s^m_t) − ˇC_{P,t} − F − δ_m ˇn^m_t. ### Capital goods producers and investment - Capital good production subject to investment adjustment costs C_{I,t} = (φ_I / 2) I_t (I_t / I_{t−1}^x − 1)^2. - Capital accumulation k_t = (1−∆) k_{t−1} + I_t. ### Capital investment funds - Balance sheet: q_t ˇk_t = ˇn^k_t + ˇℓ^k_t. (18) - Ex-post return to capital ret^k_t = (r_{k,t} + (1−∆) q_t − τ_{k,t} (r_{k,t} − ∆ q_t)) / q_{t−1}. - Optimal loan contract condition given in (6) (see capital investment funds section). - Net worth accumulation (19): ˇn^k_t = ret^k_t x q_{t−1} ˇk_{t−1} (1−ξ_k G_{k,t}) + ˇΛ^k_t − r_{ℓ,t}^x ˇℓ^k_{t−1} − δ_k ˇn^k_t. *Italic source: _wp12202 - introduction, such balances are vanishingly small relative to the size of bank deposits.* ### 1. Monetary Policy ### 1. Monetary Policy ### Pre-transition monetary policy (current monetary regime) - Policy rule (inflation forecast-based interest rate rule): - i_t = (i_{t−1})^{m_i} (x^{β_u} π (1+φ_b (b_{rat,t} − \bar b_{rat})) )^{(1−m_i)} (π_{4,t+3}/(\bar π)_4)^{(1−m_i) m_{π4,}} (equation label in source: (1) and (20)) - π_{4,t} = π_t π_{t−1} π_{t−2} π_{t−3} - Institutional features and transmission: - Government controls a policy interest rate that affects both money and credit, but control is weak. - For credit: policy rate influences deposit rate by arbitrage, but banks’ lending standards and spreads have a much stronger effect on availability and cost of credit. - Because money equals credit under the current system (except for banks’ retained earnings), policy rate effect on money is also weak compared to banks’ lending decisions. ### Prudential policy (pre-transition) - Assumption: prudential policy follows a fixed Basel rule with constant minimum capital adequacy ratio: - γ_t = \bar γ - Alternatives referenced but not detailed in this content. ### Fiscal policy (pre-transition) - Fiscal policy follows a structural deficit rule: - Government long-run target for the deficit-to-GDP ratio is fixed at gd_rat. - Deficit allowed to fluctuate with the output gap via automatic stabilizers: - gd_rat_t = gd_rat − d_{gdp} ln( \tilde g_{dp,t} / gdp_{ss} ) (equation (21) in source) - Labor income tax τ_{L,t} adjusts to make the rule hold over the business cycle. - Other distortionary taxes follow labor income tax proportionally: - (τ_{c,t} − \bar τ_c)/\bar τ_c = (τ_{L,t} − \bar τ_L)/\bar τ_L - (τ_{k,t} − \bar τ_k)/\bar τ_k = (τ_{L,t} − \bar τ_L)/\bar τ_L - Lump-sum taxes: - \tilde τ_{ls,t} = ω \tilde τ_{uu,t} + (1−ω) \tilde τ_{cc,t} - Portion affecting constrained agents: \tilde τ_{cc,t} = f_{cc} \tilde τ_{ls,t} / (1−ω) - Government spending \tilde g_t equals fixed fraction s_g of GDP. ### Government budget constraint & steady-state relationship - Government budget constraint: - \tilde b_{g,t} = r_t^x \tilde b_{g,t−1} + \tilde g_t − \tilde τ_t (equation (22)) - Tax revenue: \tilde τ_t = τ_{c,t} \tilde c_t + τ_{L,t} \tilde w_h_t h_t + τ_{k,t} (r_{k,t} − Δq_t) \tilde k_{t−1}^x + \tilde τ_{ls,t} - Steady state relationship between debt- and deficit-to-GDP ratios: - b_{rat} = (gd_rat / 4) x̄π / (x̄π − 1) - Note: factor of proportionality 4 due to quarterly model. ### Market clearing conditions (pre-transition) - Goods market: \tilde y_t = \tilde c_t + \tilde I_t + \tilde g_t + F + r ( \tilde M_t + \tilde T_t ) - r is fraction of monitoring and transactions costs that is a real resource cost; 1 − r is lump-sum transfer to households. - Labor market: h_t = ω h_{u,t} + (1−ω) h_{c,t} - Land market: a = ω a_{u,t} + (1−ω) a_{c,t} (a is fixed exogenous supply) - Bonds market: ω \tilde b_{u,t} + \tilde b_{b,t} = \tilde b_{g,t} - Aggregate consumption: c_t = ω c_{u,t} + (1−ω) c_{c,t} - GDP: \tilde gdp_t = \tilde c_t + \tilde I_t + \tilde g_t --- ### IV. The Model under the Chicago Plan (post-transition economy) ### Overview of transition - Transition occurs in exactly one period; a dummy parameter d = 1 in transition period and d = 0 thereafter. - Transition involves large one-off stock changes on balance sheets; governments, banks, households, and manufacturers exhibit differences post-transition. - Except where specified, structures and calibration identical between pre- and post-transition economies. ### A. Banks (post-transition under Chicago Plan) - Key requirement: banks must back 100% of deposits \tilde d_t by government-issued reserves \tilde m_t: - \tilde d_t = \tilde m_t (equation (23)) - Consequence: banks cannot create deposits to lend. - Loan funding: - Loan portfolio must be backed by bank equity and non-monetary liabilities \tilde f_t; authors assume \tilde f_t supplied exclusively by government treasury ("treasury credit"), with private agents limited to holding bank equity or monetary instruments \tilde d_t that do not fund lending. - Credit function: \tilde ℓ_{k,t} = \tilde f_t + \tilde n_{b,t} (equation (24)) - Transition stages (within single transition period): 1. Banks increase reserve backing for deposits from 0% to 100% by borrowing from the treasury: \tilde f_t = \tilde m_t = \tilde d_t. 2. Government cancels government debt on banks’ balance sheets against treasury credit and transfers part of remaining treasury credit claims to constrained households and manufacturers via restricted accounts used to repay outstanding bank loans. Leaves only investment loans \tilde ℓ_{k,t} outstanding; \tilde m_t unchanged and \tilde f_t much reduced. - Government sets interest rate on reserves i_{m,t}; deposit function perfectly competitive and banks face zero marginal cost => i_{m,t} = i_{d,t}. - Loan losses/gains simplify: \tilde Λ_{b,t} = \tilde Λ_{k,t} - Capital adequacy regulation applies only to credit portion; banks still determine allocation of credit. - Banks’ net worth accumulation (post-transition): - \tilde n_{b,t} = 1/x ( r_{ℓ,t} \tilde ℓ_{t−1} + r_{hℓ,t} \tilde ℓ_{h,t−1} + r_t \tilde b_{b,t−1} − r_{d,t} \tilde d_{t−1} − x \tilde Λ_{b,t} ) − χ/x ( \tilde ℓ_{t−1} + \tilde ℓ_{h,t−1} + \tilde b_{b,t−1} ) F_b_t(\bar ω_{b,t}) − δ_b \tilde n_{b,t} + 1/x ( r_{d,t} \tilde m_{t−1} − r_{f,t} \tilde f_{t−1} ) − d \tilde Δ nw_t (equation (25)) - Third line terms (new): - Gross interest on reserve backing of deposits paid by government. - Gross interest on treasury credit paid by banks to government. - One-off equity payout in transition period: \tilde Δ nw_t = \tilde n_{b,t−1} − \bar γ_a \tilde ℓ_{k,t}, where \bar γ_a is unchanged steady state capital adequacy ratio. - Heterogeneity considerations: - If government uses flat per capita transfer \tilde d_{new,t} to avoid penalizing low-debt individuals, individuals without debt would hold \tilde d_{new,t}, those with higher debt would have residual debt; net savers’ balances can be converted into equity shares or non-monetary debt instruments of investment trusts. - Treasury-funded banks remain core; investment trusts less important than in Simons’ vision. ### B. Households (post-transition) - Upon announcement and full household debt buy-back, all households become unconstrained; set population share parameter ω_t = 1 from transition period onwards. - Post-transition household financial position: - Zero net bank debt from transition moment onward (gross positions could persist with heterogeneity). - Financial assets: government bonds and deposits (now 100% reserve backed). - Post-transition household budget constraint (transition period includes additional terms): - ( \tilde b_{u,t} + \tilde d_{u,t} ) (1 + φ_b ( b_{rat net,t} − \bar b_{rat} )) + \tilde p_a,t a = r_t^x ω_{t−1} \tilde b_{u,t−1} + r_{d,t}^x ( ω_{t−1} \tilde d_{u,t−1} + (1−ω_{t−1}) \tilde d_{c,t−1} ) + \tilde p_a,t a + \tilde Ψ_{u,t} − \tilde c_{u,t} (1+s_{u,t})(1+τ_{c,t}) − \tilde τ_{ls,t} + \tilde w_h_t h_{u,t} (1−τ_{L,t}) − d (1−ω_{t−1}) ( r_{ℓ,t}^x − 1) \tilde ℓ_{c,t−1} − d (1−ω_{t−1}) ( r_{hℓ,t}^x − 1) \tilde ℓ_{a,t−1} + \tilde o_t − d τ_{once,t} (equation (26)) - Transition-only terms: households pay net interest on past consumer loans and mortgages in transition period; principal cancelled against banks’ new borrowing from treasury after transfers to restricted private accounts. - Dividend portion of other income \tilde o_t includes d Δ nw_t (one-off equity distribution/share buyback). - One-off lump-sum tax τ_{once,t} is set equal to Δ nw_t so government taxes away benefits of equity distribution to finance additional treasury credit without higher distortionary taxation. - Government-debt-related interest premium determined by b_{rat net,t} rather than b_{rat,t}: - b_{rat net,t} = ( \tilde b_{g,t} − θ \tilde f_t ) / (4 g \tilde gdp_t) (equation (27)) - θ indicates weight investors attach to treasury credit (government assets vis-à-vis private sector) in computing net government debt; calibration determined by relative interest burdens of instruments. ### C. Manufacturers (post-transition) - Technology, optimal input choice, and inflation dynamics unchanged. - Transition period: manufacturers pay net interest on past bank debt; principal cancelled as with households => manufacturing sector attains zero net bank debt. - Main financial asset remains bank deposits (fully reserve-backed), implying large net worth increase and financing almost exclusively by equity. - Post-transition manufacturers can access market for riskless debt due to lower credit risk; net steady state borrowing is zero. Denote manufacturers’ net holdings of riskless debt by \tilde b_{m,t}. - Post-transition manufacturers’ balance sheet: - \tilde d_{m,t} + \tilde b_{m,t} = \tilde n_{m,t} (equation (28)) - Opportunity cost of holding bank deposits given by spread between riskless debt rate and deposit rate; optimal money holdings: - i_t = i_{d,t} + s_m^{\prime}_t (v_{m,t})^2 (equation (29)) - Manufacturers’ net worth accumulation: - \tilde n_{m,t} = r_{d,t}^x \tilde d_{m,t−1} + r_t^x \tilde b_{m,t−1} − d ( r_{ℓ,t}^x − 1 ) \tilde ℓ_{m,t−1} − δ_m \tilde n_{m,t} + \tilde y_t − ( \tilde w_t h_t + r_{k,t} \tilde k_{t−1}^x ) (1+s_{m,t}) − \tilde C_{P,t} − F ### D. Government policy under the Chicago Plan 1. Monetary policy (post-transition) - Instrumentation and control: - Pre-transition: single instrument (nominal interest rate on short-term government bonds) affects both money and credit weakly. - Post-transition: government directly controls quantity of money; control over credit indirect but potentially much more powerful. - Money rule (Friedman money growth rule): - \tilde d_t = π_m \tilde d_{t−1}^x π_t (equation (30)) - Under Chicago Plan this rule directly controls the broadest monetary aggregate; monetarism becomes effective at controlling inflation. - Government sets nominal interest rate on reserves; long-run deposit rate set to \bar i_d = 1 (government eventually pays zero interest on money). - To avoid volatility in immediate post-transition period, nominal deposit interest follows autoregressive path: - i_{d,t} = (1 − ρ_d) \bar i_d + ρ_d i_{d,t−1} (equation (31)) - Credit policy: - Government controls nominal interest rate on treasury credit i_{f,t} and countercyclical component of capital adequacy γ_t (prudential policy). - Because inflation controlled by money growth rule, nominal control of i_{f,t} equivalent to control of real treasury credit rate and indirectly real bank credit rate. - Zero lower bound not relevant for treasury credit (only accessible to banks for funding investment loans); i_{f,t} not constrained by zero lower bound => government can charge negative nominal/real rates on treasury credit in severe downturns. - Policy rules for treasury credit rate: - Around post-transition steady state, feedback rule: - i_{f,t} = (\bar i_f)^{1−m_i} (i_{f,t−1})^{m_i} (π_{4,t+3}/(\bar π)_4)^{(1−m_i) m_{π}} (equation (32)) - Differences vs. pre-transition rule: no natural rate for i_{f,t} (government chooses steady state \bar i_f), no zero lower bound, rate directly affects investment decisions. - Immediate post-transition path (gradual lowering from pre-transition deposit rate i_{d,t−1} to long-run target \bar i_f): - i_{f,t} = (1 − ρ_f) \bar i_f + ρ_f ( d i_{d,t−1} + (1−d) i_{f,t−1} ) (equation (33)) - For transition simulation, policy feedback to inflation ignored; authors choose high ρ_f to calibrate slow reduction in i_{f,t} to avoid immediate explosion in investment demand and destabilizing effects. - Long-run calibration objective: - Policymaker sets \bar i_f so that long-run steady state wholesale bank lending rate \bar i_ℓ (before risk spreads) equals steady state rate on government bonds \bar i. *Source: _wp12202 - 1. Monetary Policy* ### 2. Prudential Policy ### 2. Prudential Policy ### Countercyclical Prudential Rule - Policy can control credit via the interest rate on treasury credit and via quantitative lending targets enforced through costly penalties on excessively volatile lending, implemented here as countercyclical capital adequacy regulations. - Pre-transition assumption: a Basel regime with a constant MCAR, γ_t = γ, retained when simulating the transition to the Chicago Plan. - Under the Chicago Plan, prudential policy is assumed to have a strong countercyclical component. With banks exclusively financing investment projects, prudential policy targets the quantity of investment directly rather than the price or quantity of credit. - Prudential rule (verbatim from source): - γ_t = γ (ˇI_t  I)_pℓ,(34) - where p_ℓ > 0. - Mechanism: raising the minimum reserve requirement when the quantity of investment is at a cyclical high forces banks to hold more equity per unit of loans, producing reduced lending and higher lending rates on remaining loans; this limits business cycle effects of banks’ attitudes towards credit risk. ### Fiscal Policy (Transition) - Fiscal policy rule under the Chicago Plan remains unchanged in form; rules endogenizing tax rates and the exogenous process for government spending are unchanged. - The fiscal rule targets the government deficit (change in stock of government debt) and must be modified for the transition period because of a large discontinuous change in the stock of government debt from repayment of government debt held by the banking system. - Modified fiscal rule (verbatim from source): - gd_rat_t = (1−d) (gd_rat − d_gdp ln (gˇdp_t gdp_ss)) + d∆bg_t,(35) - ∆bg_t = 4 (b_rat_t − b_rat_t−1 xπ_t (gˇdp_t/gˇdp_t−1)),(36) - last expression follows from the long-run relationship between debt and deficits. - Note: long-run debt-to-GDP ratios are shown with time subscripts because the transition involves an instantaneous and permanent reduction in the steady state debt-to-GDP ratio due to buy-back of bank-held government debt against cancellation of treasury credit. ### Government Budget Constraint (Post-transition and Transition Stock Effects) - Post-transition government budget constraint includes new flow terms related to money issuance and treasury credit issuance and one-off stock adjustment terms in the transition period. - Post-transition budget constraint (verbatim from source): - ˇb_g_t + ˇm_t − ˇf_t − d∆comp_t = r_t x ˇb_g_t−1 + r_d,t x ˇm_t−1 − r_f,t x ˇf_t−1 + ˇg_t − ˇτ_t,(37) - ˇτ_t = ˇτ_ls,t + dτ_once_t + τ_c,t ˇc_t + τ_L,t ˇw_h_t h_t + τ_k,t (r_k,t − ∆q_t) ˇk_t−1 x .(38) - Two new steady-state flow items highlighted: - Net seigniorage: ˇm_t − r_d,t x ˇm_t−1, which with r_d = 1 and positive growth rate x represents a cash inflow. - Net cash flow from government credit provision: −ˇf_t + r_f,t x ˇf_t−1, which in steady state is a cash outflow when r_f < x (government keeps real interest rate on treasury credit below growth rate). - Transition one-off stock items and cash flows: - Initial one-off cash flow ˇm_t − ˇf_t is zero at the moment banks purchase new reserve backing, followed instantaneously by government buy-backs and cancellations reducing ˇf_t. - One-off negative cash flow ˇb_g_t − r_t x ˇb_g_t−1 balanced by reduction in ˇf_t due to repayment of government debt held by banks. - One-off negative cash flow from cancellation of principal of private debts against treasury credit: - ∆comp_t = (1−ω_t−1) (ˇℓ_c_t−1 + ˇℓ_a_t−1) + ˇℓ_m_t−1.(39) - Banks distribute part of their stock of equity ∆nw_t to households in the transition period; to avoid a spike in distortionary taxes the government raises a one-off lump-sum tax τ_once_t = ∆nw_t to tax away households’ gain from the bank equity distribution, smoothing government cash flow. - Stock reallocation effects: - Government swaps debt for equity as the new stock of irredeemable government-issued money represents government equity rather than government debt (equity in the commonwealth with returns via lower government interest costs, lower distortionary taxes, and lower financial market monitoring costs). - Treasury credit to banks dramatically reduces the government’s overall net debt. - Non-bank private sector swaps debt for equity via government transfers increasing private sector wealth and reducing debt levels. ### Controlling Boom-Bust Cycles - Additional Considerations - Two qualitative considerations outside the formal model that enhance countercyclical policy effectiveness under the Chicago Plan: 1. Under a 100% reserve requirement banks cannot create their own funds to fuel a lending boom; they must borrow funds from the government at rates that increase in a lending boom and may face much higher capital requirements, making intermittent bouts of optimism and pessimism less likely. 2. Under the present monetary regime, during booms capital adequacy requirements are ineffective because equity injections need not represent savings: Bank B can create money as credit to a household who then injects those funds as equity into Bank A. This is impossible under the Chicago Plan since the banking system cannot create its own funds through credit and government credit is earmarked for investment projects. - Conclusion: a prudential MCAR rule becomes far more effective under the Chicago Plan, akin to the effectiveness of the money growth rule. ### Calibration (Steady State and Key Parameter Values) - Data basis: steady state calibrated on U.S. data for 1990-2006; balance sheet data use final years preceding the crisis. One period = one quarter. - Real economy parameters: - Trend real growth rate x = 2% per annum. - Average inflation rate π at 3% per annum. - Historical average real interest rate on U.S. government debt calibrated at 3% per annum. - Population share of unconstrained households ω = 0.1. - Parameter ι set to obtain unconstrained:constrained per capita consumption ratio of 4:1. - Parameter r = 0.25 (share of monitoring and transactions costs that are real resource costs). - Labor income share calibrated at 61% (α fixed accordingly). - Private investment to GDP ratio = 19% of GDP. - Implied depreciation rate close to 10% per annum. - Investment adjustment cost parameter φ_I = 2.5. - Price and wage markups A_p = A_w = 1.1 (10% markups). - Price and wage stickiness parameters φ_p = 200 and φ_w = 200 imply average duration of price and wage contracts of 5 quarters (Calvo with full indexation). - Unions’ dividends fully distributed to constrained households δ_u = 1. - Government accounts and fiscal calibration: - Government spending to GDP ratio = 18% of GDP. - Historical tax revenue ratios to GDP: labor income taxes 17.6%, capital income taxes 3.2%, consumption taxes 4.6%. - Implied steady state tax rates: τ_L = 0.317, τ_k = 0.259, τ_c = 0.073. - Implied steady state lump-sum transfer τ_ls = 6.6% of GDP; constrained households receive 95% of it f_cc = 0.95. - Calibrated government debt-to-GDP ratio = 80%. - Elasticity of real interest rate w.r.t. government debt: 3 basis points for each percentage point increase in debt-to-GDP ratio. - Degree of automatic stabilizers d_gdp = 0.34 (OECD estimate for United States) used for business cycle comparison; for transition-dynamics illustration a balanced budget rule with d_gdp = 0 is assumed. - All three distortionary tax rates assumed to move in proportion. - Monetary and prudential policy calibration: - Monetary policy rule: m_i = 0.7 and m_π = 2.0. - Prudential rule parameter p_ℓ = 0 except for one post-transition simulation of business cycle shocks. - Household and bank parameters: - Labor supply elasticity 1/η = 1. - Habit persistence v = 0.7. - Basel minimum capital adequacy ratio parameter γ = 8% of risk-weighted assets. - Risk weight for mortgages ζ = 0.5 (intermediate between 35% residential and 100% commercial real estate). - Banks’ average actual capital adequacy ratio = 10.5% (buffer of 2.5% as envisaged under Basel III). - Percentage of banks violating the minimum capital adequacy ratio = 2.5% of all banks per quarter. - Interest rate margins and penalty costs: - Steady state interest rate margin between policy rate i_t and banks’ deposit rate i_d,t = 1%. - Steady state interest rate margin between deposit rate i_d,t and rate that banks would charge on riskless private loans i_ℓ,t = 1.5% per annum. - Implied margin of the riskless private lending rate over policy rate = 0.5%. - Implied penalty costs χ ≈ 0.7% of the value of assets (applies only to small fraction of violating banks); as fraction of total banking system assets penalty equals 0.02% per period in steady state. - Financial system balance sheet sizes: - Overall size = 200% of GDP. - Liabilities = 184.25% of GDP. - Bank equity = 15.75% of GDP. *Source: _wp12202 - 2. Prudential Policy* ### 2010. Gorton (2010) emphasizes that a key component of the shadow banking system is ### _wp12202 - 2010. Gorton (2010) emphasizes that a key component of the shadow banking system is ### Shadow banking scale and role - Repo market estimates for the most recent period range between U.S.$ 10 trillion (gross) according to Hördahl and King (2008) and U.S.$ 12 trillion according to Gorton (2010). - The paper includes a conservative estimate of shadow banking liabilities because these liabilities perform money-like functions and must be included in models of the modern U.S. financial system. - Gorton et al. (2012) characterization: “To the extent that debt is information-insensitive, it can be used efficiently as collateral in financial transactions, a role in finance that is analogous to the role of money in commerce.” ### Calibration of aggregate financial liabilities and loan composition - Adopted compromise calibration: approximately 185% of GDP as the size of the safe-asset liabilities considered in the model. - Matching Flow of Funds and other data: - Non-financial business credit market debt reached 80% of GDP just before the crisis. - Short-term debt (maturity up to one year) for non-financial businesses around 20%-25% (Ueda and Brooks (2011)); steady state short-term or working capital loans ℓ̄m t set equal to 20% of GDP. - Remaining 60% of GDP allocated to long-term or investment loans ℓ̄k t. - Residential mortgages ratio to GDP reached around 80% of GDP prior to the crisis; allocate one quarter (20% of GDP) of mortgage stock to ℓ̄k t (housing component of aggregate investment), taking total investment loans to 80% of GDP. - Remaining 60% of GDP allocated to mortgage loans ℓ̄a t. - Short-term consumer loans set to ℓ̄c t = 20% of GDP in steady state. - Domestic financial system intermediates government debt equal to 20% of steady state GDP (≈ 25% of total outstanding marketable debt). ### Leverage, spreads, and default-rate calibrations - Leverage (debt-to-equity ratios): - Overall non-financial listed U.S. companies around 140% since early 1990s; core manufacturing and services around 110%. - Steady state leverage ratio chosen at 100% for working capital loans and investment loans; consumer loans leverage fixed at 100%. - Mortgage leverage calibrated from Flow of Funds and Fannie Mae; mortgage-free one third of housing stock removed (based on 2005 U.S. census); ratio of mortgages to remaining equity ≈ 200% in two decades prior to crisis used for steady state. - Steady state interest rate spreads over the policy rate (over 3-month U.S. treasury bill rates): - Mortgages: 2% - Consumer loans: 5% - Working capital loans: 3% - Investment loans: 1.5% (deviates from Ashcraft and Steindel (2008) due to inclusion of shadow banking where spreads tend to be lower; commercial paper prior to the crisis averaged less than 0.5%). - Steady state default rates: - Investment loans: 1.5% of all firms per period. - Working capital loans: 3%. - Mortgages: 2.5%. - Short-term household loans: 4%. - Household delinquency context: 15% of households fall into a score range with a delinquency rate of 50% or more; another 12% with delinquency around one third. ### Money demand and interest semi-elasticities - Interest semi-elasticity = percent change in money demand in response to a one percentage point increase in the opportunity cost of holding money. - Adopted semi-elasticities: - Unconstrained households: -1.00 (high elasticity to keep deposit rates from rising sharply during lending booms). - Constrained households and manufacturers: -0.05 (conventional value). - Rationale: low semi-elasticities in a broad-money general equilibrium model produce counterfactual large increases in deposit rates during lending booms; empirical behavior suggests marginal depositors are willing to increase deposits with little increase in deposit rates. ### Liability-side composition and steady state balance sheet - Resulting liability composition implied by assumptions: - Equity = 15.75% of GDP. - Constrained households’ deposits = 40% of GDP. - Manufacturers’ deposits = 40% of GDP. - Unconstrained households’ deposits = 104.25% of GDP. ### Chicago Plan: policy parameters and post-transition calibration - Post-transition policy parameters: - Nominal growth rate of money πm set equal to real growth rate of output x (ensures zero inflation in steady state). - Net nominal interest rate paid on reserves set equal to zero, īd = 1. - Interest rate charged by government on treasury loans to banking system set so banks’ wholesale rate equals government bond rate in steady state, īℓ = ī. - Convergence rates during transition: ρd = 0.25 and ρf = 0.9. - Gross government debt-to-GDP ratio reduced from 80% to 60% following permanent repayment of government debt held by banking system. - Coefficient θ used to determine net government debt-to-GDP ratio set to θ = 0.5. - Steady state nominal (and real) interest rates in Chicago Plan economy: - Government bonds: 1.07% - Treasury credit: 0.49% - Deposits: 0% - Monetary policy rule parameters for treasury credit rate: mi = 0.7 and mπ = 2.0. - Prudential rule pℓ = 0 in baseline; alternative calibration with pℓ = 8 considered for countercyclical policies. - Post-transition Basel ratio for banks maintained at 10.5%; manufacturers’ steady state leverage ratio remains at 0% after debt cancellation in transition. ### Transition dynamics and balance-sheet effects - Transition period mechanics (summary of key impacts): - Banks borrow from treasury to fully back deposits; treasury credit and reserves increase by 184.25% of GDP on first stage. - Principal of banks’ original loans to government and private sector, except investment loans, cancelled against treasury credit in debt buy-back. - Banks pay out part of equity to align net worth with reduced capital adequacy requirements. - Overall deposits drop very slightly long-run (~4% of GDP decline), with household deposits falling and manufacturer deposits rising. - Reserves rise from zero to around 180% of GDP to back deposits. - Loans to private sector and to government drop by 100% and 20% of GDP on impact respectively; bank net worth drops by around 7% of GDP on impact. - Treasury credit initially rises to just over 70% of GDP, later to around 90% of GDP. - Investment loans increase subsequently by almost 20% of GDP gradually. - Share of banks violating MCAR drops from 2.5% to around 0.8% per period. - Monitoring costs as a share of GDP drop from 2.0% to 0.7%. ### Macroeconomic outcomes under the Chicago Plan - Long-run macro gains: - Output eventually approaches a 10% gain for GDP. - Investment increases by 27%. - Consumption eventually increases by almost 5%; short-run consumption initially drops due to investment crowding-out. - Interest rate and fiscal effects: - Gross government debt drops from 80% to 60% of GDP. - Treasury credit jumps to around 70% of GDP on impact and to 90% eventually, making unadjusted net government debt negative; adjusted net government debt b̄rat net,t (with θ = 0.5) drops from 80% of GDP to an eventually much lower but still positive 16% of GDP. - Gradual reduction in real bond and deposit rates of 1.93% per annum; additional 3% per annum reduction in nominal rates due to elimination of steady state inflation. - Real treasury credit rate drops by 1.51% per annum to 0.49% per annum. - Real wholesale lending rates drop by 2.43% per annum. - Retail real rates on investment loans drop by 1.64% per annum (less due to increased corporate leverage in new steady state). - Tax and budgetary effects: - Very large drops in distortionary tax rates: - Labor income tax rate: almost 5 percentage points. - Capital income tax rate: 4 percentage points. - Consumption tax rate: just over one percentage point. - Budgetary impacts (steady state): - Debt service (net nominal interest charges) drops by 4.2% of GDP. - Government deficit ratio reduced by 2.8% of GDP. - Treasury credit requires ongoing budgetary expenditure of 1.3% of GDP (0.49% real rate below 2% economy growth). - Seigniorage collected due to large reserves stock: 3.6% of GDP (reserves over 180% of GDP with zero nominal and real rate on reserves but positive growth). - Seigniorage used to finance reduction in distortionary taxes equal to 3.6% of GDP. - Transfers held constant in real terms and therefore decline by 0.6 percentage points relative to GDP. - Monitoring and inflation considerations: - Monitoring costs fall sharply as debt-free government money replaces private creation of money. - The model permits zero steady state inflation and argues monetarist money-growth rules become feasible and effective. - Under Chicago Plan the policy interest rate is the cost of a specific credit type (treasury credit to banks) and can enter negative territory without the traditional zero lower bound problems, provided treasury credit is strictly constrained to finance investment projects. ### Credit boom-and-bust experiments: pre-transition vs post-transition - Experiment design: - “Good news” shocks εnews t reduce standard deviation of borrower riskiness cumulatively by 60% by end of quarter 12. - At quarter 13 borrowers’ riskiness jumps to 125% of steady state value (from 40% of steady state value), then reverts gradually. - Pre-transition economy (solid line behavior): - Bank loans grow strongly over the boom, by over 50% of GDP; banks create corresponding deposits endogenously. - Decomposition: ~70% of additional lending due to higher mortgage loans; remaining three loan types ~10% each. - Boom outcomes by end of quarter 12: - Investment grows by 2.5% relative to trend. - Consumption grows by 1.5%. - GDP ends just under 2% higher. - Inflation exceeds target by over 3% per annum. - Real policy rate rises by 2% per annum. - Bust outcomes: output drops by over 5%, consumption around 3%, investment well over 10%; banks face large lending losses, capital adequacy ratios drop by well over 2 percentage points, and more than 20% of banks violate MCAR; wholesale real lending rate rises ≈ 2% per annum; average real retail lending rate rises ≈ 5% per annum. - Post-transition Chicago Plan with interest-rate-only policy (dashed blue): - Quantities of credit and money evolve independently; credit increase much smaller as a share of GDP. - Investment loans rise and continue rising after negative shock due to capital stock financing needs; consumption crowded out by investment. - Treasury credit rate swings large, going well into negative territory in real and nominal terms. - Volatility in investment and lending remains high; reversal yields larger valuation losses in capital and higher spikes in retail lending rates compared to pre-transition. - Post-transition with countercyclical quantitative tool (red dotted): aggressive countercyclical adjustments of minimum capital adequacy requirements (MCAR) - Example: banks raise capital adequacy ratio from 10.5% to 15% during the boom. - Wholesale and retail lending rates remain much higher during boom, reducing investment increase to one third of the interest-only scenario. - At reversal, banks are more resilient; reductions in capital adequacy easier; spikes in lending rates are milder and smaller than pre-transition. - Amplitude of GDP fluctuations about half that under other scenarios. - Policy implication: under Chicago Plan, price-based credit policy alone may be insufficient; combining treasury credit rate rule with flexible quantitative lending targets (countercyclical MCAR) stabilizes investment and macro outcomes effectively. ### Key analytical conclusions and policy recommendations - Fisher’s main claims validated by model: 1. Chicago Plan can reduce business cycle volatility from rapid changes in bank credit risk attitudes, but requires appropriate tools (interest-rate rule for treasury credit plus quantitative lending targets). 2. Bank runs can be eliminated because money is debt-free and independent of banks’ credit performance. 3. Government debt net of treasury credit becomes much smaller (adjusted net government debt drops to a much lower but positive fraction of GDP). 4. Private debts can be dramatically reduced because money creation no longer requires simultaneous debt creation. - Additional advantages identified: - Large steady state output gains approaching 10% due to lower real interest rates, lower distortionary taxes, and lower monitoring costs. - Ability to achieve zero steady state inflation without liquidity-trap problems because government controls broad monetary aggregates. - Seigniorage from large reserve stock provides a recurring fiscal revenue source (3.6% of GDP in calibration) that can finance tax reductions or alternative public spending. - Operational policy recommendations under Chicago Plan: - Maintain strict separation between monetary (government-issued, debt-free money) and credit (bank-provided investment loans) functions. - Use a monetary rule for nominal money growth equal to real growth to target zero inflation in steady state. - Set net nominal interest on reserves to zero and manage treasury credit rates to align wholesale lending and government bond rates in steady state. - Use countercyclical capital adequacy requirements (MCAR) as a quantitative tool to limit credit-driven investment booms and stabilize the economy. - Ensure treasury credit is strictly disbursed only to finance investment projects to avoid arbitrage by banks. *Italic source: _wp12202 - 2010. Gorton (2010) emphasizes that a key component of the shadow banking system is (PDF chapter/section).* ### References ### References ### Bibliographic scope and themes - Contains comprehensive bibliographic entries covering monetary theory, banking history and reform, financial crises, macroeconomic modeling, fiscal policy, and financial regulation. - Representative topics and seminal works included: - Monetary theory and history: Allais, M. (1947), Économie et Intérêt; Knapp, G.F. (1924), The State Theory of Money; Smith, A. (1776), The Wealth of Nations; Graeber, D. (2011), Debt: The First 5000 Years. - Banking reform and the Chicago Plan: Fisher, I. (1935), “100% Money: Designed to keep checking banks 100% liquid ...”; Graham, F. (1936), “Partial Reserve Money and the 100 Per Cent Proposal”; Phillips, R. (1994), The Chicago Plan & New Deal Banking Reform. - Financial crises, leverage, and shadow banking: Gorton, G. (2010), “Questions and Answers about the Financial Crisis”; Pozsar, Z., Adrian, T., Ashcraft, A. and Boesky, H. (2010), “Shadow Banking”; Schularick, M. and Taylor, A. (2012), “Credit Booms Gone Bust ... 1870-2008”. - Macroeconomic modeling with financial frictions: Bernanke, B., Gertler, M. and Gilchrist, S. (1999), “The Financial Accelerator ...”; Christiano, L., Eichenbaum, M. and Evans, C. L. (2005), “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy”; Gerali, A., Neri, S., Sessa, L. and Signoretti, F. (2010), “Credit and Banking in a DSGE Model of the Euro Area”. - Fiscal policy, debt, and interest rates: Engen, E.M. and Hubbard, R.G. (2004), “Federal Government Debt and Interest Rates”; Laubach, T. (2009), “New Evidence on the Interest Rate Effects of Budget Deficits and Debt”; Gale, W. and Orszag, P. (2004), “Budget Deficits, National Saving, and Interest Rates”. - Bank capital, regulation, and prudential policy: Benes, J. and Kumhof, M. (2011), “Risky Bank Lending and Optimal Capital Adequacy Regulation”, IMF Working Paper WP/11/130; Van den Heuvel, S. (2005), “The Bank Capital Channel of Monetary Policy”; Angeloni, I. and Faia, E. (2009), “A Tale of Two Policies: Prudential Regulation and Monetary Policy with Fragile Banks”. - Includes working papers, journal articles, books, historical sources, and institutional reports (e.g., Federal Accounting Standards Advisory Board (2012); Federal Bureau of Investigations (2007); Federal Financial Institutions Examination Council (2007)). ### Notable bibliographic details (selected exact entries as listed) - Benes, J. and Kumhof, M. (2011), “Risky Bank Lending and Optimal Capital Adequacy Regulation”, IMF Working Paper WP/11/130. - Bernanke, B., Gertler, M. and Gilchrist, S. (1999), “The Financial Accelerator in a Quantitative Business Cycle Framework”, in: Taylor, J.B., Woodford, M. (eds.), Handbook of Macroeconomics, Volume 1C. Elsevier, Amsterdam, pp. 1341-1393. - Fisher, I. (1935), “100% Money: Designed to keep checking banks 100% liquid; to prevent inflation and deflation; largely to cure or prevent depressions; and to wipe out much of the National Debt”, New York: The Adelphi Company. - Gorton, G., Lewellen, S. and Metrick, A. (2012), “The Safe-Asset Share”, NBER Working Paper No. 17777. - Kumhof, M., Lebarz, C., Rancière, R., Richter, A. and Throckmorton, N. (2012), “Income Inequality and Current Account Imbalances”, IMF Working Paper WP/12/08. - Pozsar, Z., Adrian, T., Ashcraft, A. and Boesky, H. (2010), “Shadow Banking”, Federal Reserve Bank of New York Staff Reports, No. 458. - Reinhart, C. and Rogoff, K. (2009), This Time Is Different: Eight Centuries of Financial Folly, Princeton and Oxford: Princeton University Press. - Ueda, K. and Brooks, R. (2011), “User Manual for the Corporate Vulnerability Utility: The 4th Edition”, International Monetary Fund. ### Figures listed in this unit - Figure 1. Changes in Bank Balance Sheet in Transition Period (percent of GDP) - Figure 2. Changes in Government Balance Sheet in Transition Period (percent of GDP) - Figure 3. Changes in Bank Balance Sheet - Details (percent of GDP) - Figure 4. Transition to Chicago Plan - Bank Balance Sheets (panels include Private Loans/GDP (pp Difference); Treasury Credit/GDP (pp Difference); Net Worth/GDP (pp Difference); Investment Loans/GDP (pp Difference); Mortgage Loans/GDP (pp Difference); Government Bonds/GDP (pp Difference); Working Capital Loans/GDP (pp Difference); Consumer Loans/GDP (pp Difference); Reserves/GDP (pp Difference); Deposits/GDP (pp Difference); Household Deposits/GDP (pp Difference); Corporate Deposits/GDP (pp Difference); Basel Capital Adequacy Ratio (pp Difference); Banks Violating Minimum CAR (pp Difference); Monitoring Costs/GDP (pp Difference)) - Figure 5. Transition to Chicago Plan - Main Macroeconomic Variables (panels include GDP (% Difference); Consumption (% Difference); Investment (% Difference); Nominal Bond Rate (pp Difference); Nominal Deposit Rate (pp Difference); Nominal Treasury Credit Rate (pp Difference); Real Bond Rate (pp Difference); Real Deposit Rate (pp Difference); Real Treasury Credit Rate (pp Difference); Real Wholesale Rate (pp Difference); Real Investment Loans Retail Rate (pp Difference); Inflation (pp Difference); Labor Tax Rate (pp Difference); Capital Tax Rate (pp Difference); Consumption Tax Rate (pp Difference)) - Figure 6. Transition to Chicago Plan - Fiscal Variables (panels include Government Debt/GDP (pp Difference); Gross Debt Service/GDP (pp Difference); Government Deficit/GDP (pp Difference); Net New Treasury Credit/GDP (pp Difference); Seigniorage/GDP (pp Difference); Tax Revenue/GDP (pp Difference); Government Spending/GDP (pp Difference); Lump-Sum Transfers/GDP (pp Difference)) - Figure 7. Business Cycle Properties Pre-Transition versus Post-Transition (panels include GDP (% Difference); Consumption (% Difference); Investment (% Difference); Bank Loans/GDP (pp Difference); Bank Deposits/GDP (pp Difference); Bank Basel Ratio (pp Difference); Nominal Bond Rate (pp Difference); Nominal Deposit Rate (pp Difference); Nominal Treasury Credit Rate (pp Difference); Real Bond Rate (pp Difference); Real Deposit Rate (pp Difference); Real Treasury Credit Rate (pp Difference); Real Wholesale Rate (pp Difference); Real Investment Loans Retail Rate (pp Difference); Inflation (pp Difference)). Legend: __ = Pre-Transition, - - - = Post-Transition, pℓ = 0, .... = Post-Transition, pℓ = 8. *Source: _wp12202 - References* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12202.pdf_