## wp17259 — Tax on the return to capital (KRT) and corporate tax extensions in GIMF

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### Model and key innovations
- Extensions to the Global Integrated Monetary and Fiscal model (GIMF):
  - Introduces a corporate income tax (CIT) that taxes firms’ economic profits from sales.
  - Introduces a corporate cash flow tax (CFT) and a destination-based cash flow tax (DBCFT).
  - Embeds CIT and CFT/DBCFT into a model with a financial accelerator a la BGG (Bernanke, Gertler and Gilchrist (1999)) and related financial frictions.
- Model features:
  - Multicountry DSGE with sticky prices/wages, real adjustment costs, liquidity-constrained households, finite planning horizons (OLG) and incomplete asset markets.
  - Three-region setup: two countries each represent around 1/4 of the world economy and the rest of the world.
  - Fiscal instruments include taxes on labor income, capital returns (KRT), consumption, plus CIT and CFT/DBCFT introduced here.
- Simulation protocol for permanent tax increases:
  - All four business tax rates start at zero.
  - Each tax rate is increased so that on impact it raises additional fiscal revenue of 1 percent of GDP.
  - Tax proceeds redistributed to OLG households as lumpsum transfers.
  - Analysis considers steady-state (long-run) impacts and short-run adjustment.

### Long-run impacts and distortionary properties
- KRT (tax on the return to capital):
  - Permanent introduction reduces desired capital sharply → GDP reduced by roughly 2 percent below baseline.
  - KRT falls exclusively on the required return to capital, severely distorting capital accumulation.
  - Fiscal revenue as a share of GDP is higher than the initial 1 percent of GDP calibration because the decline in the capital stock raises the pre-tax physical return to capital; additional revenue returned as lumpsum transfers.
  - Corporate debt declines in level; leverage ratio remains unchanged in the long run.
  - Net foreign assets (NFA) as a share of GDP is higher in the new steady state; current account increases slightly as a share of GDP.
- CIT (corporate income tax) versus KRT:
  - Qualitatively similar to KRT but quantitatively less damaging to capital and output.
  - CIT taxes both the economic return and corporate rents (under monopolistic competition), making it less distortionary than the KRT.
  - Interest expense deductibility under CIT acts as an implicit debt subsidy, increasing leverage and mitigating negative effects on investment and output.
  - Under CIT private saving falls by more than the decline in capital stock → foreigners hold more domestic assets → small deterioration in the current account.
- CFT and DBCFT:
  - Permanent introduction of CFT or DBCFT is non-distortionary in the long run: they do not reduce capital accumulation or steady-state GDP.
  - CFT/DBCFT fall on cash flows after deducting investment and thus do not tax the required return to capital in steady state.
  - DBCFT differs from CFT only through real exchange rate adjustments: any destination-based competitive gain (loss) is offset by exchange rate appreciation (depreciation) in steady state to maintain external balance.

### Interaction with financial frictions and corporate financing
- Financial accelerator structure:
  - Entrepreneurs finance capital with internal funds and bank loans; banks charge an external finance premium that rises with entrepreneur leverage.
  - Calibration targets (following Kumhof and others (2011)):
    - Leverage ratio (corporate debt to corporate equity): 100 percent in all sectors and regions.
    - Share of firms that go bankrupt in any given year: 8 percent.
    - Steady-state external finance premium, excluding tax effects: 2.5 percent.
  - Introduction of the CIT increases financial-accelerator parameter values (borrower riskiness, cost of bankruptcy, dividend redistribution) to match targets because CIT encourages higher leverage.
    - Borrower riskiness: 0.52 (Extended GIMF with CIT) vs 0.45 (Standard GIMF with KRT)
    - Cost of bankruptcy: 0.38 vs 0.36
    - Dividend redistribution: 0.14 vs 0.13
- Tax interactions with loan contracts:
  - Under KRT: pre-tax return rises so after-tax return is unchanged → no change in ability to repay, external premium, or leverage.
  - Under CIT: interest deductibility reduces entrepreneurs’ tax burden → implicit debt subsidy → after-tax returns can rise → external finance premium falls and optimal leverage increases.
  - CFT changes affect dividend policies and Q (shadow price of capital), producing balance-sheet mismatches that spike leverage and the external finance premium in the short run.

### Short-run (transitional) dynamics, rigidities, and amplification
- Role of nominal and real rigidities plus financial accelerator:
  - With these frictions, introduction of CFT/DBCFT causes temporary contractions in investment and GDP.
  - Without rigidities/financial accelerator, CFT and DBCFT become non-distortionary at all horizons and short-run contraction disappears.
- Transitional dynamics for permanent tax increases:
  - KRT and CIT: both lower after-tax return to capital → investment declines gradually due to adjustment costs; contraction larger under KRT than CIT.
  - Under CIT, monetary policy eases on impact to lower real rates, supporting consumption; under KRT exchange rate depreciates in the short run due to a larger drop in real interest rate.
  - CFT/DBCFT: lower expected dividends reduce Q → Q overshoots downward → entrepreneurs’ net worth falls → leverage spikes → external finance premium rises sharply → investment collapses initially → as leverage falls back, premium declines and investment recovers.
  - DBCFT-specific short-run: the destination-based component immediately affects real exchange rate (appreciation to maintain external balance). Sticky prices limit pass-through, producing short-run asymmetries relative to pure CFT (imports fall more under DBCFT, net exports provide additional temporary demand support).

### Temporary tax cuts and fiscal multipliers (two-year, 1 percent of GDP shocks)
- Experiment: two-year temporary cut in each corporate-related tax, with magnitude "Two-Year 1% of GDP Reduction in all Corporate-Related Taxes."
- Key transmission differences:
  - Temporary cuts to KRT or CIT:
    - Boost capital returns → stimulate business investment and GDP in the short run.
    - For KRT: increases return on capital → higher investment, employment, real wages → consumption up → monetary policy tightens → real interest rate rises → real effective exchange rate appreciates → net exports fall → dampens demand.
    - For CIT: similar but interest deductibility effects alter financial risk premium dynamics and damp some investment gains relative to pure KRT reduction.
  - Temporary cuts to CFT and DBCFT:
    - Can incentivize firms to postpone investment because CFT permits immediate deduction of investment; a temporary reduction in CFT reduces the immediate tax rebate on investment → firms may delay investment → private investment and output can fall in the short run.
    - CFT/DBCFT cuts improve firm value and reduce leverage/external premium, partially offsetting the postponement effect, but overall can lower investment and output temporarily.
    - DBCFT decline produces larger GDP contraction than CFT decline due to destination-based component reducing exporters’ rebates and lowering implicit taxes on imports → exports fall and imports rise → trade balance deteriorates → sharper negative GDP impact.
- Selected two-year multiplier results (Average GDP Impact After First Two Years):
  - Extended version of GIMF (CIT only):
    - Consumption tax: GDP 0.25
    - Labor income tax: GDP 0.26
    - Corporate income tax: GDP 0.12
    - Dest. based cash flow tax: GDP -1.33
  - Standard version of GIMF (KRT only):
    - Consumption tax: GDP 0.26
    - Labor income tax: GDP 0.26
    - Capital return tax: GDP 0.30
- Selected consumption and private investment multipliers (Extended version of GIMF (CIT only)):
  - Transfers to LIQ households: Consumption 0.99 (Avg. after two years), GDP 0.48
  - Government investment: GDP 1.17, Private Invest. 0.68
  - Corporate income tax cut: Private Invest. 0.62 (GDP 0.12, Consumption 0.09)
  - Dest. based cash flow tax cut: Private Invest. -3.50 (Consumption -0.08)
- Comparative insights:
  - Among firm taxes, the largest positive multiplier is for the capital return tax (when operational) followed by the corporate income tax; the DBCFT can deliver negative multipliers in the extended (CIT) specification.
  - Multipliers are broadly similar across model versions but slightly higher with KRT because of tax-base dynamics; stronger financial frictions in the extended version raise investment responses to demand shocks.

### Policy implications and recommendations highlighted
- Long-run neutrality:
  - CFT and DBCFT are non-distortionary in steady state and do not reduce desired capital or steady-state GDP.
  - KRT is the most distortionary tax on investment and output among business taxes commonly modeled.
  - CIT is distortionary but less so than KRT due to taxation of rents and interest deductibility.
- Short-run policy use:
  - Temporary reductions in KRT and CIT can stimulate investment and output in the short run, but effects are temporary and can tighten monetary policy via higher real rates; using these instruments for countercyclical policy is not necessarily optimal.
  - Temporary cuts to CFT/DBCFT can perversely reduce investment and output by encouraging investment postponement; thus these instruments are poor temporary stimulus tools in the presence of investment expensing and adjustment costs.
- Financial-friction considerations:
  - Introducing CIT requires recalibration of the financial accelerator because interest deductibility directly alters debt contracts and the financial premium.
  - Optimal leverage decisions and amplification of tax shocks depend critically on tax treatment of interest and the specification of the financial accelerator.

### Appendix: calibration and algebraic modifications (key numeric targets and representative equations)
- Financial accelerator calibration targets:
  - Leverage ratio: 100 percent.
  - Bankruptcy rate: 8 percent.
  - External finance premium (steady state, excluding tax effects): 2.5 percent.
- Representative illustrative calculation for CFT mechanism:
  - With r = 3 percent, δ = 10 percent, π = 2 percent, ρ = r + π, τ = 30 percent:
    - Present value of tax on investment’s normal return and depreciation = τ·(r+δ)/(ρ+δ-π) = 30%·(3%+10%)/(5%+10%-2%) = 30%.
    - Illustrates why a CFT that fully deducts investment does not tax required return to capital.
- Key modified first-order conditions and dividend expressions preserve tax-rate ratios (τ^CI, τ^CF, τ^KR) and show how taxes enter price-setting and investment rules; under flexible prices or first-order log-linearization tax terms in price-setting equations disappear.

*Source: IMF Working Paper wp17259 (chapter/sections: "Tax on the return to capital (KRT)"; GIMF description; CIT, CFT, DBCFT comparisons; financial accelerator calibration; APPENDIX II fiscal multipliers).*

### 1. Tax on the return to capital (KRT) ............................................................................. 11

### 1. Tax on the return to capital (KRT)

### Key innovations and scope
- Documents changes to the International Monetary Fund’s Global Integrated Monetary and Fiscal model (GIMF) to incorporate:
  - a corporate income tax (CIT) that taxes firms’ economic profits from sales, and
  - a corporate cash flow tax (CFT) that permits a destination-based component (DBCFT).
- Extends GIMF beyond the original single business tax (KRT) specification to analyze richer corporate tax bases and their macro-financial interactions.
- Introduces the CIT and CFT/DBCFT into a model with a financial accelerator a la BGG (Bernanke, Gertler and Gilchrist (1999)) and related financial frictions.

### Long-run impacts and distortionary properties
- Permanent increases in the KRT and the CIT are distortionary in the long run:
  - Lead to notable reductions in business investment and GDP.
  - The reduction is largest under a KRT relative to the CIT because:
    - The KRT falls exclusively on the return to capital (severely distorting capital accumulation).
    - The CIT falls on returns to capital and on corporate rents (the latter being less distortionary).
- Permanent changes to the CFT and the DBCFT are not distortionary in the long run:
  - Their long-run introduction does not reduce capital accumulation or GDP in steady state.

### Interaction with financial frictions and corporate financing
- The CIT interacts richly with financial frictions:
  - Interest expense deductibility under the CIT acts as an implicit debt subsidy and is internalized in debt contracts, reducing the financial premium.
  - Removing interest deductibility amplifies the distortionary impact of the CIT.
  - Because the CIT affects the financial contract directly, financial accelerator parameters need to be recalibrated.
- CFT changes affect dividend payment policies and lead to short-term changes in business investment and the price of capital:
  - These affect firm value and create balance-sheet mismatches that alter the financial risk premium.
- Overall, optimal leverage decisions depend on the CIT rate through the interaction of interest deductibility, debt contracts, and the financial premium.

### Short-run (transitional) dynamics and rigidities
- The introduction of a CFT or DBCFT results in temporary contractions in business investment and GDP in the short run due to nominal and real rigidities.
  - In the absence of these rigidities, the contractionary short-run effect from introducing these taxes is eliminated; their introduction becomes non-distortionary at all horizons.
- The border-adjustment component that distinguishes the CFT from the DBCFT manifests through real exchange rate movements:
  - Any competitive gains (losses) from the destination-based component are eradicated by an appreciation (depreciation) of the exchange rate to maintain external sector equilibrium.

### Temporary tax cuts and fiscal multipliers
- Temporary (two-year) cuts to all corporate-related taxes are analyzed to illustrate each tax’s effectiveness as a stimulus instrument:
  - Reductions to the KRT or the CIT boost capital returns and stimulate business investment and GDP in the short run.
  - Cuts to the CFT and the DBCFT create short-run incentives that lower private investment and thus output:
    - Because these taxes fall on corporate cash flows after deducting investment expenditures, a temporary reduction in their rate acts as an incentive to delay investment until the tax deduction returns to its previously higher level.
- The paper documents equilibrium properties, transmission mechanisms, and (fiscal) multipliers associated with the new taxes and compares them to multipliers reported in Anderson and others (2013).

### Model, calibration and literature context
- Few DSGE papers have previously introduced a proper CIT; even fewer examine CIT or CFT interactions with financial frictions of the BGG type.
- The paper recalibrates the financial accelerator block to account for CIT effects on debt contracts and the financial premium.
- The CFT/DBCFT introduction permits analysis of destination-based tax implications in a general equilibrium setting and their interaction with financial frictions.

*Source: IMF Working Paper wp17259 (chapter: "Tax on the return to capital (KRT)")*

### Section III. Section IV presents the key transmission mechanism of all corporate taxes

### wp17259 - Section III. Section IV presents the key transmission mechanism of all corporate taxes

### Summary of the Global Integrated Monetary and Fiscal Model (GIMF)
- GIMF is a multicountry DSGE model with optimizing behavior by households and firms, and full intertemporal stock-flow accounting.
- Frictions: sticky prices and wages, real adjustment costs, liquidity-constrained households, finite-planning horizons of households.
- The assumption of finite horizons allows well-defined steady states where countries can be long-run debtors or creditors and permits study of transitions between steady states driven by fiscal policy and private saving behavior.
- Non-Ricardian features produce non-neutrality in both spending-based and revenue-based fiscal measures; fiscal policy can stimulate short-run activity but sustained government deficits crowd out private investment and net foreign assets.
- Asset markets are incomplete: government debt is only held domestically as nominal, non-contingent, one-period domestic-currency bonds; internationally traded assets are nominal, non-contingent, one-period U.S. dollar bonds issued by the U.S. government and private agents.
- Firms are domestically owned; equity is not traded domestically; households receive lump-sum dividend payments.
- The model used comprises 3 regions (two countries that represent around 1/4 of the total world economy each, plus the rest of the world) to analyze regional and global policy spillovers.

### Household Sector
- Two household types:
  - Overlapping-generation households (OLG) that optimize over a 20-year planning horizon.
  - Liquidity-constrained households (LIQ), who do not save and have no access to credit.
- All households pay direct taxes on labor income, indirect taxes on consumption spending, and a lump-sum tax.
- OLG households save via domestic government bonds, international U.S. dollar bonds, and fixed-term deposits; aggregate consumption is a function of financial wealth and the present discounted value of after-tax wage and investment income.
- LIQ households: consumption equals current net income; marginal propensity to consume out of current income is unity.
- For OLG households, a tax cut has a short-run positive effect on output even if matched by future tax increases that leave government debt unchanged in the long run, because OLG households discount future tax liabilities at a higher rate than the market rate of interest.
- Increases in the interest rate negatively affect consumption mainly through wealth valuation; the intertemporal substitution effect is moderate and calibrated to empirical evidence.

### Production Sector
- Firms produce tradable and nontradable intermediate goods; firms are managed according to preferences of finitely-lived household owners (finite planning horizons).
- Firms face nominal price rigidities and real adjustment costs in hiring and investment; they pay capital income taxes, wages, and dividends to OLG households.
- Retained earnings are insufficient to fully finance investment; firms borrow from financial intermediaries and face bankruptcy/auditing costs if earnings fall short.
- Firms operate in monopolistically competitive markets; goods prices contain a markup over marginal cost; exports priced to local destination markets; imports face quantity adjustment costs.
- Government capital (public infrastructure) is an input and augments productivity.

### Financial Sector
- Limited menu of financial assets: one-period domestic nominal government bonds; banks offer one-period fixed-term deposits; OLG households may issue/purchase tradable U.S.-dollar-denominated obligations.
- Banks pay market rate on deposits and charge a risk premium on loans; lending rate includes an external financing premium that varies directly with the debt-to-equity (leverage) ratio — the financial accelerator effect.
- Non-linearities imply steep increases in the risk premium for large negative shocks to net worth.
- Uncovered interest parity may not hold due to country risk premiums, producing deviations between interest rates across regions.

### International Dimensions and Spillovers
- All bilateral trade flows and relative prices (including exchange rates) are explicitly modeled and calibrated to match recent steady-state data flows.
- International linkages are driven by global saving and investment decisions, producing uniquely defined current account balances and net foreign asset positions for each region.
- Net foreign asset positions are represented by nominal non-contingent one-period bonds denominated in U.S. dollars.
- Magnitude of international trade linkages and uncovered interest parity, along with long-term movements in the world real interest rate, determine spillover magnitudes.

### Fiscal and Monetary Policy in GIMF
- Fiscal instruments: consumption or investment government spending, lumpsum transfers (to all households or targeted to LIQ), taxes on labor income, capital returns, consumption, and additionally corporate income and cash flow taxes in this paper; tariffs may also be revenue sources.
- Government investment augments public infrastructure, which depreciates at a constant rate.
- A fiscal policy rule ensures long-run sustainability (debt-to-GDP ratio converges to target) and allows short-run countercyclical policy and automatic stabilizers.
- Monetary policy: central bank uses an inflation-forecast-based interest rate rule, varying the gap between actual policy rate and long-run equilibrium rate to target inflation.

### Permanent changes to all business taxes: simulation design and limitations
- Two sets of simulations: (i) permanent increase in each business tax (presented in Section III), (ii) temporary decrease in each corporate tax (presented in Section IV).
- All simulations use a three-region GIMF calibrated so two countries each represent around 1/4 of the total world economy and the rest of the world.
- Several channels are omitted due to model structure: multinational firm behavior (transfer pricing, patent relocation, financial structure changes, production relocation and profit shifting) and balance-sheet effects of exchange rate movements owing to simplifying assumptions about currency denomination of foreign liabilities.
- The introduction of CIT and CFT/DBCFT affects firms, financial intermediaries, and government directly and households indirectly; after-tax profits (and dividends) are lower, financial intermediaries’ risk premia on loans are affected, and entrepreneurs’ balance sheets and debt risk premia are altered.
- Simulation protocol for permanent tax increases:
  - All four business tax rates are assumed to be zero initially.
  - Each tax rate is increased so that on impact it raises additional fiscal revenue of 1 percent of GDP.
  - No other taxes are changed.
  - Tax proceeds are redistributed to OLG households as lumpsum transfers.
  - The policy change is understood to be permanent; analysis focuses first on long-run (steady-state) impacts and then on short-run adjustment.

### Long-run impact from permanent introduction of a tax on the return to capital (KRT)
- Key mechanism:
  - Firms reduce investment sharply as desired capital is revised down because the effective return to capital declines after the tax.
  - Lower capital stock reduces the marginal product of labor and real wages, which lowers household disposable income and human wealth, leading to lower consumption.
  - Lower capital stock implies lower potential output; GDP is reduced by roughly 2 percent below the initial baseline.
  - With permanently lower output and domestic demand, imports fall and the real effective exchange rate is appreciated in the new steady state to maintain external equilibrium.
- Fiscal revenue and wealth effects:
  - The decline in the capital stock is large enough that the pre-tax physical return to capital rises so that the new after-tax return equals the return on capital prior to the imposition of the tax.
  - Fiscal revenue as a share of GDP is higher than the initial 1 percent increase the tax rate was calibrated to achieve; the additional revenue is returned to households as lumpsum transfers.
- Financial and external balance effects:
  - Lower capital stock reduces firms’ borrowing needs and corporate debt declines.
  - The leverage ratio remains unchanged in the long run.
  - With lower real wages, households save less in the new steady state, but private savings do not fall as much as the decline in the capital stock; households replace some domestic assets with foreign assets.
  - Net foreign assets as a share of GDP is higher in the new steady state, supported by a small increase in the current account as a share of GDP.
- Additional steady-state magnitudes shown in the accompanying figure (Figure 1) include percentage or percentage-point differences for: Real GDP, Real Investment, Real Consumption, Real Imports, Real Exports, Real Effective Exchange Rate (% difference, +=depreciation), Private Saving/GDP (% pt difference), NFA/GDP (% pt difference), Physical Return to Capital (% pt difference), External Finance Premium (% pt difference), Corporate Debt (% difference), and Leverage (% pt difference).

*Source: wp17259, Section III (GIMF description and permanent KRT simulation results).*

### 2. The corporate income tax (CIT)

### 2. The corporate income tax (CIT)

### Comparative macroeconomic impact: CIT versus KRT
- The qualitative macroeconomic impact of a permanent CIT increase is broadly similar to that of a KRT, but the quantitative impacts differ markedly.
- The imposition of the CIT is far less deleterious on capital accumulation and overall economic activity than the KRT for two main reasons:
  - Model structure: capital is traded in a perfectly competitive market so the KRT does not tax rents and falls only on the economic return required to make capital investment worthwhile, making the KRT highly distortionary. The CIT taxes both the economic return under perfect competition and the rents that arise because goods-producing firms operate under monopolistic competition, reducing distortions of underlying economic incentives.
  - Interest deductibility: under the CIT, interest expenses are deductible. This interacts with the model’s financial accelerator to partially offset the CIT’s distortionary impact via an increase in leverage.
- One notable difference relative to the KRT is net foreign assets (NFA): under the CIT private saving falls by more than the decline in the capital stock and foreigners are required to hold some domestic assets, producing a small deterioration in the current account.

### Interaction of the financial accelerator and the CIT
- Model structure:
  - Entrepreneurs own capital, rent it to firms each period, and finance part of capital accumulation with bank loans.
  - Entrepreneurs face an idiosyncratic shock to returns before repaying bank loans; sufficiently negative shocks can cause bankruptcy. Banks that take over wealth upon bankruptcy incur monitoring costs.
  - Entrepreneurs choose between internal funding (paying an internal finance premium, or equity premium) and external funding (bank loans). The cost of capital is a weighted average of these costs.
  - Banks charge an external finance premium over the risk-free rate to cover bankruptcy costs; this premium increases with the entrepreneur’s leverage ratio.
- Key relationships (as illustrated in Figure 3):
  - The leverage ratio is a decreasing function of the idiosyncratic shock variance and monitoring cost.
  - Bankruptcy rates are an inverted U-shaped function of idiosyncratic shock variance: from low uncertainty (high leverage), marginal increases in uncertainty raise bankruptcy rates, but sufficiently high uncertainty reduces leverage and thus bankruptcy rates.
  - Lower idiosyncratic uncertainty or lower monitoring costs lead banks to extend more credit, increasing leverage and reducing the cost of capital.
- How taxes affect loan terms:
  - Taxes are levied on entrepreneurs’ returns and, all else equal, lower the ability to repay banks.
  - Under the KRT, the pre-tax return on capital rises sufficiently to leave the after-tax return unchanged; there is no change in ability to repay, external risk premium, or leverage.
  - Under the CIT, deductibility of interest expenses reduces entrepreneurs’ tax burden, representing an implicit debt subsidy that can increase after-tax returns and reduce the external finance premium. This modifies the optimal loan contract and increases the optimal leverage ratio.
  - Figure 3 illustrates an upward shift of the leverage ratio: the blue line is the optimal debt contract with the CIT rate at zero and the red line is the optimal debt contract with the CIT rate at 30 percent.

### Quantitative role of the financial accelerator
- The presence of the financial accelerator materially mitigates the negative effects of the CIT:
  - Figure 4 comparison: the presence of the financial accelerator reduces the negative impact of the CIT on real activity by more than half, primarily through CIT interest deductibility raising corporate leverage and sustaining investment and the capital stock.
  - A smaller reduction in the capital stock implies less decline in marginal product of labor, real wages, consumption, and imports.

### Illustrative accounting example of the CFT mechanism (contrast)
- The text provides an illustrative calculation (for the CFT example) preserving parameter values:
  - Assume real interest rate r = 3 percent, depreciation rate δ = 10 percent, inflation π = 2 percent, discount rate ρ = r + π, and tax rate τ = 30 percent.
  - The present value of the tax on the investment’s normal return and depreciation equals τ·(r+δ)/(ρ+δ-π) = 30%·(3%+10%)/(5%+10%-2%) = 30%, which exactly equals the corporate tax rate.
  - (This illustrates why a Cash Flow Tax (CFT) that fully deducts investment expenditure does not tax the required return to capital and thus does not reduce firms’ desired capital stock.)

### Implications highlighted in the chapter
- CIT vs KRT: CIT is less distortionary on capital accumulation because it taxes rents and allows interest deductibility; KRT is more distortionary because it falls only on the required return to capital.
- Financial accelerator effect: interest deductibility under the CIT reduces the external finance premium and raises leverage, cushioning investment and output declines.
- External balance: under the CIT, private saving can fall by more than capital declines, increasing foreign holdings of domestic assets and slightly deteriorating the current account.

*Source: wp17259 - 2. The corporate income tax (CIT)*

### 4. The Cash Flow Tax vs a Destination-Based Cash Flow Tax (DBCFT)

### 4. The Cash Flow Tax vs a Destination-Based Cash Flow Tax (DBCFT)

### Main comparison: DBCFT vs CFT
- The addition of the destination-based component to the cash flow tax only has implications for the real exchange rate; all other macro impacts remain unchanged relative to the CFT.
- Under a destination-based system, sales of exporting firms in foreign markets are not taxed; domestic inputs continue to give the right to a tax deduction, creating a tax benefit for exporters that, under monopolistic competition, is eventually passed-through into a lower export price in the long run.
- For importing firms, the cost of imported intermediate inputs is no longer deductible from their tax base under a destination-based tax, so the price of goods entering the taxing country is increased by the tax as they enter. The destination-based component thus reproduces the price implications of a depreciation of the exchange rate.
- Maintaining balance in the current account and desired holdings of net foreign assets requires a compensatory real appreciation of the currency in response to the destination-based treatment.

### Long-run impacts (summary of Figure 6)
- The long-run DBCFT simulations relative to the CFT simulations satisfy the conditions for border-adjustment neutrality on real variables within the framework referenced; however, short-run neutrality does not hold during the transition to the long-run equilibrium.
- Figure 6 variable axis ranges and labels (as presented):
  - Real GDP (% difference): axis ticks shown -2.0, -1.5, -1.0, -0.5, 0.0, 0.5
  - Real Investment (% difference): axis ticks shown -6, -5, -4, -3, -2, -1, 0, 1
  - Real Consumption (% difference): axis ticks shown -1.4, -1.2, -1.0, -0.8, -0.6, -0.4, -0.2, 0.0, 0.2
  - Real Imports (% difference): axis ticks shown -0.5, -0.4, -0.3, -0.2, -0.1, 0.0, 0.1, 0.2
  - Real Exports (% difference): axis ticks shown -1.6, -1.4, -1.2, -1.0, -0.8, -0.6, -0.4, -0.2, 0.0
  - Real Effective Exchange Rate (% difference, +=depreciation): axis ticks shown -4.5, -4.0, -3.5, -3.0, -2.5, -2.0, -1.5, -1.0, -0.5, 0.0
  - Private Saving/GDP (% pt difference): axis ticks shown -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8
  - NFA/GDP (% pt difference): axis ticks shown -1.5, -1.0, -0.5, 0.0, 0.5, 1.0, 1.5, 2.0, 2.5
  - Physical Return to Capital (% pt difference): axis ticks shown -0.1, 0.0, 0.1, 0.2, 0.3, 0.4
  - External Finance Premium (% pt difference): axis ticks shown -0.4, -0.3, -0.2, -0.1, 0.0, 0.1
  - Corporate Debt (% difference): axis ticks shown -6, -5, -4, -3, -2, -1, 0, 1, 2
  - Leverage (% pt difference): axis ticks shown 0, 1, 2, 3, 4, 5, 6

### Transitional dynamics: key mechanisms and short-run differences (summary of Figure 7)
- KRT and CIT responses:
  - Permanent increases in both the KRT (blue) and the CIT (red) lower the after-tax return to capital, prompting firms to cut investment; adjustment costs make investment decline gradually.
  - The decline in investment and the capital stock is significantly lower under a CIT relative to a KRT because the CIT is less distortionary and allows for deductible interest expensing, which interacts with the financial accelerator mechanism.
  - Monetary policy is eased on impact to produce a decline in the real rate; this supports consumption in the near term under a CIT and mitigates its drop under a KRT.
  - Under a KRT, the exchange rate depreciates in the short run due to the large decline in the real interest rate; under a CIT, the exchange rate appreciates slightly on impact. Eventually the exchange rate appreciates under both taxes as fewer exports are required to pay for the lower desired import bundle.
- CFT and DBCFT short-run dynamics:
  - Permanent increases in the CFT (black) and the DBCFT (green) have no material impact on GDP in the long run, but both cause short-run output contractions owing to declines in investment and consumption arising from nominal and real rigidities plus the financial accelerator.
  - A permanent increase in the CFT/DBCFT reduces the value of firms by lowering expected after-tax dividend streams, captured by a fall in Q (the shadow price of capital). Investment adjustment costs cause Q to overshoot in the near term.
  - The initial fall in Q reduces entrepreneurs’ assets, causing leverage to spike up and the external finance premium to increase in the near term, which sharply reduces investment initially. As firms reduce borrowing and leverage returns to baseline, the external finance premium declines and investment recovers.
  - Consumption falls in the short term because lower investment reduces labor demand and real wages (affecting hand-to-mouth consumers) and reduces both human wealth and financial wealth for OLG consumers despite transfer payments from additional tax revenue.
  - Monetary policy is eased in response to weaker domestic demand, producing a drop in real rates that leads to a depreciation in the real exchange rate under a pure cash flow tax, which supports exports and improves net trade temporarily; the external surplus then returns the exchange rate close to its initial position (with a slight appreciation due to additional saving by OLG households).
- DBCFT-specific short-run differences:
  - The propagation of the DBCFT is similar to the CFT on domestic demand (initial drops in investment and consumption).
  - The destination-based component immediately affects the real exchange rate, which appreciates to help maintain external stability.
  - Due to sticky prices, the immediate appreciation is not fully passed-through into export and import prices; imports initially fall by more under a DBCFT relative to a CFT and net exports provide additional demand support in the near term, moderating the short-run fall in output.
  - Despite temporary improvement in export competitiveness from the tax, exports do not increase as much relative to the pure cash flow tax, partly because production substitutes away from imported goods toward domestic goods; this implies less downside pressure on domestic prices, which fall by less under a DBCFT relative to a CFT.
  - These short-run asymmetries imply that the destination-based component is not neutral in this version of GIMF because export and import price changes to exchange rate movements are not symmetrical when import prices are set excluding the border adjustment (equivalent to the case labelled “border adjustment post-border”).

### Figure 7 variable axis ranges and labels (as presented)
- X-axis denotes years (0 2 4 6 8 10 12 14 16 18 20).
- Real GDP (% difference): axis ticks shown -2.0, -1.5, -1.0, -0.5, 0.0, 0.5
- Real Investment (% difference): axis ticks shown -10, -8, -6, -4, -2, 0, 2
- Real Consumption (% difference): axis ticks shown -1.5, -1.0, -0.5, 0.0, 0.5
- Real Exports (% difference): axis ticks shown -2, -1, 0, 1, 2
- Real Effective Exchange Rate (% difference, +=depreciation): axis ticks shown -6, -4, -2, 0, 2, 4
- NFA/GDP (% pt difference): axis ticks shown -0.5, 0.0, 0.5, 1.0, 1.5, 2.0
- Current Account Balance/GDP (% pt difference): axis ticks shown -0.1, 0.0, 0.1, 0.2, 0.3, 0.4
- Physical Return to Capital (% pt difference): axis ticks shown -0.5, 0.0, 0.5, 1.0, 1.5, 2.0
- Corporate Debt (% difference): axis ticks shown -6, -4, -2, 0, 2, 4
- Leverage (% pt difference): axis ticks shown -5, 0, 5, 10, 15
- Private Saving/GDP (% pt difference): axis ticks shown -1.2, -0.8, -0.4, 0.0, 0.4
- Real Imports (% difference): axis ticks shown -2.5, -2.0, -1.5, -1.0, -0.5, 0.0, 0.5

*Source: wp17259 - 4. The Cash Flow Tax vs a Destination-Based Cash Flow Tax (DBCFT).*

### 1. On the interaction between the financial accelerator, rigidities and taxes

### 1. On the interaction between the financial accelerator, rigidities and taxes

### Interaction of financial accelerator, nominal/real rigidities, and taxes
- The presence of the financial accelerator plus nominal and real rigidities materially alters short-run transmission of different taxes.
- Without the financial accelerator or nominal/real rigidities:
  - The corporate income tax (CIT) interacts with the financial accelerator, mitigating the long-run impact of a tax increase; hence the distortionary effect of the CIT is larger without financial frictions.
  - Prices and quantities adjust more rapidly, notably investment.
  - There are no short-run negative impacts on activity from either the cash-flow tax (CFT) or the destination-based cash-flow tax (DBCFT). For the DBCFT, real exchange rate appreciation is passed through immediately into higher export and lower import prices, fully offsetting short-run competitiveness gains from the destination-based component.

### Transient (two-year) changes to corporate-related taxes in GIMF: simulation setup
- Experiment: two-year temporary cut in the KRT, the CIT, the CFT and the DBCFT.
- All reported results are deviations from the steady-state baseline.
- Two key simulation assumptions:
  - To maintain a debt-to-GDP target in the long run, government adjusts general lump sum transfers which fall on both OLG and LIQ households.
  - All corporate tax revenues are raised via the tax that is being reduced temporarily with all other corporate taxes set to zero. Consequently:
    - When analyzing the CIT, the KRT, the CFT and the DBCFT rates are set to zero.
    - When analyzing the CFT and the DBCFT, the KRT and the CIT rates are set to zero.
- The KRT, the CIT, the CFT and the DBCFT all work via the corporate sector.
- Policy shock magnitude in Figure 9: Two-Year 1% of GDP Reduction in all Corporate-Related Taxes.

### Mechanisms and comparative effects of temporary reductions
- Reduction in the KRT (blue line):
  - Increases the return on capital → stimulates investment, employment, and real wages.
  - Higher employment and wages raise labor income → stimulates consumption.
  - Domestic demand pressures raise the price for domestically produced goods → monetary authority tightens policy.
  - Higher real interest rate increases cost of capital → dampens private investment and offsets consumption impact.
  - Real interest rate increase leads to appreciation of the real effective exchange rate → lowers import prices, raises export costs → imports increase, exports decrease → net exports reduce, damping demand.

- Reduction in the CIT (red line):
  - Similar to KRT reduction: increases returns from capital, supporting investment and OLG consumption (after-tax dividends increase).
  - Unlike KRT, CIT reduction reduces the rebate received by loss-making entrepreneurs → dampens some reduction to the financial risk premium that would stem from stronger activity → dampens positive investment impact.
  - Overall activity increase → higher labor demand, higher real wages → domestic prices increase → monetary authority slightly raises policy rate → higher real rates → appreciation of real effective exchange rate → deteriorates net export position, damping demand pressures.

- Temporary reductions to the CFT/DBCFT:
  - Can create important distortions as firms may postpone investment since each unit of investment temporarily receives a smaller tax rebate.
  - Lower tax rate still yields higher after-tax profits and improves firm value → reduces leverage and the external finance premium → improved financing costs help dampen the contraction in investment.
  - Investment decline reduces labor demand → lower real wages.
  - Lower labor income plus reduced government transfers (from lower tax revenue) reduce liquidity-constrained agents’ consumption → further reduces domestic demand.
  - Domestic firms’ marginal costs fall → domestic prices fall → monetary authority reduces policy rate → leads to depreciation in the real exchange rate.

- CFT versus DBCFT:
  - GDP contraction is larger for a DBCFT decline relative to a simple CFT.
  - DBCFT decline: destination-based part lowers tax rebate for exporters and lowers implicit taxes on imports. Even with a temporary depreciation of the real effective exchange rate (partially passed through due to sticky prices), exports fall and imports increase → trade balance deteriorates → sharp negative impact on GDP.
  - Under the CFT, the current account improves as imports fall in response to lower domestic demand.

- Policy note:
  - The temporary reduction in the KRT and CIT reduces distortions only temporarily. Using both instruments to temporarily reduce distortions during periods of deficient demand will not be optimal; other instruments for countercyclical policy should be deployed instead.

### Long-run neutrality and relative distortionary effects (conclusions)
- Taxes on the return to capital (KRT), typically the only business tax in DSGE models, are by far the most distortionary taxes on investment and hence output.
- Corporate income taxes (CIT) are also highly distortionary, though interaction with financial frictions and interest expense deductibility mitigates some distortionary impact.
- Cash-flow type taxes (CFT), including DBCFT, are not distortionary in the long run because they fall exclusively on rents and thus do not alter the economy’s desired level of capital. Adjustment costs and the financial accelerator can, however, cause short-run falls in investment.

### Appendix I — calibration of the financial accelerator block (key calibration targets and changes)
- Calibration strategy follows Kumhof and others (2011): choose parameters for firm riskiness, monitoring costs and the share of net worth distributed as dividends to fix three financial variables: firm leverage, firm bankruptcy rate, and external finance premium.
- Calibration targets (same values as Kumhof and others (2011)):
  - Leverage ratio (ratio of corporate debt to corporate equity): 100 percent in all sectors and regions.
  - Share of firms that go bankrupt in any given year: 8 percent.
  - Steady-state external finance premium, excluding any tax effects: 2.5 percent.
- Introduction of the CIT increases the financial accelerator parameter values to strengthen amplification effects (makes investment more sensitive to financial frictions) because the CIT, relative to the KRT or the DBCFT, encourages entrepreneurs to increase leverage; to match prior financial-variable targets, financial-friction parameters must increase.
- Table A: Financial Accelerator Parameters (Extended version of GIMF with CIT (τBI) only vs Standard version of GIMF with KRT (τK) only)
  - Borrower riskiness: 0.52 vs 0.45
  - Cost of bankruptcy: 0.38 vs 0.36
  - Dividend resdistribution: 0.14 vs 0.13

*Source: IMF Working Paper wp17259 — "On the interaction between the financial accelerator, rigidities and taxes" (GIMF simulations and model appendix).*

### APPENDIX II: AN UPDATE ON GIMF FISCAL MULTIPLIERS

### APPENDIX II: AN UPDATE ON GIMF FISCAL MULTIPLIERS

### Overview and modeling setup
- A three-region version of GIMF comprising the United States, the European Union and the Rest of the World is used to compare with Anderson and others (2013).
- All fiscal experiments are undertaken on the US block of the model.
- The qualitative propagation mechanisms for the seven fiscal instruments in the previous version of GIMF remain largely unchanged; brief descriptions and multipliers are presented for nine fiscal instruments.
- Notes on model structure and limitations (from Appendix III excerpt):
  - The module for raw materials is switched off; labor and capital are the only inputs of production.
  - No multinational firm behavior, no transfer pricing, no relocation of production, and no balance-sheet exchange-rate valuation effects due to simplifying assumptions.
  - GIMF is an OLG model with two household types (OLG and LIQ); no detailed distributional heterogeneity beyond that.
  - Rational expectations and perfect foresight are assumed; flexible prices (including the real exchange rate) immediately adjust to changes in tax rates.

### Two-Year Government Expenditure Expansions — transmission and general effects
- Aggregate demand increases directly for government consumption and investment, and indirectly via households’ income for transfers.
- Domestic and imported components of private and government goods imply notable effects in domestic and external sectors.
- Demand for final domestic goods increases demand for domestic labor → raises wages → raises marginal costs → drives up prices of domestically produced goods.
- U.S. monetary authority raises the nominal policy interest rate → higher real interest rates.
  - Higher real interest rates increase the cost of capital → dampen private investment demand.
  - Higher real interest rates partially offset higher incomes’ effect on household consumption.
- Automatic fiscal stabilizers operate: transfers adjust to dampen private demand.
- Real interest rate increase appreciates the U.S. real effective exchange rate:
  - Lowers import prices for U.S. residents → increases U.S. demand for imports.
  - Raises cost of U.S. exports abroad → decreases foreign demand for U.S. goods.
  - Net impact: temporary deterioration in the current account.
- Government investment has the largest expenditure multiplier because the government capital stock raises private sector productivity.
- Transfers have the smallest multipliers; transfers to LIQ agents have higher multipliers than general transfers due to higher propensity to consume.

### Table B — Government Expenditure Multipliers (Average GDP Impact After First Two Years)
- Extended version of GIMF (CIT only)
  - Gov’t Consumption: GDP 0.83
  - Gov’t Investment: GDP 1.17
  - General Transfers: GDP 0.12
  - Transfers to LIQ households: GDP 0.48
  - Consumption (Gov’t Consumption): 0.09
  - Consumption (Gov’t Investment): 0.45
  - Consumption (General Transfers): 0.29
  - Consumption (Transfers to LIQ households): 0.99
  - Private Invest. (Gov’t Consumption): 0.05
  - Private Invest. (Gov’t Investment): 0.68
  - Private Invest. (General Transfers): 0.06
  - Private Invest. (Transfers to LIQ households): 0.04
- Standard version of GIMF (KRT only)
  - Gov’t Consumption: GDP 0.84
  - Gov’t Investment: GDP 1.18
  - General Transfers: GDP 0.12
  - Transfers to LIQ households: GDP 0.48
  - Consumption (Gov’t Consumption): 0.13
  - Consumption (Gov’t Investment): 0.49
  - Consumption (General Transfers): 0.29
  - Consumption (Transfers to LIQ households): 1.01
  - Private Invest. (Gov’t Consumption): 0.03
  - Private Invest. (Gov’t Investment): 0.62
  - Private Invest. (General Transfers): -0.03
  - Private Invest. (Transfers to LIQ households): 0.02

- Comparative notes:
  - Multipliers are relatively similar across the two model versions, but ever so slightly higher in the version with capital taxes (KRT) versus corporate income tax (CIT) due to differences in how the tax base evolves.
  - Impact on investment is higher in the new version of GIMF because financial frictions are stronger, so domestic demand expansion propagates more strongly.

### Two-Year Decrease in Taxation — transmission and general effects
- Temporary cuts to consumption taxes, labor income taxes or corporate income taxes produce modest GDP boosts with multipliers well below unity.
- Consumption and labor income tax cuts primarily affect households (consumption); capital income tax cuts primarily affect firms (investment).
- Consumption tax cuts: reduce the price households pay for consumption goods → boost disposable real income and consumption (notably LIQ households).
- Labor income tax cuts: raise after-tax labor income → boost consumption; labor supply increases putting downside pressure on real wages and marginal costs.
- Capital income tax cuts: raise return on capital → induce firms to invest more; households receive additional dividends → private consumption accelerates.
  - Stronger private demand raises labor demand → increases marginal cost and domestic prices → monetary authority slightly raises nominal policy rate → higher real interest rate increases cost of capital → dampens private investment and offsets some consumption gains.
- Real interest rate increase appreciates U.S. real effective exchange rate → lowers import prices and raises export prices → temporary deterioration in current account.
- Automatic fiscal stabilizers: transfers decline to dampen private demand.
- Multipliers are slightly larger when capital return taxes (KRT) are operational instead of corporate income taxes (CIT) because of differences in tax base dynamics and rebate channels.

### Table C — Tax Cut Multipliers (Average GDP Impact After First Two Years)
- Extended version of GIMF (CIT only)
  - Consumption tax:
    - GDP 0.25
    - Consumption 0.51
    - Private Invest. 0.07
  - Labor income tax:
    - GDP 0.26
    - Consumption 0.41
    - Private Invest. 0.20
  - Capital return tax: NA (CIT-only extended version)
  - Corporate income tax:
    - GDP 0.12
    - Consumption 0.09
    - Private Invest. 0.62
  - Dest. based cash flow tax:
    - GDP -1.33
    - Consumption -0.08
    - Private Invest. -3.50
- Standard version of GIMF (KRT only)
  - Consumption tax:
    - GDP 0.26
    - Consumption 0.52
    - Private Invest. 0.06
  - Labor income tax:
    - GDP 0.26
    - Consumption 0.40
    - Private Invest. 0.18
  - Capital return tax:
    - GDP 0.30
    - Consumption 0.17
    - Private Invest. 1.58
  - Corporate income tax: NA (KRT-only standard version)
  - Dest. based cash flow tax: NA (KRT-only standard version)

- Key comparative points:
  - Among firm taxes, the largest multiplier pertains to the capital return tax, followed by the corporate income tax; the destination-based cash flow tax (DBCFT) produces negative multipliers in the extended (CIT) specification.
  - Under the corporate income tax, two factors dampen the investment response relative to a capital return tax:
    1. Firms can deduct investment adjustment costs, reducing rebates associated with additional investment when the tax decrease lowers tax rates.
    2. Temporary declines in the corporate income tax affect bankruptcy rebates, raising corporate insolvencies relative to capital return tax reductions.

### Appendix III excerpt — modifications to introduce new business taxes (CIT, CFT, DBCFT)
- Purpose: present algebraic derivation for CIT, CFT and DBCFT in the case without a financial accelerator; Appendix IV adds the financial accelerator algebra.
- Assumptions on tax incidence:
  - CIT: economic profits (income) of corporates taxed; revenues from domestic and foreign sales subject to tax; all costs deductible (labor, rent, capital depreciation, interest expenses, intermediate inputs including imports).
  - CFT: cash flows from total sales after deducting cost of labor, investment, and intermediate inputs are taxed.
  - DBCFT: only domestic sales are taxed; only domestic component of intermediate inputs deductible; export revenues not taxed; cost of imports not deductible.
- Taxes affect after-tax profits of manufacturers, capital producers, exporters and importers, investment and consumption goods retailers, entrepreneurs and financial intermediaries; generate additional government revenue.
- Representative replacement of dividend equation for manufacturers (Equation (45) replacement):
  - D^J_t(i) = (1−τ^CI_t − τ^CF_t) (P̃^J_t(i) Z^J_t(i) − [V_t U^J_t(i) + R^J_{k,t} K^J_t(i)] − P̃^J_t T^J_t ω^J − P̃^J_t G^J_{P,t}(i) )
- Rescaled aggregate dividends replacement (equation (57) replacement):
  - ˇd^J_t = (1−τ^CI_t − τ^CF_t) ( p̃^J_t ˇZ^J_t − [ˇv_t ˇU^J_t + r^J_{k,t} ˇK^J_t] − p̃^J_t ω^J − p̃^J_t ˇG^J_{P,t}(i) )
- Taxes create wedges in optimal price setting under sticky prices and sticky inflation; modified price-setting equations include tax-rate ratios:
  - Sticky inflation replacement (Equation (47) replacement) includes term { (1−τ^CI_{t+1} − τ^CF_{t+1}) / (1−τ^CI_t − τ^CF_t) × (p̃^J_{t+1} / p̃^J_t) × (ˇZ^J_{t+1} / ˇZ^J_t) × (π̃^J_{t+1}/π̃^J_t) × (π̃^J_{t+1}/π̃^J_t −1) } in expectations.
  - Sticky prices replacement (Equation (48) replacement) includes analogous tax-rate ratio term multiplying future price, productivity and inflation terms.
- Setting τ^CI = 0 and τ^CF = 0 returns original dividend and price-setting equations; taxes have only second-order effects on price setting (tax terms disappear under first-order log-linearization); under flexible prices (φ^J_P = 0), introduction of CIT and CFT does not matter.
- Taxes do not alter optimal conditions for labor demand (equation (49)) or capital demand (equation (53)); market clearing conditions (equations (60) and (61)) are unaffected.
- Utilization rate of capital optimality condition (Equation (79)) is not modified by business taxes, but the section is maintained to simplify presentation of capital good producers’ and entrepreneur’s problems.

*Source: wp17259 - APPENDIX II: AN UPDATE ON GIMF FISCAL MULTIPLIERS*

### introduction of notations that are not present in the original working paper.

### wp17259 - introduction of notations that are not present in the original working paper.

### Capital utilization and real capital return
- In each sector (J = T or N), utilization rate of capital, u_J_t, is chosen to maximize capital return per unit of capital:
  - ̄R_J_k,t ≡ (R_J_k,t u_J_t − P_t a(u_J_t)), (5)
- The real capital return is defined by:
  - ̄r_J_k,t = ̄R_J_k,t / P_t. (6)
- Total real adjustment costs associated with capital accumulation:
  - ˇrcu_t ≡ a(u_J_t) ̄K_J_t / p_J_t (as in equation (80) p.21).

### Capital goods producers — general remarks
- CIT and CFT affect after-tax dividends of capital producers and multiple first-order conditions.
- Accumulation of capital (equation (71) p.20) is unchanged across model variants.

### Capital goods producers without financial accelerator
- Capital producers produce capital stock, rent it to manufacturers, choose investment and capital services, are competitive price takers.
- After-tax dividends of capital goods producers (modified vs. Equation (76) pg. 20):
  - D_K_J,t = (1 − τ_KR_t − τ_CI_t − τ_CF_t) ̄R_J_k,t ̄K_J_t 
    + (τ_KR_t + τ_CI_t) δ_J_t Q_J_t ̄K_J_t 
    − τ_CI_t (Q_J_t − Q_J_t−1) ̄K_J_t 
    − (1 − τ_CF_t) P_I_t I_J_t 
    − (1 − τ_CI_t − τ_CF_t) P_I_t G_J^I,t
  - where Q_J_t is shadow price of capital and τ_KR is capital returns tax.
- Real value of dividends (equation (81) p.21):
  - ˇd_K_J,t = (1 − τ_KR_t − τ_CI_t − τ_CF_t) ̄r_J_k,t ˇ ̄K_J_t 
    + (τ_KR_t + τ_CI_t) δ_J_t q_J_t ˇ ̄K_J_t 
    − τ_CI_t (q_J_t − q_J_t−1 / π_t) ˇ ̄K_J_t 
    − (1 − τ_CF_t) p_I_t ˇI_J_t 
    − (1 − τ_CI_t − τ_CF_t) p_I_t ˇG_J^I,t. (7)
- Optimal investment equation (replacing Equation (77) p.20):
  - S_inv_t q_J_t − (1 − τ_CF_t) p_I_t φ_I = (1 − τ_CI_t − τ_CF_t) p_I_t (ˇI_J_t / ˇI_J_t−1)(ˇI_J_t / ˇI_J_t−1 − 1)
    − θ_gn_r_t E_t { (1 − τ_CI_t+1 − τ_CF_t+1) p_I_t+1 (ˇI_J_t+1 / ˇI_J_t)(ˇI_J_t+1 / ˇI_J_t − 1) }. (8)
  - Interpretation: q_J_t equals dividend reduction required to add marginal unit of capital, (1 − τ_CF_t) p_I_t, broken by φ_I > 0 in short term.
- First-order condition for capital (optimal capital decision, replaces equation (78) p.20):
  - q_J_t = θ_gn_r_t E_t { [1 − τ_KR_t+1 − τ_CI_t+1 − τ_CF_t+1] ̄r_J_k,t+1 + [1 − (1 − τ_KR_t+1 − τ_CI_t+1) δ_J_t+1] q_J_t+1 − τ_CI_t+1 [q_J_t+1 − q_J_t / π_t+1] }.
  - Three tax impacts: taxes on excess returns/profits; depreciation expensing (KRT and CIT); CIT on capital gains.

### Capital goods producers with financial accelerator
- Capital producers purchase existing capital from entrepreneurs and investment goods from producers, produce new capital, sell to entrepreneurs.
- Dividends modified (replacing equation (65) p.19):
  - D_K_J,t = Q_J_t S_inv_t I_J_t − P_I_t [ (1 − τ_CF_t) I_J_t + (1 − τ_CI_t − τ_CF_t) G_J^I,t ]. (9)
  - First bracket: immediate expensing of investment under CFT; second: expensing for adjustment costs.
- Real dividends (equation (70) p.19):
  - ˇd_K_J,t = q_J_t S_inv_t ˇI_J_t − p_I_t [ (1 − τ_CF_t) ˇI_J_t + (1 − τ_CI_t − τ_CF_t) ˇG_J^I,t ]. (10)
- Investment first-order condition (replacing Equation (66)) is identical to (8):
  - S_inv_t q_J_t − (1 − τ_CF_t) p_I_t φ_I = (1 − τ_CI_t − τ_CF_t) p_I_t (ˇI_J_t / ˇI_J_t−1)(ˇI_J_t / ˇI_J_t−1 − 1)
    − θ_gn_r_t E_t { (1 − τ_CI_t+1 − τ_CF_t+1) p_I_t+1 (ˇI_J_t+1 / ˇI_J_t)(ˇI_J_t+1 / ˇI_J_t − 1) }. (11)
- Expressions for optimal capital decisions and loan contract are covered in Appendix IV.

### Exporting firms and their price setting (destination vs source taxation)
- Terminology: exporting firms (origin country j) sell in destination country i; importing firms (destination i) aggregate imports.
- Switch Ω_SB activated (=1) if CFT is source-based, deactivated (=0) if destination-based.
- Dividends of representative exporting firm k (sector J, triplet o = (j,i,J)), replacing Equation (150) p.31:
  - D_M_o,t(k) = (1 − τ_CI_j,t − Ω_SB_j τ_CF_j,t) P_M_o,t(k) Y_M_o,t(k)
    − (1 − τ_CI_j,t − τ_CF_j,t) (P_M_o,t G_MP_o,t(k) + P_M,cif_o,t Y_M_o,t(k)). (12)
  - P_M,cif_o,t denotes nominal costs in i-currency; G_MP_o,t(k) are adjustment costs depending on destination inflation.
- Price setting under sticky inflation (replaces Equation (151) p.31):
  - 1 / φ_MP (μ_M − 1) ( μ_M (1 − τ_CI_j,t − τ_CF_j,t) / (1 − τ_CI_j,t − Ω_SB_j τ_CF_j,t) p_M,cif_o,t / p_M_o,t−1 )
    = (π_M_o,t / π_M_o,t−1)(π_M_o,t / π_M_o,t−1 − 1)
    − θ_gn_r_t E_t { (1 − τ_CI_j,t+1 − τ_CF_j,t+1) / (1 − τ_CI_j,t − τ_CF_j,t) p_M_o,t+1 / p_M_o,t ˇY_M_o,t+1 / ˇY_M_o,t (π_M_o,t+1 / π_M_o,t)(π_M_o,t+1 / π_M_o,t − 1) }. (13)
- Price setting under sticky prices (does not appear in original paper; presented for completeness):
  - 1 / φ_MP (μ_M − 1) ( μ_M (1 − τ_CI_j,t − τ_CF_j,t) / (1 − τ_CI_j,t − Ω_SB_j τ_CF_j,t) p_M,cif_o,t / p_M_o,t−1 )
    = π_M_o,t (π_M_o,t − ̄π_i)
    − θ_gn_r_t E_t { (1 − τ_CI_j,t+1 − τ_CF_j,t+1) / (1 − τ_CI_j,t − τ_CF_j,t) p_M_o,t+1 / p_M_o,t ˇY_M_o,t+1 / ˇY_M_o,t π_M_o,t+1 (π_M_o,t+1 − ̄π_i) }. (14)
- Under pure destination-based CFT (Ω_SB_j = 0) at steady-state or flexible prices:
  - P_M_o = (1 − τ_CF_j) μ_M P_M,cif_o.
- Rescaled real dividends:
  - ˇd_M_o,t = (1 − τ_CI_j,t − Ω_SB_j τ_CF_j,t) p_M_o,t ˇY_M_o,t − (1 − τ_CI_j,t − τ_CF_j,t) (p_M_o,t ˇG_MP_o,t + p_M,cif_o,t ˇY_M_o,t). (15)

### Importing firms and destination-based effects
- Importing firms in country i (sector J, triplet o = (i,j,J)) aggregate goods from j ≠ i; foreign good considered domestic for destination-based CFT.
- Dividends of importing firm (not present in original GIMF unless destination-based CFT is active):
  - D_F_i,J,t(k) = (1 − τ_CI_i,t − τ_CF_i,t) P_F_i,J,t Y_F_i,J,t − (1 − τ_CI_i,t − Ω_SB_i τ_CF_i,t) ∑_{j ≠ i} P_M_o,t Y_M_o,t. (16)
- Real rescaled dividends:
  - ˇd_F_i,J,t(k) = (1 − τ_CI_i,t − τ_CF_i,t) p_F_i,J,t ˇY_F_i,J,t − (1 − τ_CI_i,t − Ω_SB_i τ_CF_i,t) ∑_{j ≠ i} p_M_o,t ˇY_M_o,t. (17)
- Price level for aggregated imported good (modification of equation (160) p.33):
  - P_F_i,J,t = (1 − τ_CI_i,t − Ω_SB_i τ_CF_i,t) / (1 − τ_CI_i,t − τ_CF_i,t) ( ∑_{j ≠ i} ζ_o P_M_o,t^{1 − ξ_MI} )^{1 / (1 − ξ_MI)}.
- Destination-based CFT modifies relative prices similarly to an import tariff; with perfect competition and CRS dividends of importing firms are zero except when destination-based CFT generates tax payments by import agents.

### Investment and consumption goods producers; price setting
- Dividends for investment and consumption goods producers include CIT and CFT (replacing Equations (199) and (220)):
  - D_I_t(i) = (1 − τ_CI_t − τ_CF_t) ( (P_I_t(i) − P_II_t(i)) Z_I_t(i) − P_I_t G_I_P,t(i) − P_I_t T_t ω_I ). (18)
  - D_C_t(i) = (1 − τ_CI_t − τ_CF_t) ( (P_t(i) − P_CC_t(i)) Z_C_t(i) − P_t G_C_P,t(i) − P_t T_t ω_C ). (19)
- Investment goods price setting under sticky inflation (modified Equation (200)):
  - 1 / φ_P_I (μ_I_t − 1) ( μ_I_t p_II_t / p_I_t−1 )
    = (π_ZI_t / π_ZI_t−1)(π_ZI_t / π_ZI_t−1 − 1)
    − θ_gn_r_t E_t { (1 − τ_CI_t+1 − τ_CF_t+1) / (1 − τ_CI_t − τ_CF_t) p_I_t+1 / p_I_t ˇZ_I_t+1 / ˇZ_I_t (π_ZI_t+1 / π_ZI_t)(π_ZI_t+1 / π_ZI_t − 1) }. (20)
- Investment goods price setting under sticky prices (optional in GIMF):
  - 1 / φ_P_I (μ_I_t − 1) ( μ_I_t p_II_t / p_I_t−1 )
    = π_ZI_t (π_ZI_t − ̄π)
    − θ_gn_r_t E_t { (1 − τ_CI_t+1 − τ_CF_t+1) / (1 − τ_CI_t − τ_CF_t) p_I_t+1 / p_I_t ˇZ_I_t+1 / ˇZ_I_t π_ZI_t+1 (π_ZI_t+1 − ̄π) }. (21)
- Consumption goods price setting under sticky inflation (modified Equation (221); price of consumption is numeraire):
  - 1 / φ_P_C (μ_C_t − 1) ( μ_I_t p_CC_t−1 )
    = (π_t / π_t−1)(π_t / π_t−1 − 1)
    − θ_gn_r_t E_t { (1 − τ_CI_t+1 − τ_CF_t+1) / (1 − τ_CI_t − τ_CF_t) ˇZ_C_t+1 / ˇZ_C_t (π_t+1 / π_t)(π_t+1 / π_t − 1) }. (22)
- Consumption goods price setting under sticky prices (optional in GIMF):
  - 1 / φ_P_C (μ_C_t − 1) ( μ_I_t p_CC_t−1 )
    = π_t (π_t − ̄π)
    − θ_gn_r_t E_t { (1 − τ_CI_t+1 − τ_CF_t+1) / (1 − τ_CI_t − τ_CF_t) ˇZ_C_t+1 / ˇZ_C_t π_t+1 (π_t+1 − ̄π) }. (23)

### Tax revenues (no financial accelerator)
- Total tax revenue (replaces equation (244), p.44):
  - ˇτ_t = τ_L_t ˇw_t ˇL_t + τ_C_t p_c_t ˇC_t + ˇτ_ls,t + ∑_{J = KR,CI,CF} ˇTR_J_t. (24)
- Tax revenue for KRT:
  - ˇTR_KR_t = τ_KR_t ∑_{J = T,N} [ ̄r_J_k,t − δ_J_t q_J_t ] ̄K_J_t. (25)
  - Base includes net of depreciation capital services only.
- Tax revenue for CIT:
  - ˇTR_CI_t = τ_CI_t ∑_{J = T,N} [ p ̃_J_t (ˇZ_J_t − ω_J − ˇG_J_P,t − ˇrcu_t) − ˇv_t ˇU_J_t + ( (1 − δ_J_t) q_J_t − q_J_t−1 / π_t ) ̄K_J_t − p_I_t ˇG_J^I,t ]
    + τ_CI_t [ (p_I_t − p_II_t) ˇZ_I_t − p_I_t ˇG_I_P,t − p_I_t ω_I ]
    + τ_CI_t [ (p_t − p_CC_t) ˇZ_C_t − p_t ˇG_C_P,t − p_t ω_C ]
    + τ_CI_t ∑_{i ∈ I} ∑_{J = T,N} E_i,t / E_j,t [ p_M_i,J,t ˇY_M_i,J,t − p_M,cif_i,J,t ˇY_M_i,J,t − p_M_i,J,t ˇG_M_P,i,J,t ]
    + τ_CI_t ∑_{J = T,D} [ p_F_J,t ˇY_F_J,t − ∑_{i ∈ I} p_M_i,J,t ˇY_F_i,J,t ]. (26)
  - Notes: CIT base includes domestic sales, revaluation effects, minus depreciation allowance, labor costs, adjustment costs; plus profits of distributors, exporters, and (if destination-based CFT) importers.
  - The only part affected by financial accelerator is the first line of the CIT (interest deductibility on debt).
- Tax revenue for CFT:
  - ˇTR_CF_t = τ_CF_t ∑_{J = T,N} [ p ̃_J_t (ˇZ_J_t − ω_J − ˇG_J_P,t − ˇrcu_t) − ˇv_t ˇU_J_t − p_I_t (ˇI_J_t + ˇG_I_t) ]
    + τ_CF_t [ (p_I_t − p_II_t) ˇZ_I_t − p_I_t ˇG_I_P,t − p_I_t ω_I ]
    + τ_CF_t [ (p_t − p_CC_t) ˇZ_C_t − p_t ˇG_C_P,t − p_t ω_C ]
    + τ_CF_t ∑_{i ∈ I} ∑_{J = T,N} E_i,t / E_j,t [ Ω_SB p_M_i,J,t ˇY_M_i,J,t − p_M,cif_i,J,t ˇY_M_i,J,t − p_M_i,J,t ˇG_M_P,i,J,t ]
    + τ_CF_t ∑_{J = T,D} [ p_F_J,t ˇY_F_J,t − Ω_SB ∑_{i ∈ I} p_M_i,J,t ˇY_F_i,J,t ]. (27)
  - Notes: CFT base includes domestic sales minus investment expenses, labor costs, adjustment costs; plus distributor profits; exporters under source-based system; and importers depending on source/destination basis.
- Footnotes in text:
  - The fourth line in CIT (profits made by importers) equals zero unless destination-based CFT is in operation.
  - The last term in CFT revenue is zero in a source-based system.

### Appendix IV — Financial accelerator: entrepreneurs and banks
- Entrepreneurs' problem:
  - Entrepreneur j in sector J (N or T) purchases capital at end of t, faces idiosyncratic shock ω_J_t+1(j) on ̄K_J_t+1; shocks i.i.d. lognormal with Pr(ω_J_t+1(j) ≤ w) = F_J_t+1(w).
  - Financing identity (real terms):
    - q_J_t ̄K_J_t(j) = NW_J_t(j) + B_J_t(j). (28)
  - State verification costs: time-varying fraction μ_J_t+1 of remaining worth of monitored entrepreneur.
  - Optimal debt contract features leverage l_J_t, statutory real interest factor r_J_B,t+1, monitoring policy, and state-dependent interest r_J_B,t+1(ω).
  - Introduction of KRT, CIT, CFT:
    - All business taxes are levied on entrepreneur’s return to capital used to repay loans; taxes reduce ability to repay and raise default threshold ̄ω_J_t+1.
    - CIT permits interest expensing on debt which reduces threshold and interacts directly with debt contract via increasing rebate with leverage.
- Entrepreneurs' leverage and net worth:
  - Assume NW of entrepreneurs at t equals q_J_t (value of one unit of capital). Let l_J_t(j) ≡ B_J_t(j) / NW_J_t(j). With internal and external funds, entrepreneur purchases 1 + l_J_t(j) units of capital.
- No-bankruptcy (idiosyncratic shock above threshold) net income (after tax, after loan repayment):
  - NI_J_t+1(j) ≡ [ ret_J_k,t+1 ω_J_t+1(j) (1 + l_J_t) − (1 − τ_CI_t+1) r_J_B,t+1 l_J_t + τ_CI_t+1 π_t+1 ] q_J_t. (29)
  - where ret_J_k,t+1 is:
    - ret_J_k,t+1 ≡ (1 − τ_KR_t+1 − τ_CI_t+1 − τ_CF_t+1) ̄r_J_k,t+1 + [ (1 − τ_CI_t+1) − (1 − τ_KR_t+1 − τ_CI_t+1) δ_J_t+1 ] q_J_t+1 / q_J_t. (30)
  - Interpretation: all business taxes reduce net income from renting capital; CFT has largest impact, mitigated partly by CIT depreciation/interest expensing effects.

*Italic: Source: wp17259 - introduction of notations that are not present in the original working paper (canonical PDF: https://www.imf.org/-/media/files/publications/wp/2017/wp17259.pdf).*

### Box 1Entrepreneurs’ Income and Expenditures Decomposition Without Bankruptcy

### Box 1Entrepreneurs’ Income and Expenditures Decomposition Without Bankruptcy

### Income and expenditures (no bankruptcy)
- Income
  - [I1] Entrepreneur’s capital return:
    - ( ̄r_J^k,t+1 + (1−δ_J,t+1) q_J,t+1 ) ω_J,t+1(j) (1 + l_J,t).
- Expenditures
  - [E1] Entrepreneur’s capital return tax (KRT):
    - τ_KR,t+1 ( ̄r_J^k,t+1 − δ_J,t+1 q_J,t+1 ) ω_J,t+1(j) (1 + l_J,t).
  - [E2] Entrepreneur’s corporate cash-flow tax (CFT):
    - τ_CF,t+1 ̄r_J^k,t+1 ω_J,t+1(j) (1 + l_J,t).
    - Note: investment expenditures tax rebate does not appear for entrepreneurs (capital goods producers receive the tax allowance).
  - [E3] Entrepreneur’s corporate income tax (CIT):
    - τ_CI,t+1 [ ( ̄r_J^k,t+1 − δ_J,t+1 q_J,t+1 ) ω_J,t+1(j) (1 + l_J,t)
      + ( ω_J,t+1(j) q_J,t+1 − q_J,t π_t+1 ) (1 + l_J,t)
      − ( r_J^B,t+1 − 1/π_t+1 ) l_J,t q_J,t ].
    - If the tax base is negative, the entrepreneur receives a subsidy from the fiscal authorities.
  - [E4] Entrepreneur’s loan repayment (no bankruptcy):
    - r_J^B,t+1 l_J,t q_J,t.
- Net income (no bankruptcy)
  - [NI] Entrepreneur’s net income = total income [I1] − expenditures [E1 to E4] (see equation (29) in main text).

### Threshold level and default decision
- Threshold definition: entrepreneur defaults when net income is negative; threshold productivity ̄ω_J,t+1 satisfies:
  - ̄ω_J,t+1 ≡ ( (1 − τ_CI,t+1) r_J^B,t+1 l_J,t − τ_CI,t+1 π_t+1 ) / ( ret_J^k,t+1 (1 + l_J,t) ). (31)
- Key dependencies:
  - KRT, CFT and CIT reduce entrepreneur net income and increase the threshold ̄ω_J,t+1.
  - For the CIT, interest expensing of debt acts to lower the threshold.
  - The threshold depends on r_J^B,t+1, determined by the bank’s participation constraint.

### Bankruptcy case (summary)
- In default:
  - Corporate taxes are paid first; then the bank seizes remaining real income (partial loan repayment).
  - Net income at end of t+1 is zero: NI_J,t+1(j) = 0 if ω_J,t+1(j) < ̄ω_J,t+1.
  - Capital return, KRT and CFT are the same as in no-bankruptcy case.
  - CIT and loan repayment are modified because the interest payment depends on the amount the bank is able to seize after taxes. (See Box 2 for modified expressions.)
  - Net income in bankruptcy equals zero by construction.

*Source: wp17259 - Box 1Entrepreneurs’ Income and Expenditures Decomposition Without Bankruptcy*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17259.pdf_