## 1. Consumption taxes and government debt

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### Introduction and context
- Cash flow taxes (CFTs) proposed as alternative to corporate income taxes (CITs) because they can be less distortionary.
- Key comparative points:
  - CFT falls exclusively on rents and does not alter desired level of capital, unlike CIT or taxes on return to capital.
  - CFT affords equal treatment of debt and equity capital since CIT allows interest deductibility.
- Destination-based cash-flow tax (DBCFT) proposed to be implemented via a value-added tax (VAT) or consumption tax combined with a payroll subsidy (labor income subsidy) — referred to as CLS.
- Distinctions in an open-economy context:
  - Source-based taxes tax production where it occurs; VAT/consumption taxes apply in destination (where sale takes place).
  - DBCFT taxes domestic consumption and imports while excluding investment and exports.
- Legal/political constraint: principal obstacle to DBCFT is incompatibility with WTO rules; CLS implementation is motivated by VAT border-adjustment compatibility considerations.

### Key mechanisms and conditions for equivalence
- Paper objective: identify conditions under which “full” equivalence (both “tax revenue” and “economic” equivalence) between a DBCFT and CLS holds.
- Two critical conditions:
  - Tax treatment of government expenditure affects “tax revenue” equivalence: whether government consumption is subject to the consumption tax matters.
  - Household perception of government debt affects “economic” equivalence:
    - If households treat government debt as net wealth (finite horizons, q<1), equivalence can break down.
    - Mechanism when equivalence breaks: consumption tax raises consumption deflator, reduces real value of government debt held by households, lowers household real wealth → households increase saving under CLS relative to DBCFT → real interest rate falls → investment and output respond.
    - If households are infinitely lived (q=1) and do not value government debt as net wealth, the distortion from this channel disappears and “economic” equivalence holds.

### Modeling approach and simulations
- Uses IMF’s Global Integrated Monetary and Fiscal (GIMF) model (latest version incorporating DBCFT) and a stylized overlapping-generations (OLG) model to demonstrate results.
- Stylized OLG model highlights analytically:
  - National accounts identities and DBCFT base: DBCFT Base = C + G − W (equation (4) in source).
  - Labor-market condition for distortion eradication: (1+τ^L_t)(1+τ^C_t) = 1.
  - Modified Euler equation with finite horizons: a_t = 1/(1+r_t) a_{t+1} + Θ (1−q)/(1+τ^C_t) v_t (equation (9) in source) — real wealth term vanishes when q = 1.
- GIMF features used in simulations:
  - Multicountry DSGE with sticky prices/wages, finite planning horizons, liquidity-constrained households, asset market incompleteness, financial accelerator.
  - Multi-region calibration: version used comprises 3 regions; Country A ≈ 95 percent of world output.
  - Fiscal instruments include consumption taxes, labor taxes/subsidies, cash-flow taxes including destination-based component (DBCFT) as defined (CFT taxes corporate cash flows after deducting labor, investment, intermediate inputs; DBCFT excludes exports and disallows deduction of imports).

### GIMF simulation design (baseline experiments)
- Baseline assumptions:
  - Model without financial accelerator unless otherwise stated.
  - Initially no distortionary taxes (consumption, labor, capital = zero); any revenue otherwise via lump-sum taxes.
  - External sector in equilibrium (net foreign asset position = zero); no government budget deficit.
- Experiment:
  - DBCFT introduced only in Country A at rate of 10 percent.
  - Equivalent CLS implemented by consumption tax of 10 percent with labor income subsidy of 10 percent.
  - Additional revenue rebated to OLG households as non-distortionary lump-sum transfers.

### Simulation findings — Cases and mechanisms
- Case 1: Infinitely lived households and no government expenditure (G = 0, approximated by agents living 900 years)
  - Finding:
    - Permanent increase in the CFT rebated lump-sum to OLG households does not create long-run distortions: no impact on labor market, firms’ desired capital, investment, or output.
    - Destination-based component affects only real exchange rate (export price effects, import non-deductibility) while nominal exchange rate adjusts to maintain current account.
    - CLS (consumption tax + labor subsidy) leaves labor supply, after-tax real wages, consumption and investment unchanged — economic equivalence holds when government debt = 0 and G = 0.
  - Equivalence extends to finitely-lived OLG households if government debt = 0.

- Case 2: Infinitely lived households with government expenditure ≈ 20 percent of GDP (government debt = 0)
  - Finding:
    - Government expenditure not subject to consumption tax in practice causes DBCFT and CLS tax bases to differ — breaks “tax revenue” equivalence.
    - “Economic” equivalence remains given infinitely-lived households (q ≈ 1) because supply-side distortions are offset.

- Case 3: Finitely-lived households and government debt
  - Finding:
    - DBCFT with transfers rebated to OLG households is non-distortionary in the long run; only real exchange rate appreciates.
    - CLS is distortionary:
      - Consumption tax raises consumption deflator and lowers real value of government debt and household real wealth.
      - OLG households increase saving → reduces real interest rate → raises investment, capital, and output.
      - Household saving increases current account balance.
    - Quantitative outcomes (reported in simulations) show larger impacts under CLS than under DBCFT for GDP, Consumption, Investment, Tax Revenue/GDP, Nominal Effective Exchange Rate, Current Account Balance/GDP, Interest Rate, Real Effective Exchange Rate.

- DBCFT vs CLS with corporate debt (government debt = 0; corporate debt part of household wealth)
  - Under DBCFT:
    - Dividends lowered by tax → firm value falls → firms borrow less → corporate borrowing declines → household financial wealth falls → households save more → global real interest rate falls → investment and capital accumulation supported → current account increases.
  - Under CLS:
    - Consumption tax reduces real value of corporate debt and household wealth → households increase saving → real interest rate falls → investment, capital and output rise; current account improves.
  - Quantitative note: impacts are larger under CLS than under DBCFT.

- Case 1 Alt (non-zero initial tax rates calibrated to OECD averages)
  - Initial calibrations:
    - consumption tax ≈ 12 percent (τC = 0.12),
    - labor income tax ≈ 32 percent (τL = 0.32),
    - business (corporate) income tax ≈ 10 percent (τCIT = 0.10).
  - Condition to eliminate distortions from consumption and labor taxes in GIMF:
    - (1−τL)(1+τC) = 1 (equation (11) in source).
    - With τL = 0.32 and τC = 0.12 the product is less than one, so combination depresses labor supply and output relative to no-tax case.
  - Policy experiment: applying ∆τC = ∆τL = 0.1 (increase consumption tax 10 percentage points and decline labor tax 10 percentage points) boosts labor supply, output, consumption and investment.
  - Interaction with corporate income tax:
    - DBCFT non-distortionary only when τCIT = 0.
    - Interaction formula for rental rate of capital:
      - RK = (1−τDBCFT)(1−τCIT)/(1−τDBCFT−τCIT) [ r(1−τCIT) + δ ] (equation (13) in source).
    - Any τCIT > 0 means DBCFT interacts with CIT to increase rental rate and lower investment; larger initial τCIT amplifies interaction.
    - Practical note: co-existence of DBCFT and CIT may be unlikely but possible where taxes are levied at different government levels.

### Analytical propositions and channels (stylized OLG model results)
- Labor and output distortion eradication necessary but not sufficient condition:
  - (1+τ_l)(1+τ_c) = 1 and δ = 0 and q = 1 needed for full economic equivalence.
- Propositions summarized from the model:
  - Proposition 1 (Economic equivalence): Necessity of (1+τ_l)(1+τ_c) = 1 and δ = 0 (and implicitly q = 1 for full equivalence).
  - Proposition 2: Cash flow taxes do not distort labor or output.
  - Proposition 3 (Revenue equivalence): Cash flow tax can generate same revenue as consumption plus payroll subsidy iff g_t = 0 and τ_{cf} = τ_c = − τ_l.
  - Proposition 4: Consumption tax + labor payroll subsidy cannot exactly replicate a cash flow tax in both revenue and economic effects in general.
  - Proposition 5: When government expenditure differs from zero tax bases differ and revenue equivalence fails.
  - Proposition 6: CFTs are non-distortionary and equivalent to lump-sum taxes; they only appear in government resource constraint.
  - Proposition 7: Condition (1+τ_l)(1+τ_c) = 1 insufficient to offset asset-market distortions from consumption tax.
  - Proposition 8 (Full economic equivalence): q = 1, δ = 0, and (1+τ_l)(1+τ_c) = 1 together sufficient for consumption and payroll taxes to be non-distortionary like CFTs.
  - Proposition 9: Revenue equivalence additionally requires g_t = 0.

- Two economic channels creating persistent distortions from consumption taxes:
  1. Money demand channel: consumption taxes reduce purchasing power of real money balances → households hold more money per unit of consumption (vanishes if δ = 0).
  2. Financial wealth channel: consumption taxes erode real financial wealth → households increase wealth accumulation to smooth consumption (vanishes if q = 1).

### Policy implications and conclusions
- Full equivalence between DBCFT and CLS holds only under restrictive conditions:
  - No government expenditure (for "tax revenue" equivalence).
  - Agents infinitely lived and no existing taxes (for "economic" equivalence).
- Deviations from these conditions break equivalence; therefore:
  - Approximating DBCFT by consumption taxes/VAT plus labor income/payroll subsidies will generally not yield equivalent macroeconomic outcomes.
  - Simulations show an increase in consumption taxes together with a reduction in labor taxes can have a larger impact on output than introducing a DBCFT because consumption tax-induced increases in household saving reduce real interest rates and boost investment.
  - Earlier estimates of cash-flow tax benefits may be overstated if based on approximations that replace DBCFT with consumption taxes and labor income changes.
- Scale dependence: the larger the economy, the larger the impact on global interest rates from household saving responses.

*Source: IMF working paper "1. Consumption taxes and government debt" (excerpt).*

### 1. Consumption taxes and government debt ................................................................... 16

### 1. Consumption taxes and government debt

### Introduction and context
- Cash flow taxes (CFTs) have long been proposed as an alternative to corporate income taxes (CITs) because they can be less distortionary.
- Key advantage of a CFT relative to a CIT: the former falls exclusively on rents and does not alter the economy’s desired level of capital, whereas the latter (as do taxes on the return to capital) does so.
- Other noted advantage: a CFT affords equal treatment of debt and equity capital since the CIT allows for interest deductibility.
- Proponents of the destination-based version of the cash-flow tax (DBCFT) suggest implementation via a value-added tax (VAT) (or a consumption tax) combined with a payroll subsidy (or labor income subsidy), hereafter referred to as CLS.
- Prior claims typically assert equivalence between DBCFT and CLS with respect to tax bases (“tax revenue” equivalence) but do not always establish “economic” equivalence (identical macroeconomic outcomes).
- In an open-economy context:
  - “Source-based” taxes fall on domestic and foreign sources of revenue where production occurs.
  - A VAT or consumption tax falls on domestic (consumption) sales and applies in the “destination” country where the sale takes place.
  - A DBCFT combines cash-flow taxation with a destination-based component, resembling a VAT in that it taxes domestic consumption and imported consumption goods while excluding investment and exports.
- Legal and political implementation issues: principal obstacle to DBCFT is incompatibility with WTO rules; implementing a DBCFT as a CLS is motivated by VAT border-adjustment compatibility with WTO rules.

### Key mechanisms and conditions for equivalence
- The paper aims to show conditions under which “full” equivalence—both “tax revenue” and “economic” equivalence—between a DBCFT and the CLS holds.
- Two key conditions identified:
  - Tax treatment of government expenditure matters for “tax revenue” equivalence: whether government expenditure is subject to the consumption tax affects the tax bases of DBCFT and CLS.
  - Household perception of government debt matters for “economic” equivalence:
    - If households treat government debt as net wealth (occurs when households have finite lives and discount the probability of paying future tax liabilities), equivalence breaks down.
    - Mechanism when equivalence breaks: the consumption tax increases the consumption deflator and reduces the real value of government debt owned by households; this creates a distortion that forces households to increase saving under CLS relative to DBCFT.
    - If households are infinitely lived and do not value government debt as net wealth, the distortion disappears and “economic” equivalence between a DBCFT and CLS holds.

### Modeling approach and simulations
- Uses the latest version of the International Monetary Fund’s Global Integrated Fiscal and Monetary (GIMF) model that incorporates a DBCFT (see Carton and others, 2017) to demonstrate the conditions and to show when “full” equivalence breaks down.
- The paper complements the GIMF simulations with a stylized small model to provide formal demonstration of the results.

### Main contributions
- Contribution 1: Contributes to literature showing that CFTs can be less distortionary than other taxation forms by formally demonstrating this through both a stylized small model and GIMF simulations.
- Contribution 2: Formally documents conditions under which DBCFTs are "economic" and "tax revenue" equivalent to a CLS; emphasizes that prior research primarily examined "tax revenue" equivalence.
- Contribution 3: Connects to literature on effects of consumption taxes in growth and general equilibrium models by showing that consumption taxes are distortionary in an overlapping-generations framework.

### Paper structure (as presented)
- Section II: provides intuition for the conditions under which a DBCFT and a CLS are equivalent.
- Section III: presents an overview of GIMF.

*Source: IMF working paper "1. Consumption taxes and government debt" (excerpt).*

### Section IV presents the GIMF simulations. Section V concludes. An Appendix presents the

### wp17276 - Section IV presents the GIMF simulations. Section V concludes. An Appendix presents the

### II. HOW TO BREAK EQUIVALENCE: INTUITION
- Purpose: provide an intuitive explanation for conditions needed to guarantee “full” equivalence between a DBCFT and a CLS using a simple overlapping-generations (OLG) model with endogenous labor supply (no capital), based on Ascari and Rankin (2007). Appendix I contains more detail and derivations.
- National accounts identities and DBCFT base:
  - Expenditure side: Y = C + Id + G + X – M.         (1)
  - Income side: Y = R + W.          (2)
  - DBCFT Base (taxes domestic sales, permits expensing of investment and labor): DBCFT Base = Y - (X - M) - Id – W .      (3)
  - Substituting (1) into (3): DBCFT Base = C + G – W.        (4)
  - Alternative to tax only private final consumption sales: DBCFT Base = Y – G - Id – (X - M) – W.      (3b)
- Key conceptual points:
  - A DBCFT “looks like” a CLS (tax on private sector and government consumption plus a wage subsidy) under the algebra above, but practical differences arise because some forms of government consumption are typically not subject to consumption taxes.
  - Consumption taxes and labor income subsidies/cuts can approximate a DBCFT; simulations examine “full” equivalence between a pure DBCFT and a CLS implemented via a consumption tax and a labor income tax cut (these are the corresponding instruments in GIMF).
- A. Cash-flow taxes (CFTs) create few distortions (without financial frictions)
  - CFTs do not alter firms’ optimal choice of inputs or relative prices when incidence falls on pure profits; supply side unaffected if dividend-income losses are rebated lump-sum to consumers.
- B. Labor market equilibrium is distorted by consumption and labor taxes
  - Consumer price vs producer price under consumption tax: P^C_t ≡ (1+τ^C_t) P_t.         (5)
  - Consumption taxes reduce real wage received by consumers relative to producer wage; payroll subsidy creates negative wedge between labor costs faced by firms and marginal product of labor.
  - Labor supply, demand, and equilibrium:
    - w_t = ϑ (1+τ^C_t) l_t^{ε−1} .        (6)
    - w_t = α l_{s,t}^{α−1} (1+τ^L_t) .         (7)
    - l_t = Γ[1 / ((1+τ^L_t)(1+τ^C_t))]^{1/(ε−α)} .        (8)
      - w = real producer wage (marginal product of labor)
      - l = labor
      - τ_c = consumption tax
      - τ_L = payroll subsidy
      - α and ε are labor demand elasticity and inverse labor supply elasticity respectively
      - Γ>0 a constant
  - Distortion eradication condition: (1+τ^L_t)(1+τ^C_t) = 1 (payroll subsidy exactly offsets consumption tax).
- C. OLG structure, household wealth, and distortionary consumption and cash-flow taxes
  - OLG households treat government debt as net wealth; finite horizons imply government debt raises perceived wealth because future taxes fall partly beyond their planning horizon—modifies Euler equation for consumption.
  - Modified Euler equation (consumption-related variable a proportional to consumption):
    - a_t = 1/(1+r_t) a_{t+1} + Θ (1−q)/(1+τ^C_t) v_t ,       (9)
      - a = variable proportional to consumption
      - r = real interest rate
      - v = real household wealth (deflated by producer prices), includes government debt
      - q = probability of surviving into next period
      - Θ>0 parameter
    - Key observation: real wealth enters Euler when households have finite lives (q<1) but vanishes under infinitely-lived representative households (q=1).
  - Mechanism: Permanent increase in consumption tax decreases real financial wealth → lowers current consumption → households rebuild wealth by increasing saving → reduces real interest rate → supports investment and output; in an open economy additional saving results in a trade surplus.
  - Household resource constraint (abstracting from money holdings):
    - q/(1+r_t) v_{s,t} = v_{s,t−1} + w_t l_t + (1−τ^{CF}_t) d_t − τ^{LS}_t − (1+τ^C_t) c_{s,t} .       (10)
      - τ^{LS} = lump-sum tax
      - τ^{CF} = cash flow tax levied on firms’ dividends d
    - Taxing dividends and rebating them exactly as lump-sum taxes (τ^{CF}_t d_t = − τ^{LS}_t) has no impact on the OLG household resource constraint → CFTs are equivalent to a lump-sum tax in this respect.

### III. SUMMARY OF THE GLOBAL INTEGRATED MONETARY AND FISCAL MODEL (GIMF)
- Model characteristics:
  - Multicountry DSGE model with optimizing households and firms, full intertemporal stock-flow accounting, sticky prices and wages, real adjustment costs, liquidity-constrained households, finite-planning horizons.
  - Finite horizons allow well-defined steady states where countries can be long-run debtors or creditors; suited to study transitions between steady states where fiscal policy and private saving behavior matter.
  - Non-Ricardian features produce non-neutrality in spending- and revenue-based fiscal measures.
  - Asset markets incomplete: government debt held domestically as nominal one-period domestic-currency bonds; internationally traded assets are nominal one-period U.S. dollar bonds issued by U.S. government and private agents.
  - Firms owned domestically; equity not traded domestically; households receive lump-sum dividends.
  - Financial sector with a procyclical financial accelerator: cost of external finance rises with indebtedness.
  - Multi-region: version used comprises 3 regions; Country A ≈ 95 percent of world output.
- A. Household sector
  - Two household types:
    - OLG households optimize over a 20-year planning horizon.
    - Liquidity-constrained households (LIQ) do not save and have no access to credit; LIQ consumption equals current net income (marginal propensity to consume = unity).
  - All households pay direct labor taxes, indirect consumption taxes, and a lump-sum tax.
  - For OLG, tax cuts have short-run positive effect on output even if matched later (tilt consumption toward present); permanent increases in government debt can crowd out private capital by raising real interest rates.
- B. Production sector
  - Firms produce tradable and nontradable intermediate goods; firms have finite planning horizons; nominal price rigidities and real adjustment costs; pay capital taxes, wages, dividends.
  - Retained earnings insufficient for investment; firms borrow; default leads to intermediary seizure of capital net of costs.
  - Firms operate under monopolistic competition; exports priced to local markets; imports subject to quantity adjustment costs.
  - Government capital (public infrastructure) augments productivity.
- C. Financial sector
  - Limited assets: domestic government bonds, bank deposits; domestic assets and firm ownership not tradable across borders; OLG can issue/purchase tradable U.S.-dollar obligations.
  - Lending rate includes external financing premium rising with debt-to-equity ratio (financial accelerator); steep non-linear risk-premium increases for large negative shocks to net worth.
  - Uncovered interest parity may not hold due to country risk premiums.
- D. International dimensions and spillovers
  - All bilateral trade flows and relative prices (including exchange rates) explicitly modeled; steady-state calibration matches recent data flows.
  - International linkages driven by global saving and investment decisions, with finite horizons leading to uniquely defined current account balances and net foreign asset positions.
  - Net foreign assets represented by nominal non-contingent one-period U.S.-dollar bonds.
- E. Fiscal and monetary policy
  - Fiscal instruments include consumption or investment government spending, lump-sum transfers (general or targeted to LIQ), and taxes on labor income, capital returns, consumption, lump-sum.
  - Latest GIMF (Carton and others, 2017) allows revenue from corporate income and cash flow taxes, including destination-based component (DBCFT). CFT taxes corporate cash flows after deducting labor, investment, intermediate inputs; DBCFT excludes exports and disallows deduction of imports.
  - Tariffs may be included as revenue source. Government investment augments public infrastructure which depreciates at a constant rate.
  - Fiscal policy rule ensures long-run sustainability (debt-to-GDP ratio converges to target) and allows short-run countercyclical policies; instruments typically changes in labor and capital income taxes but can be replaced.
  - Monetary policy: central bank uses an inflation-forecast-based interest rate rule, varying gap between actual policy rate and long-run equilibrium rate to stabilize inflation.

### IV. ON THE EQUIVALENCE BETWEEN CONSUMPTION AND LABOR TAXES AND CASH-FLOW TAXES
- Simulation setup (three-region GIMF; Country A ≈ 95 percent of world output):
  - Version without financial accelerator (unless otherwise stated).
  - No distortionary taxes initially (consumption, labor, capital = zero); any tax revenue otherwise raised via lump-sum taxes.
  - External sector in equilibrium (net foreign asset position = zero); no government budget deficit.
  - DBCFT introduced only in Country A at rate of 10 percent; equivalent CLS achieved by consumption tax of 10 percent with labor income subsidy of 10 percent.
  - Additional revenue rebated to OLG households as a non-distortionary lump-sum transfer.
- A. Full equivalence holds: Infinitely lived households and no government expenditure
  - Assumptions: agents almost infinitely lived and no population growth (Ricardian equivalence); no government expenditure (G=0); no government debt.
  - Numerical device: agents assumed to live for 900 years (q very close to 1) to approximate infinite lives.
  - Findings (Case 1):
    - Permanent increase in the CFT rebated lump-sum to OLG households does not create long-run distortions: no impact on labor market, firms’ desired capital stock or investment, hence no negative impact on output.
    - Destination-based component affects only real exchange rate: exporters receive a tax benefit on foreign sales that leads to lower long-run export prices; import costs no longer deductible raise price of goods entering the taxing country → replicates effect of real exchange rate depreciation offset by nominal appreciation to maintain current account balance and desired net foreign assets.
    - CLS (consumption tax + labor subsidy) works through households: consumption tax lowers consumption and private saving; labor subsidy raises after-tax labor income and labor supply; combined effect leaves labor supply, after-tax real wages, consumption and investment unchanged → no overall impact on output. Nominal exchange rate unchanged under CLS; real exchange rate appreciates due to higher consumption tax.
    - Equivalence holds when government debt = zero, no government expenditure, tax revenues fully rebated to infinitely-lived households; extends to finitely-lived OLG households if government debt = zero (v=0 in Equation (9)).
- B. Breaking tax revenue equivalence: Infinitely-lived households with government expenditure
  - Assumptions: government expenditure ≈ 20 percent of GDP; government debt = zero percent of GDP.
  - Finding (Case 2):
    - Government expenditure not assumed to be subject to consumption tax (e.g., national defense, law and order, education), making DBCFT and CLS tax bases different → breaks “tax revenue” equivalence but not “economic” equivalence.
    - Economic equivalence remains because consumption tax increase + labor subsidy offset leave supply side undistorted and infinitely-lived households do not value government debt.
- C. Breaking economic equivalence: Finitely-lived households and debt
  - Preview: forthcoming simulations will show that “economic” equivalence can be broken in presence of finitely-lived households and debt. In those simulations government expenditure is set to zero (so tax equivalence holds) and additional tax revenue is rebated to OLG households as lump-sum transfers. Simulations with government debt assume no financial accelerator; simulations with corporate debt activate the financial accelerator block.

*Source: GIMF simulations and model description in the supplied content.*

### 1. Consumption taxes and government debt

### 1. Consumption taxes and government debt

### Finitely-lived households and government debt (Figure 3 / Case 3)
- DBCFT with transfers rebated back to OLG households as a lump-sum transfer and no initial distortionary taxes is non-distortionary in the long-run; the only real variable affected in the long run is the real exchange rate which appreciates.
- The CLS is distortionary: the consumption tax component of the CLS
  - raises the consumption deflator and lowers the real value of government debt and hence household real wealth;
  - induces OLG households to increase saving, which reduces the real interest rate;
  - the reduction in the real interest rate raises investment, capital and hence output;
  - additionally, household saving increases and leads to an improvement in the current account balance.
- Simulation visualizations reported as percent deviations from baseline for GDP, Consumption, Investment, Tax Revenue/GDP, Nominal Effective Exchange Rate, Current Account Balance/GDP, Interest Rate, and Real Effective Exchange Rate (source: GIMF simulations).

### DBCFT vs CLS with corporate debt (Figure 4)
- Setup: government debt set to zero; corporate debt is part of households’ wealth.
- Under a DBCFT:
  - the dividend stream produced by firms is lowered by the tax, so the value of the firm falls;
  - with a smaller balance sheet to finance, firms need to borrow less and corporate borrowing declines;
  - the decline in corporate debt reduces household financial wealth, prompting households to save more;
  - higher saving in a large economy lowers the global real interest rate, supporting investment and capital accumulation;
  - higher household saving is reflected in an increase in the current account balance.
- Under the CLS:
  - the consumption tax component reduces the real value of corporate debt and hence households’ real wealth;
  - OLG households increase saving which reduces the real interest rate;
  - lower real rates raise investment, capital and output;
  - higher household saving improves the current account balance.
- Quantitative note: these impacts are all larger under the CLS than under the DBCFT.
- Simulation visualizations reported as percent deviations/differences from baseline across the same set of macro variables (source: GIMF simulations).

### Breaking equivalence when initial tax rates are non-zero (Case 1 Alt; Case 1 Alt CIT) (Figure 5)
- Calibration of initial tax rates to match OECD average tax revenues yields:
  - consumption tax ≈ 12 percent (휏C = 0.12),
  - labor income tax ≈ 32 percent (휏L = 0.32),
  - business (corporate) income tax ≈ 10 percent (휏CIT = 0.10).
- Key analytical condition in GIMF to eliminate distortions from consumption and labor taxes:
  - (1−휏L)(1+휏C) = 1 ,          (11)
  - With 휏L = 0.32 and 휏C = 0.12 the ratio in (11) is less than one, so the combination depresses labor supply and output relative to no-tax case.
- Policy experiment: applying ∆휏C = ∆휏L = 0.1 (increase of 10 percentage points for consumption taxes and decline in labor income tax of 10 percentage points)
  - yields:
    (1−휏L)(1+휏C) < (1−휏L+∆휏L)(1+휏C+∆휏C) < 1.        (12)
  - The CLS therefore acts to boost labor supply, output, consumption and investment.
- DBCFT behavior:
  - With infinitely-lived households, DBCFT remains non-distortionary in the presence of consumption and labor income taxes (but with 훑퐶퐼푇 = 0).
  - When corporate income tax (CIT) is non-zero, a DBCFT generates distortions via interaction with the existing CIT and distorts firms' investment and capital accumulation decisions.
- Interaction in capital rental formula (Carton and others (2017), pp.42):
  - RK = (1−휏DBCFT)(1−휏CIT)/(1−휏DBCFT−휏CIT) [ r(1−휏CIT) + δ ]      (13)
    - where RK is the rental rate of capital, r is the risk-free interest rate and δ is the depreciation rate.
  - Only when 휏CIT = 0 is the DBCFT non-distortionary for capital accumulation.
  - Any increase in the DBCFT interacts with the CIT to increase the rental rate of capital and hence lowers investment and the capital stock; the higher the initial level of the CIT, the larger the interaction effect with the DBCFT.
- Practical note: the interaction effect between corporate income and cash-flow taxes is unlikely in practice because fiscal authorities are unlikely to use both taxes simultaneously, though co-existence may occur where taxation is levied by both Central and Regional governments.
- Simulation visualizations compare Case 1, Case 1 Alt, and Case 1 Alt_CIT across macro variables (source: GIMF simulations).

### Summary of equivalence conditions and policy implications (Conclusions)
- Full equivalence between destination-based cash-flow taxes (DBCFT) and a combination of consumption taxes and labor income subsidies (CLS) occurs only under very restrictive conditions:
  - no government expenditure (for "tax revenue" equivalence);
  - agents are infinitely lived and no existing taxes exist (for "economic" equivalence).
- Deviations from these conditions break equivalence; approximating DBCFT with consumption taxes/VAT plus labor income/payroll subsidies will not yield equivalent outcomes.
- Several implications:
  - Using a consumption tax plus labor income subsidy will not exactly approximate the impact of introducing a DBCFT.
  - Simulations show that the impact on output from an increase in consumption taxes together with a reduction in labor taxes can be greater than introducing a DBCFT.
    - Mechanism: consumption tax leads households to increase savings, thereby reducing the real interest rate which boosts investment.
  - Earlier estimates of the benefits of a cash flow tax may have been overestimated if they approximated the DBCFT by consumption taxes and labor income changes.
- Scale dependence: the overall effect on real rates depends on the size of the economy — the larger the economy, the greater the impact on global interest rates.

*Source: IMF Working Paper (GIMF simulations and analytical OLG model content provided in the chapter "1. Consumption taxes and government debt")*

### 1. As in AR, the real money balance to consumption ratio of cohorts,z

### wp17276 - 1. As in AR, the real money balance to consumption ratio of cohorts,z

### Household first-order conditions and cohort implications
- Real money balance to consumption ratio of cohorts, z_{s,t}, and labor supply, l_{s,t}, are cohort independent and equal to their aggregate counterparts (follows from (27) and (28)).
- Increases in real money balances increase labor supply because money balances are complements to consumption and raise the marginal utility of consumption.
- Consumption taxes:
  - Affect all household FOCs with both indirect and direct effects.
  - Indirect effect: lower money balances per unit of consumption.
  - Direct effect: "tilt" the Euler equation (26) since higher expected future consumption taxes increase consumption growth and lower current consumption.
  - In (27), demand for real money balances increases, for a given consumption and interest rate, in response to higher consumption taxes because higher consumption taxes raise the price of consumption, necessitating higher money balances to purchase a given level of consumption.
  - In (28), consumption taxes reduce the purchasing power of real wages, so labor supply falls in response to higher consumption taxes.
  - Overall: consumption taxes are distortionary for households.
- Cash-flow taxes (CFTs) affect households via non-human wealth, ω_{nh,s,t}, such that higher CFTs lower non-human wealth and hence consumption. As (29) shows, CFTs are similar to lump-sum taxes, τ_{LS}. The impact of the CFT depends on fiscal policy assumptions.

### Aggregate household behavior and Euler equation
- Aggregation identities:
  - x_t = (1−q)^t ∑_{s=−∞}^{t} q^{t−s} x_{s,t} (33), except v_t = q(1−q)^t ∑_{s=−∞}^{t} q^{t−s} v_{s,t} (34).
- Aggregate consumption evolution:
  - a_{t+1} = (1−q) a_{t+1,t+1} + q^t ∑_{s=−∞}^{t} (1−q) q^{t−s} a_{s,t+1} (35).
  - Newcomers' consumption: a_{t+1,t+1} = a_{t+1} − v_t (36).
- Aggregate Euler equation:
  - E_t{a_{t+1}} = β E_t{(1+r_t) (1+τ^C_t)/(1+τ^C_{t+1})} a_t − (1−δ)(1−βq)/(1+τ^C_t) 1−q q v_t. (37)
  - With infinitely lived households, q = 1, the last term vanishes and the standard Euler equation holds.
- Consumption taxes affect aggregate Euler equation threefold:
  1. Expected changes in consumption taxes, E_t{(1+τ^C_{t+1})/(1+τ^C_t)}, affect the slope (real interest rate discount factor).
  2. The level of consumption taxes depresses real wealth, lowering consumption but increasing its growth rate.
  3. Increases in consumption taxes lower z_t and hence, all else equal, lower a_t.

### Government budget and fiscal instruments
- Nominal government resource constraint (38):
  - 6 B_t + M_t + T^{LS}_t + [τ^c_t + τ^{cf}_t] P_t y_t + [τ^l_t − τ^{cf}_t (1+τ^l_t)] W_t l_t = (1+τ^c_t) P_t g_t + (1+i_{t−1}) B_{t−1} + M_{t−1}.
- Real government constraint (39):
  - (1+τ^c_t) g_t − τ^{LS}_t − [τ^c_t + τ^{cf}_t] y_t − [τ^l_t − τ^{cf}_t (1+τ^l_t)] w_t l_t = b_t − (1+r_{t−1}) b_{t−1} + m_t − m_{t−1} P_{t−1}/P_t.
- For purposes of government constraint, it does not matter if labor taxes are levied as payroll taxes or labor income taxes.

### Policy closures and exogenous assumptions (as in AR)
- Government expenditure and nominal money balances are exogenous and constant over time.
- Consumption, payroll and cash-flow taxes are exogenous and constant over time.
- Government debt is treated as independent policy instrument with stock of real debt fixed exogenously:
  - b′_t = (1+r_t) b_t. (40)
- Lump-sum taxes, τ_{LS}, operate as the residual.

### Labor market and goods market equilibria
- Labor market equilibrium (17) = (28) yields:
  - α l_t^{α−1} = (1+τ^l)^{εη} (1+τ^c)^{1−δ} (z_t)^{−δ} l_t^{ε−1}. (41)
- Closed-form solutions:
  - l_t = [α(1−δ) / (εη (1+τ^l) (1+τ^c) (z_t)^δ )]^{1/(ε−α)}. (42)
  - y_t = l_t^α = [α(1−δ) / (εη (1+τ^l) (1+τ^c) (z_t)^δ )]^{α/(ε−α)}. (43)
- Goods market equilibrium: y_t = c_t + g_t (44).
  - c_t = [α(1−δ) / (εη (1+τ^l) (1+τ^c) (z_t)^δ )]^{α/(ε−α)} − g_t. (45)
- Cash-flow taxes do not affect labor or output equilibrium.

### Propositions on economic and revenue equivalence (summary)
- Proposition 1 (Economic equivalence): A necessary but not sufficient condition to mitigate labor and output distortions from consumption and payroll taxes is:
  - (1+τ_l)(1+τ_c) = 1 (46)
  - δ = 0 (47)
  - This implies positive consumption taxes must be offset by payroll subsidies and households do not value real money balances.
  - Relation for τ_l implied by (45):
    - τ_l = − τ_c / (1+τ_c). (48)
- Proposition 2: Cash flow taxes do not distort labor or output.
- Proposition 3 (Revenue equivalence): A cash flow tax can generate the same revenue as consumption and payroll subsidies iff:
  - g_t = 0 (49)
  - τ_{cf} = τ_c = − τ_l (50)
  - Tax revenue expressions:
    - Tax Revenue from CFT = τ_{cf} y_t − τ_{cf} w_t l_t. (51)
    - Tax Revenue from CLS = τ_c y_t − τ_c w_t l_t. (52)
- Proposition 4 (Necessary Conditions for Revenue and Economic equivalence): A consumption tax and labor payroll subsidy cannot exactly replicate a cash flow tax so that matching revenue equivalence would not obtain economic equivalence and vice-versa.
  - Under (49) and (48):
    - l_t = [α(1−δ) / (εη (1−τ_c)(1+τ_c) (z_t)^δ )]^{1/(ε−α)}. (53)
    - y_t = c_t = [α(1−δ) / (εη (1−τ_c)(1+τ_c) (z_t)^δ )]^{α/(ε−α)}. (54)
  - Since (1−τ_c)(1+τ_c) < 1, (49) would be expansionary for labor, output and consumption.
  - Revenue comparison:
    - Tax revenue from CFT = τ_{cf} y_t − τ_{cf} w_t l_t. (55)
    - Tax revenue from CLS = τ_c y_t − τ_c/(1+τ_c) w_t l_t. (56)
    - Since τ_c/(1+τ_c) < τ_{cf}, revenue from cash flow tax is greater than that from a consumption tax and labor subsidy.
- Proposition 5 (No revenue equivalence redux): When government expenditure is different from zero, but (49) holds, the tax bases are different and will not generate the same amount of tax revenue.
  - Tax bases:
    - From CLS: τ_c (y_t − g_t) − τ_c w_t l_t. (57)
    - From CFT: τ_{cf} y_t − τ_{cf} w_t l_t. (58)

### Asset market equilibrium and monetary interactions
- Aggregate real wealth:
  - v_t = (1+r_t) b_t + E_t{M_t/P_{t+1}}, with M_{t+1} = M_t = M as (59).
  - v_t = b′ + E_t{m_{t+1}} (59) where m_{t+1} = M/P_{t+1}.
- Asset-market Euler condition (60):
  - β E_t{(1+r_t)} a_t = E_t{a_{t+1}} + (1−δ)(1−βq)/(1+τ_c) (1−q)/q E_t{[ b′ + m_{t+1} ]}. (60)
- Re-expressing with nominal interest and money growth yields (61):
  - β(1+i_t) a_t m_t = E_t{a_{t+1} m_{t+1}} + (1−δ)(1−βq)/(1+τ_c) (1−q)/q E_t{[ b′ m_{t+1} + 1 ]}. (61)
- Expressions used:
  - m_{t+1} = [α(1−δ) / (η ε (1+τ_l) (1+τ_c) (z_{t+1})^δ )]^{α/(ε−α)} z_{t+1}. (62)
  - a_t m_t = 1/z_t (1 − α(1−δ)/(ε (1+τ_l) (1+τ_c))). (63)
  - 1+i_t = (1−δ) z_t + δ τ_c (1−δ) z_t − δ. (64)
- Combined asset-market condition (65) (full equilibrium expression in z_t and z_{t+1}) is:
  - ((1−δ) z_t + δ τ_c t (1−δ) z_t − δ) β [ε(1+τ_l)(1+τ_c) − α(1−δ)] / (ε(1+τ_l)(1+τ_c) z_t) = E_t{ [ε(1+τ_l)(1+τ_c) − α(1−δ)] / [ε(1+τ_l)(1+τ_c) z_{t+1}] } + (1−δ)(1−βq)/(1+τ_c) (1−q)/q E_t{ [ 1 + b′ [α(1−δ)/(η ε (1+τ_l)(1+τ_c))]^{α/(α−ε)} (z_{t+1})^{(1+δ) α/(ε−α)} ] }. (65)

### Key asset-market propositions and implications
- Proposition 6 (CFTs non-distortionary): Cash flow taxes are non-distortionary and equivalent to lump-sum taxes. CFTs do not appear in equilibrium conditions and only appear in the government resource constraint.
- Proposition 7: The condition (1+τ_l)(1+τ_c) = 1 is not sufficient to offset distortions in the asset market brought about by the consumption tax.
  - Setting (1+τ_l)(1+τ_c) = 1 in (64) yields (66), showing remaining distortions.
- Proposition 8 (Full economic equivalence): For consumption and payroll taxes to be non-distortionary (like CFTs) all of the following must hold:
  - q = 1, δ = 0, and (1+τ_l)(1+τ_c) = 1. (67)
  - Under q = 1 and δ = 0, (65) reduces to E_t{ c_{t+1} m_{t+1} } = β c_t m_t. (68)
- Proposition 9: For taxes to raise the same amount of revenue requires (49) to hold too. If (66) holds, (49) will not, so consumption and payroll subsidies do not raise the same revenue.

### Economic channels creating persistent distortions
- Two channels through which consumption taxes distort equilibrium:
  1. Money demand channel: consumption taxes reduce the purchasing power of real money balances, so households must hold additional money balances to purchase consumption goods. This channel disappears if households do not value money, i.e., δ = 0.
  2. Financial wealth channel: consumption taxes erode the real value of financial wealth and require additional financial wealth to smooth consumption. This channel disappears when agents are infinitely lived, q = 1.
- Net effects on nominal interest rate are ambiguous:
  - Increased demand for money raises nominal interest rate (MET shift).
  - Increased demand for financial wealth lowers the real interest rate.
  - Overall, money balances are greater in the economy with consumption taxes.

### Steady-state characterization and Figure intuition
- Steady-state generalized expression (69):
  - δ(1+τ_c)/( (1−δ) z − δ ) = (1/β − 1) + ε(1−δ)(1/(β q) − 1)(1−q) / ( (1+τ_c)(ε − α(1−δ)) ) [ z + (η ε / (α(1−δ)))^{α/(ε−α)} b′(z) − α δ/(ε−α) ]. (69)
- Figure 6 (described):
  - LHS corresponds to money-as-medium-of-exchange schedule with taxes (MET) and without taxes (ME), both downward sloping. MET is shifted up and right relative to ME.
  - RHS corresponds to store-of-value schedules with taxes (SVT) and without taxes (SV). With b′ = 0, SVT and SV are upward-sloping straight lines with vertical intercept at 1/β − 1.
  - Consumption tax increases required real money balances and financial wealth; MET shifts outward while SVT shifts, so the net effect on interest rate is model-parameter dependent but z (money per unit consumption) increases.

*Source: wp17276 (excerpt).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17276.pdf_