## sipea2025088

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### Developments of CIT Revenues: vulnerability and need for a stronger national fiscal framework
- Ireland’s reliance on corporate income tax (CIT) from multinational enterprises (MNEs), concentrated in a small number of companies, presents significant risks to the budget.
- Context and constraints:
  - Previous government’s spending rule: limited annual growth of nominal expenditure net of discretionary revenue measures to 5 percent during 2021–25; it was repeatedly breached and has lapsed.
  - EU fiscal framework uses GDP as denominator; Modified Gross National Income (GNI*) is more appropriate for Ireland given MNE activities.
- Policy rationale:
  - Strengthen macroeconomic stabilization and debt sustainability.
  - Build fiscal buffers to meet substantial spending needs (infrastructure, housing, long-term pressures such as climate, aging, defense, digital transformation).
- Recommended design elements (summary):
  - Adopt a prudent medium-term debt anchor (evidence supports around 40 percent of GDP/GNI* depending on net/gross and measurement choice), with a safety buffer relative to the 60 percent EU benchmark.
  - Implement a multi-year expenditure ceiling operational rule (expenditure net of discretionary revenue measures) calibrated to stabilize debt at the anchor while accounting for the economy’s cyclical position.
  - Use GNI* as preferred output measure for domestic debt-servicing capacity and net debt when designing Ireland-specific anchors.
  - Broaden the tax base over time to reduce reliance on CIT from a small set of MNEs.

### Calibrating a prudent debt anchor — approach, simulations, and numeric findings
- Methodology and data sources:
  - Risk-based framework modeling customized MNE-related shocks; producing debt “fan charts.”
  - Two quantitative approaches:
    - Top-down: cross-country FDI panel dataset of 58 small open economies.
    - Bottom-up: Compustat firm-level data to estimate firm/sector-specific profitability shocks (chemical and IT sectors) and calibrate shocks for the top 10 CIT payers; an exit rate of 5 percent per year assumed for firm exits.
- Measurement considerations:
  - Gross debt/GDP (consistent with EU rules) versus net debt/GNI* (more appropriate for domestic debt-servicing capacity when excess CIT is unavailable).
  - The gap between the debt benchmark and the estimated debt anchor functions as a safety buffer.
- Top-down FDI risk approach — baseline assumptions:
  - FDI and the domestic economy grow by 4.25 percent in nominal terms over the medium-term.
  - Nominal expenditure grows by 5 percent annually.
  - CIT is assumed to grow in line with FDI; other revenues grow in line with the domestic economy.
- Top-down simulation insights:
  - Simulations suggest debt anchors ranging from 30 to 40 percent of GDP or GNI* would put Ireland on a comfortable medium-term path.
  - If gross debt starts at about 40 percent of GDP as of end 2024, there is a 5 percent probability of exceeding 60 percent of GDP by 2030 under the assumed output and expenditure growth path.
- Bottom-up firm risk approach — calibration and results:
  - Top 10 corporate taxpayers account for more than 50 percent of Ireland’s total CIT; firm- or sector-specific shocks can materially affect CIT receipts.
  - Historical distribution of firm profits from Compustat used to calibrate profitability shocks; a 5 percent annual exit rate assumed.
  - Simulation result alignment with top-down:
    - A gross debt-to-GDP ratio of 43 percent or below would ensure the probability of breaching 60 percent by 2030 is no more than 10 percent.
    - Net debt to GNI* implies a lower anchor: to ensure net debt does not breach 60 percent of GNI* by 2030 with 90 percent probability, net debt would need to be around 36 percent of GNI*, compared to the current level of about 60 percent.
  - Overall recommendation emerging from both approaches: a debt anchor set at 40 percent of GNI* (for net debt) would be prudent to avoid breaching the EU benchmark in most scenarios.

### Expenditure-growth scenarios and implications for anchors
- Spending-growth findings:
  - A 5 percent annual nominal spending growth assumed in the baseline would ensure a downward path for debt over a ten-year period.
  - A 6-percent expenditure growth annually could still anchor debt over the medium term, although the debt trajectory would begin to trend up toward the end of the simulation horizon.
  - Higher constant expenditure growth rates would cause debt to rise sooner and may be incompatible with long-term fiscal sustainability.
  - In the very long term, even a 5-percent spending growth may not be sufficient for debt stabilization under the annual revenue growth assumption of 4.25 percent.
- Policy implication:
  - Annual spending growth targets should be set consistent with the chosen prudent debt anchor and allow fiscal policy to perform its stabilization role rather than mechanically increasing spending at a constant rate.

### Policy recommendations and operational rule design (detailed)
- Operational rule necessity:
  - A debt anchor alone is insufficient; an operational rule is required to guide short-term decisions, ensure compliance, and avoid procyclicality and delayed adjustments.
- Preference for expenditure rules:
  - Expenditure rules usually more effective than budget balance or revenue rules because governments control spending, automatic stabilizers can operate, and they are less vulnerable to optimistic revenue forecasts.
  - Empirical evidence: Belu Manescu and Bova (2020) find procyclical bias of fiscal policy lower with expenditure rules.
- Recommended operational design for Ireland:
  - Multi-year expenditure ceilings covering all institutions under the general government classification.
  - Expenditure ceilings tied to macro projections and debt anchor; in positive revenue shocks, ceilings help prevent procyclical spending.
  - Use GNI* for net debt and domestic capacity measures; net expenditure defined net of discretionary revenue measures.
  - Include escape clause with predefined triggering conditions for exceptional circumstances and a correction mechanism specifying remedial actions if rules are breached.
  - Independent fiscal oversight: role for the Irish Fiscal Advisory Council in monitoring compliance and assessing forecasts.
  - Periodic review to recalibrate rules as macro-fiscal conditions evolve.
  - Integrate the two savings funds established in 2024—the Future Ireland Fund and the Infrastructure, Climate and Nature Fund—into the strengthened fiscal framework.
- Design choices for ceilings (trade-offs preserved exactly):
  - Nominal vs. real ceilings:
    - Nominal ceilings: simplicity and transparency; may fail in unstable inflation environments.
    - Real ceilings: preserve purchasing power; harder to communicate and require an appropriate price index choice (HICP, CPI, or GDP deflator).
  - Levels vs. growth rates:
    - Growth-rate ceilings are easier to communicate and continuous; with full compliance equivalent to level ceilings.
  - Treatment of cyclical expenditure:
    - Consider excluding automatic stabilizers (e.g., unemployment benefits) from ceilings.
  - Public investment treatment:
    - Avoid placing full consolidation burden on capital outlays.
    - Consider overall ceiling with separate subceilings for current and capital expenditure; do not recommend excluding public investment (no golden rule).
  - Link to financial assets:
    - Ireland has substantial financial assets (about 40 percent of GNI*); part counted in net debt, part outside the rule serving as buffer and financing source.
  - Caveats on net worth rules:
    - Net worth is volatile due to discount rate revisions, hard to communicate, and can create perverse incentives.

### Revenue shock scenarios and buffer use (numeric scenario)
- Illustrative permanent revenue shock:
  - Assume the CIT windfall estimated at about 4.5 percent of GNI* disappears over three years.
  - Result: revenue ratio falls to about 38 percent and remains at that level thereafter.
- Two expenditure response scenarios:
  - Full adjustment to model-prescribed primary balance:
    - Nominal expenditure increases between 1 and 3 ½ percent in the first three years, with growth catching up later.
    - In level terms, expenditure remains lower—about 90 percent of that in the baseline.
  - Smoothing scenario:
    - Nominal expenditure grows at about 4 percent per annum during the adjustment period, postponing the time when debt reaches the anchor (debt reaches the anchor toward the end of the simulation horizon).
- Use of fiscal buffers:
  - Drawing on financial assets outside net debt (e.g., the two savings funds) would cushion the shock and allow achievement of the debt anchor within a reasonable timeframe.

### Cross-country panel dataset, model structure, and parameter assumptions
- Data and sample:
  - Cross-country panel covering 212 countries and regions, 1990–2023.
  - Small and open economy sample (58 countries): countries in the 30th to 90th percentiles for GDP size and the 50th to 99th percentiles for openness (FDI-GDP ratio).
- Model specification — stage 1:
  - Panel VAR(1) for cyclical components of GNI and FDI; cyclical components obtained by HP-filter per country.
  - Stationarity tests: IPS test rejects panel unit-root null for FDI; LLC test p-value 0.00 rejecting null of unit roots; DF tests reject unit root for most countries but DF test fails to reject unit root for Ireland.
  - Caveat: model assumptions may not be appropriate for Ireland when shocks to MNE operations and associated CIT revenues are permanent.
- Model specification — stage 2 (translation to GDP, taxes, and debt):
  - Key assumptions linking FDI to taxable income and fiscal revenue summarized in exact model relationships in source (Cobb-Douglas production, monopolistic competition, shares definitions).
  - Government budget and debt dynamics: PB_t = T_t − G_t; B_t = (1 + R_t) B_{t−1} − PB_t.
- Parameter assumptions for simulations (preserved exactly):
  - Assumed trend real growth rate for GDP, GNI* and FDI stock: 2¼ percent.
  - Assumed trend growth for real government spending: 3 percent.
  - Interest rate for government debt: 2 percent per annum.
  - Inflation: 2 percent per annum.

### Firm-concentration model, exit calibration, and alternative assumptions
- Firm-level data and selection:
  - Compustat North America Fundamental Annual dataset for corporate financials; Index Monthly Prices dataset for delisting information.
  - Top 100 US firms in tech and pharmaceutical industries selected in 1990.
- Two-stage simulation approach:
  - Panel VAR(1) for firm cyclical log revenue and pre-tax income-to-revenue ratio.
  - Add independent Poisson exiting rule with constant arrival rate λ to capture non-stationary firm dynamics and downside risk.
  - Baseline calibration: λ = 0.045 matches average duration of 17 years in sample.
- Ireland-specific mechanics:
  - Top 10 MNEs contributed over 95 percent of total CIT from MNEs in Ireland.
  - Simulate each firm’s pre-tax income with survival indicator reist_{i,t} (survives with probability 1−λ each period); aggregate to total MNE pre-tax income and derive corporate tax growth.
- Alternative revenue-growth assumption (unit root):
  - Firm revenue growth has a unit root; revenue growth rate and income-to-revenue jointly follow a VAR (non-stationary).
  - Implications: more extreme upside and downside risks, amplified downside through lower GDP and higher debt ratios, wider fan charts, and lower debt anchors.

### Fiscal Reaction Functions (FRFs), unemployment-gap estimation, and policy optimization
- Measuring cyclical position:
  - Output-gap estimation difficult due to GDP distortions; alternatives include GNI* (annual, delayed), modified domestic demand, or unemployment gap (timely, fewer revisions).
  - Unemployment natural-rate estimated via two-state Markov switching model:
    - Low-unemployment state estimate: about 4 ¾ percent.
    - High-unemployment state estimate: slightly over 10 ½ percent.
    - Transition probabilities imply 96 percent probability of staying in low-unemployment regime next period if currently in that regime.
    - Recent unemployment gap u_t^� in range of -0.3 to -0.6 percentage points, implying positive output gaps between 1 and 2 percent using Okun’s law coefficient −0.3.
- Optimization and robust control approaches:
  - FRF specification: p_{t+1} = β0 p_t + β1 γ_t + β2 b_t; given a revenue path, FRF determines expenditure trajectory.
  - Optimization methods identify FRF parameters that minimize quadratic loss (unemployment gap and debt deviations) subject to model dynamics.
  - Robust control methods account for uncertainty (misspecification, shocks, measurement errors).

### Baseline FRF, calibrated parameters, and expenditure-growth profiles (numeric fidelity preserved)
- Parameterization and baseline calibration (preserved exactly):
  - ρ = 0.72
  - α = 0.2
  - Okun’s law parameter = -0.3
  - Nominal potential growth and interest rate = 4 ¼ and 2 ½ , percent respectively (2 ½ percent real potential growth, 2 percent inflation and 0.5 percent equilibrium real interest rate)
  - Tax to GNI ratio = 43 percent (alternative scenario: drop to about 38 percent)
  - Weights: unemployment gap = 1; fiscal impulse R = 10; debt anchor weight baseline = 0.5 (alternatives 1.0 and 0.1 tested)
- Baseline FRF coefficients (exact):
  - −0.43, −0.57, 0.15
- Expenditure-growth implications under baseline FRF (exact profiles):
  - Expenditure can increase at an average rate of about 6.2 percent in the first 5 years.
  - Expenditure can increase at an average rate of about 5.4 percent in the first 10 years.
  - Eventually, expenditure growth should converge to 4 ¼ percent in line with potential growth.
- Sensitivity results (coefficients and scenarios preserved exactly):
  - Debt weight of 1 FRF coefficients: −0.46, −0.65, 0.21
  - Debt weight of 0.1 FRF coefficients: −0.36, −0.40, 0.07
  - Multiplier of 0.4 FRF coefficients: −0.56, −0.68, 0.15
  - Minimax FRF (θ used = 70; threshold ≈ 62) coefficients: −0.73, −1.09, 0.29
  - Robust-stabilizing FRF (parametric uncertainty between τ = 43 percent and τ ≈ 38 percent) coefficients: −0.53, −0.89, 0.28
- Expenditure-growth implications under robustness approaches (exact averages reported):
  - Minimax: about 6.3 percent (first 5 years), 5.3 percent (first 10 years).
  - Robust stabilizing: about 6.4 percent (first 5 years), 5.4 percent (first 10 years).
- Example initial condition used in invariant-set illustration (exact):
  - -0.3 percent unemployment gap and 53.5 percent net debt to GNI*.
- Disturbance bounds in invariant-set example (exact):
  - Unemployment shocks ≈ 0.75 ppts, debt shocks ≈ 0.5 ppts (absolute value).

### Concluding policy implications (concise)
- A prudent debt anchor of about 40 percent provides a fiscal buffer to absorb shocks while maintaining prudent indebtedness.
- Operational rule recommendation: multi-year expenditure ceilings (net of discretionary revenue measures), informed by cyclical conditions and debt levels, to limit procyclicality, enhance transparency, and facilitate monitoring and enforcement.
- Use GNI* and net debt when designing Ireland-specific anchors; retain scope to draw on substantial financial assets (about 40 percent of GNI*) and the two savings funds to cushion shocks and finance priorities.
- Complementary institutional features: escape clause, correction mechanism, independent fiscal oversight, periodic review, integration with MTFF and annual budgets, and transparent treatment of public investment.

*Source: sipea2025088 (IMF).*

### 1. Developments of CIT Revenues ______________________________________________________ 1

### 1. Developments of CIT Revenues

### Introduction: vulnerability of CIT and need for a stronger national fiscal framework
- Ireland’s reliance on corporate income tax (CIT) from multinational enterprises (MNEs), concentrated in a small number of companies, presents significant risks to the budget.
- Key contextual points:
  - The previous government’s spending rule limited annual growth of nominal expenditure net of discretionary revenue measures to 5 percent during 2021–25; it was repeatedly breached and has lapsed.
  - The EU fiscal framework uses GDP as the denominator, but Modified Gross National Income (GNI*) is a more appropriate measure for Ireland given MNE activities.
  - The paper proposes a prudent medium-term debt anchor and a multi-year expenditure ceiling operational rule calibrated to stabilize debt while accounting for cyclical positions.
- Policy rationale:
  - Strengthen macroeconomic stabilization and debt sustainability.
  - Build fiscal buffers to meet substantial spending needs (infrastructure, housing, long-term pressures such as climate, aging, defense, digital transformation).

### Calibrating a prudent debt anchor — approach and criteria
- Methodology:
  - A risk-based framework is applied to calibrate a medium-term debt anchor by modeling and simulating customized MNE-related shocks and producing debt “fan charts.”
  - Two complementary quantitative approaches are used:
    - Top-down: cross-country FDI panel dataset of 58 small open economies to gauge FDI-related risks.
    - Bottom-up: Compustat firm-level data to estimate firm/sector-specific profitability shocks for the largest multinational companies (chemical and IT sectors) and calibrate shocks for the top 10 CIT payers; an exit rate of 5 percent per year is assumed for firm exits.
- Design considerations:
  - Debt anchors should encourage fiscal buffers and limit the probability of debt breaching the EU’s 60 percent debt-to-GDP benchmark.
  - Measurement choices matter: gross debt/GDP (consistent with EU rules) versus net debt/GNI* (more appropriate for domestic debt-servicing capacity when excess CIT is unavailable).
  - The difference between the debt benchmark and the estimated debt anchor functions as a safety buffer.

### Top-down FDI risk approach: assumptions and simulations
- Concept:
  - Changes in FDI capture shocks affecting MNE output and CIT; FDI variation across peer countries is used to simulate risks Ireland may face.
- Baseline assumptions for central scenario:
  - FDI and the domestic economy grow by 4.25 percent in nominal terms over the medium-term.
  - Nominal expenditure grows by 5 percent annually (in line with the previous government’s rule).
  - CIT is assumed to grow in line with FDI; other revenues grow in line with the domestic economy.
- Simulation insights:
  - Fan charts for macro variables and debt illustrate uncertainty around future debt paths derived from FDI shocks.
  - Simulations suggest debt anchors ranging from 30 to 40 percent of GDP or GNI* would put Ireland on a comfortable medium-term path.
  - If gross debt starts at about 40 percent of GDP as of end 2024, there is a 5 percent probability of exceeding 60 percent of GDP by 2030 under the assumed output and expenditure growth path.

### Bottom-up firm risk approach: firm concentration and results
- Rationale:
  - The top 10 corporate taxpayers account for more than 50 percent of Ireland’s total CIT; firm- or sector-specific shocks can materially affect CIT receipts.
- Calibration:
  - Historical distribution of firm profits from Compustat used to calibrate firm-specific profitability shocks; a 5 percent annual exit rate is assumed.
- Simulation results:
  - Broad alignment with top-down results: a gross debt-to-GDP ratio of 43 percent or below would ensure the probability of breaching 60 percent by 2030 is no more than 10 percent.
  - Net debt to GNI* implies a lower anchor: to ensure net debt does not breach 60 percent of GNI* by 2030 with 90 percent probability, net debt would need to be around 36 percent of GNI*, compared to the current level of about 60 percent.
  - Overall recommendation emerging from both approaches: a debt anchor set at 40 percent of GNI* (for net debt) would be prudent to avoid breaching the EU benchmark in most scenarios.

### Expenditure paths, spending-growth scenarios, and implications for anchors
- Spending-growth findings:
  - A 5 percent annual nominal spending growth assumed in the baseline would ensure a downward path for debt over a ten-year period.
  - A 6-percent expenditure growth annually could still anchor debt over the medium term, although the debt trajectory would begin to trend up toward the end of the simulation horizon.
  - Higher constant expenditure growth rates would cause debt to rise sooner and may be incompatible with long-term fiscal sustainability.
  - In the very long term, even a 5-percent spending growth may not be sufficient for debt stabilization under the annual revenue growth assumption of 4.25 percent.
- Policy implication:
  - Annual spending growth targets should be set consistent with the chosen prudent debt anchor and allow fiscal policy to perform its stabilization role rather than mechanically increasing spending at a constant rate.

### Policy recommendations and operational rule design
- Recommended framework elements:
  - Adopt a prudent medium-term debt anchor (evidence supports around 40 percent of GDP/GNI* depending on net/gross and measurement choice), with a safety buffer relative to the 60 percent EU benchmark.
  - Implement a multi-year expenditure ceiling operational rule (expenditure net of discretionary revenue measures) calibrated to stabilize debt at the anchor while accounting for the economy’s cyclical position.
  - Use GNI* as a preferred output measure for domestic debt-servicing capacity and net debt (gross debt – cash balance) when designing anchors that reflect Ireland-specific MNE risks.
  - Broaden the tax base over time to reduce reliance on CIT from a small set of MNEs and allow higher investment spending while remaining within net expenditure limits.

*Source: Considerations for a Stronger Fiscal Framework in Ireland, May 20, 2025.*

### 15.      An operational rule is needed to guide near-term fiscal policy. A debt anchor alone

### 15.      An operational rule is needed to guide near-term fiscal policy. A debt anchor alone

### Need for an operational rule
- A debt anchor alone is insufficient for effective fiscal management because it lacks a mechanism to guide short-term policy decisions and ensure compliance over time.
- An operational rule (e.g., expenditure or fiscal balance rule) is needed to provide a clear and actionable framework that helps achieve and maintain the debt objective while considering economic conditions and implementation constraints.
- Without an operational rule, risks increase of procyclical policies and delayed adjustments undermining credibility and effectiveness of the debt anchor.

### Expenditure rules versus balance/revenue rules
- Expenditure rules are usually considered more effective than budget balance or revenue rules because:
  - Governments have direct control on spending, making them easier to monitor and enforce.
  - They allow automatic stabilizers to operate.
  - They are less vulnerable to overly optimistic revenue forecasts.
- Empirical evidence: Belu Manescu and Bova (2020) find that the procyclical bias of fiscal policy is lower in the presence of expenditure rules.
- Design matters: coverage, legal basis, monitoring, and consequences for non-compliance are critical.

### Recommendation for Ireland: multi-year expenditure ceilings
- Multi-year expenditure ceilings covering all institutions under the general government classification are appropriate for Ireland.
- Such frameworks link the debt anchor to annual fiscal outcomes and, given a revenue path consistent with medium-term macro projections, allow expenditure ceilings to be informed by macro stability and debt sustainability considerations.
- In times of positive revenue shocks, expenditure ceilings help prevent procyclical spending.
- International examples: Netherlands (four-year ceilings in coalition agreements) and Denmark (four-year expenditure ceilings in the Budget Act).

### Fiscal Reaction Functions (FRFs) as a calibration framework
- Typical FRF specification (primary balance as function of cyclical position, public debt, and past primary balance):
  - p_{t+1} = β0 p_t + β1 γ_t + β2 b_t
  - where p_t is the primary balance, γ_t is the output gap (or other cycle measure), and b_t is public debt.
- Given a revenue path, the FRF determines uniquely the expenditure trajectory.
- Key empirical/calibration issues:
  - Estimating the output gap is difficult in Ireland because GDP is distorted by large MNE sector activity.
  - Alternatives: use GNI* (annual, delayed), modified domestic demand (focuses on domestic activity), or unemployment gap (timely, fewer revisions). The paper estimates natural unemployment via a two-state Markov switching model (Appendix I).
- FRFs can be:
  - Estimated econometrically (evidence from Bohn (1998); Plödt and Reicher (2015) report debt response coefficient between 0.05 and 0.08 and cyclical response coefficient between 0.4 and 0.7 for euro area panel).
  - Calibrated using economic models with policy objectives, fiscal multipliers, and sustainability conditions — useful when historical data are limited.

### Optimization and robust control approaches
- Optimization methods identify FRF parameter values that align with policy objectives using a linear model with unemployment gap, primary balance, and debt equations and a quadratic cost function.
- Robust control methods are used to account for uncertainty (misspecification, shocks, measurement errors).

### Simulation outcomes: expenditure growth consistent with sustainability
- Optimization-based results indicate:
  - An average nominal expenditure growth around 5 percent over the next ten years, with somewhat higher growth initially, is consistent with sustainability.
  - Simulations use net debt and GNI* with 2024 estimates from Budget 2025 as initial values (outcomes similar with gross debt and GDP).
  - The optimized FRFs stabilize debt at the anchor (assumed at 40 percent) and the unemployment gap at zero under plausible parameter assumptions.
- Profile of spending growth across methods:
  - First 5 years: rates range between 6 ¼ and 6 ½.
  - First 10 years: around 5½ percent.
  - After that: FRFs prescribe expenditure should grow at the same rate as nominal revenue.
- Trade-offs:
  - Tension between closing a negative unemployment (positive output) gap (which implies tighter fiscal policy) and reducing a substantial primary surplus (which requires higher expenditure).
  - Weights on objectives and fiscal multipliers affect speed and profile of adjustment; higher weight on cyclical position yields faster gap closure.
  - Opportunity to step up productive public investment in the initial period given persistent gap and higher initial spending growth.

### Revenue shock scenarios and buffers
- Illustrative permanent revenue shock:
  - Assume the CIT windfall estimated at about 4.5 percent of GNI* disappears over three years.
  - Result: revenue ratio falls to about 38 percent and remains at that level thereafter.
- Two expenditure response scenarios:
  - Full adjustment to model-prescribed primary balance: nominal expenditure increases between 1 and 3 ½ percent in the first three years, with growth catching up later. (In level terms, expenditure remains lower — about 90 percent of that in the baseline.)
  - Smoothing scenario: nominal expenditure grows at about 4 percent per annum during the adjustment period, postponing the time when debt reaches the anchor (debt reaches the anchor toward the end of the simulation horizon).
- Use of fiscal buffers:
  - Drawing on financial assets outside net debt (e.g., the two savings funds) would cushion the shock and allow achievement of the debt anchor within a reasonable timeframe.
  - Ireland has substantial financial assets (about 40 percent of GNI*); part counted in net debt, part remaining outside the rule serving as buffer and financing source for future pressures.

### Concluding policy implications
- Recommended fiscal framework features:
  - A prudent debt anchor of about 40 percent provides a fiscal buffer to absorb shocks while maintaining prudent indebtedness.
  - Consider both gross debt to GDP and net debt to GNI; GNI may better reflect domestic economy size.
  - Set the operational rule as an expenditure rule (net of discretionary revenue measures) to limit procyclicality, enhance transparency, and facilitate monitoring and enforcement.
  - Expenditure ceilings informed by cyclical conditions and debt levels provide stability and predictability.
- Additional elements to enhance credibility, flexibility, and transparency:
  - Escape clause with predefined triggering conditions for exceptional circumstances.
  - Correction mechanism specifying remedial actions if rules are breached (automatic spending adjustments or corrective budget plans).
  - Independent fiscal oversight: role for the Irish Fiscal Advisory Council in monitoring compliance and assessing forecasts.
  - Periodic review to recalibrate rules as macro-fiscal conditions and structures evolve.
  - Link fiscal rule to annual budgets and the MTFF so satisfying the operational rule implies the fiscal anchor is achieved.
  - Integrate the two savings funds established in 2024—the Future Ireland Fund and the Infrastructure, Climate and Nature Fund—into the strengthened fiscal framework.

### Design choices for multi-year expenditure ceilings
- Nominal vs. real ceilings:
  - Nominal ceilings: simplicity and transparency; may fail in unstable inflation environments.
  - Real ceilings: preserve purchasing power; harder to communicate and require an appropriate price index choice (HICP, CPI, or GDP deflator).
- Levels vs. growth rates:
  - Growth-rate ceilings are easier to communicate and continuous; with full compliance equivalent to level ceilings.
  - If ceilings are breached, growth-rate ceilings require subsequent adjustments due to higher base.
- Treatment of cyclical expenditure:
  - Consider excluding automatic stabilizers (e.g., unemployment benefits) from ceilings to preserve countercyclical policy space.
- Public investment:
  - Avoid placing the full burden of consolidation on capital outlays given Ireland’s investment needs.
  - Consider an overall expenditure ceiling with separate subceilings for current and capital expenditure, and strengthen public investment management.
  - Do not recommend excluding public investment from the ceiling (golden rule) because it raises risks of creative accounting, low-return project selection, and excessive borrowing.
  - A slower adjustment path toward the debt anchor could provide space for upfront growth-enhancing investment in a transparent way.
- Link to financial assets:
  - Substantial financial assets (about 40 percent of GNI*) provide buffers; part counted in net debt, part outside the rule.
  - Two savings funds should play an important role in an integrated fiscal strategy.
- Caveats on net worth rules:
  - Net worth is volatile due to discount rate revisions, hard to communicate, can create perverse incentives (no borrowing limits for investment), and is an imperfect indicator of fiscal sustainability given illiquidity of nonfinancial assets.

*Source: sipea2025088 (IMF).*

### 2.      A cross-country panel dataset covering 212 countries and regions from 1990 to 2023 is

### 2.      A cross-country panel dataset covering 212 countries and regions from 1990 to 2023 is

### Data and sample construction
- Cross-country panel covering 212 countries and regions, 1990–2023.
- Inward FDI stock: nominal US dollars, sourced from countries’ official external sector statistics.
- Domestic macroeconomic and fiscal variables (measured in current prices in local currency): GDP, GNI (GNI* for Ireland), GDP deflator, fiscal revenue, government spending, primary balance, gross domestic debt — sourced from the IMF’s WEO database.
- Model estimated in real terms; GNI deflated by country GDP deflators. Revenues, spending and gross debt used only for Ireland’s debt simulations.
- Small and open economy sample selection:
  - Countries in the 30th to 90th percentiles for GDP size and the 50th to 99th percentiles for openness (measured by FDI-GDP ratio).
  - Resulting sample: 58 countries (Table 1).
- Example country-level sample statistics (as reported):
  - Albania: FDI/GDP 160.623; Lithuania: FDI/GDP 270.578; Luxembourg: FDI/GDP 2148.286; Ireland: FDI/GDP 183.4546.
  - (Full per-country table presented in source.)

### Model specification — stage 1 (FDI and GNI dynamics)
- Panel VAR(1) for cyclical components of GNI and FDI:
  - GNI and FDI assumed trend-stationary; cyclical components obtained by HP-filter per country and expressed as percentage deviations from trend.
  - Estimated model for country i at time t (cyclical components):
    - [y*_it, i_it]' = u_i + B [y*_{i,t-1}, i_{i,t-1}]' + ε_it (as specified in source).
- Stationarity and unit-root testing:
  - Im-Pesaran-Shin (IPS) panel unit root test on FDI rejects the null that all countries’ FDI series have unit roots (alternative: at least one country trend-stationary).
  - Levin-Lin-Chu (LLC) test with alternative that all countries’ FDI are stationary: p-value 0.00, rejecting null of unit roots.
  - Dickey-Fuller (DF) tests for individual countries: null of unit root rejected at the 95 percent confidence level for most countries.
- Caveat for Ireland:
  - DF test fails to reject unit root for Ireland (likely due to Global Financial Crisis turmoil and a large one-off transfer of intangible assets in 2015).
  - Model assumptions may not be appropriate for Ireland when shocks to MNE operations and associated CIT revenues are permanent; parameter values should be revisited when structural shifts occur.

### Model specification — stage 2 (translation to GDP, taxes, and debt)
- Key assumptions linking FDI → capital → output → taxable income → fiscal revenue:
  - One-for-one translation of FDI to capital in domestic production (physical capital or intellectual property).
  - MNEs’ production function: Cobb-Douglas Yn_it = A_it K_it^α L_it^{1−α}, with α the capital income share (capital share close to one for intellectual property).
  - Labor supply: perfectly elastic at fixed wage, matching increases in capital as FDI settles; Δy_it = Δk_it = Δl_it (log differences).
  - In monopolistic competition, firm profits proportional to output with demand elasticity η>1; percentage changes in corporate income taxes (CIT) proportional to changes in FDI:
    - Δτ_{i,t}^c = Δπ_{i,t} = (1/η) Δy_{i,t} = (1/η) Δk_{i,t}.
  - Personal income tax (PIT) from MNEs: Δτ_{i,t}^p = Δl_{i,t}.
  - Aggregate percentage changes of CIT are share-weighted sums of domestic CIT and MNE CIT:
    - Δτ_t^c = s_{c,dom} Δτ_{t,c,dom} + s_{i}^c Δτ_{i,t}^c = s_{dom} Δτ_{t,c,dom} + (1/η) s_{c,FDI} Δk_t
  - Define shares: s_{c,dom} and s_{c,FDI} sum to one; similarly s_{p,dom} and s_{p,FDI} for PIT shares.
  - Domestic firm CIT and PIT track GNI* one-for-one: Δτ_{t,p,dom} = Δτ_{t,c,dom} = Δy_t^*.
  - Total percentage change of fiscal revenue:
    - Δτ_t = μ Δτ_t^c + (1−μ) Δτ_t^p = (μ s_{c,dom} + (1−μ) s_{p,dom}) Δy_t^* + [μ/η s_{c,FDI} + (1−μ) s_{p,FDI}] Δk_t
    - μ is share of tax revenue from corporate income.
  - Difference between GDP and GNI* equals value added generated by MNE operations; its growth rate assumed to track FDI growth:
    - Δ ln(Y_t − Y_t^*) = Δk_t.
- Government budget and debt dynamics:
  - Primary balance: PB_t = T_t − G_t.
  - Domestic debt evolution: B_t = (1 + R_t) B_{t−1} − PB_t.

### Parameter assumptions for simulations
- Cyclical components simulated per VAR(1) estimates and added to predetermined trends:
  - Assumed trend real growth rate for GDP, GNI* and FDI stock: 2¼ percent.
  - Assumed trend growth for real government spending: 3 percent.
  - Interest rate for government debt: 2 percent per annum.
  - Inflation: 2 percent per annum.

### Concentration risks — data and sample
- Firm-level data from Compustat:
  - North America Fundamental Annual dataset for corporate financials; Index Monthly Prices dataset for delisting information.
  - Top 100 US firms in tech and pharmaceutical industries (GIND codes 502030, 352020, 451030, 452020, 452010) in 1990 selected by average 1990 revenue.
  - Delisting treatment: “bankruptcy” → bankrupt; “merger and acquisition” → survival.
  - Collected top 10 MNEs’ revenue in Ireland in the base year from local sources.
  - For simulations: assume real log trend growth of 2¼ percent for all MNEs; other assumptions same as FDI risk model.

### Firm-concentration model specification and simulation
- Two-stage approach for public debt projections under firm concentration risks:
  - Panel VAR(1) for individual firm cyclical log revenue (rrrev_it) and pre-tax income to revenue ratio (pti_it):
    - [rrrev_it, pti_it]' = u_i + B [rrrev_{i,t−1}, pti_{i,t−1}]' + ε_it.
  - Add independent Poisson exiting rule with constant arrival rate λ to capture non-stationary firm dynamics and downside risk.
    - Baseline constant survival/exit assumption; match average duration of top firms 1990–2020.
    - With constant arrival rate λ, average duration:
      - E[mim(T,30)] = (1/λ) [1 − r^{−30 λ}] (as specified in source).
  - Historical evidence:
    - Revenue trajectories for top 52 tech and pharmaceutical firms since 1990 show bankruptcies distributed across 30 years with clustering during two major financial crises.
    - Bankruptcy more likely with revenue declines but can occur on growing revenue paths.
  - Baseline calibration:
    - λ = 0.045 matches average duration of 17 years in the sample.

- Simulation mechanics for Ireland:
  - Top 10 MNEs contributed over 95 percent of total CIT from MNEs in Ireland.
  - Simulate pre-tax income for each firm i:
    - PI_{i,t} = (ppp_i + ppp_{i,t}) reep( rrrevhat_{i,t} + rrrevtrend_{i,t} ) * reist_{i,t}
      - where ppp_i is historical average pretax income to revenue ratio; rrrevtrend_{i,t} is predetermined log trend of firm revenue growth; reist_{i,t} indicates survival in market (survives with probability 1−λ each period).
  - Total pre-tax income from MNEs Π_t = sum_{i=1}^{10} PI_{i,t} divided by top 10 pre-tax income share in all MNEs in 2024.
  - Growth rate of total MNE pre-tax income Δπ_t used in corporate tax growth calculations:
    - Δτ_t^c = s_{c,dom} Δτ_{t,c,dom} + s_{c,FDI} Δπ_t.
  - Rest of procedure same as FDI risk model.

### Alternative revenue-growth assumption and implications
- Alternative assumption: firm revenue growth has a unit root; revenue growth rate and income-to-revenue jointly follow a VAR (non-stationary) process:
  - [rrrevg_{it}, pti_{it}]' = u_i + B [rrrevg_{i,t−1}, pti_{i,t−1}]' + ε_it.
- Implications of unit-root firm growth model:
  - Simulation for Ireland’s domestic debt with this model produces more extreme upside and downside risks.
  - Significant asymmetry: downside risks amplified because declines in top MNE revenues reduce GDP and raise debt-to-GDP; upside limited asymmetrically.
  - Model tends to generate wider fan charts and lower debt anchors.

### Fiscal reaction function — estimating unemployment gap
- Natural-rate estimation approach:
  - Use a simple two-state Markov switching model for unemployment: low and high regimes.
  - Observed unemployment u_t = u^*_{s_t} + ε_t, ε_t ~ N(0, σ_{s_t}^2); regime-specific constants u_0 (low) and u_1 (high).
  - Transition matrix:
    - P = [[p_00, p_10], [1−p_00, 1−p_10]] (as specified in source).
- Estimation results (summary):
  - Low-unemployment state estimate: about 4 ¾ percent.
  - High-unemployment state estimate: slightly over 10 ½ percent, with large variance.
  - Transition probabilities imply 96 percent probability of staying in low-unemployment regime next period if currently in that regime.
  - Probability plot indicates economy in low-unemployment regime since recovery from financial crisis except a short Covid-19 period.
  - Recent unemployment gap defined as u_t^� = u_t − u^*_{s_t} has been negative in range of -0.3 to -0.6 percentage points, which using Okun’s law coefficient −0.3 translates to positive output gaps between 1 and 2 percent.

### Simple model of fiscal policy (fiscal reaction function)
- Unemployment gap dynamics influenced by fiscal policy:
  - u^�_{t+1} = ρ u^�_t + α η_t
    - η_t = fiscal impulse = change in cyclically adjusted balance expressed as ratio to potential output Y^_t; ρ is autoregressive parameter.
- Cyclically adjusted balance:
  - Nominal primary balance PB_t decomposed: PB_t = PB_{t}^{cax} + PB_{t}^{c}.
  - Standard assumption: revenue elasticity = 1; expenditure elasticity = 0.
  - PB_{t}^{cax} = R_t (Y^_t / Y_t) − G_t ⇒ cyclical component PB_t^{c} = R_t − G_t − R_t (Y^_t / Y_t) + G_t = R_t (1 − Y^_t / Y_t) = R_t / Y_t (Y_t − Y^_t).
  - Define output gap γ_t = (Y_t − Y^_t) / Y^_t; assume revenue-to-GDP ratio τ constant (subject to random fluctuations). Then PB_t^{c} = τ γ_t Y^_t.
  - In ratios to potential output (lowercase): p_t = p_{t}^{cax} + τ γ_t.
  - Fiscal impulse: η_t := Δ p_{t+1}^{cax} = p_{t+1} − τ γ_{t+1} − (p_t − τ γ_t).
  - Unadjusted primary balance next period:
    - p_{t+1} = p_t + τ γ_{t+1} − τ γ_t + η_t.
- Public debt evolution (relative to potential output):
  - b_{t+1} = [(1 + r) / (1 + g_p)] p_t b_t − p_{t+1}
    - where r is interest rate and g_p denotes potential growth rate (notation as in source).
- Combining unemployment gap, cyclically adjusted balance, and debt evolution yields a compact fiscal policy representation capturing policy impact on activity and debt sustainability.

*Source: IMF staff calculations.*

### 17.      To derive a fiscal reaction function based on this model, it is convenient to rewrite it in

### sipea2025088 - 17.      To derive a fiscal reaction function based on this model, it is convenient to rewrite it in

### Model setup and state-space representation
- The model is rewritten in state-space form by moving (t+1) variables to the left-hand side, forming a matrix of parameters and premultiplying the right-hand side by its inverse.
- The preferred cyclical measure is the unemployment gap rather than the output gap; the latter is restated via Okun’s law: 푢푢
푡푡
�=βγ
푡푡
.
- A disturbance vector (v_t) is added to capture uncertainty and measurement errors in the unemployment equation, and shocks to the tax ratio and public debt in the primary balance and debt equations.
- Vector notation summary (as given):
  - 퐴퐴
    푑푑
    푦푦
    푡푡+1
    =퐴퐴
    1
    푦푦
    푡푡
    +퐵퐵
    1
    휂휂
    푡푡
    +푣푣
    푡푡
  - 푦푦
    푡푡+1
    =퐴퐴
    0
    −1
    퐴퐴
    1
    푦푦
    푡푡
    +퐴퐴
    0
    −1
    퐵퐵
    1
    휂휂
    푡푡
    +퐴퐴
    0
    −1
    푣푣
    푡푡
  - Final compact form (equation (4)):
    - 푦푦
      푡푡+1
      =퐴퐴푦푦
      푡푡
      +퐵퐵휂휂
      푡푡
      +퐶퐶푣푣
      푡푡

### Objective and loss function
- Policymaker objective: minimize deviations of unemployment from equilibrium (unemployment gap) and debt from target.
- Quadratic loss function assumed (equation (5)):
  - min_{ {η_t} } E_0 sum_{t=0}^{∞} 1/2 [ (y_t − ȳ)^⊤ Q (y_t − ȳ) + η_t^⊤ R η_t ]
- Target vector: ȳ = [0, p̄, b̄]^⊤ (p̄ is debt-stabilizing primary balance; b̄ is debt anchor).
- Q matrix form (weights):  
  - 푄푄=
    [ w_u 0 0
      0 0 0
      0 0 w_b ]
- R is a positive scalar. The fiscal impulse η_t in the objective penalizes large year-to-year swings in the primary balance.

### Transformation to equilibrium-at-origin
- Define e_t = y_t − ȳ. Objective becomes (equation (6)):
  - min_{ {η_t} } E_0 sum_{t=0}^{∞} 1/2 [ e_t^⊤ Q e_t + η_t^⊤ R η_t ]
- Dynamics in transformed variables (equation (7)):
  - e_{t+1} = A e_t + B η_t + C v_t + r, where r = (A − I)^{−1} ȳ.
- For the specific choice of ȳ, r = 0.

### Parameterization and baseline calibration
- Parameters used for scenarios:
  - Autoregressive coefficient for the unemployment gap ρ is fixed at 0.72.
  - Fiscal multiplier for unemployment α is set at 0.2.
  - Okun’s law parameter is fixed at -0.3.
  - Nominal potential growth and interest rate are assumed to be 4 ¼ and 2 ½ , percent respectively (2 ½ percent real potential growth, 2 percent inflation and 0.5 percent equilibrium real interest rate).
  - Tax to GNI ratio is set at 43 percent.
- Objective weights (baseline):
  - Weight on the unemployment gap = 1.
  - Weight on the fiscal impulse (control variable) R = 10.
  - Weight on the debt anchor w_b = 0.5 in the baseline.
- Motivation for weights: high R (10) justified by desire for smoothness—avoiding abrupt changes in the primary balance.

### Baseline Fiscal Reaction Function (FRF) and implications
- With the above parametrization and normally distributed disturbances with zero mean, the solution to the control problem yields the baseline FRF (coefficients given):
  - 푝푝
    푡푡+1
    =−0.43푢푢
    푡푡
    �−0.57
    (
    푝푝
    푡푡
    −푝푝̅
    )
    +0.15�푏푏
    푡푡
    −푏푏
    �
- Interpretation:
  - Primary balance should increase (fiscal tightening) when the unemployment gap is negative (output gap positive).
  - Primary balance should increase when debt level is above target.
- Trajectory implications (Figure 3 referenced):
  - Primary surpluses need to be maintained for the first 5 years to allow net debt to converge to the desired level; surpluses decline gradually.
  - Under constant revenue-to-GDP ratio assumption:
    - Expenditure can increase at an average rate of about 6.2 percent in the first 5 years.
    - Expenditure can increase at an average rate of about 5.4 percent in the first 10 years.
    - Eventually, expenditure growth should converge to 4 ¼ percent in line with potential growth.

### Sensitivity analysis: alternative weights and multipliers
- Alternative FRF coefficients shown in text table (hats denote deviations from targets):
  - Baseline: -0.43, -0.57, 0.15
  - Debt weight of 1: -0.46, -0.65, 0.21
  - Debt weight of 0.1: -0.36, -0.40, 0.07
  - Multiplier of 0.4: -0.56, -0.68, 0.15
- Findings:
  - Increasing weight on debt objective (to 1) yields a stronger reaction to debt deviations.
  - Increasing fiscal multiplier to 0.4 increases response to unemployment gap; reaction to debt similar to baseline.
  - Time profile of expenditure growth varies somewhat; differences in average growth rates in first 5 years are less than 0.5 ppts and essentially disappear over 10 years.

### Robustness to uncertainty: two approaches
- Context: Normality of disturbances implies certainty equivalence; but non-normality and desire for policy robustness motivate alternative approaches.

- Minimax optimal (Hansen and Sargent style):
  - Add robustness term and constraint v_t^⊤ v_t ≤ δ to the optimization problem; leads to minimax formulation (equation (8)).
  - Parameter θ must be above a threshold (threshold ≈ 62); simulations use θ = 70.
  - Resulting minimax FRF:
    - 푝푝
      푡푡+1
      =−0.73푢푢
      푡푡
      �−1.09
      (
      푝푝
      푡푡
      −푝푝̅
      )
      +0.29� 푏푏
      푡푡
      −푏푏
      �
  - Implication: stronger response to deviations from targets.
  - Implementing this rule suggests average expenditure growth of about 6.3 and 5.3 percent in the first 5 and 10 years, respectively; higher initial-year growth causes temporary deterioration in unemployment gap but differences vanish over time.

- Robust stabilization (stabilizing invariant set approach):
  - Goal: find feedback rule and region around equilibrium (invariant set) such that if the system state starts in that region and shocks are bounded, it remains there indefinitely.
  - Use ellipsoidal sets for disturbances (interpretable as confidence regions). Example assumes disturbances around 0.75 ppts in unemployment equation and around 0.5 ppts in the debt equation in absolute value.
  - Robust FRF under parametric uncertainty (modeled as alternative system matrices A_1 and A_2 differing in τ to capture tax ratio drop from 43 percent to about 38 percent) yields:
    - 푝푝
      푡푡+1
      =−0.53푢푢
      푡푡
      �−0.89
      (
      푝푝
      푡푡
      −푝푝̅
      )
      +0.28� 푏푏
      푡푡
      −푏푏
      �
  - Robust stabilizing rule results:
    - Somewhat lower expenditure growth in the first year relative to alternatives, but average results similar:
      - 6.4 percent average expenditure growth in the first 5 years.
      - 5.4 percent average expenditure growth in the first 10 years.
  - Illustration: starting from initial condition (-0.3 percent unemployment gap and 53.5 percent net debt to GNI*), applying the robust FRF steers the system to the invariant set; additive disturbances keep the state close to, but not exactly at, equilibrium.

### Key numeric values and calibration summary (preserved exactly)
- ρ = 0.72
- α = 0.2
- Okun’s law parameter = -0.3
- Nominal potential growth and interest rate = 4 ¼ and 2 ½ , percent respectively (2 ½ percent real potential growth, 2 percent inflation and 0.5 percent equilibrium real interest rate)
- Tax to GNI ratio = 43 percent (alternative scenario: drop to about 38 percent)
- Weights: unemployment gap = 1; fiscal impulse R = 10; debt anchor weight baseline = 0.5 (alternatives 1.0 and 0.1 tested)
- Baseline FRF coefficients: −0.43, −0.57, 0.15
- Minimax FRF coefficients: −0.73, −1.09, 0.29 (θ used = 70; threshold ≈ 62)
- Robust-stabilizing FRF coefficients (parametric uncertainty between τ = 43 percent and τ ≈ 38 percent): −0.53, −0.89, 0.28
- Expenditure growth implications:
  - Baseline: about 6.2 percent (first 5 years), 5.4 percent (first 10 years), converge to 4 ¼ percent
  - Minimax: about 6.3 percent (first 5 years), 5.3 percent (first 10 years)
  - Robust stabilizing: about 6.4 percent (first 5 years), 5.4 percent (first 10 years)
- Example initial condition used in invariant-set illustration: -0.3 percent unemployment gap and 53.5 percent net debt to GNI*.
- Disturbance bounds in invariant-set example: unemployment shocks ≈ 0.75 ppts, debt shocks ≈ 0.5 ppts (absolute value).

*Source: IMF staff calculations*

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_Source: https://www.imf.org/-/media/files/publications/selected-issues-papers/2025/english/sipea2025088.pdf_