## Annex I. RRF implementation in Greece

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### Introduction and research question
- Greece’s external vulnerabilities and targets:
  - Greece’s net international investment position (NIIP) stood at -136% of GDP at end-2023.
  - Greece has persistent current account deficits; forecasts point to sustained deficits (Table 1 — Forecasts of Greece’s current account balance, % of GDP):
    - IMF (April 2024): -10.1-6.9-6.5-5.3-4.5-3.6-3.1-3.0
    - EC (May 2024): -10.3-6.3-5.7-5.3- -
    - OECD (May 2024): -10.1-6.7-6.0-4.0- -
- Policy experiment: assess whether the EU Recovery and Resilience Plan (RRP), financed by the Recovery and Resilience Facility (RRF), can fundamentally alter Greece’s external trajectory.
  - RRF allocation to Greece: about €36 billion over 2021-26, split into €18.2 billion of grants and €17.7 billion in subsidized loans, equivalent to 16% of Greece’s 2023 GDP.
- Method: dynamic general-equilibrium Debt Investment Growth (DIG) model calibrated to a pro-RRF baseline and used to simulate savings, investment, current account, external debt, NIIP dynamics, and policy experiments.

### Main findings and key quantitative results
- Baseline (well-executed RRP/RRF):
  - Current account improvements by up to 2.6 percentage points of GDP (relative to a no RRP/RRF scenario) in 15 years.
  - NIIP improvement close to 30 percentage points of GDP in the baseline scenario.
  - Fiscal balances rise by about 2.6 percentage points of GDP in the same timeframe under a successful RRP/RRF.
  - Implied fiscal balance–current account association: 0.98.
- Growth dividend context:
  - Literature estimates of the RRF’s positive effect vary between 2%-6% of GDP by 2026.
- Risks and conditionality:
  - Loose macroeconomic policies (e.g., large tax cuts) or large household borrowing in anticipation of future income gains can markedly erode external benefits.
  - Political-economy pressures to consume rather than repay debt after an investment-led boom could undermine external sustainability.
- Implementation status:
  - Greece has successfully unlocked more than half of its allocated RRF resources as of the first quarter of 2025.

### Mechanisms: savings, informality, public capital, and consumption behavior
- Savings–investment identity:
  - current account = gross national savings − gross capital formation; cumulative current accounts determine NIIP evolution (plus valuation effects).
- Drivers of Greece’s deficits:
  - External deficits over the past ten years rooted in weak private-sector savings more than in the public sector.
  - Public sector savings improved under macroeconomic adjustment programs (2010–18); private savings deteriorated from 2015 onwards.
- Household savings and informality:
  - Informality estimates: informal income range between 20-30% of the size of the official economy.
  - Only 9% of the poorest 40% of the adult population in Greece were able to save any money (GPFI and World Bank, 2021).
  - Low household savings linked to low labor force participation, low income per capita, and informality.
- Two channels through which RRF can raise savings and productivity:
  - Formalization channel: modernizing and digitalizing government processes, improving tax collection capacity (electronic invoicing, real-time reporting), and SME assistance to shrink informality.
  - Public capital/productivity channel: RRF investment (green energy, 5G/fibreoptic, digital labour skills, health, education) raises public capital, increases productivity, creates higher-paying formal jobs, and enables higher household savings.
- Empirical implication:
  - RRP’s success in raising public savings is central to translating growth dividends into durable external adjustments; prudent macro policy is required.

### Model structure and key equations (overview)
- Model type and solution:
  - Flexible-price small open-economy dynamic general equilibrium DIG model distinguishing optimizing households and rule-of-thumb households; firms in traded (T) and non-traded (NT) sectors.
  - Fully non-linear perfect foresight solution where agents anticipate government fiscal reaction.
- Public capital and production:
  - Sectoral production: y_{i,t} = z_{i,t} (k_{i,t−1})^{1−α_i} (L_{i,t})^{α_i} (k_{G,t−1})^{α_G}, with z_{i,t} = z̅_{i} + ε_{t}^{TFP,RRP}.
  - Public capital accumulation: k_{G,t} = (1−δ_{G,t}) k_{G,t−1} + ε (g_{I} + ε_{t}^{I,RRP}), with ε ∈ (0,1].
- Households:
  - Two types: optimizing (OPT) who can borrow abroad and may anticipate higher future income, and rule-of-thumb (RoT) who cannot smooth consumption.
  - Aggregate consumption: c_{t} = ω c_{t}^{OPT} + (1−ω) c_{t}^{ROT}; share of optimizing households = 65 percent.
- External sector and NIIP:
  - Trade balance identity and current account expressed in domestic-currency terms including grants, remittances, and debt service.
  - NIIP dynamics: NIIP_{t} = (s_{t} / s_{t−1}) NIIP_{t−1} + ca_{t}^{d} / s_{t}.
- Fiscal rule and debt financing:
  - Consumption tax adjusts with lag to deviations from a balanced budget: τ_{t}^{C} − τ_{t−1}^{C} = ζ(τ̅^{C} + GAP_{t}^{C} − τ_{t−1}^{C}); baseline ζ = 0.02.
  - Debt financing split parameter ω̄ governs use of external commercial debt vs domestic public debt; baseline uses external debt for fiscal surpluses (ω̄ = 1).

### Shock construction, calibration, and key parameters
- RRP/RRF shocks modeled as six shocks:
  - official grants (ε_{t}^{GR,RRP}), public investment (ε_{t}^{I,RRP}), public consumption (ε_{t}^{C,RRP}), official loans (ε_{t}^{LN,RRP}), total factor productivity (ε_{t}^{TFP,RRP}), reduction in disutility of labor (ε_{t}^{κ,RRP}).
- Financial flows and amounts:
  - Grants: €18.2 billion increase in official grants, split 2/3 to public investment and 1/3 to public consumption.
  - Loans: €17.7 billion in loans, with ten-year grace period and repayments equally sized over twenty years.
  - Shock series expressed in percent of 2020 GDP (€167.5 billion).
- Reform calibration target:
  - Match Malliaropulos et al. (2021): overall RRP/RRF effect on GDP = 7 percent and employment = 3.9 percent (relative to initial steady state) over ten years.
- Selected calibration parameters:
  - Risk aversion σ = 1.78.
  - Share of optimizing households = 65 percent.
  - Inverse-Frisch elasticity ψ = 1.
  - Output elasticity to public capital α_{G} = 0.083.
  - Steady-state efficiency of public investment = 0.87.
  - Investment adjustment costs for private capital = 5.
  - Depreciation rate of public capital = 0.0421.
  - Private demand biases: φ = 0.366 and φ_{T} = 0.781.
  - Private consumption composition: 40.5% domestic traded goods, 34.9% domestic non-traded goods, 24.6% imports.
  - Government purchases composition: 6% domestic traded goods, 88.7% domestic non-traded goods, 5.3% imports.
  - Non-traded bias of additional government spending ν = 0.887 and ν^{*} = 0.33.
  - Elasticity between non-traded and traded goods χ = 0.44; between domestic traded and imported goods χ_{T} = 1.5; Armington export elasticity χ_{x} = 2.6.
  - Labour income shares α_{T} = α_{N} = 0.6323.
  - Labour supply share to non-traded sector = 0.4750.
  - Fiscal reaction parameter ζ = 0.02 (baseline).
  - Elasticity of portfolio adjustment costs η^{*} = 1.

### Baseline scenario narrative and quantitative dynamics
- Transmission summary:
  - Public investment increases public capital → raises productivity of private capital and labor → expected returns on capital rise → domestic interest rates rise → firms accumulate private capital.
  - Consumption: optimizing households increase consumption early (smoothing over anticipated income gains); RoT households increase consumption gradually as incomes rise.
  - Labor market reforms initially lower real wages and raise labor force participation.
  - Trade dynamics: initial import rise (incl. RRP-funded imports) outweighs export gains; over time productivity gains and wage compression reduce import share and exports increase.
- Savings and fiscal effects (quantities preserved exactly):
  - Private savings rise as much as 1.4 percentage points of GDP during implementation, then revert close to initial levels over time.
  - Public savings increase permanently, enabling repayment of external liabilities.
- External outcomes (quantitative):
  - Current account balance improves by 2.6 percentage points of GDP after 15 years.
  - NIIP-to-GDP ratio rises steadily, reaching close to 30 percentage points of GDP after 15 years.
  - The impulse to the current account peaks at around 12 years after the start of the RRP.
  - Bulk of NIIP improvement owes to repayment of public external debt; partially offset by negative valuation effects and new RRF-related liabilities carried forward.
- Interpretation:
  - Model suggests more optimistic RRP/RRF success could bring 2029 current account projections closer to balance compared to a conservative IMF WEO projection of about a 3 percent of GDP deficit by 2029.

### Policy experiments and alternative scenarios (quantitative outcomes)
- Overview:
  - Three alternative scenarios illustrate sensitivity to domestic policies: (1) Fiscal slippages; (2) Unproductive capital inflows; (3) Smaller export penetration.
- Scenario 1 — Fiscal slippages:
  - Change: increase fiscal reaction parameter ζ to 0.25 (consumption tax more responsive; captures use of fiscal dividend to cut taxes).
  - Outcomes:
    - Public external debt remains significantly higher—by over 25 percentage points of GDP—15 years into the RRP.
    - NIIP is only higher by about 7 percentage points of GDP (compared to baseline improvement of around 30 percentage points of GDP).
  - Policy implication: using RRP-generated surpluses for tax cuts weakens external improvement from debt reduction.
- Scenario 2 — Unproductive capital inflows:
  - Change: lower portfolio adjustment costs parameter to η^{*} =0.0001 (looser macroprudential policy).
  - Outcomes:
    - After 15 years, households would borrow an additional 10 percentage points of GDP, with this borrowing used solely for consumption.
  - Policy implication: looser macroprudential regimes can trigger large private external borrowing that undermines external sustainability.
- Scenario 3 — Smaller export penetration:
  - Change: lower export elasticity to the real effective exchange rate to χ_{x} =1.
  - Outcomes:
    - NIIP improves by about 19 percentage points of GDP (compared to baseline improvement of 30 percentage points of GDP).
  - Policy implication: incomplete export-enhancing reforms materially reduce external benefits of the RRP/RRF.

### Policy implications and recommendations (preserved wording and priorities)
- Core policy priorities:
  - Preserve fiscal discipline as investment gains materialize to convert temporary income windfalls into higher public savings and NIIP improvements.
  - Pursue structural reforms and public investment targeting formalization, tax administration modernization, and public investment management to raise productivity and household incomes in the formal sector.
  - Guard against politically driven consumption or tax-cutting measures that could reverse external gains by increasing domestic absorption and private borrowing.
  - Monitor household credit growth and macroprudential stances to avoid private-sector leverage undermining external sustainability.
- Additional recommendations:
  - Prioritize fiscal policies that reduce external public debt rather than channeling RRP/RRF-generated fiscal dividends into distortionary tax cuts.
  - Strengthen macroprudential frameworks to limit incentives for unproductive foreign borrowing that would amplify private external debt.
  - Complete structural reforms that improve export competitiveness to ensure traded-sector gains materialize and support NIIP improvements.
  - Consider policies to boost private savings, including greater tax incentives to contribute to the fully-funded auxiliary pension system, particularly for low- and middle-income households.
  - Tilt capital inflows toward productive foreign direct investment (FDI) by establishing a world-class regulatory framework for FDI and targeted incentives in strategic sectors such as manufacturing, renewable energy, and research and development.

### Model limitations (as stated)
- Exclusions and simplifications:
  - Foreign direct investment omitted; RRP/RRF affects domestic investment only endogenously via public capital and productivity.
  - No detailed banking sector or differentiated macroprudential instruments modeled.
  - No provision for defaults or sudden stops; borrowing behavior does not reflect these risks.
  - Informal sector not covered (could amplify RRP/RRF benefits).
  - No demographic or lifecycle considerations.
- Suggested extension:
  - Exploration of these limitations in the DIG model left for future research.

*Italic: Source — wpiea2025110-print-pdf (Annex I. RRF implementation in Greece) — IMF working paper content provided in the input.*

### Annex I. RRF implementation in Greece ..................................................................................

### Annex I. RRF implementation in Greece

### Introduction and research question
- Greece has persistent current account deficits and high external debt, leaving the country vulnerable to changes in external financing conditions; Greece’s net international investment position (NIIP) stood at -136% of GDP at end-2023.
- Recent forecasts point to sustained current account deficits into the foreseeable future:
  - Table 1 — Forecasts of Greece’s current account balance, % of GDP
    - IMF (April 2024): -10.1-6.9-6.5-5.3-4.5-3.6-3.1-3.0
    - EC (May 2024): -10.3-6.3-5.7-5.3- -
    - OECD (May 2024): -10.1-6.7-6.0-4.0- -
- The paper asks whether a major new investment program, the EU-funded Recovery and Resilience Plan (RRP), financed by the Recovery and Resilience Facility (RRF), can fundamentally alter Greece’s external economic trajectory.
- RRF allocation to Greece: about €36 billion over 2021-26, split into €18.2 billion of grants and €17.7 billion in subsidized loans, equivalent to 16% of Greece’s 2023 GDP.
- Approach: a dynamic general-equilibrium Debt Investment Growth (DIG) model calibrated to a pro-RRF baseline (aligned with Malliaropulos et al., 2021) and used to simulate savings, investment, current account, external debt, and NIIP dynamics, plus policy experiments.

### Main findings and key quantitative results
- Positive potential outcome if RRP/RRF is well executed:
  - Baseline scenario shows current account improvements by up to 2.6 percentage points of GDP (relative to a no RRP/RRF scenario) in 15 years.
  - NIIP improvement is close to 30 percentage points of GDP in the baseline scenario.
  - Fiscal balances rise by about 2.6 percentage points of GDP in the same timeframe under a successful RRP/RRF.
  - The implied fiscal balance–current account association is 0.98.
- Growth dividend literature cited: estimates of the RRF’s positive effect vary between 2%-6% of GDP by 2026.
- Risks and conditionality:
  - The positive external outcome is not automatic; loose macroeconomic policies (e.g., large tax cuts) or large household borrowing in anticipation of future income gains can erode the RRP’s benefits, producing much smaller improvements in the external position.
  - Political-economy pressures to consume rather than repay debt after an investment-led boom could undermine external sustainability.
- Structural and institutional context:
  - Greece historically ran long-lasting deficits (over 40 years current account never in surplus, average -5% of GDP).
  - About two-thirds of Greece’s external liabilities are held by public-sector creditors at ultra-long maturities with low interest rates, moderating short-run external financing vulnerabilities.
- Implementation status:
  - Greece has successfully unlocked more than half of its allocated RRF resources as of the first quarter of 2025.

### Related literature and methodological framing
- Builds on studies assessing the RRF/RRP impact on output through investment, productivity, and labor force participation (Bańkowski et al. 2022; EC, 2024a; Malliaropulos et al., 2021; Pfeiffer et al. 2023).
- Connects to broader literature on structural funds within a monetary union and on savings–investment and external sustainability (Becker et al. 2013; Brueckner et al. 2023; Feldstein and Horioka 1980; Blanchard and Giavazzi 2002; Chinn and Prasad 2003; Obstfeld and Rogoff 2005 and 2009; Lane and Milesi-Ferretti 2012).
- Method: dynamic general-equilibrium DIG model capturing (i) large public investment scale-ups on output and debt, (ii) detailed fiscal sector with several debt types and policy rules, and (iii) household and government spending effects on the balance of payments.

### Greece’s external position (diagnosis)
- NIIP and historical context:
  - Greece’s NIIP was the most negative across euro area countries that received financial assistance at end-2023.
  - From 2009 onwards, large current account deficits and a severe economic contraction (real GDP per capita fell by 25% from peak to trough) increased external indebtedness.
- External debt structure and financing needs:
  - About two-thirds of external liabilities are held by public-sector creditors at ultra-long maturities and low interest rates, reducing immediate rollover and financing pressures.
  - Nonetheless, the net debtor position implies a need to generate external surpluses over a sustained period to improve the NIIP.
- Investment opportunity:
  - Figure 2 shows a sharp decline in Greece’s net capital stock, which boosted the return on capital, suggesting significant potential for new productive investments.
  - If RRF-funded investments are efficiently allocated and generate returns that exceed cost of funds, they can support higher future output and justify current account deficits during the transition.

### National savings, informality, and the RRP/RRF (mechanisms)
- Current account determinant: current account = gross national savings − gross capital formation (investment); cumulative current accounts determine NIIP evolution (plus valuation effects).
- Historical savings–investment pattern:
  - Greece’s external deficits over the past ten years are rooted in weak private-sector savings more than in the public sector.
  - Public sector savings improved under macroeconomic adjustment programs (2010–18).
  - Private savings deteriorated from 2015 onwards.
- Household savings and informality:
  - Household sector saves abnormally little in Greece; corporate savings are close to euro area average.
  - Causes of low household savings: low labor force participation (especially female and youth), low income per capita (Greece among lowest in euro area at PPP), and informality (estimates of informal income range between 20-30% of the size of the official economy).
  - Only 9% of the poorest 40% of the adult population in Greece were able to save any money (GPFI and World Bank, 2021).
  - Informality correlates with low productivity, low and unstable incomes, and limited access to formal financial services—factors that constrain savings and can amplify fiscal risks.
- Two channels through which RRF can raise savings and productivity:
  - Formalization channel: RRF-financed investments and reforms aim at shrinking informality by modernizing and digitalizing government processes, improving tax collection capacity (electronic invoicing, real-time reporting), and providing financial and technical assistance to SMEs.
  - Public capital/productivity channel: RRF investment raises public capital (green energy, 5G/fibreoptic, digital labour skills, health, education), which can increase productivity, create higher-paying formal jobs, and raise incomes, thereby enabling higher household savings.
- Empirical implication:
  - The RRP’s success in raising public savings is central to translating growth dividends into durable external adjustments; without prudent macroeconomic policy, growth gains may not reduce external vulnerabilities.

### Policy implications (from model experiments and interpretation)
- A well-executed RRP/RRF plus prudent macroeconomic policies can substantially improve Greece’s external position and NIIP.
- Key policy priorities inferred from the analysis:
  - Preserve fiscal discipline as investment gains materialize to convert temporary income windfalls into higher public savings and NIIP improvements.
  - Pursue structural reforms and public investment targeting formalization, tax administration modernization, and public investment management to raise productivity and household incomes in the formal sector.
  - Guard against politically driven consumption or tax-cutting measures that could reverse external gains by increasing domestic absorption and private borrowing.
  - Monitor household credit growth and macroprudential stances to avoid private-sector leverage undermining external sustainability.

_Italic: Source — wpiea2025110-print-pdf (Annex I. RRF implementation in Greece) — IMF working paper content provided in the input._

### 4. Modelling the domestic savings and the

### 4. Modelling the domestic savings and the external position

### Model overview and solution method
- Starting point: Debt, Investment, Growth (DIG) model (Melina et al., 2016). Footnote: latest member used is DIGNAR-19 model (Aligishiev et al., 2021).
- Model type: flexible-price small open-economy dynamic general equilibrium model that distinguishes optimizing households (who can borrow abroad) and financially constrained (rule-of-thumb) households; firms in traded (T) and non-traded (NT) sectors.
- Prices are perfectly flexible; monetary policy, incomplete exchange-rate pass-through, and intra-/extra-currency union trade differences abstracted away.
- Solution method: fully non-linear perfect foresight solution where households know government’s fiscal reaction function and anticipate future income.
- Focus: paths of investment-savings balance and external sector variables (current account, external debt, NIIP) determined by behavior of optimizing households and firms.
- Full set of equations: see Annex V (in source).

### Production and public capital
- Sectoral production function (for i = T, NT):  
  푦푖,푡 = 푧푖,푡 (푘푖,푡−1)1−훼푖 (퐿푖,푡)훼푖 (푘퐺,푡−1)훼퐺  
  where 푧푖,푡 = 푧̅푖 + 휀푡TFP,RRP; 퐿푖,푡 labor; 푘푖,푡 private capital; 푘퐺,푡 public capital; 훼퐺∈(0,1) and 훼푖∈(0,1).
- Public capital accumulation:  
  푘퐺,푡 = (1−훿퐺,푡)푘퐺,푡−1 + 휖(푔𝐼 + 휀푡𝐼,RR P)  
  where 푔𝑡𝐼 = 푔𝐼 + 휀푡𝐼,RR P; 훿∈(0,1) depreciation rate; 휖∈(0,1] efficiency of public investment.
- Productivity-enhancing and product market reforms modeled as a permanent, gradual increase in total factor productivity (following Fournier and Koske, 2010).
- Mechanisms: higher public capital and TFP raise marginal product of private factors and real output; higher marginal product of capital incentivizes private investment; reforms increase marginal product of capital.

### Domestic interest rates and distortions
- Domestic gross interest rate linked to expected return on domestic private capital (for i = T, NT):  
  푅푡 = (1−훿푖) + 퐸푡⌈(1−휏̅𝑘)(1−휃푡+1)(1−훼푖) 푝푖,푡+1 푦푖,푡+1 푘푖,푡⌉  
  where zero adjustment costs assumed; (1−휏̅𝑘)(1−휗푡)(1−훼푖)푝푖,푡푦푖,푡/푘푖,푡−1 is marginal product of capital.
- Capital tax distortion: constant distortionary capital tax 휏𝑘 and capital market distortion 휗𝑡 lower investment.
- Distortion responsiveness to RRP/RRF:  
  휗𝑡 / 휗̅ = exp(−휂휃(푘퐺,푡 − 푘̅퐺))  
  where 휂휃 governs sensitivity between distortion size and RRP investments; allows catalyzing role of RRP/RRF on private investment (persistent effects).

### Households and consumption dynamics
- Two household types: optimizing (OPT) and rule-of-thumb (RoT). Both set labor supply optimally.
- Labor supply (for j = OPT, ROT):  
  휀푡휅,RR P 휅𝑗 = 휆𝑡𝑗 (1−휏𝑡𝐿) 푤𝑡 (퐿𝑡𝑗) − 휓  
  where 퐿𝑡𝑗 labour supply, 푤𝑡 aggregate wage index, 휏𝑡𝐿 labor tax, 휆𝑡𝑗 marginal utility of consumption, 휓≥0 inverse Frisch elasticity, 휅𝑗>0 disutility parameter, and 휀𝑡휅,RR P shock to disutility of labor from structural reforms (negative values increase labour supply and put downward pressure on wages).
- Optimizing households: anticipate higher future income from RRP/RRF and may increase current consumption; higher domestic real interest rates and anticipated consumption tax changes may lead them to defer consumption. Euler-like condition (augmented with optimizing household income 푖𝑡):  
  ( (𝑐𝑡+1OPT / 𝑖𝑡+1) / (𝑐𝑡OPT / 𝑖𝑡) )^𝜎 = 훽푅푡 (1+휏𝑡𝐶) / (1+휏𝑡+1𝐶) (𝑖𝑡+1 / 𝑖𝑡)^−𝜎  
  where 푐𝑡OPT consumption of optimizing households; 휏𝑡𝑐 consumption tax; 휎≥0 risk aversion; 훽∈(0,1) discount factor. Larger 휎 amplifies impact of tax and interest changes on consumption.
- RoT households: cannot smooth consumption or respond to anticipated productivity improvements; aggregate consumption:  
  푐𝑡 = 휔 푐𝑡OPT + (1−휔) 푐𝑡ROT  
  where 휔 is share of optimizing households.
- RoT consumption specification:  
  푐𝑡ROT = (1−휏𝑡𝐿) 푤𝑡 퐿𝑡ROT + 푠𝑡 𝑟𝑚∗ + 푧𝑡 − 휇𝑘𝐺,𝑡−1 (1+휏𝑡𝐶)  
  where 푠𝑡 real effective exchange rate, 𝑟𝑚∗ remittances (set at steady state), 푧𝑡 government transfers, and 휇푘𝐺,𝑡−1 user fees for government infrastructure.
- Lower 휔 diminishes link between aggregate consumption and future income growth.
- User fees for public capital and wage reductions from labor reforms put downward pressure on current income.

### Relative prices and home bias
- Three relative prices: domestically produced traded good price 푝𝑇𝐻,푡 ≡ 𝑃𝑇𝐻,푡 / 𝑃𝑡; non-traded good price 푝𝑁,푡 ≡ 𝑃𝑁,푡 / 𝑃𝑡; real effective exchange rate 푠𝑡 ≡ 𝑃𝐹,푡 / 𝑃𝑡 (domestic price of foreign good).
- Home bias affects composition of demand and thus relative prices and trade: consumption demand functions (private consumption) given by:  
  푝𝑁,푡^휒 𝑐𝑁,푡 = 휑 𝑐𝑡  
  푝𝑇,푡^(휒−휒𝑇) 푝𝑇𝐻,푡^휒𝑇 𝑐𝑇,푡 = 휑𝑇 (1−휑) 𝑐𝑡  
  where 푐𝑇,푡 and 푐𝑁,푡 are domestic consumption of traded and non-traded goods; 휑∈(0,1) share of non-traded goods in aggregate consumption; 휑𝑇∈(0,1) share of domestically produced tradable goods in traded goods consumption.
- Elasticities: 휒>0 (traded vs non-traded) and 휒𝑇>0 (domestically produced vs imported traded goods) govern relative price responses.
- Government expenditure composition may deviate from steady state because RRP/RRF spending skews toward imported goods:  
  휈𝑡 = (𝑝̅𝐺 𝑔̅) 휈 + (𝑝𝑡𝐺 𝑔𝑡 − 𝑝̅𝐺 𝑔̅) 휈∗ / (𝑝𝑡𝐺 𝑔𝑡)  
  where 휈 steady-state share of non-traded goods in government expenditures and 휈∗ share in additional fiscal expenditures.
- Labor market effects on relative prices:
  - Demand side: higher productivity increases sectoral output, lowers relative prices, raises labor demand and average wage:  
    푤𝑖,푡 퐿𝑖,푡 / 푝𝑖,푡 = 훼𝑖 푦𝑖,푡 for i = T, NT (훼𝑖∈(0,1)).
  - Supply side: labor market reforms increase labor supply, lowering wages and prices:  
    (푤𝑖,푡 / 푤𝑡)^−휌 퐿𝑖,푡 = 휃𝑖 퐿𝑡 for i = T, NT  
    where 휃𝑖∈(0,1) steady-state labor share by sector, 휃𝑇 + 휃𝑁 = 1, and 휌≥0 governs labor mobility. Higher 휃𝑖 ⇒ larger wage reduction following reform.
- Model allows asymmetric sectoral effects due to differences in labor share and imperfect mobility.

### External sector: trade balance, current account, NIIP
- Trade balance identity:  
  푡𝑏𝑡 = 푦𝑡 − 푐𝑡 − 푖𝑡 − 푝𝑡𝐺 𝑔𝑡𝐼 − 푝𝑡𝐺 𝑔𝑡𝐶 − Θ𝑡OPT∗  
  where 푡𝑏𝑡 ≡ 푝𝑇𝐻,푡 𝑥𝑡 − 푠𝑡 𝑚𝑡 (exports minus imports in domestic consumption basket price), 푦𝑡 aggregate output, 푝𝑡𝐺 𝑔𝑡𝐼 government investment, 푝𝑡𝐺 𝑔𝑡𝐶 = 푝𝑡𝐺(𝑔̅𝐶 + 휀𝑡𝐶,RR P) government consumption including RRP/RRF, 푐𝑡 and 푖𝑡 aggregate consumption and investment, Θ𝑡OPT∗ portfolio adjustment costs.
- Current account (domestic-currency terms) includes primary/secondary income flows and external debt service:  
  푐𝑎𝑡𝑑 = 푡𝑏𝑡 + 푠𝑡 𝑟𝑚∗ + 푠𝑡 𝑔𝑟𝑡∗ − ( (푅̅𝑑 − 1) ) 푠𝑡 𝑑𝑡−1 − ( (푅𝑑𝑐,𝑡−1 − 1) ) 푠𝑡 𝑑𝑐,𝑡−1 − ( (푅∗ − 1) ) 푠𝑡 𝑏𝑡−1∗  
  where 푠𝑡 𝑟𝑚∗ net remittances, 푠𝑡 𝑔𝑟𝑡∗ = 푠𝑡(𝑔̅𝑟∗ + 휀𝑡𝐺R,RR P) official grants (including RRP/RRF), terms representing interest payments on external private, public commercial, and concessional debt, and external private interest rate 푅∗.
- NIIP dynamics:  
  푁퐼퐼푃𝑡 = (푠𝑡 / 푠𝑡−1) 푁퐼퐼푃𝑡−1 + 푐𝑎𝑡𝑑 / 푠𝑡  
  where valuation changes from real effective exchange rate movements and current account determine NIIP path.
- Financial account/current account relationship:  
  푐𝑎𝑡𝑑 = 푠𝑡 𝑓𝑎𝑡 = 푠𝑡 (Δ𝑑𝑡 + Δ𝑑𝑐,𝑡 + Δ𝑏𝑡∗ + Δ𝑏𝐸𝑈,𝑡∗)  
  where 푓𝑎𝑡 financial account balance; 푏𝑡∗ external private debt; 푑𝑐,𝑡 and 푑𝑡 external public concessional and commercial debt; Δ denotes first differences.

### Fiscal rule, budget constraint, and debt repayment
- Government budget constraint (domestic-currency terms):  
  푝𝑡𝐺 𝑔𝑡𝐼 + 푝𝑡𝐺 𝑔𝑡𝐶 + 푧𝑡 + ( (푅̅𝑑 − 1) ) 푠𝑡 𝑑𝑡−1 + ( (푅𝑑𝑐,𝑡−1 − 1) ) 푠𝑡 𝑑𝑐,𝑡−1 + ( (푅𝑡−1 − 1) ) 𝑏𝑡−1  
  = 휏𝑡𝐶 𝑐𝑡 + 휏𝑡𝐿 푤𝑡 𝐿𝑡 + (1−휇𝐾) 휏̅𝑘 (𝑟𝑇,𝑡𝐾 𝑘𝑇,𝑡−1 + 𝑟𝑁,𝑡𝐾 𝑘𝑁,𝑡−1) + 휇𝑘𝐺,𝑡−1 + 푠𝑡 𝑔𝑟𝑡∗ + 푠𝑡 Δ𝑑𝑡 + Δ𝑏𝑡 + 푠𝑡 Δ𝑑𝑐,𝑡
  where 푏𝑡 public domestic debt held by optimizing households; 휇𝐾 share of capital tax receipts rebated to optimizing households.
- Fiscal rule: government uses distortionary consumption tax to adjust fiscal balance with a lag to deviations from a balanced budget rule (stabilizing debt-to-GDP over long term):  
  휏𝑡𝐶 − 휏𝑡−1𝐶 = 휁(휏̅𝐶 + GAP𝑡𝐶 − 휏𝑡−1𝐶)  
  where GAP𝑡𝐶 is deviation from target balanced-budget position (positive = fiscal deficit) relative to consumption; 휁≥0 governs speed of closing fiscal gap via consumption taxes.
- Debt composition choice for covering fiscal gap:  
  휔̄ Δ𝑏𝑡 = (1−휔̄) 푠𝑡 Δ𝑑𝑐,𝑡  
  where 휔̄∈[0,1] governs split; 휔̄ = 1 ⇒ only external commercial debt used to cover fiscal gap.
- Implications: tax responsiveness affects external position via consumption, labor supply, wages, marginal product of capital, private investment, and the government’s ability to repay foreign debt. Faster tax cuts in response to surpluses increase consumption and can limit debt reduction.

### Private capital inflows and macroprudential policies
- Private capital inflows amplify initial consumption response during RRP/RRF.
- Model assumes inverse relationship between private capital inflows and macroprudential policy stringency (Eller et al., 2021); implemented via reduced-form adjustment to cost of issuing bonds to foreign investors.
- As domestic interest rates rise and foreign rate fixed at 푅∗, relative cost of foreign borrowing declines, leading to inflows and real exchange rate appreciation that stimulates imports and weighs on exports.
- Portfolio adjustment costs (elasticity 휂∗ > 0) enter intertemporal interest rate relation:  
  푅푡 = 퐸𝑡[ (𝑠𝑡+1 / 𝑠𝑡) 푅∗ − 휂(𝑏𝑡OPT∗ − 𝑏̅OPT∗) ]  
  where 푏𝑡OPT∗ = 푏𝑡 휔 is stock of foreign debt by optimizing households. Looser macroprudential policies lower borrowing costs and increase private external debt via lower adjustment costs.

### Exports penetration and terms of trade
- Exports respond to traded sector supply and relative demand for foreign goods:  
  푥𝑡 / 𝑦̅ = ( (𝑠𝑡 𝑝𝑡𝑇𝐻) )^휒𝑥  
  where 𝑠𝑡 𝑝𝑡𝑇𝐻 = 𝑃𝑡𝐹 / 𝑃𝑡𝑇𝐻 represents terms of trade; 𝑦̅ steady-state external demand; 휒𝑥 governs sensitivity of exports to terms-of-trade changes.
- Interpretation of 휒𝑥: lower 휒𝑥 ⇒ easier export penetration (smaller relative price reduction needed to boost exports). High 휒𝑥 (difficult penetration) implies larger relative price decline required, entailing: (i) larger shift of domestic demand toward traded goods; (ii) lower wages and labor income in tradable sector; (iii) lower marginal product of capital and lower investment.
- Higher domestic demand for traded goods combined with reduced traded-sector output can offset import demand declines, limiting trade balance improvement.

### Model limitations
- Foreign direct investment omitted; RRP/RRF affects domestic investment only endogenously via public capital and productivity.
- No detailed banking sector or differentiated macroprudential instruments modeled.
- No provision for defaults or sudden stops; borrowing behavior does not reflect these risks (contrasts with models that include such risks, e.g., Mendoza, 2010; Bianchi, 2011).
- Informal sector not covered (could amplify RRP/RRF benefits).
- No demographic or lifecycle considerations.
- Exploration of these limitations in DIG model left for future research.

*Source: wpiea2025110-print-pdf - 4. Modelling the domestic savings and the external position*

### 5. The RRP/RRF shock and model parameters

### 5. The RRP/RRF shock and model parameters

### Shock construction and implementation
- The RRP/RRF is modelled through six shocks: an increase in official grants (휀tGR,RRP), public investment (휀tI,RRP), public consumption (휀tC,RRP), official loans (휀tLN,RRP), total factor productivity (휀tTFP,RRP), and a reduction in the disutility of labor (휀tκ,RRP).
- Financial flows follow the publicly available disbursement schedule at the time of writing (Hellenic Republic, 2023).
- Grants: a €18.2 billion increase in official grants (휀tGR,RRP) is assumed and split into 2/3 public investment spending (휀tI,RRP) and 1/3 public consumption (휀tC,RRP), in line with current government plans.
- Post-implementation: government investment remains permanently higher to replace depreciating capital. Depreciation-related replacement investment is not financed by EU grants (i.e., not from the grants shocks).
- Loans: loans of €17.7 billion (휀tLN,RRP) increase external liabilities in line with the disbursement schedule; loans carry a ten-year grace period followed by equally sized repayments over a twenty-year period.
- Figure 4 displays the shock series expressed in percent of 2020 GDP (€167.5 billion).
- Reform approximation: sequences of TFP shocks (휀tTFP,RRP) and labor disutility shocks (휀tκ,RRP) are calibrated to match exactly the profile for GDP and employment from 2021 to 2030 in Malliaropulos et al. (2021).
  - According to Malliaropulos et al. (2021), the overall effect of the RRP/RRF on GDP and employment is 7 and 3.9 percent (relative to the initial steady state), respectively, over a period of ten years.
- Modeling note: capturing reforms via TFP is an approximation; shocks to markups and barriers can generate quantitatively different trajectories for some variables, though headline indicators follow similar paths.

### Calibration and key model parameters
- Model frequency and matching: calibrated at an annual frequency by matching the steady state to Greek data.
- Preferences and households:
  - Risk aversion parameter σ = 1.78 (matches intertemporal elasticity of substitution from Havranek et al. (2015)).
  - Share of optimizing households = 65 percent.
  - Inverse-Frisch elasticity ψ = 1.
- Public capital and investment:
  - Output elasticity to public capital 훼G = 0.083.
  - Steady-state efficiency of public investment = 0.87.
  - Investment adjustment costs for private capital = 5 (one-fifth of value in Melina et al. (2016)) to capture positive impact of loan-financed RRP on private investment.
  - Depreciation rate of public capital = 0.0421.
- Goods composition and elasticities:
  - Private demand biases: 휑 = 0.366 and 휑T = 0.781.
  - Domestic private consumption basket: 40.5% domestic traded goods, 34.9% domestic non-traded goods, 24.6% imports.
  - Government purchases composition: 6% domestic traded goods, 88.7% domestic non-traded goods, 5.3% imports.
  - Non-traded bias of additional government spending 휈 = 0.887 and 휈∗ = 0.33.
  - Elasticity of substitution between non-traded and traded goods 휒 = 0.44.
  - Elasticity of substitution between domestic traded and imported goods 휒T = 1.5.
  - Elasticity of substitution between traded domestic and imported goods for exports (Armington) 휒x = 2.6.
- Labor and sectoral shares:
  - Labour income shares in traded and non-traded sectors 훼T = 훼N = 0.6323.
  - Labour supply share to the non-traded sector = 0.4750.
- Fiscal and portfolio parameters:
  - Fiscal reaction parameter ζ = 0.02 (government accommodates changes in fiscal gap primarily through net external borrowing).
  - Government uses fiscal surpluses from the RRP/RRF for repayment of external debt (휘 = 1).
  - Elasticity of portfolio adjustment costs 휂∗ = 1 (limits foreign borrowing of optimizing households).
- Additional calibration references:
  - Steady-state allocation of demand across traded, non-traded, and imported goods calibrated using OECD Input-Output tables for 2019.
  - Table 2 lists baseline calibration values for initial values and parameters (selected entries preserved in the text).

### Baseline scenario narrative and macro dynamics
- Mechanism summary:
  - New public investments increase public capital stock → raises productivity of private capital and labor → expected returns on capital increase → upward pressure on domestic interest rates.
  - Firms accumulate private capital; diminishing returns and slowing effect of reforms cause expected marginal product of capital, Tobin’s Q, and domestic interest rates to decline over time.
- Consumption and borrowing:
  - Aggregate consumption initially rises rapidly then slows; optimizing households smooth consumption anticipating higher future income.
  - Households borrow against future income due to lower rates abroad, increasing foreign private debt to finance initial consumption surge.
  - Rule-of-thumb households increase consumption gradually, driven by rising incomes and a reduction in the consumption tax rate.
- Labor market and wages:
  - Labor market reforms initially reduce real wages; higher labor force participation stimulates output while containing aggregate consumption growth.
- Investment frictions and trade dynamics:
  - Investment adjustment costs slow capital accumulation, dampen output growth, and allow domestic absorption to outpace output (partly due to rapid government expenditure and debt-financed consumption).
  - Productivity gains and wage compression reduce relative price of traded goods → exports gradually increase.
  - Initial rise in imports (partly RRF-grants funded) outweighs export rise, worsening trade balance as domestic absorption exceeds output; over time, productivity gains reduce import share in domestic demand.
- Fiscal and savings effects:
  - Private savings increase temporarily but public savings are permanently higher.
    - Private savings rise as much as 1.4 percentage points of GDP during implementation, driven by higher employment and firm profits and a relative tilt from consumption to investment.
    - Over time private savings (relative to GDP) revert close to initial levels as investment tapers and replacement of the capital stock stabilizes private savings as a share of GDP.
    - Public savings increase permanently because higher tax revenue and relative decline in expenditures (relative to GDP) boost fiscal balances and enable repayment of external liabilities.
  - The decline in public external debt reflects the muted fiscal reaction to changes in the fiscal gap implied by ζ = 0.02.
- External position, current account, and NIIP:
  - Greece’s external position improves substantially, mirroring the permanent increase in national savings.
  - Current account balance improves by 2.6 percentage points of GDP after 15 years.
  - The impulse to the current account peaks at around 12 years after the start of the RRP and then gradually falls.
  - NIIP-to-GDP ratio rises steadily, reaching close to 30 percentage points of GDP after 15 years. The bulk of the improvement owes to the repayment of public external debt; partially offset by negative valuation effects (real exchange rate depreciation) and new RRF-related liabilities carried forward indefinitely.
- Interpretation note:
  - The model’s simulated current account trajectory suggests that more optimistic assumptions about RRP/RRF success could bring 2029 current account projections closer to balance compared to a more conservative IMF WEO projection of about a 3 percent of GDP deficit by 2029.

### Figures, tables, and sensitivity
- Figure 4 displays the non-reform RRF/RRP shocks in percent of 2020 GDP (€167.5 billion).
- Table 2 presents baseline calibration values necessary to pin down the steady state (selected values summarized in the Calibration subsection).
- Figure 5 and Annex II show key macroeconomic variables under the baseline scenario.
- Figure 6 decomposes RRP impact under the baseline scenario (in percentage points of GDP) across private savings, public savings, current account, and NIIP.
- Annex IV presents sensitivity checks for key assumptions, including intratemporal elasticities, fiscal rules, and composition of reform shocks.

*Source: IMF staff calculations as presented in "5. The RRP/RRF shock and model parameters."*

### 7. Policy experiments

### 7. Policy experiments

### Overview
- The RRP/RRF can materially improve Greece’s external position, but success is not pre-ordained. Long-run external outcomes critically depend on domestic policies in three areas: (i) fiscal policy; (ii) macroprudential policy; and (iii) structural policies.
- The paper contrasts a baseline simulation (where the RRP/RRF successfully boosts productivity and employment and fiscal policy prioritizes debt reduction) with three alternative policy scenarios to illustrate how different domestic policy settings can alter outcomes.

### Scenario 1: Fiscal slippages
- Experimental change:
  - Increase fiscal reaction parameter 휁 to 0.25, making the consumption tax rate more responsive to rising tax revenues (capturing use of the “fiscal dividend” to cut distortionary taxes rather than repay external debt).
- Mechanism and outcomes:
  - Tax cuts stimulate aggregate consumption, reduce labor supply, and increase wages, partially offsetting reductions in domestic prices.
  - Higher imports and lower exports follow, slowing external debt repayment.
- Key quantitative outcomes:
  - Public external debt remains significantly higher—by over 25 percentage points of GDP—15 years into the RRP.
  - The NIIP is only higher by about 7 percentage points of GDP (compared to the improvement under the baseline of around 30 percentage points of GDP).
- Policy implication:
  - Channeling surplus tax revenue into tax cuts can permanently raise household consumption and diminish the improvement in external vulnerabilities that debt reduction would deliver.

### Scenario 2: Unproductive capital inflows
- Experimental change:
  - Lower portfolio adjustment costs parameter to 휂* =0.0001 (instead of 1 in the baseline), representing looser macroprudential policies and cheaper household borrowing abroad.
- Mechanism and outcomes:
  - Households borrow more in anticipation of rising incomes to smooth consumption, raising domestic prices (especially non-traded goods), wages, and imports; private foreign borrowing increases.
- Key quantitative outcomes:
  - After 15 years, households would borrow an additional 10 percentage points of GDP, with this borrowing used solely for consumption.
- Policy implication:
  - Success of the RRP/RRF in raising expected future incomes can create incentives for a new surge in foreign borrowing; macroprudential policies that limit unproductive capital inflows are important to preserve external sustainability.

### Scenario 3: Smaller export penetration
- Experimental change:
  - Lower the elasticity of exports to the real effective exchange rate to 휒_x =1 to model weaker export competitiveness (partial implementation of export-enhancing structural reforms).
- Mechanism and outcomes:
  - Lower traded-sector prices needed to boost exports reduce wages; under limited labor mobility this lowers household incomes and consumption.
  - Domestic demand shifts toward domestic goods but traded-sector output declines; the trade balance deteriorates.
  - Exchange rate depreciation increases negative valuation effects on external debt.
- Key quantitative outcomes:
  - The NIIP improves by about 19 percentage points of GDP (compared to the baseline improvement of 30 percentage points of GDP).
- Policy implication:
  - Incomplete structural reforms that weaken export penetration materially reduce the external benefits of the RRP/RRF.

### Figures and diagnostic results (as described)
- Figure 7 (described): RRP/RRF impact under alternative scenarios in percentage points of GDP for:
  - Private savings, Public savings, Current account balance, Net international investment position.
- Figure 8 (described): Fiscal policy, debt, and real exchange rate under alternative scenarios in percentage points of GDP and percent deviations for:
  - Fiscal balance, External public debt, External private debt, Real exchange rate (increase means depreciation).
- Notes on measurement:
  - Charts are measured relative to either the balanced growth path (which does not enjoy the benefits of the RRP/RRF) or the initial steady state, as specified in the annotated figures.

### Discussion and conclusion
- Baseline magnitudes:
  - Under the baseline, the current account and the NIIP improve by up to 2.6 percentage points and 30 percentage points of GDP, respectively, after 15 years (compared to a scenario without the RRP/RRF).
- Key nuanced conclusions:
  - The RRP/RRF can deliver sustained improvements in external positions, but these gains are highly contingent on accompanying domestic policies.
  - Fiscal prudence that prioritizes debt reduction is critical; redirecting the fiscal dividend into tax cuts substantially weakens external outcomes.
  - Loose macroprudential regimes that reduce borrowing costs for households can produce unproductive capital inflows that undermine the RRP/RRF’s benefits.
- Recommendations for policy design:
  - Prioritize fiscal policies that reduce external public debt rather than channeling RRP/RRF-generated fiscal dividends into distortionary tax cuts.
  - Strengthen macroprudential frameworks to limit incentives for unproductive foreign borrowing that would amplify private external debt.
  - Complete structural reforms that improve export competitiveness to ensure traded-sector gains materialize and support NIIP improvements.
  - Consider policies to boost private savings, including greater tax incentives to contribute to the fully-funded auxiliary pension system, particularly for low- and middle-income households.
  - Tilt capital inflows toward productive foreign direct investment (FDI) by establishing a world-class regulatory framework for FDI and targeted incentives in strategic sectors such as manufacturing, renewable energy, and research and development.

*Source: IMF staff calculations and analysis in "7. Policy experiments" from the supplied content unit.*

### Annex V. Equilibrium conditions

### Annex V. Equilibrium conditions

### Model setup and steady state
- The steady state is calculated numerically by solving a system of non-linear equations (using Matlab’s fsolve function).
- The non-linear model is solved under perfect foresight.
- For simplicity, the below equilibrium conditions ignore trend growth rate under the balanced growth path.

### Unit prices and price indices
- Unit price of the consumption basket:
  - 1 = [φ p_{N,t}^{1−χ} + (1−φ) P_{T,t}^{1−χ}]^{1/(1−χ)}
- Price of the traded good basket:
  - P_{T,t} = [φ_{T} p_{TH,t}^{1−χ_{T}} + (1−φ_{T}) s_{t}^{1−χ_{T}}]^{1/(1−χ_{T})}
- Government purchases price index:
  - p_{t}^{G} = [ν p_{N,t}^{1−χ} + (1−ν) p_{T,t}^{1−χ}]^{1/(1−χ)}
- Price index for government purchases of traded goods:
  - p_{T,t}^{G} = [ν_{T} p_{TH,t}^{1−χ_{T}} + (1−ν_{T}) s_{t}^{1−χ_{T}}]^{1/(1−χ_{T})}

### Labor and wage relations
- Relative labor supply to tradable sector:
  - L_{T,t} = (1−θ) (w_{T,t} / w_{t})^{ρ_{L}}_{t}
- Relative labor supply to non-traded good sector:
  - L_{N,t} = θ (w_{N,t} / w_{t})^{ρ_{L}}_{t}
- Real wage index:
  - w_{t} = [θ w_{N,t}^{1+ρ} + (1−θ) w_{T,t}^{1+ρ}]^{1/(1+ρ)}
- Demand for labor (Non-traded good):
  - w_{N,t} = α_{N} p_{N,t} y_{N,t} / L_{N,t}
- Demand for labor (Traded good):
  - w_{T,t} = α_{T} p_{T,t} y_{T,t} / L_{T,t}

### Household optimization: consumption, labor, and Euler equations
- Marginal utility of consumption (Optimizers):
  - λ_{t} (1+τ_{t}^{C}) = (c_{t}^{OPT})^{−σ}
- Labor supply (Optimizers):
  - ε_{t} κ^{κ}_{OPT} (L_{t}^{OPT})^{ψ} = λ_{t} (1−τ_{t}^{L}) w_{t}
- Euler equation 1 (Optimizers):
  - λ_{t} = β E_{t} (λ_{t+1} R_{t})
- Euler equation 2 (Optimizers):
  - λ_{t} = β E_{t} [λ_{t+1} s_{t+1} R_{∗} s_{t}^{−η} (b_{t}^{OPT∗} − b^{OPT∗})]
- Risk premium for private debt (Optimizers):
  - R_{t}^{∗} = R_{dc,t} + u

### Rule-of-thumb agents (consumption and labor)
- Consumption demand (Rule of Thumb):
  - (1+τ_{t}^{C}) c_{t}^{ROT} = (1−τ_{t}^{L}) w_{t} L_{t}^{ROT} + s_{t} r_{m}^{∗} + z_{t} − μ_{k} G_{t−1}
- Labor supply (Rule of Thumb):
  - L_{t}^{ROT} = [1 / (ε_{t} κ^{κ}_{ROT} (1−τ_{t}^{L}) (1+τ_{t}^{C}) (c_{t}^{ROT})^{−σ} w_{t})]^{1/ψ}

### Aggregation across agent types
- c_{t} = ω c_{t}^{OPT} + (1−ω) c_{t}^{ROT}
- L_{t} = ω L_{t}^{OPT} + (1−ω) L_{t}^{ROT}
- b_{t}^{∗} = ω b_{t}^{OPT∗}
- b_{t} = ω b_{t}^{OPT}

### Production, capital, and investment (Non-traded and Traded)
- Production function (Non-traded good):
  - y_{N,t} = z_{N,t} (k_{N,t−1})^{1−α_{N}} (L_{N,t})^{α_{N}} (k_{G,t−1})^{α_{G}}
- Capital law of motion (Non-traded good):
  - k_{N,t} = (1−δ_{N}) k_{N,t−1} + [1 − κ_{N}/2 (i_{N,t}/i_{N,t−1} − 1)^{2}] i_{N,t}
- Tobin’s Q (Non-traded good):
  - q_{N,t} = E_{t}[β (λ_{t+1}/λ_{t}) ((1−δ_{N}) q_{N,t+1} + (1−τ_{K})(1−ϑ_{t+1})(1−α_{N}) p_{N,t+1} y_{N,t+1} / k_{N,t})]
- Investment (Non-traded good):
  - 1/q_{N,t} = 1 − κ_{N}/2 (i_{N,t}/i_{N,t−1} − 1)^{2} − κ_{N} (i_{N,t}/i_{N,t−1} − 1) i_{N,t}/i_{N,t−1} + E_{t}[β (λ_{t+1}/λ_{t}) κ_{N} q_{N,t+1}/q_{N,t} (i_{N,t+1}/i_{N,t})^{2} (i_{N,t+1}/i_{N,t} − 1)]
- Production function (Traded good):
  - y_{T,t} = z_{T,t} (k_{T,t−1})^{1−α_{T}} (L_{T,t})^{α_{T}} (k_{G,t−1})^{α_{G}}
- Capital law of motion (Traded good):
  - k_{T,t} = (1−δ_{T}) k_{T,t−1} + [1 − κ_{T}/2 (i_{T,t}/i_{T,t−1} − 1)^{2}] i_{T,t}
- Tobin’s Q (Traded good):
  - q_{T,t} = E_{t}[β (λ_{t+1}/λ_{t}) ((1−δ_{T}) q_{T,t+1} + (1−τ_{K})(1−ϑ_{t+1})(1−α_{T}) p_{T,t+1} y_{T,t+1} / k_{T,t})]
- Investment (Traded good):
  - 1/q_{T,t} = 1 − κ_{T}/2 (i_{T,t}/i_{T,t−1} − 1)^{2} − κ_{T} (i_{T,t}/i_{T,t−1} − 1) i_{T,t}/i_{T,t−1} + E_{t}[β (λ_{t+1}/λ_{t}) κ_{T} q_{T,t+1}/q_{T,t} (i_{T,t+1}/i_{T,t})^{2} (i_{T,t+1}/i_{T,t} − 1)]

### Investment distortion and productivity
- Investment distortion:
  - ϑ_{t} / ϑ̅ = exp(−η_{θ} (K_{t−1}^{G} − K_{G̅}))
- Total factor productivity:
  - z_{T,t} = z̅_{T} ε_{t}^{z}
  - z_{N,t} = z̅_{N} ε_{t}^{z}

### Fiscal sector: gap, financing, and rules
- Fiscal gap:
  - gap_{t} = f_{out,t} − f_{in,t}
- Fiscal gap expanded:
  - gap_{t} = Δ b_{t} + s_{t} Δ d_{c,t} + (τ_{t}^{C} − τ_{C̅}) c_{t} + (τ_{t}^{L} − τ_{L̅}) w_{t} L_{t} − p_{t}^{G} (g_{t}^{C} − g_{C̅}) − (z_{t} − z̅)
- Fiscal inflows:
  - f_{in,t} = τ_{C̅} c_{t} + τ_{L̅} w_{t} L_{t} + (1−ϑ_{K}) τ_{K̅} (r_{T,t}^{K} k_{T,t−1} + r_{N,t}^{K} k_{N,t−1}) + μ_{k} G_{t−1} + s_{t} g_{r,t}^{∗} + s_{t} Δ d_{t}
- Fiscal outflows:
  - f_{out,t} = p_{t}^{G} g_{t}^{I} + p_{t}^{G} g_{C̅}^{C} + z̅ + (R_{d̅} − 1) s_{t} d_{t−1} + (R_{dc,t−1} − 1) s_{t} d_{c,t−1} + (R_{t−1} − 1) b_{t−1}
- Financing the fiscal gap:
  - ω Δ b_{t} = (1−ω) s_{t} Δ d_{c,t}
- Fiscal targets:
  - τ_{target,t}^{C} = τ_{C̅} + λ_{1} gap_{t} / c_{t}
  - τ_{target,t}^{L} = τ_{L̅} + λ_{2} gap_{t} / (w_{t} L_{t})
  - z_{target,t} = z̅ + λ_{4} gap_{t}
- Fiscal rules:
  - τ_{t}^{C} = τ_{t−1}^{C} + ζ_{1} (τ_{target,t}^{C} − τ_{t−1}^{C}) + ζ_{2} (b_{t−1} + s_{t−1} d_{c,t−1} / y_{t−1} − b̅ + s̅ d_{c̅} / y̅)
  - τ_{t}^{L} = τ_{t−1}^{L} + ζ_{3} (τ_{target,t}^{L} − τ_{t−1}^{L}) + ζ_{4} (b_{t−1} + s_{t−1} d_{c,t−1} / y_{t−1} − b̅ + s̅ d_{c̅} / y̅)
  - z_{t} / z̅ = z_{t−1} / z̅ + ζ_{7} (z_{target,t} − z_{t−1}) / z̅ − ζ_{8} (b_{t−1} + s_{t−1} d_{c,t−1} / y_{t−1} − b̅ + s̅ d_{c̅} / y̅)

### Government spending and public capital
- Government spending:
  - g_{t} = g_{t}^{C} + g_{t}^{I}
  - g_{t}^{C} = g_{C̅} + ε_{t}^{RRFC}
  - g_{t}^{I} = g_{I̅} + ε_{t}^{R R F I}
- Law of motion for public capital:
  - k_{G,t} = (1−δ_{G,t}) k_{G,t−1} + ε_{g,t}^{I}

### Debt and risk premia
- Debt-elastic risk premium on external government debt:
  - R_{dc,t} = R_{f} + v_{dc} exp [η_{dc} ((d_{t} + d_{c,t}) / y_{t} − (d̅ + d_{c̅}) / y̅)]

### External sector: trade, current account, and balance of payments
- Exports:
  - x_{t} / x̅ = (s_{t} p_{TH,t})^{χ_{X}}
- Imports:
  - s_{t} m_{t} = p_{TH,t} x_{t} + c_{t} + i_{N,t} + i_{T,t} + p_{t}^{G} g_{t} + Θ_{t}^{OPT∗} − y_{t}
- Current account deficit:
  - ca_{t}^{d} = p_{TH,t} x_{t} − s_{t} m_{t} + s_{t} r_{m}^{∗} + s_{t} g_{r,t}^{∗} − (R_{d̅} − 1) s_{t} d_{t−1} − (R_{dc,t−1} − 1) s_{t} d_{c,t−1} − (R_{t−1}^{∗} − 1) s_{t} b_{t−1}^{∗}
- Balance of payment condition:
  - ca_{t}^{d} / s_{t} = Δ d_{t} + Δ d_{c,t} + Δ b_{t}^{∗}

### Market clearing and aggregate output
- Total output:
  - y_{t} = p_{N,t} y_{N,t} + p_{TH,t} y_{T,t}
- Market clearing condition for non-traded goods:
  - y_{N,t} = φ p_{N,t}^{−χ} (c_{t} + i_{N,t} + i_{T,t} + Θ_{t}^{OPT∗}) + ν p_{t}^{G} − χ g_{t}
- Market clearing condition for traded goods:
  - y_{T,t} = φ_{T} (p_{TH,t} / P_{T,t})^{−χ_{T}} (1−φ) P_{T,t}^{−χ_{T}} (c_{t} + i_{N,t} + i_{T,t}) + ν_{T} (p_{TH,t} / p_{T,t}^{G})^{−χ_{T}} (1−ν) (p_{T,t}^{G} / p_{t}^{G})^{−χ_{T}} − χ_{T} (1−ν) (p_{T,t}^{G} / p_{t}^{G})^{−χ_{T}} − χ g_{t} + ω x_{t}

*Source: Annex V. Equilibrium conditions, wpiea2025110-print-pdf.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025110-print-pdf.pdf_