## 2.1 Some Stylized Facts (wpiea2025213-source-pdf)

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### Historical trajectory and structural features
- Post-1948: high unemployment, low foreign currency reserves; austerity (rationing) until 1959.
- Recovery after 1952 reparations: annual growth rates exceeding 10 percent in the following decade and rising per capita consumption.
- 1970s setbacks (Yom Kippur War) and hyperinflation peaking at nearly 450 percent after the 1983 banking crisis; subsequent stabilization.
- 1990s: over one million immigrants from the former Soviet Union; favorable environment after 1991 peace process.
- Early 2000s: downturn from dot-com bubble burst and the Second Intifada; recovery from 2002 driven by new export markets (notably East Asia) and HT sector resurgence.
- Financial sector: limited exposure to high-risk foreign assets helped withstand the 2007-2008 Global Financial Crisis.

### Key model-relevant structural characteristics
- Household heterogeneity:
  - OLG households: overlapping generations, high labor skills, savers (can smooth consumption via asset accumulation).
  - LIQ households: liquidity-constrained, low labor skills, consume current income each period (non-savers).
- Real rigidities and amplifiers:
  - External habit formation and real wage rigidities.
  - Presence of OLG and LIQ breaks Ricardian equivalence, amplifies Keynesian demand effects and fiscal multipliers.
  - OLG introduces Pigouvian wealth effects on demand.
- Two main production sectors:
  - High-Tech (HT): export-oriented, sector-specific capital, skilled labor, public capital; monopolistic competition, nominal price rigidities, real adjustment costs on labor and imports.
  - Non-High-Tech (non-HT): domestic and external markets, oil imports, sector-specific capital, skilled and unskilled labor; CES production with capital-skill complementarity (capital substitutes low-skill labor; capital complements high-skill labor); monopolistic competition and price rigidities.
- Additional agents: physical capital producers (perfect competition), oil and non-oil importers (law of one price for oil; monopolistic competition for non-oil imports with imperfect exchange-rate pass-through), exporters and retailers (aggregate HT and non-HT outputs with adjustment costs).

### External sector and fiscal-monetary framework (model representation)
- Foreign variables (foreign inflation, foreign interest rate, oil prices, foreign GDP) follow AR(1) processes with stochastic shocks.
- Foreign interest rate includes a country risk premium that increases with total foreign debt-to-GDP ratio.
- Fiscal block:
  - Government budget constraint: deficits financed by issuing domestic and external debt.
  - Revenues: lump-sum taxes and distortionary taxes on labor income, capital income, and consumption.
  - Expenditures: current expenditures, targeted transfers, public investment (possibly inefficient).
  - Fiscal policy rule: forward-looking primary surplus instrument responding to deviations of total public debt from a target; simple rules for debt issuance with exogenously determined domestic vs external financing fractions.
  - Other revenue and expenditure instruments: exogenous AR(1) processes with shocks.
- Central bank: inflation-targeting, forward-looking interest-rate rule with smoothing and monetary policy shocks; interest rate responds to deviations of expected future CPI inflation from the target.
- Market equilibrium closes goods, labor, capital, bonds, and current account (growth of net foreign debt equals current account deficit).

### Shocks included in the ISM
- Households: preference shocks, labor supply shocks (preferences and endowments), wage markup shocks.
- Capital producers: investment adjustment shocks.
- HT and non-HT firms: productivity shocks, cost-push shocks, balanced-growth-path (BGP) shocks.
- Importers: foreign price shocks, cost-push shocks, oil price shocks.
- Fiscal block: shocks to distortionary tax rates, lump-sum taxes, targeted transfers, government consumption, government investment and its efficiency, primary surplus, debt targets, domestic financing.
- Monetary policy: discretionary shocks.
- Foreign sector: shocks to foreign interest rates, inflation, GDP, and country risk premium.

### Stylized numerical outcomes (2020–2022 episode)
- Baseline (applied end-2022 with data up to 2021):
  - GDP decline of more than 4 percent during 2020–2021.
  - Increase in public debt of approximately 9 percentage points of GDP.
  - Real appreciation of over 9 percent.
  - Significant contraction in consumption of both savers and non-savers and notable redistributional effects.
- Role of HT in 2021:
  - Positive HT developments raised real GDP by more than 3 percent relative to trend and reduced public debt-to-GDP by about 2 percentage points (pp).
- HT expansion assumptions for policy scenarios:
  - HT expansion of 0.5 pp of GDP in 2022 and 0.7 pp in 2023.
  - Additional government revenues of approximately 2.9 pp of GDP in 2022 and 1.3 pp in 2023.
- Policy scenario common outcomes:
  - All three policies (expedited debt reduction, redistribution via transfers, increased public investment) accelerate GDP convergence to pre-pandemic trend, reduce public debt-to-GDP ratios, and produce positive redistributional effects.
  - All policies induce further real exchange rate appreciation—additional appreciation between 8.2 and 10.5 percent in 2022 relative to trend—raising competitiveness concerns for non-HT sector.
  - Comparative preference: increased public investment most favorable on balance—accelerates GDP return to long-term trajectory, reduces public debt-to-GDP ratios, mitigates real appreciation and competitiveness losses for non-HT, and offers some protection to disadvantaged consumers.

---

### Macroeconomic performance and HT role (2010–2021 context)

### Macroeconomic averages and targets (2010–2019)
- GDP potential growth: 3.8
- GDP growth (constant prices): 4.2 — Average 2010-2019
- Inflation target: 2.0 — Between 1-3 percent
- Inflation rate: 1.1 — Average 2010-2019
- Unemployment rate: 5.6 — Average 2010-2019, 2019 level: 3.8 percent
- Debt-to-GDP target: 60.0 — 58.9 percent in 2019
- Private consumption-to-GDP: 53.46 — Average 2010-2019
- Export-to-GDP: 31.81 — Average 2010-2019
- Import-to-GDP: 30.34 — Average 2010-2019
- Government current expenditure-to-GDP: 19.0 — Average 2010-2019
- Government capital expenditure-to-GDP: 2.0 — Average 2010-2019
- Government financial transfer to household-to-GDP: 9.9 — Average 2010-2019
- Government consumption tax-to-GDP: 7.26 — Average 2010-2019
- Government labor income tax-to-GDP: 4.58 — Average 2010-2019
- Government non-tax revenues-to-GDP: 2.66 — Average 2010-2019
- Source: Ministry of Finance, Israel.

### High-Tech (HT) sector statistics and dynamics
- By 2021:
  - HT sector ≈ 15 percent of GDP.
  - HT employment ≈ 10 percent of total workforce.
  - HT exports > 50 percent of Israel’s total exports in 2021.
- HT production shifted from goods to services.
- VC investment in HT reached an all-time high in 2021.
- Tax dynamics note: most venture capital investment flows almost immediately into wages (increasing income tax revenues); corporate tax revenues materialize later.

### COVID-19 impacts (2020–2021)
- Two lockdowns: 2020 and early 2021.
- Bank of Israel interest rate was 0.25 percent before limited quantitative easing.
- Government increased expenditures and introduced an economic aid plan.
- Government debt rose to 70.6 percent of GDP in 2021, up from 58.9 percent in 2020.
- HT sector remained at full capacity in 2020–2021, increasing employment and exports.
- Real GDP grew by 8.1 percent year-on-year in 2021.
- By 2021 many sectors approached pre-pandemic employment levels; tourism lagged.

### Fiscal framework and outcomes
- Historical hyperinflation in 1980s (100 to 500 percent) led to 1985 stabilization and fiscal rules.
- Fiscal rules:
  - Target Deficit Rule (1992).
  - Expenditure Rule (2004).
  - Numerator (2017): restricts accumulation of future liabilities; requires planned three-year budget publication.
- Pandemic fiscal path:
  - Deficit rose to 11.3 percent of GDP in 2020.
  - Gross debt rose to 70.6 percent of GDP in 2021.
  - 2021: deficit fell to 4.4 percent of GDP; gross debt decreased to 68 percent.
- Tax revenues:
  - Total tax revenues: 24.3 percent of GDP in 2021 (from 21.9 percent in 2020).
  - Direct taxes: 56.2 percent of total revenues.
  - Indirect taxes: 42.0 percent of total revenues.
  - Tax revenue growth: average real growth 3.3 percent (1996–2019); −1.5 percent in 2020; +21.7 percent in 2021 coinciding with GDP growth of 8.6 percent.
  - First half of 2022: tax revenues remained high, exceeding projections, driven primarily by HT growth.
- 2022 budget allocations:
  - 43.1 percent for social services.
  - 20.1 percent for security.
  - 13.1 percent for debt payments (4.1 percent principal; 9.1 percent interest).

### Monetary policy and inflation (selected facts)
- BOI inflation-targeting since early 1990s.
- Inflation fell to approximately 10 percent by 1996; reduced interest rates to stimulate growth thereafter.
- BOI reduced benchmark rate from around 8 percent (early 2000s) to as low as 0.25 percent by 2015.
- COVID-19 era:
  - By January 2022 inflation surpassed BOI’s target; interest rate increased to 0.35 percent in April meeting.
  - Inflation reached 5.1 percent in October 2022.
  - BOI tightened policy, raising policy rate to 3.25 percent through six decisions.

---

### ISM structure, growth, and calibration

### ISM overview
- ISM: open-economy DSGE (New Keynesian small-open economy) for policy scenario analysis.
- Key features:
  - Two household types: OLG (middle-/high-income, savers) and LIQ (low-income, liquidity-constrained).
  - Two productive sectors: HT and non-HT.
  - Four high-level blocks: Household; Production (non-HT firms, HT firms, physical capital producers, importers, exporters, retailers); Policy block (MOF and BOI); Rest of world.
  - Exogenous long-term growth from productivity and population growth.

### Growth trend and normalization
- Balanced growth components:
  - Productivity growth: g_A_t
  - Population growth: g_N_t
- Trend relation: 1 + g_t = (1 + g_N_t)(1 + g_A_t).
- Simplifying assumption: g_N_t = g_N and g_A_t = g_A.
- Variables rescaled by (1 + g)_t to ensure stationarity.

### Household block specifics (selected equations)
- OLG budget and aggregated consumption (period t):
  - (1 + τ_C_t) P_C_t C_OLG_a,t + (1 - !) (B_a,t + S_t B*_a,t) + T_a,t = (1 - τ_L,OLG_t) W_OLG,r_t L_OLG_a,t + pr_a,t + (1 + i_t-1) B_a-1,t-1 + (1 + i*_t-1)(1 + Prem_t-1) S_t B*_a-1,t-1.
  - Aggregated consumption: (1 + τ_C_t) C_OLG_t = MPC_t · Inc_t + (1 + r_t-1) B_t-1 + (1 + r*_t-1) REER_t B*_t-1, where REER_t = S_t P_C*_t / P_C_t.
- LIQ budget (period t):
  - (1 + τ_C_t) C_LIQ_a,t = (1 - τ_L,LIQ_t) w_LIQ,r_t L_LIQ_a,t + TR_a,t.
- Real wage rigidity (j ∈ {OLG, LIQ}):
  - log(w^j_t) = ρ_w,j log( w^j_t-1 / (1 + g_A_t) ) + (1 - ρ_w,j) log(w^j,r_t).

### Production block (selected highlights)
- Physical capital producers:
  - K_j_t = (1 - δ) K_j_{t-1} + Inv_j_t [1 - S_j(·)], j ∈ {H; N}.
  - Investment adjustment cost: S_j(·) = θ_Inv_j · (Inv_j_t^2) [ (1 + ξ_Inv_j_t) Inv_j_t / Inv_j_{t-1}  - 1 ]^2 / 2.
  - Investment FOC (Tobin’s Q) and non-arbitrage condition detailed (equations preserved in source).
- Non-HT firms:
  - Dixit-Stiglitz demand: Y_{N,t}(i) = (P_{N,t}(i) / P_{N,t})^{-φ_N} Y_{N,t}.
  - Rotemberg price adjustment costs R_N(·) with indexation parameter #_N.
  - Production: multi-level CES with public capital term (K_{Gov,t-1}/\bar{K}_{Gov,t-1})^{α_{G,N}} and oil/non-oil components; capital-skill complementarity via nested CES (parameters θ, α_N, κ_N).
  - New-Keynesian Phillips curve for non-HT (equation (33)).
- HT firms:
  - HT production (equation (34)) with public capital elasticity α_{G,H}, capital share α_H, substitution κ_H.
  - Marginal cost and demand for sector-specific capital and skilled labor defined (equations (35)-(37)).
  - New-Keynesian Phillips curve for HT (equation (38)).
- Importers and exporters:
  - Oil importers: law of one price; P_{Oil,t} = P_{Oil,*,t} S_t.
  - Non-oil importers: monopolistic competition, Rotemberg costs, imperfect exchange-rate pass-through.
  - Export retailers aggregate sector outputs and imports via CES (equation (44)); final export price p_{X,j,t} given by equation (48).
- Retailers aggregate HT, non-HT, oil and non-oil imports into final goods (equation (50)); demand functions and final prices follow (equations (51)-(55)).

### External block and current account
- Foreign variables (i*, π*, P_Oil,*, GDP* ) follow AR(1) processes.
- Export demand X_j t depends on effective foreign demand GDP*,j t, relative export price p_X,j t, and REER_t with sensitivity θ_j.
- Country risk premium prem_t increases with total net foreign debt-to-GDP D* t / GDP_t via an exponential specification.
- Current account and trade balance identities preserve exact model expressions (e.g., CAB_t, TB_t formulas preserved in source).

### Key calibration values (selected exact entries)
- Balanced growth path:
  - g = 0.029
  - g_N = 0.019
  - g_A = 0.01
  - Steady-state growth implied by g_A and g_N = 2.9 percent per year
- Household and production parameters:
  - ! = 0.05 (implied by 20 year planning horizon)
  - ̄A_OLG_N = 1; ̄A_OLG_H = 1; ̄A_LIQ = 1
  - ̄S = 1
  - _OLG = 0.65
  - _LIQ = 0.5
  - h = 0.35
  - Relative risk aversion  = 1
  -  = 0.1 (depreciation rate of private capital)
  - α_H = 0.5872
  - α_N = 0.3792
  - α_G_H = 0.01
  - α_G_N = 0.02
  - _Inv,j t = 0.10
  - _L,OLG,j = 0.5
  - _L,LIQ = 5
  - ' _N = 6
  - κ_N = 1.01
  - % = 1.67
- Fiscal and monetary steady-states and ratios:
  - ̃Rev / ̃GDP = 31.05
  - ̃Tax_C / GDP = 10.0
  - ̃Tax_L / GDP = 12.0
  - ̃Tax_K / GDP = 1.0
  - ̃T / GDP = 8.05
  - ̃Exp / ̃GDP = 31.0
  - p_Gov ̃Gov / ̃GDP = 19.0
  - ̃p_Gov_Inv_Gov / GDP = 2.0
  - ̃TR / ̃GDP = 10.0
  - ̃GS / ̃GDP = 2.84
  - ̃PS / ̃GDP = -0.31
  - ̃IntCost / ̃GDP = 3.15
  - Domestic debt servicing cost-to-GDP = 2.42
  - Foreign debt servicing cost-to-GDP = 0.73
  - ̃Debt / ̃GDP = 62.0
  - ̃Debt_Dom / ̃GDP = 53.0
  - ̃Debt* / ̃GDP = 9.0
  - ̄e = 0.75
  - _Gov = 0.1
  - τ_C = 0.17
  - τ_L,OLG = 0.24
  - τ_L,LIQ = 0.12
  - τ_K = 0.10
  - ̄r = 0.03
  - ̄π_tar = 0.02
  - _π = 2.5
  - ρ_i = 0.4
  - ρ_r,trend = 0.95
- National accounts / external steady-state shares (percent of GDP):
  - ̃C / ̃GDP = 58.68
  - ̃C_OLG / ̃GDP = 47.46
  - ̃C_LIQ / ̃GDP = 10.61
  - p_Inv_Inv_H / GDP = 6.0
  - p_Inv_Inv_N / GDP = 17.0
  - p_Gov ̃Gov / GDP = 19.0
  - p_X,H ̃X_H + p_X,N ̃X_N / ̃GDP = 30.0
  - p_X,H ̃X_H / ̃GDP = 15.0
  - p_X,N ̃X_N / ̃GDP = 15.0
  - p_M ̃M + p_Oil ̃M_Oil / ̃GDP = 31.07
  - p_M ̃M / ̃GDP = 26.71
  - p_Oil ̃M_Oil / ̃GDP = 4.37
- Supply and income shares:
  - p_N ̃Y_N − p_Oil ̃M_Oil / ̃GDP = 83.59
  - p_H ̃Y_H / ̃GDP = 16.41
  - W_OLG ̃L_OLG + W_LIQ ̃L_LIQ / ̃GDP = 51.64
  - W_OLG ̃L_OLG / ̃GDP = 47.34
  - W_LIQ ̃L_LIQ / ̃GDP = 4.3
  - Capital income / ̃GDP = 32.8
  - ̃Profit_N + ̃Profit_H / ̃GDP = 15.56
- External position:
  - REER ̃D* / ̃GDP = -75.0
  - REER ̃B* / ̃GDP = -66.0
  - REER ̃Debt* / ̃GDP = -9.0
  - p_X,H ̃X_H + p_X,N ̃X_N − p_M ̃M − p_Oil ̃M_Oil / ̃GDP = -2.68

---

### Policy scenarios using HT-related fiscal windfall (2022 onward)

### Baseline calibration (COVID-19 episode summary)
- Baseline simulation: three-year horizon beginning in 2020.
- Macro outcomes:
  - GDP contracted by 1.9 percent (annualized) in 2020.
  - Growth of 8.6 percent in 2021.
  - Growth of 6.5 percent in 2022.
  - Aggregate decline in GDP of over 4 percent (2020–2021).
  - Public debt increased by approximately 10 percentage points of GDP.
  - Real exchange rate appreciation exceeding 10 percent.
- External shocks in 2020:
  - 10 percent decline in effective foreign demand.
  - Fed reduced policy rate by 120 basis points and signaled rates at the zero lower bound.
  - Effective foreign inflation declined by 1 percent in 2020.
  - Positive 30 percent shock to HT-related foreign demand in 2020.
- Domestic shocks include negative productivity and preference shocks, labor supply and demand disturbances, and investment adjustment cost shock.

### Mitigating role of HT sector (quantified)
- HT sector dynamics:
  - Pushed real GDP up by more than 3 percent relative to trend.
  - Reduced public debt-to-GDP ratio by 3 percentage points (pp).
- Distributional effects:
  - LIQ households: large reductions in labor hours and persistent consumption declines.
  - OLG (non-HT): larger but more temporary consumption decline.
  - OLG in HT: relatively insulated and benefited.

### Alternative scenarios (beginning in 2022) — common assumptions
- HT sector performs significantly better relative to baseline, generating additional tax revenues (higher income taxes and lump-sum taxes).
- Government consumption fixed relative to baseline in all scenarios.

### Scenario 1 — Faster reduction of public debt
- Surplus revenues used to service public debt.
- Effects:
  - Strongest impact on fiscal sustainability.
  - Public debt-to-GDP returns to pre-pandemic levels by 2023.
  - Could boost growth by approximately one percent above baseline.
  - Contributes to additional real exchange rate appreciation (part of 8.2 to 10.5 percent range in 2022).

### Scenario 2 — Redistribution via transfers
- Surplus revenues allocated to transfers: two-thirds to LIQ households and one-third to OLG households.
- Effects:
  - Shields vulnerable households.
  - LIQ household consumption increases by nearly 11 percent in 2022 and 4 percent in 2023 relative to trend.
  - Greater protection for vulnerable populations than debt reduction.
  - Slower pace of public debt reduction in the medium term.
  - More pronounced real exchange rate appreciation under this policy; redistribution captured mainly through savings/consumption channel (model does not allow reservation wage to respond to transfers).

### Scenario 3 — Increased public investment
- Surplus revenues allocated to public investment (subject to inefficiencies).
- Effects:
  - Faster GDP recovery; closes output gap within a couple of years.
  - Through growth effects, faster consolidation of public debt relative to baseline.
  - Short-term accentuation of real appreciation but helps counteract appreciation in medium term.
  - Stimulates non-HT output and productive capacity, mitigating competitiveness losses.
  - Provides some protection to LIQ households relative to baseline.
  - Model usable for sensitivity analyses on public investment efficiency.

### Comparative outcomes (key statistics and trade-offs)
- All three policies:
  - Accelerate return of GDP to pre-pandemic trend.
  - Lower public debt-to-GDP ratios.
  - Yield favorable redistributive outcomes.
- Highlights:
  - Accelerated debt consolidation: most pronounced on fiscal sustainability; debt back to pre-crisis by 2023.
  - Redistribution/transfers: most effective at shielding vulnerable populations; LIQ consumption ~11 percent in 2022 and ~4 percent in 2023 above trend.
  - Increased public investment: most effective at enhancing pace of output recovery and best across debt stabilization, redistribution, and output growth.
- Real exchange rate:
  - All policies induce additional appreciation between 8.2 and 10.5 percent above trend in 2022, raising competitiveness concerns for non-HT sector.
  - Increased public investment partially mitigates this by boosting non-HT productive capacity.

### Policy implications and model utility
- Increased public investment emerges as the most favorable single policy option by the model: accelerates recovery, strengthens debt indicators, tempers real appreciation over the medium term, and offers targeted support to LIQ households.
- ISM is an open-economy DSGE tailored to Israeli economy structural features; supports scenario-based policy analysis for the Ministry of Finance.
- ISM developed through multi-year IMF technical assistance emphasizing institutional capacity building; MOF staff have since applied ISM independently to real-time policy topics.

---

*Source: wpiea2025213-source-pdf — chapter content and authors’ calculations.*

### 2.1  Some Stylized Facts...............................11

### 2.1  Some Stylized Facts

### Historical macroeconomic trajectory and structural features
- Post-1948 challenges: high unemployment, low foreign currency reserves; austerity measures (rationing) until 1959.
- Recovery after 1952 reparations agreement led to annual growth rates exceeding 10 percent in the following decade and rising per capita consumption.
- Growth setbacks in the 1970s (Yom Kippur War) and hyperinflation peaking at nearly 450 percent following the 1983 banking crisis; subsequent successful stabilization plan.
- 1990s transformation: waves of Jewish immigration from the former Soviet Union (over one million educated individuals entering the HT sector) and a favorable environment after the 1991 peace process.
- Early 2000s downturn from the dot-com bubble burst and the Second Intifada; recovery from 2002 driven by new export markets (notably East Asia) and a resurgence in the HT sector.
- Financial sector limited exposure to high-risk foreign assets helped withstand the 2007-2008 Global Financial Crisis.

### Key model-relevant structural characteristics of the Israeli economy
- Two heterogeneous household types:
  - OLG households: overlapping generations, high labor skills, can smooth consumption via asset accumulation (savers).
  - LIQ households: liquidity-constrained, low labor skills, consume current income each period (non-savers).
- Real rigidities and amplifiers: external habit formation and real wage rigidities; presence of OLG and LIQ households breaks Ricardian equivalence and amplifies Keynesian demand effects and fiscal multipliers; OLG introduces Pigouvian wealth effects on demand.
- Two main production sectors:
  - High-Tech (HT) sector: produces mainly for export using sector-specific capital, skilled labor, and public capital; monopolistic competition, nominal price rigidities, and real adjustment costs on labor and imports.
  - Non-High-Tech (non-HT) sector: produces for domestic and external markets using oil imports, sector-specific capital, skilled and unskilled labor; CES production function calibrated for capital-skill complementarity (capital substitutes low-skill labor; capital complements high-skill labor); monopolistic competition and price rigidities.
- Additional production agents: physical capital producers (perfect competition, flexible prices, investment adjustment costs), oil and non-oil importers (law of one price for oil; monopolistic competition for non-oil imports with imperfect exchange-rate pass-through), exporters and retailers (aggregate HT and non-HT outputs with adjustment costs).

### External sector and fiscal-monetary framework (model representation)
- Foreign variables (foreign inflation, foreign interest rate, oil prices, foreign GDP) follow AR(1) processes with stochastic shocks; foreign GDP affects export demand for HT and non-HT goods via real exchange rate and relative prices.
- Foreign interest rate includes a country risk premium that increases with total foreign debt-to-GDP ratio.
- Comprehensive fiscal block:
  - Government budget constraint: deficits financed by issuing domestic and external debt.
  - Revenues: lump-sum taxes and distortionary taxes on labor income, capital income, and consumption.
  - Expenditures: current expenditures, targeted transfers, public investment (possibly inefficient).
  - Fiscal policy rule: forward-looking primary surplus instrument responding to current and anticipated deviations of total public debt from a target; simple rules for debt issuance with exogenously determined fractions of domestic vs external financing.
  - Other revenue and expenditure instruments: exogenous AR(1) processes with shocks.
- Central bank: inflation-targeting, forward-looking interest-rate rule with smoothing and monetary policy shocks; interest rate responds to deviations of expected future CPI inflation from the target.
- Market equilibrium conditions close the model across goods, labor, capital, bonds, and the current account (growth of net foreign debt equals current account deficit).

### Shocks included in the ISM
- Households: preference shocks, labor supply shocks (preferences and endowments), wage markup shocks.
- Capital producers: investment adjustment shocks.
- HT and non-HT firms: productivity shocks, cost-push shocks, balanced-growth-path (BGP) shocks.
- Importers: foreign price shocks, cost-push shocks, oil price shocks.
- Fiscal block: shocks to distortionary tax rates, lump-sum taxes, targeted transfers, government consumption, government investment and its efficiency, primary surplus, debt targets, domestic financing.
- Monetary policy: discretionary shocks.
- Foreign sector: shocks to foreign interest rates, inflation, GDP, and country risk premium.

### Application to the 2020–2022 episode and stylized numerical outcomes (model-based)
- Baseline capturing 2020–2021 pandemic effects (ISM applied end-2022 with data up to 2021):
  - GDP decline of more than 4 percent during 2020–2021.
  - Increase in public debt of approximately 9 percentage points of GDP.
  - Real appreciation of over 9 percent.
  - Significant contraction in consumption of both savers and non-savers and notable redistributional effects.
- Role of HT sector developments in 2021:
  - Positive HT developments mitigated adverse effects, generating additional government revenue that pushed up real GDP by more than 3 percent relative to trend and reduced the public debt-to-GDP ratio by about 2 percentage points (pp).
- HT sector expansion assumptions for policy scenarios:
  - HT sector expansion of 0.5 pp of GDP in 2022 and 0.7 pp in 2023.
  - Additional government revenues of approximately 2.9 pp of GDP in 2022 and 1.3 pp in 2023.
- Policy scenario comparative outcomes (three policy options considered: expedited debt reduction, redistribution via transfers, increased public investment):
  - All three policies accelerate convergence of GDP to its pre-pandemic trend, reduce public debt-to-GDP ratios, and produce some positive redistributional effects.
  - Expedited debt reduction: largest impact on debt levels; public debt-to-GDP returns to pre-pandemic levels by 2023.
  - Transfer redistribution: greatest protection for vulnerable households; consumption among LIQ households increases by nearly 11 percent in 2022 and 4 percent in 2023 relative to trend.
  - Increased public investment: faster GDP recovery, closing the gap from trend within a couple of years.
  - Common side effect: all policies induce further real exchange rate appreciation—an additional appreciation of between 8.2 and 10.5 percent in 2022 relative to trend—raising competitiveness concerns for the non-HT sector.
- Comparative conclusion: increasing public investment is found most favorable—accelerates GDP return to long-term trajectory, reduces public debt-to-GDP ratios, mitigates real appreciation and competitiveness losses for the non-HT sector, and offers some protection to disadvantaged consumers.

*Source: wpiea2025213-source-pdf - 2.1  Some Stylized Facts (canonical IMF chapter content).*

### 2008. By 2009, Israel achieved positive real GDP growth and concluded the decade with

### wpiea2025213-source-pdf - 2008. By 2009, Israel achieved positive real GDP growth and concluded the decade with

### Macroeconomic performance (2010–2019)
- GDP potential growth: 3.8
- GDP growth (in constant prices): 4.2 — Average 2010-2019
- Inflation target: 2.0 — Between 1-3 percent
- Inflation rate: 1.1 — Average 2010-2019
- Unemployment rate: 5.6 — Average 2010-2019, 2019 level: 3.8 percent
- Debt-to-GDP target: 60.0 — 58.9 percent in 2019
- Private consumption-to-GDP: 53.46 — Average 2010-2019
- Export-to-GDP: 31.81 — Average 2010-2019
- Import-to-GDP: 30.34 — Average 2010-2019
- Government current expenditure-to-GDP: 19.0 — Average 2010-2019
- Government capital expenditure-to-GDP: 2.0 — Average 2010-2019
- Government financial transfer to household-to-GDP: 9.9 — Average 2010-2019
- Government consumption tax-to-GDP: 7.26 — Average 2010-2019
- Government labor income tax-to-GDP: 4.58 — Average 2010-2019
- Government non-tax revenues-to-GDP: 2.66 — Average 2010-2019
- Source: Ministry of Finance, Israel.

### High-Tech (HT) sector: role and dynamics
- By 2021, HT sector represented approximately 15 percent of GDP and employed around 10 percent of the total workforce.
- HT production shifted from goods to services.
- HT exports accounted for over 50 percent of Israel’s total exports in 2021.
- High demand for HT workers drove wages upward, creating and widening a wage gap relative to other sectors as the HT share of the economy expanded.
- VC investment in HT reached an all-time high in 2021, resuming pre-pandemic growth trajectories.
- Note on tax dynamics: "Most venture capital investment flows almost immediately and directly into wages, thereby increasing income tax revenues. By contrast, corporate tax revenues materialize only at much later stages."

### COVID-19 shock and 2020–2021 economic developments
- Israel implemented two lockdowns: one in 2020 and another in early 2021.
- Bank of Israel interest rate was 0.25 percent before resorting to limited quantitative easing measures.
- Government increased expenditures and introduced an economic aid plan supporting workers, households, health services, and businesses.
- Government debt rose to 70.6 percent of GDP in 2021, up from 58.9 percent in 2020.
- HT sector remained at full capacity in 2020–2021, increasing employment and exports and mitigating recessionary effects.
- Real GDP grew by 8.1 percent year-on-year in 2021.
- As vaccines became widely available, restrictions were lifted and labor-market recovery occurred across most non-HT sectors; tourism continued to struggle.
- Many sectors approached pre-pandemic employment levels by 2021.

### Fiscal framework, history, and rules
- Historical context: hyperinflation in the 1980s (inflation rates ranging from 100 to 500 percent) led to the 1985 economic stabilization plan emphasizing reductions in government expenditures and deficit and preventing central bank monetization of debt.
- Fiscal rules enacted:
  - Target Deficit Rule (1992): maximum limit on fiscal deficit as a percentage of GDP.
  - Expenditure Rule (2004): ties growth of government expenditure to GDP growth and deviations from the debt target.
  - Numerator (2017): restricts accumulation of future liabilities, mandates publication of a planned budget for the next three years twice a year; new laws with fiscal liabilities must fit within the planned three-year budget or require offsetting expenditure reductions.
- Objective: achieve debt target of 60 percent of GDP (anchor of 1985 plan).

### Fiscal outcomes and the pandemic-period fiscal path
- From 1990s to 2020, deficit fluctuated between 0 and 5 percent of GDP; debt levels declined from 143 percent of GDP in 1988 to 58.9 percent in 2019.
- 2020 pandemic effect:
  - Deficit rose to 11.3 percent of GDP in 2020.
  - Gross debt rose to 70.6 percent of GDP in 2021.
- 2021 improvements:
  - Deficit fell from 11.3 percent of GDP in 2020 to 4.4 percent in 2021.
  - Gross debt decreased from 70.6 percent of GDP to 68 percent.
- Tax revenue composition and dynamics in 2021:
  - Total tax revenues: 24.3 percent of GDP in 2021, up from 21.9 percent in 2020.
  - Direct taxes: 56.2 percent of total revenues.
  - Indirect taxes: 42.0 percent of total revenues.
  - Remaining revenue from fees.
  - Tax revenue growth: average real growth of 3.3 percent from 1996 to 2019; decline of 1.5 percent in 2020; rebound of 21.7 percent in 2021, coinciding with a GDP growth rate of 8.6 percent.
  - First half of 2022: tax revenues remained high, exceeding projections, driven primarily by HT sector growth.
- Government expenditure trends:
  - From 2004 to 2019 government expenditure stabilized around 28 percent of GDP.
  - 2020 surge in spending due to COVID-19; decline in 2021 after pandemic-related expenditure reductions.
  - 2022 budget allocations: 43.1 percent for social services, 20.1 percent for security, 13.1 percent for debt payments (4.1 percent for principal and 9.1 percent for interest).

### Monetary policy and inflation dynamics
- Bank of Israel (BOI) has practiced inflation targeting since the early 1990s.
- Inflation fell to approximately 10 percent by 1996; BOI gradually reduced interest rates to stimulate growth.
- Early 2000s shocks (Second Intifada, dot-com bubble) raised inflationary pressures; BOI contained pressures and reduced inflation below 1 percent by 2003.
- BOI reduced benchmark rate from around 8 percent in the early 2000s to as low as 0.25 percent by 2015.
- COVID-19 era:
  - By January 2022, inflation surpassed BOI’s target range; interest rate increased to 0.35 percent in April policy meeting.
  - Inflation reached 5.1 percent in October 2022.
  - BOI tightened policy, raising the policy rate to 3.25 percent through six separate monetary policy decisions.

### The ISM (Israeli Structural Model): structure and purpose
- ISM is an open-economy DSGE (New Keynesian small-open economy) model designed for policy scenario analysis.
- Key model features:
  - Two types of households: OLG (middle- and high-income) and LIQ (low-income) consumers, each with distinct saving patterns and labor skills.
  - Two productive sectors: HT sector and non-HT sector.
  - Four high-level blocks:
    1. Household block
    2. Production block (non-HT firms, HT firms, physical capital producers, importers, exporters, retailers)
    3. Policy block (MOF and BOI)
    4. Rest of the world block
  - Exogenous long-term growth driven by productivity increases and population growth.

### Growth trend in the ISM
- Balanced growth components:
  - Productivity growth: g_A_t
  - Population growth: g_N_t
- Trend growth relation:
  - 1 + g_t = (1 + g_N_t)(1 + g_A_t)
- Simplifying assumption in the model: g_N_t = g_N and g_A_t = g_A.
- Model variables are rescaled by the factor (1 + g)_t to ensure stationarity.

### Household sector: OLG and LIQ specification and key equations
- Two household populations: a mass of OLG consumers and a mass of 1 - (implied) LIQ consumers; both face a constant probability of dying !.
- OLG households:
  - Represent middle- and higher-income groups; provide skilled labor to HT and non-HT firms.
  - Optimization problem follows Blanchard (1985) and Yaari (1965) methods; surviving probability (1 - !) and finite planning horizon used.
  - Budget constraint (period t):
    (1 + τ_C_t) P_C_t C_OLG_a,t + (1 - !) (B_a,t + S_t B*_a,t) + T_a,t = (1 - τ_L,OLG_t) W_OLG,r_t L_OLG_a,t + pr_a,t + (1 + i_t-1) B_a-1,t-1 + (1 + i*_t-1)(1 + Prem_t-1) S_t B*_a-1,t-1.
  - Aggregated consumption (Modigliani-type):
    (1 + τ_C_t) C_OLG_t = MPC_t · Inc_t + (1 + r_t-1) B_t-1 + (1 + r*_t-1) REER_t B*_t-1,
    where REER_t = S_t P_C*_t / P_C_t.
  - Intra-temporal condition (labor supply implicit):
    C_OLG_t^S_t - L_OLG_t = ( (φ_OLG)^( -1/γ_OLG ) ) ( (1 - τ_L,OLG_t) / (1 + τ_C_t) ) w_OLG,r_t.
  - Uncovered interest parity (approximate, suppressing expectations):
    1 + i_t = (1 + i*_t) (1 + Prem_t) S_t+1 / S_t.
- LIQ households:
  - Cannot save or obtain credit; consume all disposable income each period; supply unskilled labor exclusively to non-HT firms.
  - Budget constraint (period t):
    (1 + τ_C_t) C_LIQ_a,t = (1 - τ_L,LIQ_t) w_LIQ,r_t L_LIQ_a,t + TR_a,t.
  - Aggregated intra-temporal labor supply condition:
    C_LIQ_t^(1 - η) S_t - L_LIQ_t = ( (φ_LIQ)^( -1/γ_LIQ ) ) ( (1 - τ_L,LIQ_t) / (1 + τ_C_t) ) w_LIQ,r_t.
- Real wage rigidity:
  - Differentiates between market wages w^j_t and reservation wages w^j,r_t for j ∈ {OLG, LIQ}.
  - Market wages adjust per:
    log(w^j_t) = ρ_w,j log( w^j_t-1 / (1 + g_A_t) ) + (1 - ρ_w,j) log(w^j,r_t),
    where ρ_w,j is the persistence parameter in wage dynamics.

*Source: Ministry of Finance, Israel; excerpts from the ISM model documentation as provided in the source content.*

### 3.3  Production Sector

### 3.3  Production Sector

### 3.3.1  Physical Capital Producers
- Firm ownership and output:
  - Firms producing physical capital are owned by OLG households and supply sector-specific capital to both HT and non-HT firms.
- Capital accumulation technology (equation (11)):
  - K_j_t = (1 - δ) K_j_{t-1} + Inv_j_t [1 - S_j(·)], where j ∈ {H; N} and δ is the depreciation rate.
- Investment adjustment costs (equation (12)):
  - S_j(·) = S(Inv_j_t / Inv_j_{t-1}) = θ_Inv_j · (Inv_j_t^2) [ (1 + ξ_Inv_j_t) Inv_j_t / Inv_j_{t-1}  - 1 ]^2 / 2, with parameter θ_Inv_j and stochastic shocks ξ_Inv_j_t.
- Pricing and objective:
  - Capital producers operate under perfect competition with flexible prices and maximize profits from renting capital R_{K,j,t} K_{j,t-1} minus investment costs P_{Inv,j,t} Inv_{j,t} [1 + S_j(·)].
- Investment first-order condition (Tobin’s Q) (equation (13)):
  - Q_j_t (1 - τ_{K,t}) P_{Inv,j,t} = 1 + S_j(Inv_j_t / Inv_j_{t-1}) + S'_j(Inv_j_t / Inv_j_{t-1}) · (Inv_j_t / Inv_j_{t-1} - 1) + (1 + i_t)^{-1} E_t [ (1 - τ_{K,t+1})/(1 - τ_{K,t}) · (P_{Inv,t+1} / P_{Inv,j,t}) S'_j(Inv_j_{t+1} / Inv_j_t) · (Inv_j_{t+1} / Inv_j_t)^2 ].
- Non-arbitrage condition equating bond and capital returns (equation (14)):
  - 1 + i_t = E_t [ (1 - δ) Q_j_t^{-1} ( (1 - τ_{K,t+1}) R_{K,j,t+1} + Q_{j,t+1} (1 - δ) ) ]^{-1} (presented in source as: 1+i_t = E_t [ (1-δ) Q_j_t h (1-τ_{K,t+1}) R_{K,j,t+1} + Q_{j,t+1} (1-δ) i ] ).

### 3.3.2  Non-High-Tech (non-HT) Intermediate Firms
- Market structure and demand:
  - Representative non-HT firm operates under monopolistic competition producing for domestic and external markets.
  - Dixit-Stiglitz demand (equation (15)): Y_{N,t}(i) = (P_{N,t}(i) / P_{N,t})^{-φ_N} Y_{N,t}, where φ_N is the price demand elasticity.
- Price adjustment costs (Rotemberg, equation (16)):
  - R_N(·) = R_N [ P_{N,t}(i) / P_{N,t-1}(i) - (1 + π_{tar,t}) (1 + \hat{π}_{N,t-1})^{-1} ]_{+}^{2} with parameters P_N (adjustment cost), #_N (indexation degree), and 1 + \hat{π}_{N,t-1} = (1 + π_{N,t-1})/(1 + π_{tar,t-1}).
  - Full indexation when #_N = 1; no indexation when #_N = 0.
- Real adjustment costs for inputs:
  - Skilled labor adjustment cost H_{OLG,N}(·) (equation (17)) with parameter L_{OLG,N}. Similar H_{LN}(·) for unskilled labor.
  - Oil import adjustment cost G(·) (equation (18)) with parameter M_{Oil,N}.
- Production technology (multi-level CES, equation (19)):
  - Y_{N,t}(i) = (K_{Gov,t-1} / \bar{K}_{Gov,t-1})^{α_{G,N}} [ μ_Y (Y_{Noil,t}(i))^{(ξ-1)/ξ} + (1 - μ_N) (M_{N,Oil,t}(i))^{(ξ-1)/ξ} ]^{ξ/(ξ-1)}, with μ_Y share, ξ elasticity of substitution, α_{G,N} public capital elasticity.
- Non-oil component and capital-skill complementarity (equations (20)-(21)):
  - Y_{Noil,t}(i) aggregates Z_t(i) and skilled/unskilled labor via nested CES with parameters θ, α_N, κ_N, and technology terms A_{LIQ,t}, A_{OLG,N,t}.
- Marginal cost and internal marginal components (equations (22)-(24)):
  - mc_{N,t} = (K_G,t-1 / \bar{K}_G,t-1)^{-α_{G,N}} [ μ_N (mc_{Noil,t})^{1-ξ} + (1 - μ_N) p_{Oil,t}^{1-ξ} ]^{1/(1-ξ)}.
  - mc_{Noil,t} defined by combination of p_Z,t and effective wage ˆw_{LIQ,t} (equation (23)).
  - p_Z,t defined by combination of r_{K,N,t} and ˆw_{OLG,N,t} (equation (24)).
- Effective labor cost (equation (25)):
  - ˆw_j_t = w_{OLG,t} [ 1 + H_j (L_{j,t} / L_{j,t-1}) + H'_j (L_{j,t} / L_{j,t-1}) (L_{j,t} / L_{j,t-1})^2 - E_t w_{OLG,t+1} (1 + r_t)^{-1} H'_j (L_{j,t+1} / L_{j,t}) (L_{j,t+1} / L_{j,t})^2 ], for j ∈ {OLG, N; LIQ}.
- Demand conditions (equations (26)-(31)):
  - K_{N,t-1} = α_N (p_Z,t / r_{K,N,t})^{κ_N} Z_t.
  - L_{OLG,N,t} = (1 - α_N) (p_Z,t / ˆw_{OLG,N,t})^{κ_N} (A_{OLG,N,t})^{κ_N - 1} Z_t.
  - Z_t = [ (mc_{Noil,t} / p_Z,t)^{σ} ] Y_{Noil,t}.
  - L_{LIQ,t} = (1 - θ) (mc_{Noil,t} / ˆw_{LIQ,t})^{σ} (A_{LIQ,t})^{σ-1} Y_{Noil,t}.
  - Y_{Noil,t} = μ_N (mc_{N,t} / mc_{Noil,t})^{ξ} (K_G,t-1 / \bar{K}_G,t-1)^{α_{G,N} (ξ-1)} Y_{N,t}.
  - M_{Oil,N,t} = (1 - μ_N) (mc_{N,t} / ˆp_{Oil,N,t})^{ξ} (K_G,t-1 / \bar{K}_G,t-1)^{α_{G,N} (ξ-1)} Y_{N,t}.
- Effective oil import price (equation (32)):
  - ˆp_{Oil,N,t} defined by p_{Oil,t} times adjustment terms G(·) and expectations.
- New-Keynesian Phillips curve for non-HT sector (equation (33)):
  - Complex forward-looking relation involving indexation parameters #_N, real rates 1 + i_t, expectations E_t, sectoral markup term ' _N, and gap (mc_{N,t} / p_{N,t} - (φ_N - 1)/φ_N).

### 3.3.3  High-Tech (HT) Intermediate Firms
- Inputs and focus:
  - HT firms produce primarily for export and use skilled labor L_{OLG,H,t}, sector-specific capital K_{H,t-1}, and public capital.
- Production function (equation (34)):
  - Y_{H,t} = (K_{Gov,t-1} / \bar{K}_{Gov,t-1})^{α_{G,H}} [ α_H (K_H,t-1)^{(κ_H-1)/κ_H} + (1 - α_H) (A_{OLG,H,t} L_{OLG,H,t})^{(κ_H-1)/κ_H} ]^{κ_H/(κ_H-1)}.
  - Parameters: α_{G,H}, α_H, κ_H, A_{OLG,H,t}.
- Market structure and frictions:
  - Monopolistic competition, Rotemberg nominal price adjustment costs R_H(·) as in equation (16), and labor adjustment costs H_{OH}(·) as in equation (17).
- Equilibrium conditions:
  - Marginal cost (equation (35)):
    - mc_{H,t} = (K_{Gov,t-1} / \bar{K}_{Gov,t-1})^{-α_{G,H}} [ α_H (r_{K,H,t})^{1-κ_H} + (1 - α_H) (ˆw_{OLG,H,t} / A_{OLG,H,t})^{1-κ_H} ]^{1/(1-κ_H)}.
  - Demand for sector-specific capital (equation (36)):
    - K_{H,t-1} = α_H (mc_{H,t} / r_{K,H,t})^{κ_H} (K_{Gov,t-1} / \bar{K}_{Gov,t-1})^{α_{G,H} (κ_H - 1)} Y_{H,t}.
  - Demand for skilled labor (equation (37)):
    - L_{OLG,H,t} = (1 - α_H) (mc_{H,t} / ˆw_{OLG,H,t})^{κ_H} (K_{Gov,t-1} / \bar{K}_{Gov,t-1})^{α_{G,H} (κ_H - 1)} (A_{OLG,H,t})^{κ_H - 1} Y_{H,t}.
  - New-Keynesian Phillips curve for HT sector (equation (38)):
    - Forward-looking relation similar in structure to non-HT Phillips curve with indexation #_H, expectation terms, and markup gap involving mc_{H,t} and p_{H,t}.

### 3.3.4  Oil Importers
- Role and pricing:
  - Oil importers purchase oil abroad and sell domestically without markup; they face the law of one price.
- Price conversions (equations (39)-(40)):
  - P_{Oil,t} = P_{Oil,*,t} S_t.
  - Relative (real) price: p_{Oil,t} = p_{Oil,*,t} REER_t, where p_{Oil,*,t} is the relative foreign oil price.

### 3.3.5  Non-Oil Importers
- Market structure and frictions:
  - Non-oil importers operate under monopolistic competition with Rotemberg-type price adjustment costs, causing imperfect exchange rate pass-through.
- Demand for non-oil imports (equation (41)):
  - M_t(i) = (P_{M,t}(i) / P_{M,t})^{-φ_M} M_t, where φ_M is the price elasticity of substitution.
- Price adjustment cost for non-oil imports (equation (42)):
  - R_M(·) analogous to R_N(·) with parameter P_M and indexation #_M; 1 + \hat{π}_{M,t-1} = (1 + π_{M,t-1})/(1 + π_{tar,t-1}).
- Imperfect pass-through condition (equation (43)):
  - Forward-looking equation relating 1 + \hat{π}_{M,t}, indexation #_M, real rate 1 + i_t, expectations E_t, elasticity φ_M, and terms involving REER_t and relative price p_{M,t}.

### 3.3.6  Exporters
- Production and inputs:
  - Export retailers produce X_{j,t} combining sector-specific inputs Y_{j,t} (j ∈ {H; N}) and imports (oil and non-oil) subject to adjustment costs G_{Oil,X,j}(·) and G_{M,X,j}(·).
- CES aggregator for export goods (equation (44)):
  - X_{j,t} aggregates Y_{j,t}, M_{Oil,X,j,t}, and M_{X,j,t} with parameters μ_{Y,j}, μ_{M,j}, and elasticity κ_{x,j}.
- Derived demands (equations (45)-(47)):
  - Y_{j,t} = μ_{Y,j} (p_{j,t} / p_{X,j,t})^{-κ_{x,j}} X_{j,t}.
  - M_{Oil,X,j,t} = μ_{M,j} (ˆp_{Oil,X,j,t} / p_{X,j,t})^{-κ_{x,j}} X_{j,t}.
  - M_{X,j,t} = (1 - μ_{Y,j} - μ_{M,j}) (ˆp_{M,X,j,t} / p_{X,j,t})^{-κ_{x,j}} X_{j,t}.
- Final export price (equation (48)):
  - p_{X,j,t} = [ μ_{Y,j} p_{j,t}^{1-κ_{x,j}} + μ_{M,j} ˆp_{Oil,X,j,t}^{1-κ_{x,j}} + (1 - μ_{Y,j} - μ_{M,j}) ˆp_{M,X,j,t}^{1-κ_{x,j}} ]^{1/(1-κ_{x,j})}.
- Effective import costs (equation (49)):
  - ˆp_{s,t} = p_t [ 1 + G(M_{s,t}/M_{s,t-1}) + G'_t (M_{s,t}/M_{s,t-1}) (M_{s,t}/M_{s,t-1}) - E_t p_{t+1} (1 + r_t)^{-1} G'_t (M_{s,t+1}/M_{s,t}) (M_{s,t+1}/M_{s,t})^2 ], with p_t = p_{Oil,t} if s = Oil,X,j and p_t = p_{M,t} if s = M,X,j.

### 3.3.7  Retailers
- Role and aggregator:
  - Retailers produce aggregate output Z_{j,t} for consumption and investment by combining HT intermediate goods Y_{H,j,t}, non-HT intermediate goods Y_{N,j,t}, oil imports M_{Oil,Z,j,t}, and non-oil imports M_{Z,j,t}.
- CES retail production function (equation (50)):
  - Z_{j,t} = [ (μ_{N,j})^{1/κ_j} Y_{N,j,t}^{(κ_j-1)/κ_j} + (μ_{H,j})^{1/κ_j} Y_{H,j,t}^{(κ_j-1)/κ_j} + (μ_{Oil,j})^{1/κ_j} M_{Oil,Z,j,t}^{(κ_j-1)/κ_j} + (1 - μ_{N,j} - μ_{H,j} - μ_{Oil,j})^{1/κ_j} M_{Z,j,t}^{(κ_j-1)/κ_j} ]^{κ_j/(κ_j-1)}, for j ∈ {C; Inv_N; Inv_Gov; Inv_H; Gov; Inv_N S_N(·); Inv_H S_H(·)}.
  - Imports subject to adjustment costs G_{Oil,Z,j}(·) and G_{M,Z,j}(·) as in equation (18).
  - Retailers also satisfy demand from adjustment costs associated with private investment, Inv_N S_N(·) and Inv_H S_H(·).
- Demand functions from retailer optimization (equations (51)-(54)):
  - Y_{N,j,t} = μ_{N,j} (p_{N,t} / p_{j,t})^{-κ_j} Z_{j,t}.
  - Y_{H,j,t} = μ_{H,j} (p_{H,t} / p_{j,t})^{-κ_j} Z_{j,t}.
  - M_{Oil,Z,j,t} = (1 - μ_{N,j} - μ_{H,j} - μ_{Oil,j}) (ˆp_{M,Z,j,t} / p_{j,t})^{-κ_j} Z_{j,t}.
  - M_{Z,j,t} = μ_{Oil,j} (ˆp_{Oil,Z,j,t} / p_{j,t})^{-κ_j} Z_{j,t}.
- Final retail prices (equation (55)):
  - p_{j,t} = [ μ_{N,j} p_{N,t}^{1-κ_j} + μ_{H,j} p_{H,t}^{1-κ_j} + μ_{Oil,j} ˆp_{Oil,Z,j,t}^{1-κ_j} + (1 - μ_{N,j} - μ_{H,j} - μ_{Oil,j}) ˆp_{M,Z,j,t}^{1-κ_j} ]^{1/(1-κ_j)}.
  - Retail inflation satisfies 1 + π_{j,t} = (1 + π_{C,t})^{-1} p_{j,t} / p_{j,t-1}.
- Effective import cost expression (equation (56)):
  - ˆp_{s,t} defined analogously to exporters’ effective cost (equation (49)), with p_t = p_{Oil,t} if s = Oil,Z,j and p_t = p_{M,t} if s = M,Z,j.

_Italic: Source — wpiea2025213-source-pdf — 3.3 Production Sector_

### 3.5  External Sector

### 3.5 External Sector

### Modeling of foreign variables and world prices
- Israel is treated as a small open economy with foreign-sector variables modeled exogenously.
- Foreign variables follow either simple structural equations or AR(1) processes.
- Foreign interest rate i* t is determined by a forward-looking Taylor rule (forward-looking response to expected foreign inflation, interest-rate persistence, steady-state foreign real interest rate, and stochastic shock ✏ i* t).
- Foreign inflation π* t follows a persistent process that can be affected by world oil prices P_Oil,* t (persistence parameter ρ_π*, response to oil deviations, and shock ✏_π* t).
- World oil prices P_Oil,* t follow a persistent process with persistence ρ_Oil,* and shock ✏_Oil,* t.

### Export demand and effective foreign demand
- Export demands X_j t for non-HT (j = N) and HT (j = H) goods depend on effective foreign demand GDP*,j t, relative export price p_X,j t, and the real exchange rate REER_t, with sensitivity parameter θ_j.
- Effective foreign demand GDP*,j t follows a persistent process (persistence parameter ρ_GDP*,j), responds to deviations of the foreign interest rate r* t from its steady-state ̄r*, and includes stochastic shock ✏_GDP*,j t.

### Country risk premium and foreign debt dynamics
- Foreign creditors charge a premium prem_t over the risk-free rate that increases with the total net foreign debt-to-GDP ratio D* t / GDP_t, where D* t = Debt* t − B* t.
- The premium is modeled exponentially and depends on deviations of REER_t and D* t / GDP_t from their steady-state values, sensitivity parameter (denoted in source by a parameter), and shocks ✏_D,* t and ✏_Prem t.
- ̄D* / GDP represents the sustainable long-term external debt-to-GDP ratio (including government foreign debt).

### Equilibrium conditions and current account
- Market equilibrium conditions equalize demand and supply of skilled and unskilled labor, sector-specific capital, and bonds.
- Goods market equilibrium for non-HT and HT sectors implies total supply equals aggregate demand from households, investors, government, and exporters.
- GDP_t is defined as the sum of consumption, investment (with adjustment costs), government consumption and investment, exports net of imports, wage income for all household types, and other modeled terms (see model equations).
- Resource constraint pins down current account CAB_t as accumulation of net foreign assets:
  - CAB_t = S_t P_C,* t (B* t − Debt* t) − S_t P_C,* t−1 (B* t−1 − Debt* t−1).
  - CAB_t = TB_t + i* t−1 S_t P_C,* t−1 (B* t−1 − Debt* t−1).
  - Trade balance TB_t = P_X,N t X_N t + P_X,H t X_H t − S_t P*_t M_t − S_t P_Oil,* t M_Oil t.
- Imports M_t and oil imports M_Oil t are aggregated across components with import markup and adjustment functions.

### Exogenous shocks included in the foreign sector and model
- Foreign sector shocks: foreign interest rates, foreign inflation, foreign GDP, and country risk premium.
- The model also incorporates a comprehensive set of exogenous shocks across other blocks:
  - Households: preference shocks, labor supply shocks, wage markup shocks.
  - Capital producers: investment adjustment shocks.
  - HT and non-HT firms: productivity shocks, cost-push shocks, balanced growth path (BGP) shocks.
  - Importers: foreign price shocks, cost-push shocks, oil price shocks.
  - Fiscal policy: shocks to distortionary tax rates, lump-sum taxes, targeted transfers, government consumption, government investment (including efficiency shocks), primary surplus, debt targets, and domestic financing.
  - Monetary policy: discretionary shocks.

### Key calibration values used in the external-sector and macro framework
- Steady-state and growth parameters:
  - Balanced growth path g = 0.029
  - g_N = 0.019
  - g_A = 0.01 (Productivity growth rate)
  - Steady-state growth rate implied by g_A and g_N = 2.9 percent per year
- OLG / household parameters:
  - ! = 0.05 (implied by 20 year planning horizon)
  - ̄A_OLG_N = 1, ̄A_OLG_H = 1, ̄A_LIQ = 1 (normalized steady-state productivities)
  - ̄S (level of time endowment) = 1 (normalized)
  - _OLG = 0.65 (share of consumption in OLG households’ utility)
  - _LIQ = 0.5 (share of consumption in LIQ households’ utility)
  - h = 0.35 (consumption habit formation)
  - Relative risk aversion parameter  = 1
- Production and adjustment parameters:
  -  = 0.1 (depreciation rate of private capital in non-HT and HT sectors)
  - ̃S1 Level of time endowment (normalized in table to 1)
  - α_H = 0.5872 (HT capital share)
  - α_N = 0.3792 (Non-HT capital share)
  - α_G_H = 0.01 (share of public capital in HT production)
  - α_G_N = 0.02 (share of public capital in non-HT production)
  - _Inv,j t = 0.10 (investment adjustment cost parameter)
  - _L,OLG,j = 0.5 (real adjustment cost parameter for OLG labor)
  - _L,LIQ = 5 (real adjustment cost parameter for LIQ labor)
  - ' _N = 6 (price-elasticity/demand parameter for intermediate non-HT goods; captures 20 percent markup)
  - κ_N = 1.01 (elasticity of substitution between private capital and skilled labor)
  - % = 1.67 (elasticity of substitution between unskilled and combined private capital & skilled labor)
- Fiscal and monetary calibration (Table 3 exact entries):
  - Public finance ratios:
    - ̃Rev / ̃GDP = 31.05 (Total tax revenue-to-GDP ratio)
    - ̃Tax_C / GDP = 10.0 (Consumption tax-to-GDP ratio)
    - ̃Tax_L / GDP = 12.0 (Labor income tax-to-GDP ratio)
    - ̃Tax_K / GDP = 1.0 (Capital income tax-to-GDP ratio)
    - ̃T / GDP = 8.05 (Lump-sum tax-to-GDP ratio)
    - ̃Exp / ̃GDP = 31.0 (Total expenditures-to-GDP ratio)
    - p_Gov ̃Gov / ̃GDP = 19.0 (Current expenditure-to-GDP ratio)
    - ̃p_Gov_Inv_Gov / GDP = 2.0 (Capital expenditure-to-GDP)
    - ̃TR / ̃GDP = 10.0 (Financial transfers-to-GDP ratio)
    - ̃GS / ̃GDP = 2.84 (Overall deficit-to-GDP ratio)
    - ̃PS / ̃GDP = -0.31 (Primary deficit-to-GDP ratio)
    - ̃IntCost / ̃GDP = 3.15 (Servicing cost-to-GDP ratio)
    - Domestic debt servicing cost-to-GDP = 2.42 (formula in table)
    - Foreign debt servicing cost-to-GDP = 0.73 (formula in table)
    - ̃Debt / ̃GDP = 62.0 (Total public debt-to-GDP ratio)
    - ̃Debt_Dom / ̃GDP = 53.0 (Domestic public debt-to-GDP ratio)
    - ̃Debt* / ̃GDP = 9.0 (Foreign public debt-to-GDP ratio)
    - ̄e = 0.75 (steady-state public capital inefficiency cost parameter)
    - _Gov = 0.1 (depreciation rate parameter of public capital)
    - Steady-state tax rates and monetary parameters:
      - τ_C = 0.17 (steady-state consumption tax rate)
      - τ_L,OLG = 0.24 (steady-state OLG personal income tax rate)
      - τ_L,LIQ = 0.12 (steady-state LIQ personal income tax rate)
      - τ_K = 0.10 (steady-state capital tax rate)
      - ̄r = 0.03 (steady-state real interest rate)
      - ̄π_tar = 0.02 (steady-state inflation target)
      - _π = 2.5 (response to inflation parameter in Taylor rule)
      - ρ_i = 0.4 (interest-rate smoothing parameter in Taylor rule)
      - ρ_r,trend = 0.95 (persistence parameter of the real interest rate trend)
- National accounts and external-sector steady-state shares (Table 4 exact entries, percent of GDP):
  - ̃C / ̃GDP = 58.68 (Private consumption)
  - ̃C_OLG / ̃GDP = 47.46 (Private consumption of OLG households)
  - ̃C_LIQ / ̃GDP = 10.61 (Private consumption of LIQ households)
  - p_Inv_Inv_H / GDP = 6.0 (HT sector private investment)
  - p_Inv_Inv_N / GDP = 17.0 (Non-HT sector private investment)
  - p_Gov ̃Gov / GDP = 19.0 (Government expenditures)
  - p_X,H ̃X_H + p_X,N ̃X_N / ̃GDP = 30.0 (Exports of goods and services)
  - p_X,H ̃X_H / ̃GDP = 15.0 (HT exports)
  - p_X,N ̃X_N / ̃GDP = 15.0 (Non-HT exports)
  - p_M ̃M + p_Oil ̃M_Oil / ̃GDP = 31.07 (Imports of goods and services)
  - p_M ̃M / ̃GDP = 26.71 (Non-oil imports)
  - p_Oil ̃M_Oil / ̃GDP = 4.37 (Oil imports)
- Supply and income side shares (Table 4 exact entries):
  - p_N ̃Y_N − p_Oil ̃M_Oil / ̃GDP = 83.59 (Intermediate production)
  - p_H ̃Y_H / ̃GDP = 16.41 (HT sector)
  - W_OLG ̃L_OLG + W_LIQ ̃L_LIQ / ̃GDP = 51.64 (Labor wage income)
  - W_OLG ̃L_OLG / ̃GDP = 47.34 (Skilled labor wage income)
  - W_LIQ ̃L_LIQ / ̃GDP = 4.3 (Unskilled labor wage income)
  - Capital income (expression in table) / ̃GDP = 32.8
  - ̃Profit_N + ̃Profit_H / ̃GDP = 15.56 (Profit)
- Balance of payments and external position (Table 4 exact entries):
  - REER ̃D* / ̃GDP = -75.0 (Net foreign assets)
  - REER ̃B* / ̃GDP = -66.0 (Private net foreign assets)
  - REER ̃Debt* / ̃GDP = -9.0 (Public net foreign assets)
  - REER ̃B* / ̃GDP (formula) = (1 − 1/(1+g)) −1.87 (Current account balance; presented in table as (1 − 1/(1+g)) −1.87)
  - p_X,H ̃X_H + p_X,N ̃X_N − p_M ̃M − p_Oil ̃M_Oil / ̃GDP = -2.68 (Net export)

### Role of the HT sector in scenario analysis
- The model is calibrated to Israeli annual data (mostly 2010-2019) and used to construct baseline and alternative scenarios.
- The HT sector played a pivotal role in mitigating adverse effects of the 2020 COVID-19 shock and contributed to fiscal revenue growth during the 2021 recovery, motivating scenario experiments that emphasize HT sector dynamics.

*Source: wpiea2025213-source-pdf - 3.5 External Sector*

### 2022.  Against this backdrop, the ISM is utilized to examine alternative allocations of these

### wpiea2025213-source-pdf - 2022. Against this backdrop, the ISM is utilized to examine alternative allocations of these

### Baseline scenario and calibration (COVID-19 impact)
- Baseline simulation spans a three-year horizon beginning in 2020.
- Macro outcomes in the COVID-19 episode:
  - GDP contracted by 1.9 percent (annualized) in 2020.
  - Growth of 8.6 percent in 2021.
  - Growth of 6.5 percent in 2022.
  - The baseline captures a decline in GDP of over 4 percent (aggregate, 2020–2021).
  - Public debt increased by approximately 10 percentage points of GDP.
  - Real exchange rate appreciation exceeding 10 percent.
- Shocks and transmission channels incorporated in 2020:
  - External shocks:
    - 10 percent decline in effective foreign demand.
    - Fed reduced its policy rate by 120 basis points and signaled rates at the zero lower bound.
    - Effective foreign inflation declined by 1 percent in 2020.
    - Positive 30 percent shock to HT-related foreign demand in 2020 (partially offsetting overall external demand decline).
  - Domestic shocks:
    - Structural disturbances to household time preferences, time endowments, labor demand, and sector-specific demand for HT goods and services.
    - Negative productivity shocks (ε_A,OLG_t and ε_A,LIQ_t) reducing permanent income of LIQ and OLG households.
    - Negative preference shocks (ε_u_C_t) leading OLG households to increase precautionary savings.
    - Time endowment shock (ε_S_t) reducing labor market participation.
    - Negative labor demand shock for LIQ workers (ε_θ_t) and temporary negative wage shock (ε_wLIQ_t).
    - Investment adjustment cost shock (ε_Inv_t) reflecting heightened uncertainty and weaker investor sentiment.
- Sectoral dynamics:
  - HT sector resilience: increased international demand for digital services and technological products supported output and tax revenues.
  - The negative productivity shock in the HT sector constrained excess reallocation of skilled labor from non-HT to HT.
  - Skilled labor dynamics: skilled labor force remains relatively stable; non-HT sector decline modest relative to unskilled labor.
- Policy responses in baseline:
  - Monetary policy: interest rate gradually lowered consistent with a Taylor rule (not an exogenous shock).
  - Fiscal policy: government raised the debt target (ε̄_Debt_t) and temporarily suspended the fiscal rule (setting ρ_1 = 0 in equation (59)) to allow discretionary expansion in government consumption (ε_Gov_t).
  - Lump-sum tax shock (ε_T_t) captures unmodeled fiscal windfall from HT sector robustness.
  - In 2021 the fiscal rule was reinstated (setting ρ_1 = 1 in equation (59)) and a positive shock to the primary surplus (ε_PS_t) modestly accelerated fiscal consolidation.

### Quantified mitigating role of the HT sector
- Shock-decomposition highlights HT sector effects:
  - HT sector dynamics pushed up real GDP by more than 3 percent relative to trend.
  - HT sector dynamics pushed down the public debt-to-GDP ratio by 3 percentage points (pp).
- Distributional outcomes:
  - LIQ households: substantial reductions in labor hours and more persistent consumption declines driven by adverse employment prospects.
  - OLG households (excluding HT workers): larger but more temporary decline in consumption owing to higher steady-state consumption.
  - OLG households in HT sector: relatively insulated and benefited from sector expansion.
- By 2022 the recovery is nearly complete but global inflationary pressures intensified due to foreign output gap closure, rising global commodity prices (ε_Oil,⇤_t), and foreign inflationary shocks (ε_π_t).

### Alternative scenarios (policy uses of HT-related fiscal windfall, beginning in 2022)
- Common assumptions across scenarios:
  - Compared to baseline, HT sector performs significantly better (higher foreign demand for HT goods and increased labor demand), generating additional tax revenues including higher income taxes and increased lump-sum taxes.
  - Government consumption is fixed relative to the baseline in all scenarios.
- Scenarios analyzed:
  1. Faster reduction of public debt
     - Surplus revenues used to service public debt rather than transfers or public investment.
     - (Quantitative trajectories illustrated in Figure 12 in source.)
  2. Redistribution measures (transfers)
     - Surplus revenues allocated to transfers.
     - Allocation rule: two-thirds directed to LIQ households and one-third to OLG households.
  3. Increased public investment
     - Surplus revenues allocated to public investment.
     - Public investment is subject to inefficiencies.
- Policy objectives reflected:
  - Scenario 1 prioritizes debt sustainability.
  - Scenario 2 prioritizes distributional objectives.
  - Scenario 3 prioritizes growth-oriented (investment) strategy.
- Purpose:
  - The ISM-based scenario analysis quantifies macroeconomic effects and trade-offs of each allocation, supporting policymakers in evaluating impacts on key variables.

*Source: Authors’ calculations.*

### 12. Model projections indicate that the public debt-to-GDP ratio is expected to decrease to 5

### 12. Model projections indicate that the public debt-to-GDP ratio is expected to decrease to 5 percent by 2022, down from its 2019 level, and is anticipated to return to pre-pandemic levels by 2024

### Model projections and baseline outcomes
- Public debt-to-GDP ratio is expected to decrease to 5 percent by 2022.
- Debt anticipated to return to pre-pandemic levels by 2024.
- Accelerating debt repayment could potentially boost growth rates by approximately one percent above those observed in the baseline scenario without debt consolidation.
- Return to pre-pandemic growth rates expected by 2028 under accelerated debt repayment.
- Rapid debt reduction might result in higher real appreciation, potentially delaying recovery of the non-HT sector, while having similar redistribution effects compared to the baseline scenario.

### Policy scenario: Accelerated public debt repayment
- Uses surplus revenue from the HT sector boom to accelerate public debt repayment.
- Effects:
  - Strongest impact on fiscal sustainability among scenarios.
  - Debt ratios revert to their pre-crisis levels by 2023.
  - Could boost growth by approximately one percent above baseline (see above).
  - Contributes to additional real exchange rate appreciation (part of 8.2 to 10.5 percent range in 2022).
  - Appreciation pressures arise in the model because decline in sovereign risk premium dominates, strengthening the real exchange rate.

### Policy scenario: Transfers (redistribution) policy
- Reallocates surplus HT-sector revenue to enhance social transfers for low-income LIQ consumers.
- Represented by red-dashed lines in Figure13 (authors’ calculations).
- Effects:
  - Projected to have a more substantial impact on GDP than faster debt reduction via demand-driven (Keynesian) consumption stimulus among LIQ consumers.
  - Shields vulnerable populations: LIQ household consumption rises by approximately 11 percent in 2022 and 4 percent in 2023 above their respective trends.
  - Slower pace of public debt reduction, particularly in the medium term.
  - Real exchange rate appreciation is more pronounced under this policy, though demand-driven growth mitigates some negative effects on the non-HT sector.
- Model limitation noted: the model assumes labor supply decisions depend on the reservation wage but does not allow the reservation wage to be influenced by the level of social transfers; redistribution is captured mainly through the savings/consumption channel, not labor force participation.

### Policy scenario: Increase in public investment
- Redirects HT-sector surplus to boost public investment (green-dashed lines in Figure14; authors’ calculations).
- Effects:
  - Enhances sectoral productivity and directly impacts GDP, surpassing baseline and other policy scenarios in output gains.
  - Through growth effects, results in faster consolidation of public debt relative to the baseline.
  - Accentuates real appreciation in the short term but helps counteract appreciation in the medium term.
  - Directly stimulates output in the non-HT sector and enhances its productive capacity, mitigating competitiveness losses from appreciation.
  - Provides some small protection to low-income LIQ consumers relative to baseline.
- Model can be used for sensitivity analyses of parameters such as the efficiency of capital spending.

### Comparative outcomes and key statistics
- All three policy interventions:
  - Contribute meaningfully to accelerating return of GDP to its pre-pandemic trend.
  - Lower public debt-to-GDP ratios.
  - Yield some favorable redistributive outcomes.
- Specific comparative highlights:
  - Accelerated debt consolidation: most pronounced effect on fiscal sustainability; debt back to pre-crisis by 2023.
  - Redistribution/transfers: most effective in shielding vulnerable populations; LIQ consumption ~11 percent in 2022 and ~4 percent in 2023 above trend.
  - Increased public investment: most effective at enhancing pace of output recovery and narrowing deviation from trend GDP quickly; also best on balance across debt stabilization, fiscal redistribution, and output growth.
- Real exchange rate appreciation:
  - All three policies contribute to additional real exchange rate appreciation ranging between 8.2 and 10.5 percent above trend in 2022.
  - Appreciation raises concerns about external competitiveness for the non-HT tradable sector.
  - Increased public investment partially mitigates this adverse effect by boosting non-HT output and productive capacity.

### Policy implications and model utility
- Increased public investment emerges as the most favorable single policy option when evaluated against debt stabilization, fiscal redistribution, and output growth criteria: it accelerates macroeconomic recovery, strengthens debt indicators, tempers real exchange rate appreciation over the medium term, and offers targeted support to lower-income LIQ households.
- The ISM (Israeli Structural Model) is an open-economy DSGE framework tailored and calibrated to capture structural features of the Israeli economy and supports scenario-based policy analysis for the Ministry of Finance.
- The ISM was developed through a multi-year IMF technical assistance (TA) project with emphasis on institutional capacity building and a “coaching” approach to foster ownership by MOF staff.
- Post-TA, MOF staff have used the ISM independently to analyze the proposed 2023 judicial reform and a prospective permanent increase in defense spending beginning in 2024, demonstrating the model’s applicability for real-time policy analysis.

*Source: Authors’ calculations and text from the chapter.*

### Appendix A  Summary   of   Normalized   Model

### Appendix A  Summary   of   Normalized   Model

### Normalization and growth definitions
- All variables must be divided by A_t N_t; normalized variables denoted by ̃x_t.
- Population and technology growth:
  - N_t = N_{t-1}(1 + g^N_t) (equation 87)
  - ̄A_t = ̄A_{t-1}(1 + g^A_t) (equation 88)

### Households (OLG and LIQ)
- Consumption Euler and budget relations (normalized):
  - (1 + τ^C_t) ̃C^{OLG}_t = MPC_t [̃Inc_t + (1+r_{t-1})/(1+g_t) ̃B_{t-1} + (1+r^*_ {t-1})/(1+g_t) REER_t ̃B^*_{t-1}] (89)
  - ̃Inc_t = (1-τ^{L,OLG}_t) ̃w_{OLG,r,t} ̃S_t + ̃pr_t - ̃T_t + (1-!) E_t[(1+g_{t+1})/(1+r_t) ̃Inc_{t+1}] (90)
  - ̃pr_t = ̃pr_{N,t} + ̃pr_{Inv,t} + ̃pr_{W,t} + ̃pr_{M,t} + ̃pr_{H,t} (91)
- Intertemporal consistency and MPC dynamics:
  - Key expectation condition linking MPC_{t+1}, r_t, and OLG parameters (92)
  - Definition of ̃C^{OLG}_{t-1} dynamics and adjustment (93)
- Labor and consumption identities:
  - ̃C^{OLG}_t ̃S_t - ̃L^{OLG}_t = - (OLG/(1-OLG)) (1/(1-τ^{L,OLG}_t)) (1+τ^C_t)^{-1} ̃w_{OLG,r,t} (94)
  - ̃C^{LIQ}_t (1- ) ̃S_t - ̃L^{LIQ}_t = - (LIQ/(1-LIQ)) (1/(1-τ^{L,LIQ}_t)) (1+τ^C_t)^{-1} ̃w_{LIQ,r,t} (95)
  - (1+τ^C_t) ̃C^{LIQ}_t = (1-τ^{L,LIQ}_t) ̃w_{LIQ,r,t} ̃L^{LIQ}_t + ̃TR_t (96)
  - Aggregate consumption: ̃C_t = ̃C^{OLG}_t + ̃C^{LIQ}_t (96)

- Real effective wages follow AR(1) in logs:
  - log(̃w_{OLG,t}) = ρ_{w,OLG} log(̃w_{OLG,t-1}) + (1-ρ_{w,OLG}) log(̃w_{OLG,r,t}) (97)
  - log(̃w_{LIQ,t}) = ρ_{w,LIQ} log(̃w_{LIQ,t-1}) + (1-ρ_{w,LIQ}) log(̃w_{LIQ,r,t}) (98)
- Labor wedge/pricing term ̃pr_W,t expression (99)

### Capital producers (j ∈ {N; H})
- Capital accumulation and investment adjustment:
  - ̃K_{j,t} = ̃Inv_{j,t}[1 - S(·)] + (1-δ)/(1+g_t) ̃K_{j,t-1} (100)
  - S and S' functional forms for investment adjustment costs (101–102)
- Investment pricing condition q_{j,t} and Tobin-q expectations (103–104)
- Normalized profit from investment ̃pr_{Inv,j,t} = (1-τ^K_t) r_{K,j,t} ̃K_{j,t-1} (1/(1+g_t)) - p_{Inv,j,t} ̃Inv_{j,t} (1+S(·)) (104)

### Aggregation: total investment, profit and skilled labor
- ̃pr_{Inv,t} = ̃pr_{Inv,N,t} + ̃pr_{Inv,H,t} (105)
- ̃L_{OLG,t} = ̃L_{OLG,N,t} + ̃L_{OLG,H,t} (106)

### Non-HT firms (sector N) — pricing, marginal cost, technology, and production
- New-Keynesian price-setting with Rotemberg costs and indexation (107)
- Marginal cost specification mc_t and mc^Noil_t (108–109)
- Composite input price p_{Z,t} definition combining capital and wages (110)
- Factor shares and production relationships (111–115)
  - 1/(1+g_t) ̃K_{N,t-1} = α_N (p_{Z,t}/r_{K,N,t})^{κ_N} ̃Z_t (111)
  - ̃L_{OLG,N,t} = (1-α_N) (p_{Z,t} ̃ˆw_{OLG,N,t})^{κ_N} (̃A_{OLG,N,t})^{κ_N-1} ̃Z_t (112)
  - ̃Z_t = [ (mc^{Noil}_t/p_{Z,t})^% ̃Y_{Noil,t} ] (113)
  - ̃L_{LIQ,t} and ̃Y_{Noil,t} expressions (114–115)
- Oil import use and profit in non-HT: ̃M_{Oil,N,t} and ̃pr_{N,t} (116–117)
- Inflation definitions and price level relations:
  - 1+ˆπ_{N,t} = (1+π_{N,t})/(1+π^{tar}_t) (118)
  - 1+π_{N,t} = (1+π^C_t) p_{N,t}/p_{N,t-1} (119)
- Wage markups and wage dynamic specifications (120–121)
- Oil price indexing for producers ˆp_{Oil,N,t} (122)
- Rotemberg cost parameters and penalty functions R(·), R_0(·) (123–126)
- Labor adjustment cost H and associated specifications (125–128)
- Oil import adjustment costs G and G_0 (129–130)

### HT firms (sector H)
- Price-setting with Rotemberg and indexation for HT sector (131)
- Marginal cost mc_{H,t} (132)
- Capital-labor-production relationships (133–134)
- Profit expression ̃pr_{H,t} and inflation relations (135–137)
- Growth in OLG,H technology and productivity definitions and AR(1) processes for gr and A (138–140)
- Wage and labor adjustment cost specifications analogous to non-HT (141–145)
- Rotemberg cost R and R_0 for HT (144–145)

### Oil importers and import composition
- Imported oil inflation and domestic oil price relations:
  - 1+π_{Oil,* ,t} = (1+π^*_t) p_{Oil,* ,t}/p_{Oil,* ,t-1} (146)
  - p_{Oil,t} = p_{Oil,* ,t} REER_t (147)
  - 1+π_{Oil,* ,t} AR(1) with steady-state (148)
- Aggregation of oil import uses (149)
  - ̃M_{Oil,t} = ̃M_{Oil,N,t} + ̃M_{Oil,C,t} + ̃M_{Oil,InvN,t} + ̃M_{Oil,InvH,t} + ̃M_{Oil,Gov,t} + ̃M_{Oil,InvGov,t} + ̃M_{Oil,X,N,t} + ̃M_{Oil,X,H,t} + ̃M_{Oil,Inv,N,t} S(·) + ̃M_{Oil,Inv,H,t} S(·) (149)

### Importers and retail/retailer firms
- Importers price-setting (150–155) with indexation and Rotemberg costs; profit ̃pr_{M,t} (155)
- Aggregate import demand composition ̃M_t (156)
- Export retailer pricing p_{X,j,t}, export demand ̃Y_{X,j,t} and imported components (157–165)
- Domestic retailer aggregation for consumption, investment, government and other final goods:
  - p_{j,t} specification with input shares μ and imported oil terms (169)
  - Final good demands ̃Y_{N,j,t}, ̃Y_{H,j,t}, ̃M_{Oil,j,t}, ̃M_{j,t} (170–173)
  - Price inflation definitions 1+ˆπ_{j,t}, 1+π_{j,t} (174–175)
  - Imported oil and non-oil price indexing for retailers (176–177)
- Adjustment cost functions G and G_0 for import bundles (165–181)

### Fiscal policy block
- Revenue and tax decomposition (normalized):
  - ̃Rev_t = ̃T_t + ̃Tax^C_t + ̃Tax^L_t + ̃Tax^K_t (182)
  - ̃Tax^C_t = τ^C_t ̃C_t (183)
  - ̃Tax^L_t = τ^{L,OLG}_t ̃w_{OLG,r,t} ̃L_{OLG,t} + τ^{L,LIQ}_t ̃w_{LIQ,r,t} ̃L_{LIQ,t} (184)
  - ̃Tax^K_t expression includes τ^K_t and investment price terms (185)
- Expenditure and public capital:
  - ̃Exp_t = ̃TR_t + p_{Gov,t} ̃Gov_t + p_{Inv,N,t} ̃Inv_{Gov,t} (186)
  - ̃K_{Gov,t} = e_t ̃Inv_{Gov,t} + (1-δ_{Gov})/(1+g_t) ̃K_G_{t-1} (187)
  - e_t = e_{t-1} + ε^e_t (188)
- Primary surplus and financing:
  - ̃PS_t = ̃Rev_t - ̃Exp_t (189)
  - ̃GS_t = ̃PS_t - ̃IntCost_t (190)
  - Interest cost ̃IntCost_t formula includes i_{t-1}, π_t, REER and foreign premia (191)
  - Financing split: ̃Fin_t = K_t · ̃GS_t ; ̃Fin^*_t = (1-K_t) · ̃GS_t (192–193)
- Domestic and external debt dynamics:
  - ̃Debt^{Dom}_t = 1/((1+g_t)(1+π_t)) ̃Debt^{Dom}_{t-1} - ̃Fin_t (194)
  - REER_t ̃Debt^*_t = REER_t/( (1+g_t)(1+π^*_t)) ̃Debt^*_{t-1} - ̃Fin^*_t (195)
  - ̃Debt_t = ̃Debt^{Dom}_t + REER_t ̃Debt^*_t (196)
- Fiscal rule for primary surplus to GDP:
  - ̃PS_t / ̃GDP_t = ρ_1 ̃PS_{t-1}/̃GDP_{t-1} + (1-ρ_1)( ̄PS_t/ ̄GDP_t + #_D DebtDev_t ) (197)
  - DebtDev_t dynamics (198)

- Risk premium relation:
  - 1+prem_t = e^{- [ REER_t D^*_t / GDP_t -  ̄REER  ̄D^*/ ̄GDP ] e^{ε_{D,* ,t}} } e^{ε_{Prem,t}} (209)

### Monetary policy
- Taylor-type reaction with persistence:
  - (1+i_t) = (1+i_{t-1})^{ρ_i} [ ((1+i) (1+π^C_{t+1})/(1+π^{tar}_t) )^{-π^3} ]^{1-ρ_i} e^{ε^i_t} (199) [model expression preserved]
- Fisher relation definitions for domestic and foreign:
  - (1+i_t) = E_t[(1+r_t)(1+π^C_{t+1})] (200)
  - (1+i^*_t) = E_t[(1+r^*_t)(1+π^*_{t+1})] (201)
- Link between domestic and foreign rates via premia and S_t dynamics (202–203)

### Foreign trade and external sector
- Export demand for sectors:
  - ̃X_{N,t} = (p_{X,N,t}/REER_t)^{-κ_N} ̃GDP^*_{t} (204)
  - ̃X_{H,t} = (p_{X,H,t}/REER_t)^{-κ_H} ̃GDP_{H,* ,t} (205)
- Trade balance and current account:
  - ̃TB_t = p_{X,N,t} ̃X_{N,t} + p_{X,H,t} ̃X_{H,t} - REER_t ̃M_{Noil,t} - REER_t p_{Oil,* ,t} ̃M_{Oil,t} (206)
  - ̃TB_t = - REER_t D^*_t + (1+r^*_ {t-1})/(1+g_t) REER_t D^*_{t-1} (207)
  - External debt definition: D^*_t = ̃Debt^*_t - ̃B^*_t (208)

### Equilibrium conditions and GDP identities
- Asset equivalence: ̃B_t = ̃Debt^{Dom}_t (210)
- Sectoral GDP decomposition for ̃Y_N,t and ̃Y_H,t (211–212)
- Expenditure-side GDP identity (213)
- Supply-side GDP identity:
  - ̃GDP_t = p_{N,t} ̃Y_{N,t} + p_{H,t} ̃Y_{H,t} - p_{Oil,t} ̃M_{Oil,N,t} (214)

### Foreign block (exogenous processes)
- Foreign interest rate and inflation AR(1) processes (215–217)
- External GDP import demand and AR(1) processes for foreign GDP (218–221)

### Appendix B — Other Parametrization (selected steady-state values and calibrations)
- Table 5: Other Steady-State Variables (selected entries)
  - ̃M_{Oil,C}/̃C = 0.04 : Share of oil imports for private consumption-to-total private consumption
  - ̃M_{Oil,InvN}/̃InvN = 0.001
  - ̃M_{Oil,InvH}/̃InvH = 0.001
  - ̃M_{Oil,Gov}/(p_{Gov} ̃Gov) = 0.001
  - ̃M_{Oil,X,N}/̃X_N = 0.02
  - ̃M_{Oil,X,H}/̃X_H = 0.001
  - ̃M_{Noil,InvN}/̃InvN = 0.31
  - ̃M_{Noil,InvH}/̃InvH = 0.9
  - ̃M_{Noil,Gov}/(p_{Gov} ̃Gov) = 0.09
  - ̃M_{Noil,X,H}/̃X_H = 0.17
  - ̃M_{Noil,X,N}/̃X_N = 0.28
  - ̃Y_{H,C}/̃C = 0.06
  - ̃Y_{H,InvH}/̃InvH = 0.05
  - ̃Y_{H,InvN}/̃InvN = 0.01
  - ̃Y_{H,Gov}/(p_{Gov} ̃Gov) = 0.0001

- Table 6: Calibration of Other Parameters (selected fiscal and foreign)
  - ρ_{τ_C} = 0.4 ; ρ_{τ_{L,OLG}} = 0.4 ; ρ_{τ_{L,LIQ}} = 0.4 ; ρ_{τ_K} = 0.4
  - ρ_T = 0.75 ; ρ_{Dom} = 0.75 ; ρ_{Gov} = 0.5 ; ρ_{Inv,Gov} = 0.6
  - ρ_{TR} = 0.5 ; ρ_{PS} = 0.5 ; #_D = -0.01 (sensitivity parameter of risk premium to foreign debt)
  - π^*_{C} = 0.02 ; p_{Oil}^* = 1 ; ρ_{π^*,C} = 0.99 ; ρ_{i^*} = 0.4
  - ρ_{π^*,Oil} = 0.99 ; ρ_{GDP^*} = 0.5 ; ρ_{Debt^*} = 0.5

- Table 7: Calibration of Other Parameters (selected firm and shock parameters)
  - P_N = 20 ; P_H = 20 ; P_M = 40 (Rotemberg parameters)
  - #_N = 0.25 ; #_H = 0.25 ; #_M = 0.5 (degree of inflation indexation)
  - 'H = 11 ; 'M = 11 (price elasticities)
  - ̄M,C = 0.1 ; ̄M,InvN = 0.001 ; ̄M,InvH = 0.001 ; ̄M,InvGov = 0.001
  - ̄M,XN = 0.5 ; ̄M,XH = 0.5 ; ̄M,Oil,C = 0.1 ; ̄M,Oil,InvN = 0.001 ; ̄M,Oil,InvH = 0.001
  - κ_C = 0.5 ; κ_{InvN} = 0.5 ; κ_{InvH} = 0.5 ; κ_{InvGov} = 0.5 ; κ_{Gov} = 0.5
  - κ_{X,N} = 0.4 ; κ_{X,H} = 0.4 ; ✓_N = 0.5 ; ✓_H = 3
  - Stochastic shock persistences: ρ_{ξ,Inv} = 0.5 ; ρ_C = 0.5 ; ρ_A = 0.75 ; ρ_{Prem} = 0.5 ; ρ_{GR,H} = 0.8

- Sources for parameter choices: Authors’ expert judgement, input-out table, and empirical estimates.

*The Israeli Structural Model — Working Paper No. WP/2025/213*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025213-source-pdf.pdf_