## The Extent and Composition of Automatic Stabilization in EU Countries

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### Key findings: income stabilization
- Income stabilization at the EU level: 41.3 percent, with considerable variation among Member States.
- Stabilization is similar across income groups within countries in extent, but the source differs:
  - Income taxation is more important for high-income households.
  - Transfers are more important for low-income households.
- Income stabilization proved stable over time, with a few exceptions driven by major reforms.

### Key findings: demand stabilization
- EU-level demand stabilization averaged 84.7 percent.
- Demand stabilization increases with household income, reflecting the greater ability of richer households to smooth consumption.

### Methodology and key definitions
- Household disposable income: Y_h = M_h + NT_h + NT̅_h = M_h + B_h − T_h + NT̅_h (Equation (1))
- Marginal propensity to consume (MPC_h): ∆C_h = MPC_h * ∆Y_h (Equation (2))
- Household-level Income Stabilization Coefficient (ISC_h): ISC_h = 1 − (∆Y_h / ∆M_h) = (∆T_h / ∆M_h) − (∆B_h / ∆M_h) (Equation (3))
- Country-level ISC: weighted average of household ISCs using household share in total market income (Equation (4)).
- Household-level Demand Stabilization Coefficient (DSC_h): DSC_h = 1 − (MPC_h * ∆Y_h / ∆M_h) (Equation (5))
- Relationship: DSC_h = (1 − MPC_h) + MPC_h * ISC_h (Equation (7))
- Country-level MPC: MPC = (∑ MPC_h * ∆Y_h) / (∑ ∆Y_h) (Equation (8))
- Country-level DSC: DSC = 1 − MPC * (∑ ∆Y_h / ∑ ∆M_h) = (1 − MPC) + MPC * ISC (Equation (9))
- Elasticity measures:
  - Household-level: E_h(Y_h, M_h) = (∆Y_h / ∆M_h) * (M_h0 / Y_h0) = (1 − ISC_h) * (M_h0 / Y_h0) (Equation (10))
  - Country-level: E(Y, M) = (1 − ISC) * (∑ M_h0 / ∑ Y_h0) (Equation (11))
- Properties:
  - i. DSC_h = 1 if MPC_h = 0.
  - ii. DSC_h = ISC_h if MPC_h = 1.
  - iii. DSC_h = 1 if ISC_h = 1.
  - iv. DSC_h = (1 − MPC_h) if ISC_h = 0.
  - v. ∂DSC_h / ∂ISC_h = MPC_h.

### Data, simulation design, and scope
- Data and tools: EUROMOD version I4.0+ and EU-SILC microdata; EUROMOD maintained by the Joint Research Centre (JRC) of the European Commission in collaboration with Eurostat and national teams.
- Policy years analyzed: 2011 to 2019 for EU 27 countries.
- Simulation assumptions:
  - Full compliance and full take-up of policy rules.
  - A hypothetical negative market income shock of 5 percent applied simultaneously to all individuals with any source of market income.
  - Market income includes employment and self-employment incomes, investment and property incomes, pensions from individual private plans, and regular net inter-household transfers, reported in gross terms.

### Empirical results — income stabilization (2019)
- Country-level automatic income stabilization in 2019 averaged 41.3 percent at the EU level.
- Cross-country range in 2019: 18.9 percent in Bulgaria to 57.2 percent in Belgium.
- Composition of ISC at EU level (2019):
  - Direct income taxes: 29.3 percent.
  - Social Insurance Contributions (SICs): 10.2 percent.
  - Social benefits: 1.8 percent.
- Cross-country component variation:
  - Stabilization from direct taxes ranges from 42.7 percent in Denmark to 7.8 percent in Romania.
  - In 20 countries, direct income taxes alone comprised more than half of the total ISC.
  - Income stabilization from SICs varies from 34 percent in Romania to zero in Denmark.
  - Importance of social benefits ranges from less than 0.1 percent in Hungary and Latvia to 3.9 percent in France.
- Distributional ISC (EU-level partial reporting):
  - ISC Q1 (bottom quintile): 41.8 percent.
  - ISC Q3 (median quintile): 39.1 percent.
  - ISC Q5 (top quintile): 42.5 percent.
- Instrumental distribution:
  - Social benefits absorb about 16 percent of the market income shock for households in the lowest quintile compared to only 0.1 percent for households in the top quintile.
  - Personal income taxes stabilize 34.8 percent of the income shock at the top of the income distribution and 12.5 percent at the bottom.

### Evolution 2011–2019 and drivers of change
- EU-level ISC change: slight increase of around 2 percentage points between 2011 and 2019.
- Notable ISC increases between 2011 and 2019: Lithuania, Romania, Greece, France, Italy, Slovakia.
  - Lithuania and Romania: employers’ contributions strongly shifted to employees.
  - Slovakia: maximum social insurance contribution bases substantially increased.
  - Greece, France, Italy: adjustments enhancing progressivity of personal income taxes (France introduced an exceptional tax on high incomes in 2013).
- Notable decrease: Hungary — gradual implementation of a flat personal income tax between 2011 and 2014, replacing progressive schedules, leading to a reduction in ISC.
- Benefits-side changes: generally did not drive country-level ISC changes except Greece where a new guaranteed minimum income entered into force in 2017.
- Bottom-quintile volatility: standard deviation of ISC above 10 in the first quintile for Greece and Cyprus, mostly stemming from means-tested benefits changes.

### Elasticities of disposable income with respect to market income (2019)
- EU-level elasticity: 0.65.
- Elasticities for households with positive market incomes: vary from 0.48 in Belgium to 0.84 in Bulgaria.
- When excluding households with zero market incomes: elasticities vary from 0.79 in Bulgaria to 0.43 in Belgium.
- Correlation between elasticities and ISC: -0.72.
- Country examples:
  - Romania: middle ranking in ISC but second highest elasticity — consistent with relying less on non-means-tested transfers.
  - France: middle ISC ranking but low elasticity — consistent with relatively high reliance on non-means-tested transfers.

### Demand stabilization (DSC), MPCs, and cost-effectiveness
- MPCs and implementation:
  - Quintile-specific MPCs based on Carroll et al. (2014) for EU-15; imputed regional averages for remaining countries.
  - EU-level MPC: 26.1 percent.
  - Country-level MPCs range from 18.2 percent in Netherlands to 34.2 percent in Spain.
  - EU-level MPC by quintile: 32.5 percent for the poorest quintile and 23.3 percent for the richest quintile.
  - Note: MPCs refer to a transitory income shock; for prolonged shocks MPCs are expected to increase over time.
- DSC outcomes (2019):
  - EU-level DSC: 84.7 percent (43.3 points larger than corresponding ISC).
  - Country-level DSC range: 73.1 percent in Spain to 90.0 percent in the Netherlands.
  - DSCs by quintile across EU countries: increase from 81.1 percent in the poorest quintile to 86.6 percent in the richest quintile.
- Share of DSC attainable if ISC = 0:
  - About 87% of the demand stabilization at the EU level would be reached even in absence of income stabilization.
  - Country-specific range: 83.2 percent in Greece to 94 percent in Malta.
- Cost-effectiveness metric:
  - MPCISC=0 values are very close to baseline MPCs.
  - A unit change in ISC at the EU level will lead to an increase in DSC by 0.26 of a percentage point.
  - Implication: means-tested transfers targeting high-MPC low-income households tend to be more cost-effective in stabilizing consumption than progressive income taxes, ceteris paribus.

### Policy-relevant implications and caveats
- Aggregate and compositional insights:
  - Country-level automatic income stabilization in 2019 averaged 41.3 percent at the EU level.
  - Direct income taxes are the largest source of stabilization (29.3 percent ISC), followed by SICs (10.2 percent) and social benefits (1.8 percent).
  - Stabilization extent is similar across household income groups within countries, but instrument composition differs across income levels.
- Policy implications:
  - Strengthening fiscal stabilization may be desirable at the lower end of the income distribution even if higher ISCs do not automatically translate into higher DSCs, because high DSCs among low-income households may reflect costly or unsustainable mitigation (e.g., debt).
  - Policy design should consider MPC gradients: targeting means-tested transfers to high-MPC low-income households can be more cost-effective for consumption stabilization than relying solely on progressive income taxation.
  - The effectiveness of unemployment insurance and other transfer programs depends not only on ISC magnitudes but also on fiscal multipliers and propensity to spend versus save.
- Caveats:
  - DSC estimates depend on the assumption that shocks are transitory and on the level and gradient of MPCs; different MPC assumptions could lead to materially different DSCs.

### Annex I — Formal derivation (summary)
- Country-level response to household ISC shocks:
  - d ISC / d ISC_h = 1 (country-level ISC changes by the same amount as the household-level ISC_h).
  - d DSC / d ISC = (∑_{h=1}^{N} ΔM_h * MPC_h) / (∑_{h=1}^{N} ΔM_h) = MPC_{ISC=0} (aggregate DSC response equals weighted average of household MPCs, weights ΔM_h).
- Aggregation identities and partial derivatives used to derive the result are presented in the source, including the equivalent algebraic expression for DSC.

*Prepared by David Coady, Silvia De Poli, Adrián Hernández, Andrea Papini, and Alberto Tumino; IMF WP/23/103*

### 41.3 percent at the EU level, with considerable variation among Member States. While the extent of

### The Extent and Composition of Automatic Stabilization in EU Countries

### Key findings: income stabilization
- Income stabilization at the EU level: 41.3 percent, with considerable variation among Member States.
- Stabilization is similar across income groups within countries in extent, but the source differs:
  - Income taxation is more important for high-income households.
  - Transfers are more important for low-income households.
- Income stabilization proved stable over time, with a few exceptions driven by major reforms.

### Key findings: demand stabilization
- EU-level demand stabilization averaged 84.7 percent.
- Demand stabilization increases with household income, reflecting the greater ability of richer households to smooth consumption.

### Study details and provenance
- Title: The Extent and Composition of Automatic Stabilization in EU Countries
- Authors: David Coady, Silvia De Poli, Adrián Hernández, Andrea Papini, and Alberto Tumino
- Recommended citation: Coady, D., De Poli, S., Hernández, A., Papini, A., and Tumino, A. “The Extent and Composition of Automatic Stabilization in EU Countries”, IMF WP/23/103
- JEL Classification Numbers: H20; E62; E63
- Keywords: Income stabilization; Demand stabilization; Euromod
- The results are based on EUROMOD version I4.0+ and EU-SILC microdata, with EUROMOD maintained, developed and managed by the Joint Research Centre (JRC) of the European Commission in collaboration with Eurostat and national teams.

### Empirical scope and robustness notes
- The analysis reports EU-level aggregates and highlights considerable heterogeneity across Member States.
- Temporal stability of the income stabilization metric is emphasized, with notable exceptions tied to major policy reforms.
- Demand stabilization is measured and reported alongside income stabilization, with clear differentiation by household income quintile.

*Prepared by David Coady, Silvia De Poli, Adrián Hernández, Andrea Papini, and Alberto Tumino; IMF WP/23/103*

### 10. MPCs and MPCISC=0 for EU Countries, 2019 ...........................................................................

### 10. MPCs and MPCISC=0 for EU Countries, 2019

### Introduction
- Automatic stabilizers (AS) are fiscal policy features that operate countercyclically on household income and consumption, cushioning the transmission of economic shocks in the absence of further discretionary government intervention.
- Typical AS include personal income tax, means-tested benefits, and unemployment benefits, which automatically adjust to changes in market income.
- The paper uses the EU microsimulation model EUROMOD and household-level data from EU-SILC to assess stabilization properties of tax-benefit systems in response to a common 5 percent negative shock to market income across EU Member States.
- Contributions of the paper:
  - New estimates of income and demand stabilization coefficients in the EU for 2019, analyzing roles of tax-benefit policies and households’ marginal propensities to consume out of a transitory income shock.
  - Overview of income stabilization over the 2010s and changes caused by major tax-benefit reforms.
  - Formal framework linking income stabilization (ISC), demand stabilization (DSC), and marginal propensity to consume (MPC).

### Methodology and Data
- Key definitions and decompositions:
  - Household disposable income: Y_h = M_h + NT_h + NT̅_h = M_h + B_h − T_h + NT̅_h (Equation (1))
  - Marginal propensity to consume (MPC_h): ∆C_h = MPC_h * ∆Y_h (Equation (2))
  - Household-level Income Stabilization Coefficient (ISC_h): ISC_h = 1 − (∆Y_h / ∆M_h) = (∆T_h / ∆M_h) − (∆B_h / ∆M_h) (Equation (3))
  - Country-level ISC computed as weighted average of household ISCs using household share in total market income (Equation (4)).
  - Household-level Demand Stabilization Coefficient (DSC_h): DSC_h = 1 − (MPC_h * ∆Y_h / ∆M_h) (Equation (5))
  - Relationship: DSC_h = (1 − MPC_h) + MPC_h * ISC_h (Equation (7))
  - Country-level MPC defined as MPC = (∑ MPC_h * ∆Y_h) / (∑ ∆Y_h) (Equation (8))
  - Country-level DSC: DSC = 1 − MPC * (∑ ∆Y_h / ∑ ∆M_h) = (1 − MPC) + MPC * ISC (Equation (9))
  - Elasticities capturing stabilizing role of non-income-related net transfers:
    - Household-level elasticity: E_h(Y_h, M_h) = (∆Y_h / ∆M_h) * (M_h0 / Y_h0) = (1 − ISC_h) * (M_h0 / Y_h0) (Equation (10))
    - Country-level elasticity: E(Y, M) = (1 − ISC) * (∑ M_h0 / ∑ Y_h0) (Equation (11))
- Properties derived:
  - i. DSC_h = 1 if MPC_h = 0.
  - ii. DSC_h = ISC_h if MPC_h = 1.
  - iii. DSC_h = 1 if ISC_h = 1.
  - iv. DSC_h = (1 − MPC_h) if ISC_h = 0.
  - v. ∂DSC_h / ∂ISC_h = MPC_h (the effectiveness of income stabilization in stabilizing demand is proportional to MPC_h).
- Data and simulation details:
  - Uses EUROMOD version I4.0+ and EU-SILC microdata, policy years 2011 to 2019 for EU 27 countries.
  - Simulations assume full compliance and full take-up of policy rules.
  - A hypothetical negative market income shock of 5% is applied simultaneously to all individuals with any source of market income.
  - Market income includes employment and self-employment incomes, investment and property incomes, pensions from individual private plans, and regular net inter-household transfers, reported in gross terms.

### Empirical Results — Income Stabilization (2019)
- EU average and cross-country variation:
  - Country-level automatic income stabilization in 2019 averaged 41.3 percent at the EU level.
  - Range across countries: 18.9 percent in Bulgaria to 57.2 percent in Belgium.
- Composition of ISC at EU level (2019):
  - Direct income taxes: 29.3 percent (largest source).
  - Social Insurance Contributions (SICs): 10.2 percent.
  - Social benefits: 1.8 percent.
- Cross-country and within-country variation in components:
  - Stabilization from direct taxes ranges from 42.7 percent in Denmark to 7.8 percent in Romania.
  - In 20 countries, direct income taxes alone comprised more than half of the total ISC.
  - Income stabilization from SICs varies from 34 percent in Romania to zero in Denmark.
  - Importance of social benefits ranges from less than 0.1 percent in Hungary and Latvia to 3.9 percent in France.
- Distributional patterns:
  - At the EU level, ISC by income quintile (partial reporting in provided text):
    - ISC at the bottom of the income distribution (Q1): 41.8 percent.
    - ISC for the median quintile (Q3): 39.1 percent.

*Source: IMF Working Paper "The Extent and Composition of Automatic Stabilization in EU Countries", excerpt covering methodology, definitions, and 2019 income stabilization results.*

### 42.5 at its top (Q5).

### 42.5 at its top (Q5).

### Income stabilization: composition and cross-country variation
- EU-level ISC amounts reported in different contexts:
  - Stabilization from unemployment benefits amounts to 1 percent at the EU level in the unemployment shock scenario; EU-level ISC for that scenario is 41.5 percent.
  - Country-level automatic income stabilization in 2019 averaged 41.3 percent at the EU level.
- Composition of stabilization by instrument (EU 2019):
  - Direct income taxes: ISC of 29.3 percent at the EU level.
  - Social insurance contributions (SICs): ISC of 10.2 percent.
  - Social benefits: ISC of 1.8 percent.
- Income-distributional heterogeneity:
  - Social benefits absorb about 16 percent of the market income shock for households in the lowest quintile compared to only 0.1 percent for households in the top quintile.
  - Personal income taxes stabilize 34.8 percent of the income shock at the top of the income distribution and 12.5 percent at the bottom.
  - Direct taxes are relatively more important for high-income households; transfers are relatively more important for low-income households.
- Country examples:
  - Luxembourg, Slovenia, and Ireland show the largest income stabilization from social benefits in the lower part of the income distribution.
  - Denmark classification nuance: labor market contributions treated as taxes in EUROMOD; unemployment benefit contributions and supplementary labor market contributions do not depend directly on earnings.
  - Romania’s reform shifting social insurance contribution burden to employees explains a high stabilization coefficient on SICs.

### Evolution 2011–2019 and drivers of change
- Overall pattern:
  - ISC remained rather stable over 2011–2019; EU-level ISC experienced a slight increase of around 2 percentage points.
  - Most countries did not experience significant changes; outliers exist.
- Notable increases in ISC between 2011 and 2019:
  - Lithuania, Romania, Greece, France, Italy, Slovakia.
  - Drivers:
    - Lithuania and Romania: employers’ contributions strongly shifted to employees.
    - Slovakia: maximum social insurance contribution bases substantially increased.
    - Greece, France, Italy: adjustments that enhanced progressivity of personal income taxes (e.g., France introduced an exceptional tax on high incomes in 2013).
- Notable decrease:
  - Hungary: gradual implementation of a flat personal income tax between 2011 and 2014, replacing progressive schedules, leading to a reduction in ISC.
- Benefits-side changes:
  - Generally did not undergo significant changes sufficient to influence ISC at the country level, with the exception of Greece where a new guaranteed minimum income entered into force in 2017, replacing some existing means-tested benefits.
- Bottom-quintile volatility:
  - Significant variation over time at the bottom of the distribution in many countries (e.g., standard deviation of ISC above 10 in the first quintile for Greece and Cyprus), mostly stemming from means-tested benefits changes.

### Elasticities of disposable income with respect to market income
- Definition and interpretation:
  - Elasticities capture stabilization role of non-means-tested transfers; higher elasticity implies less stabilization (inverse interpretation to ISC).
- Key values (2019):
  - EU-level elasticity: 0.65.
  - Elasticities for households with positive market incomes vary from 0.48 in Belgium to 0.84 in Bulgaria.
  - When households with zero market incomes are excluded, elasticities vary from 0.79 in Bulgaria to 0.43 in Belgium.
- Relationship with ISC:
  - Correlation between elasticities and ISC is -0.72.
  - Country-specific examples:
    - Romania: middle ranking in ISC but second highest elasticity — consistent with relying less on non-means-tested transfers.
    - France: middle ISC ranking but low elasticity — consistent with relatively high reliance on non-means-tested transfers.

### Demand stabilization (DSC), marginal propensities to consume (MPCs), and cost-effectiveness
- MPCs used:
  - Quintile-specific MPCs based on Carroll et al. (2014) for EU-15; imputed regional averages for remaining countries.
  - EU-level MPC: 26.1 percent.
  - Country-level MPCs range from 18.2 percent in Netherlands to 34.2 percent in Spain.
  - EU-level MPC by quintile: 32.5 percent for the poorest quintile and 23.3 percent for the richest quintile.
  - Note: MPCs refer to a transitory income shock; for prolonged shocks MPCs are expected to increase over time.
- DSC results (2019):
  - EU-level DSC: 84.7 percent (43.3 points larger than corresponding ISC).
  - Country-level DSCs range from 73.1 percent in Spain to 90.0 percent in the Netherlands.
  - Across EU countries, DSCs increase from 81.1 percent in the poorest quintile to 86.6 percent in the richest quintile.
- Share of DSC arising even if ISC = 0:
  - About 87% of the demand stabilization at the EU level would be reached even in absence of income stabilization.
  - Country-specific range: 83.2 percent in Greece to 94 percent in Malta.
  - Interpretation: socio-economic groups with low MPCs (richer households) can stabilize a larger share of consumption via savings/borrowing; high DSCs for low-income households may reflect undesirable longer-term outcomes (e.g., unsustainable debt).
- Cost-effectiveness metric:
  - MPCISC=0 (the derivative of DSC w.r.t. a uniform ISC change) values are very close to baseline MPCs.
  - A unit change in ISC at the EU level will lead to an increase in DSC by 0.26 of a percentage point.
  - Implication: AS measures are less effective where households can self-protect consumption via savings/borrowings; means-tested transfers targeting high-MPC low-income households tend to be more cost-effective in stabilizing consumption than progressive income taxes, ceteris paribus.

### Methodological notes and comparability
- Microsimulation and data:
  - Results based on EUROMOD 4.0+ and EU-SILC data.
- Comparability with other studies:
  - Results broadly align with Mabbet and Schelkle (2007), Dolls et al. (2012), European Commission (2017), with differences explained by time horizon, period of policy rules analyzed, and level of analysis (household vs country).
  - European Commission (2017) finds a larger degree of progressivity overall; differences in ISC levels partly due to different unit of analysis (household-level indicators vs country-aggregated results).
  - MPC choices materially affect DSC estimates; other approaches (e.g., self-reported MPC estimates) find larger MPCs and would imply lower DSCs.

### Key conclusions and policy-relevant implications
- Aggregate and compositional findings:
  - Country-level automatic income stabilization in 2019 averaged 41.3 percent at the EU level.
  - Direct income taxes are the largest source of stabilization (29.3 percent ISC), followed by SICs (10.2 percent) and social benefits (1.8 percent).
  - Stabilization extent is similar across household income groups within countries, but instrument composition differs across income levels.
- Policy implications:
  - Strengthening fiscal stabilization may be desirable at the lower end of the income distribution even if higher ISCs do not automatically translate into higher DSCs, because high DSCs among low-income households may reflect costly or unsustainable mitigation (e.g., debt).
  - Policy design should consider MPC gradients: targeting means-tested transfers to high-MPC low-income households can be more cost-effective for consumption stabilization than relying solely on progressive income taxation.
  - The effectiveness of unemployment insurance and other transfer programs depends not only on ISC magnitudes but also on fiscal multipliers and propensity to spend versus save.
- Caveats:
  - DSC estimates depend on the assumption that shocks are transitory and on the level and gradient of MPCs; different MPC assumptions could lead to materially different DSCs.

*IMF WORKING PAPERS The Extent and Composition of Automatic Stabilization in EU Countries — excerpt.*

### Annex I. Formal Derivation

### Annex I. Formal Derivation

### Key result: country-level responses to household ISC shocks
- It can be shown that the total derivative of 퐼푆퐶 with respect to 퐼푆퐶_ℎ is equal to 1:
  - d 퐼푆퐶 / d 퐼푆퐶_ℎ = 1
  - Interpretation: the country-level 퐼푆퐶 will also change by the same amount as the household-level 퐼푆퐶_ℎ.

- The total derivative of 퐷푆퐶 with respect to 퐼푆퐶_ℎ is equal to a weighted sum of the household-level marginal propensity to consume:
  - d 퐷푆퐶 / d 퐼푆퐶 = (∑_{ℎ=1}^{N} ΔM_ℎ * MPC_ℎ) / (∑_{ℎ=1}^{N} ΔM_ℎ) = MPC_{ISC=0}
  - Interpretation: the aggregate DSC response to an ISC shock equals the weighted average of household MPCs, with weights ΔM_ℎ.

### Formal steps of the derivation
- Starting identity and chain rule decomposition:
  - d 퐷푆퐶 / d 퐼푆퐶 = (d 퐷푆퐶 / d 퐼푆퐶_ℎ) * (d 퐼푆퐶 / d 퐼푆퐶_ℎ)^{-1}
- Aggregation expressions used:
  - d 퐼푆퐶 = ∑_{ℎ=1}^{N} (∂ISC / ∂퐼푆퐶_ℎ) d 퐼푆퐶_ℎ = ∑_{ℎ=1}^{N} ΔM_ℎ d 퐼푆퐶_ℎ
  - Hence d 퐼푆퐶 / d 퐼푆퐶_ℎ = 1
- For 퐷푆퐶:
  - d퐷푆퐶 = ∑_{ℎ=1}^{N} (∂DSC / ∂퐼푆퐶_ℎ) d퐼푆퐶_ℎ
  - ∂DSC / ∂퐼푆퐶_ℎ = ΔM_ℎ / (∑_{ℎ=1}^{N} ΔM_ℎ) * MPC_ℎ
  - Therefore d퐷푆퐶 / d퐼푆퐶 = (∑_{ℎ=1}^{N} ΔM_ℎ * MPC_ℎ) / (∑_{ℎ=1}^{N} ΔM_ℎ)

### Note (equivalent expression for DSC) — exact algebra provided in source (note 21)
- 퐷푆퐶 = 1 − 푀푃퐶* (∑ Δ푌_ℎℎ / ∑ ΔM_ℎℎ) = 1 − (∑ Δ푌_ℎℎ * 푀푃퐶_ℎ / ∑ ΔY_ℎℎ) * (∑ Δ푌_ℎℎ / ∑ ΔM_ℎℎ) = 1 − ∑ ΔM_ℎ (1 − 퐼푆퐶_ℎ)_ℎ * 푀푃퐶_ℎ / ∑ ΔM_ℎℎ

### Related empirical materials in the annex (presented in source)
- Table A1: Combination of Policy Years (2011 – 2019) and EU-SILC Data in EUROMOD I4.0+ (base-year simulation note included).
- Figure A1: ISC Following Unemployment and Income Shock (Scenario 1), 2019.
- Figure A2: ISC Following Unemployment Shock (Scenario 2), 2019.
- Figure A3: Changes in ISC by Component, Q1, 2011 - 2019.

*Source: Annex I. Formal Derivation, wpiea2023103-print-pdf - Annex I. Formal Derivation (IMF Working Paper No. WP/2023/103).*

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