## INFLATION IN PORTUGAL, RECENT TRENDS, DRIVERS, AND RISKS

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---

### A. Stylized facts
- Headline and core inflation "hovered below 2 percent" for most of the last decade before the energy crisis.
- Portugal’s inflation was strongly correlated with the euro area (EA) but remained below EA levels for much of 2010–pre-energy crisis, driven largely by non-energy industrial goods (e.g., clothing and footwear).
- Tourism-related prices fell by "almost 10 percent" during the COVID pandemic, contributing to Portugal’s inflation falling further below the EA level.
- HICP composition and implications:
  - Food and non-alcoholic beverages weight in Portugal has been "above the EA level since 2012 (at over 20 percent)".
  - Housing, water, electricity, and gas weight is "10 percent" in Portugal vs "16 percent" for the EA.
  - Imputing average EA weights to Portugal would raise Portugal’s inflation by "about 0.2 pp" in 2021 and 2022.
- Inflation dynamics in 2022:
  - Passthrough from rising energy prices to Portugal’s prices was "about 9 percent increase y/y in Portugal compared to about 47 percent for EA in March 2022".
  - Headline inflation peaked in October 2022 at "10.6 percent y/y" and then trended downward.
  - Core inflation exceeded EA level in early 2022 and "has hovered around 8 percent since September 2022".
- Consumer price expectations rose from early 2021 and "eventually exceeding EA averages by end-2022", then started declining during 2022H2.

### B. Drivers of inflation — Phillips curve evidence
- Model and data:
  - Phillips curve relates q/q annualized inflation (휋) to expected inflation (휋^e), slack (y, proxied by unemployment gap), Energy, Food, and External with lags for external pressures and food.
  - Estimation sample: 2000:Q1 to 2022:Q4 for 27 advanced economies, including Portugal.
- Main empirical findings:
  - Slack (unemployment gap) has a negative and significant relationship with headline and core inflation for both Portugal and other advanced economies (AE) and of similar magnitude.
  - Backward-looking and forward-looking expectations roles are comparable between Portugal and AE.
  - Passthrough of food prices and external price pressure is present for Portugal but with smaller coefficients than AE; nevertheless, external price pressures contributed relatively large to Portugal’s inflation in 2022.
- Model performance and decomposition for 2022:
  - The Phillips-curve decomposition explains "about 3/4" of Portugal’s inflation in 2022 (model explained at most "60 percent" for the AE group).
  - Contributions to 2022 headline inflation in Portugal:
    - Food prices: "about 3.5 pp"
    - External price pressures: "about 2.5 pp"
    - Energy contribution estimated below AE average (in part due to domestic measures).
  - Unemployment gap had almost no impact on Portugal’s overall inflation in 2022 according to the model.
  - Inflation expectations, despite picking up since 2021, "remained anchored" and have driven inflation in the opposite direction from other factors since 2022H2.
- Factors explaining unexplained inflation in 2022:
  - Non-linear impacts of exceptionally large commodity price changes or structural changes since the pandemic and Russia’s war in Ukraine.
  - Labor market tightness beyond the unemployment gap: unemployment below pre-pandemic level and below estimated equilibrium; rising vacancies per unemployed; more firms reporting labor shortages.
  - Administered price policies slowed passthrough—example: Iberian cap estimated to have reduced electricity prices by "about 16 percent".
  - Wage growth: nominal wages increased less than headline inflation ("6.1 percent and 8.1 percent in 2022, respectively"), implying falling real wages in H2 2022.
  - Tourism: hotels and restaurants increased "13 percent vs 7 percent for EA average".

### C. Inflation projections and scenario sensitivity
- Baseline forecasts:
  - Phillips-curve baseline: headline and core inflation in Portugal and AE decline to "about 2 percent by the end of 2024", driven by larger slack, lower energy prices, and lower external pressures.
  - Staff baseline (March 2023): reaches 2 percent "only after 2025".
  - Banco de Portugal (March 2023): projects convergence to 2 percent "in the course of 2025".
- Scenario sensitivities (model simulations):
  - A decrease/increase in the unemployment gap by "2 pp" would change headline and core inflation by about "0.5 pp" (increase/decrease) over the next four quarters.
  - A temporary de-anchoring of inflation expectations higher by "1 pp" would raise headline and core inflation temporarily by "some 1 pp" over the next 4 quarters.
  - A "20 percent" higher/lower energy and food prices would increase headline inflation by "1 to 2 pp" and increase core inflation by "less than 1 percent".
  - If inflation formation becomes more backward-looking (raise coefficient on past inflation to "0.8"), headline inflation would increase by "about 2 pp" and core by "about 1 pp", with effects damping over time provided expectations remain unchanged.
- Uncertainty and risks:
  - Predicted deceleration is uncertain; risks include persistent supply bottlenecks, elevated commodity prices, de-anchoring of expectations, wage demands, and phased-out dampening measures.

### D. Risk of a wage-inflation spiral
- Literature and historical evidence:
  - Historical analysis of 79 wage-price spiral episodes identified 29 episodes similar to the current one; those episodes "did not tend to be followed by sustained wage-price spirals."
  - Baba and Lee (2022): in response to a 10 percent oil price shock, wages tend to increase by "0.3 percent over three years" and then stabilize; passthrough to wages is more than twice as high when underlying inflation already exceeds "4 percent".
- Portugal-specific passthrough (2000–2019) following Baba and Lee (2022):
  - Specification (i): wage inflation on lagged oil price inflation and controls; (ii) wage inflation on lagged inflation instrumented with oil price inflation.
  - First specification (Portugal): peak effect (statistically not significant) implies a "1 percent" increase in oil price raises wage growth by "0.02 percentage points" during the first year.
  - Alternative phrasing in document notes "0.03 percentage points during the first year" and the text describes oil price increases of "some 65 percent in 2021 and 40 percent in 2022" implying wage growth increases of "1.3 and 0.8 percentage point" in 2021 and 2022 respectively, ceteris paribus.
  - Second specification: a 1 percentage point increase in inflation caused by oil price shocks is associated with a peak wage growth of "1.2 percentage point" for Portugal during the first year, and "1.4 percentage point" for other advanced European economies.
- Assessment:
  - Evidence suggests a relatively low risk of an extended wage-price spiral in Portugal given historical passthrough magnitudes and empirical estimates, but findings provide caution—wage responses to large oil shocks and higher underlying inflation could amplify risks.

### Inflation dynamics and conclusions
- Recent estimated Phillips-curve analysis indicates the impact of higher oil prices on wages dissipates fully over the year and at a somewhat faster pace in Portugal compared to other European Advanced economies.
- Considering oil price increases of "some 65 percent in 2021 and 40 percent in 2022", implied wage growth increases are "1.3 and 0.8 percentage point" in 2021 and 2022 respectively, ceteris paribus (per the chapter’s arithmetic).
- Conclusions (paragraph 16):
  - Inflation in Portugal has likely peaked, but upside risks remain.
  - Surge in inflation was driven predominantly by commodity prices and external price pressures, and to some extent by labor market tightness.
  - Inflation is projected to ease in 2023 and 2024—driven by falling energy prices and in the context of anchored expectations.
  - Downward path should be sustained under most alternative assumptions.
  - Inflation would increase if:
    - the inflationary process became backward looking, or
    - energy prices remained elevated for longer, or
    - wage-inflation increases induced by pressures from energy prices become sustained.
  - Policy implication: policies should remain focused on inflation reduction given unprecedented recent inflation dynamics and unusual forecast uncertainty.
- Institutional note:
  - Results do not consider institutional factors impacting wage formation (e.g., sectoral collective agreements in Portugal negotiated during the first half of the year), which may explain moderate passthrough observed in 2022 and potential implications for 2023 contracts.

---

### Optimal fiscal path considerations (Buffer Stock model)

### Context and objective
- Public debt dynamics:
  - Despite a nearly 20 percentage points of GDP spike in 2020, public debt-to-GDP fell below its pre-pandemic level by end-2022.
  - The 2023 Stability Program forecasts a low overall deficit and public debt on a downward track.
  - The high debt ratio implies sustained effort needed for medium-term debt reduction.
- Model used: Buffer Stock model (Fournier, 2019) to illuminate optimal medium-term structural consolidation under alternative scenarios.

### Model framework and implications
- Government balances stabilization and debt sustainability with forward-looking fiscal policy subject to initial debt, stabilization function, market risk appetite, and shock distribution.
- As debt increases, borrowing costs rise; near model’s debt limit (risk of losing market access), the optimal response is to preserve fiscal room rather than smooth negative shocks.

### Baseline recommendation and sensitivities
- Baseline calibration (2023 Article IV Staff Report forecast):
  - Recommends an increase in the structural primary balance averaging around "2.1 percentages points of potential GDP relative to 2022" during 2024-2028, implying an average level of "2.7 percent of potential GDP".
  - Consolidation path is front-loaded reflecting higher initial debt.
- Sensitivity to parameters:
  - Long-run real effective interest rate:
    - Baseline assumes convergence to "2.5 percent".
    - Alternatives: "2.8 percent" (2002-19 average) and about "2.0 percent" (excluding sovereign crisis and Covid-19).
    - A 30-basis point increase in long run real interest rates implies the recommended additional annual increase in the structural primary balance would be some "0.2 percentage points" higher than the baseline.
  - Medium-term growth:
    - Baseline assumes boost from RRP investment and structural reforms.
    - Alternative with long-term potential growth of "¾ percent (average 2002-19)" would necessitate an additional "0.3 p.p." average increase in structural primary balance starting in 2024 over the medium-term relative to the baseline.
  - Market sensitivity to debt:
    - Higher sensitivity of interest rate to debt level necessitates stronger consolidation over the medium-term.

### Policy conclusion
- Appropriate fiscal consolidation critically depends on medium-term output dynamics and market risk appetite.
- While debt is forecast to decline under the model baseline, the model calls for more ambitious consolidation, and higher recommended fiscal effort under adverse scenarios.

### Annex I — model details and key calibrations (selected parameter values)
- Welfare and macro parameters:
  - Discount factor, β 0.99
  - Risk aversion, σ 2
  - Labor elasticity, η 1/0.3
  - Weight of labor, ξ 1
- Fiscal and shock parameters:
  - Fiscal multiplier, m1 0.5
  - Fiscal multiplier sensitivity to shocks, m2 3
  - Automatic stabilizers (primary balance semi-elasticity to the gap) 0.4
  - Adjustment cost, χ 3
  - Effect of debt level on the risk premium, α 2.5%
  - Effect of debt change on the risk premium, α2 0.5%
  - Debt level at which the risk to lose market access is 50%, d 150%
  - Debt limit accuracy, d1 3
  - Economy parameters: Potential growth, long-term 1.3%; Population growth -0.4%; Real interest rate 2.5%; Shock persistence 0.77; Shock size 0.032; Hysteresis 10%; Hysteresis threshold -1%.

---

### Labor market and digitalization — key findings

### Aggregate and distributional outcomes during Covid-19
- Aggregate employment rate declined and unemployment increased less during Covid-19 than in previous recessions; pattern broadly in line with median EA country and smaller than the US, reflecting extensive job retention schemes.
- Labor force participation rate dropped more sharply during Covid-19 than in previous two recessions, driven largely by low-skilled and young workers.
- Distributional impacts:
  - Young workers (15-29 years): employment share fell by around "1.1 percentage points" between 2020Q1 and 2020Q2.
  - Low-skilled workers (below tertiary): employment share fell by around "1.6 percentage points" over the same period.
  - Contact-intensive employment (e.g., hotels and restaurants): share declined by around "1 percentage point".
  - Non-digital employment share fell by around "1.7 percentage points".
  - No significant gender differential in employment changes in Portugal during the pandemic, unlike some other advanced economies.

### Digital employment dynamics and policy implications
- Portugal experienced a sharper increase in the share of jobs in digital occupations during Covid-19 compared to the rest of the EA; rise driven by increased share of “professional” occupations.
- In Portugal, digital employment increased in absolute terms while non-digital employment declined.
- Policy implications:
  - Invest in digitalization, digital skills, and higher education to build a more resilient labor market.
  - Target skills and education policies to mitigate distributional impacts on young and low-skilled, contact-intensive and non-digital workers.

---

### Household vulnerabilities and macro-financial context

### Stylized facts and exposures
- House prices:
  - Since 2018Q1 real house prices increased by 40 percent (the highest appreciation rate in Europe).
  - Real house price growth decelerated to around "2 percent y/y in 2022Q4" (versus "9.1 percent y/y" one year earlier).
  - VECM estimates put over-valuation in 2022Q3 at around "20 percent".
- Mortgages and interest rates:
  - Mortgage rates on new issuances reached "3.2 percent" at end 2022, representing a "240-bps" increase from end-2021.
  - Median household spends one third of its gross income on food and energy; bottom tercile spends "56 percent" of gross income on food and energy.
  - Share of households with non-mortgage loans: "14 percent" (bottom tercile), "28 percent" (second), "25 percent" (top).
  - Estimated average debt service among households with debt payments is around "10.4 percent" at end-2021.
- Banking sector exposures:
  - Household loans collateralized by residential real estate (RRE) account for over half of total loans to the nonfinancial private sector and amount to over "40 percent of 2022 GDP".
  - Other non-collateralized household loans represent "10 percent" of total loans or "6 percent of GDP".

### Government support and measures
- Government estimated to have spent about "1 percent of GDP" on average during 2022-23 to shield households from rising food, energy, and housing costs.
- Mortgage relief measures:
  - Decree-Law No. 80-A/2022 (published November 25, 2022): measures to encourage banks to restructure loans for borrowers at risk.
  - Decree-Law No. 20-B/2023 (came into force March 23, 2023): interest rate subsidy to absorb part of the rise in interest rates for financially stretched borrowers.

---

### Stress-testing household balance sheets: methodology, scenarios, and results

### Definitions and methodology
- Financial vulnerability: DSECTI (debt service and basic living expenditures to gross income) ≥ "70 percent". Alternative standard: DSTI ≥ "40 percent".
- Mortgage debt-at-risk: outstanding mortgages of financially vulnerable households as a share of total mortgages outstanding.
- Data: EU-SILC microdata and HFCS; EU-SILC Portugal (2020) around "30,000 households" (326,000 observations 2004-20); HFCS covers under "6,000 households" for Portugal.
- Simulation horizon: 2-year projection of household income, housing cost, other basic expenses, and repayments.

### Scenarios
- Baseline: follows IMF October 2022 WEO forecast.
- Adverse example (‘cost of living’): interest rate shock of "200 bps" and a food and energy price shock of "20 percent" relative to baseline.
- Worst-case: further interest rates increase by a further "200 bps" relative to baseline and food and energy prices rise "20 percent" above baseline.

### Stress-test results: vulnerability, arrears, and consumption-at-risk
- Arrears probability (Portugal):
  - Probability of being in arrears on mortgage payments increases by "70 percent" (from "3.1 to 5.3 percent" on average 2004–2020) when households are overburdened.
  - For EA, average probability jumps from "4.5 to 6.8 percent" for vulnerable households.
  - Probability of arrears on other retail loans in Portugal rises from "3.6 to 5.8 percent" when households are overburdened; for EA it rises from "7.3 to 10.3 percent".
- DSTI ≥ 40 percent vulnerability:
  - Share of mortgage borrowers with DSTI ≥ 40 percent is estimated to rise to "8.8 percent" under baseline and to "14.0 percent" in the ‘tightening’ scenario in Portugal.
  - Mortgage debt-at-risk could double and reach a quarter of outstanding mortgage debt under the worst-case scenario.
- Broader vulnerability (including basic living expenditure):
  - In adverse scenarios, almost half of households could struggle to afford basic expenditures in Portugal (about twice as many as before the energy crisis).
  - Share of financially vulnerable low-income families could increase to "78 percent" under the baseline (from "60 percent") and reach around "90 percent" under the ‘cost of living’ scenario.
  - Only between "5 and 13 percent" of high-income households would be financially vulnerable depending on scenario severity.
  - In the worst-case scenario, one third of consumers could be economically vulnerable and be forced to cut back on consumption of non-essential goods, accounting for over one fourth of consumption.
  - Estimated reduction in aggregate consumption would range between "2 and 5 percent" (elsewhere the chapter reports a worst-case aggregate consumption reduction of "7 percent"—both figures are presented in the document in different contexts).

---

### Banks, house-price correction, and policy mitigation

### Impact on banks: baseline versus house price correction
- Without a sharp house price correction:
  - Capital depletion would not exceed "20 basis points" in Portugal (versus "15 basis points" in the EA).
- Abrupt decline in house prices (eliminating the "20 percent" estimated overvaluation):
  - Aggregate capital depletion could reach up to "100 basis points" of capital in Portugal (versus "85 basis points" in the EA).
  - Stressed LGD assumption: increase by "20 percent" over weighted average LGD (reported 20.1 percent as of 2022Q4), yielding stressed LGD of "40 percent".

### Shock mitigation policies — cost-effectiveness (selected results)
- Government measures in 2022 included reduced tax burden on fuel, hold on planned carbon tax increase, reduced VAT rate on electricity, and exceptional income support to households.
- Simulation of selected shock mitigation policies (applied to all households):
  - Baseline:
    - Around "3.5 percent" of households would be saved from distress.
    - Fiscal cost: "0.6 percent of GDP".
    - Reduction of risky debt: "1.7 percent".
  - ‘Cost of living’ scenario:
    - Share of households shielded: "3.8 percent".
    - Cost: "0.7 percent of GDP".
    - Reduction of mortgage debt at risk: "2.5 percent".
- Hypothetical full shielding interventions (100 percent increase in food and energy prices 2022-23) — narrow targeting (bottom tercile) outcomes:
  - Baseline:
    - Saves "7.9 percent" of households.
    - Protects "0.8 percent" of mortgage debt at risk.
    - Cost "0.8 percent of GDP".
  - ‘Cost of living’ scenario:
    - Saves "12 percent" of distressed households.
    - Protects "2.5 percent" of risky debt.
    - Cost "1.5 percent of GDP".
- Mortgage relief policies:
  - Decree-Law No. 80-A/2022 (Nov 25, 2022):
    - Simulation: restructuring reduces monthly installments by reducing interest payments (half of the increase by end-2023).
    - Effects: around "0.5 to 3.2 percentage points" of mortgage-debt-at-risk protected; "0.3 to 2.3 percent" of mortgage borrowers protected; restructuring applied to "7-18 percent" of outstanding mortgage debt.
    - Bank effects: benefit for banks (lower provisions) around "5 basis points" of CET1; cost for banks (lower NII) between "10 and 20 basis points" of CET1.
  - Decree-Law No. 20-B/2023 (in force March 23, 2023):
    - Subsidy: temporary 2023 subsidy for half of the increase in benchmark rates at origination augmented by a 3-percentage point increase.
    - Eligibility: outstanding amount at origination < "EUR 250,000"; family income up to "EUR 38,632" annual; DSTI ≥ "35 percent".
    - Simulation results:
      - Mortgage debt at risk lower by up to "one percentage point" under policy in adverse scenarios.
      - Debt relief estimated subsidy: "0.46 percent" on eligible debt (around "15 percent" of outstanding mortgages).
      - Cost: around "EUR 60 million (3 basis points of GDP)".
      - Benefit for banks (lower provisions): estimated at "1 basis point" of CET1.
    - Note: projections are lower bound due to bias in reference rate at origination and exclusion of mortgage originations after 2017 HFCS.

### Key findings and policy implications
- House price overvaluation (~"20 percent" in 2022Q3) implies elevated risk of correction.
- Under adverse conditions, almost half of households could become financially stretched; these households represent over "40 percent" of mortgage debt and "45 percent" of consumer debt.
- In the worst-case scenario, one third of consumers could cut back consumption with an estimated aggregate consumption reduction up to "7 percent" in one formulation, or "2 to 5 percent" in another projection context within the chapter.
- Capital depletion under market price correction that brings house prices back to fundamentals would not exceed "100 basis points" given adequate provisioning.
- Policy cost-effectiveness:
  - Selected shock mitigation policies (VAT reductions and income support) could shield around "3.5 percent" of households and "1.7 percent" of mortgage debt at risk at a cost of "0.6 percent of GDP".
  - Targeted support to the bottom tercile is more cost-effective per unit of fiscal cost in reducing financially stretched households; including the middle tercile increases support to mortgage debt given its concentration in the middle tercile.

*Source: IMF staff chapter “INFLATION IN PORTUGAL, RECENT TRENDS, DRIVERS, AND RISKS” (content unit provided).*

### References _____________________________________________________________________________ 12

### INFLATION IN PORTUGAL, RECENT TRENDS, DRIVERS, AND RISKS

### A. Stylized Facts
- Before the recent energy crisis, headline and core inflation in Portugal "hovered below 2 percent" for most of the last decade.
- Portugal’s inflation has been strongly correlated with the euro area (EA) but remained below EA levels for much of 2010–pre-energy crisis, driven largely by non-energy industrial goods (e.g., clothing and footwear).
- Tourism-related prices fell by "almost 10 percent" during the COVID pandemic, contributing to Portugal’s inflation falling further below the EA level.
- HICP composition notes:
  - Food and non-alcoholic beverages weight in Portugal has been "above the EA level since 2012 (at over 20 percent)".
  - Housing, water, electricity, and gas weight is "10 percent" in Portugal vs "16 percent" for the EA.
  - Imputing average EA weights to Portugal would raise Portugal’s inflation by "about 0.2 pp" in 2021 and 2022.
- Inflation dynamics in 2022:
  - Passthrough from rising energy prices to Portugal’s prices was "about 9 percent increase y/y in Portugal compared to about 47 percent for EA in March 2022".
  - Headline inflation peaked in October 2022 at "10.6 percent y/y" and then trended downward.
  - Core inflation exceeded EA level in early 2022 and "has hovered around 8 percent since September 2022".
- Consumer price expectations rose from early 2021 and "eventually exceeding EA averages by end-2022", then started declining during 2022H2.

### B. Drivers of Inflation — Phillips Curve Evidence
- Model specification: Phillips curve relating q/q annualized inflation (휋), expected inflation (휋^e), slack (y, proxied by unemployment gap), energy (Energy), food (Food), and external price pressure (External), with lags for external pressures and food.
- Estimation sample: 2000:Q1 to 2022:Q4 for 27 advanced economies, including Portugal.
- Main empirical findings:
  - Slack (unemployment gap) has a negative and significant relationship with headline and core inflation for both Portugal and other advanced economies (AE) and of similar magnitude.
  - Backward-looking and forward-looking expectations roles are comparable between Portugal and AE.
  - Passthrough of food prices and external price pressure is present for Portugal but with smaller coefficients than AE; however, the contribution of external price pressures to Portugal’s inflation is nonetheless relatively large in 2022.
- Model performance:
  - The Phillips-curve decomposition explains "about 3/4" of Portugal’s inflation in 2022 (the model performs slightly better for Portugal than for the AE group, where it explained at most "60 percent").
  - Contributions to 2022 headline inflation in Portugal:
    - Food prices: "about 3.5 pp"
    - External price pressures: "about 2.5 pp"
    - Energy contribution estimated below AE average (in part due to domestic measures).
  - Unemployment gap had almost no impact on Portugal’s overall inflation in 2022 according to the model.
  - Inflation expectations, despite picking up since 2021, "remained anchored" and have driven inflation in the opposite direction from other factors since 2022H2.
- Factors potentially explaining the rise in unexplained inflation in 2022:
  - Non-linear impacts of exceptionally large commodity price changes or structural changes to the inflation process since the pandemic and Russia’s war in Ukraine.
  - Labor market tightness beyond what the unemployment gap captures: unemployment below pre-pandemic level and below estimated equilibrium, rising vacancies per unemployed, and more firms reporting labor shortages.
  - Administered price policies (tax/regulatory measures, price caps/freezes) slowed passthrough—example: Iberian cap estimated to have reduced electricity prices by "about 16 percent".
  - Wage growth: wages (compensation of employees) grew less than headline inflation in 2022 ("nominal wages increased less than headline inflation (6.1 percent and 8.1 percent in 2022, respectively)"), implying falling real wages in H2 2022.
  - Tourism: pickup in tourism-related prices — e.g., hotels and restaurants increased "13 percent vs 7 percent for EA average".

### C. Inflation Projections and Scenario Sensitivity
- Baseline model forecast (Phillips-curve) prediction: headline and core inflation in Portugal and AE decline to "about 2 percent by the end of 2024", driven by larger slack, lower energy prices, and lower external pressures.
- Staff baseline (March 2023) and Banco de Portugal (March 2023) assume slower convergence:
  - Staff baseline reaches 2 percent "only after 2025".
  - Banco de Portugal projects convergence to 2 percent "in the course of 2025".
- Key scenario/sensitivity results from model simulations:
  - A decrease/increase in the unemployment gap (slack) by "2 pp" would change headline and core inflation by about "0.5 pp" (increase/decrease) over the next four quarters.
  - A temporary de-anchoring of inflation expectations higher by "1 pp" would raise headline and core inflation temporarily by "some 1 pp" over the next 4 quarters.
  - A "20 percent" higher/lower energy and food prices would increase headline inflation by "1 to 2 pp" and increase core inflation by "less than 1 percent".
  - If inflation formation becomes more backward-looking (raising the coefficient on past inflation in the Phillips curve to "0.8"), headline inflation would increase by "about 2 pp" and core by "about 1 pp", with effects damping over time provided inflation expectations remain unchanged.
- Uncertainty summary: predicted deceleration is uncertain; risks include persistent supply bottlenecks, elevated commodity prices, de-anchoring of expectations, wage demands, and phased-out dampening measures.

### D. Risk of a Wage-Inflation Spiral
- Literature overview:
  - Historical analysis of 79 wage-price spiral episodes identified 29 episodes similar to the current one (characterized by rising y/y inflation, positive nominal wage growth, negative real wage growth, and flat/falling unemployment). Those episodes "did not tend to be followed by sustained wage-price spirals."
  - Baba and Lee (2022): in response to a 10 percent oil price shock, wages tend to increase by "0.3 percent over three years" and then stabilize; passthrough to wages is more than twice as high when underlying inflation already exceeds "4 percent".
- Portugal-specific empirical passthrough analysis (2000–2019), following Baba and Lee (2022):
  - Two specifications were estimated: (i) wage inflation on lagged oil price inflation and controls; (ii) wage inflation on lagged inflation instrumented with oil price inflation.
  - In the first specification for Portugal, the (statistically not significant) peak estimated effect implies that a "1 percent" increase in oil price raises wage growth by "0.02 percentage points" during the first year.
  - Evidence suggests a relatively low risk of an extended wage-price spiral in Portugal given historical passthrough magnitudes and the empirical estimates.

*Source: IMF staff chapter “INFLATION IN PORTUGAL, RECENT TRENDS, DRIVERS, AND RISKS” (content unit provided).*

### 0.03 percentage points during the first year. The

### 1prtea2023002 - 0.03 percentage points during the first year. The

### Inflation dynamics and conclusions
- Recent analysis based on an estimated Phillips curve for Portugal:
  - The impact of higher oil prices on wages dissipates fully over the year and at a somewhat faster pace in Portugal compared to other European Advanced economies.
  - Considering oil price increases of some 65 percent in 2021 and 40 percent in 2022, this implies some 1.3 and 0.8 percentage point increase in the wage growth in 2021 and 2022 respectively, ceteris paribus.
  - Based on the second specification, a 1 percentage point increase in inflation caused by the oil price shocks is associated with a peak wage growth of 1.2 percentage point for Portugal during the first year, and 1.4 percentage point increase for other advanced European economies during the same period.
  - These findings provide a cautionary note on the overall assessment of a low risk of wage-price spiral in Portugal.
- Conclusions (paragraph 16):
  - Inflation in Portugal has likely peaked, but upside risks remain.
  - The surge in inflation has been driven predominantly by commodity prices and external price pressures, and to some extent by labor market tightness.
  - Inflation is projected to ease in 2023 and 2024—driven by falling energy prices and in the context of anchored expectations.
  - Downward path should be sustained under most alternative assumptions.
  - Inflation would increase if:
    - the inflationary process became backward looking, or
    - energy prices remained elevated for longer, or
    - wage-inflation increases induced by pressures from energy prices become sustained.
  - Policy implication: policies should remain focused on inflation reduction given unprecedented recent inflation dynamics and unusual forecast uncertainty.
- Institutional note:
  - Results do not consider institutional factors impacting wage formation (e.g., sectoral collective agreements in Portugal negotiated during the first half of the year), which may explain moderate passthrough observed in 2022 and potential implications for 2023 contracts.

*INTERNATIONAL MONETARY FUND*

### Optimal fiscal path considerations (Buffer Stock model)
- Context and objective:
  - Despite a nearly 20 percentage points of GDP spike in 2020, public debt-to-GDP fell below its pre-pandemic level by end-2022.
  - The 2023 Stability Program forecasts a low overall deficit and public debt on a downward track.
  - The high debt ratio implies sustained effort needed for medium-term debt reduction.
  - The Buffer Stock model (Fournier, 2019) is used to illuminate optimal medium-term structural consolidation under alternative scenarios.
- Model framework:
  - Government balances economic stabilization and debt sustainability with forward-looking fiscal policy to smooth shocks and reduce scarring, subject to initial debt, stabilization function, market risk appetite, and shock distribution.
  - As debt increases, borrowing costs rise; near model’s debt limit (risk of losing market access), the optimal response is to preserve fiscal room rather than smooth negative shocks.
- Baseline recommendation and sensitivities:
  - Baseline calibration (2023 Article IV Staff Report forecast) recommends an increase in the structural primary balance averaging around 2.1 percentages points of potential GDP relative to 2022 during 2024-2028, implying an average level of 2.7 percent of potential GDP.
  - The consolidation path is front-loaded reflecting higher initial debt.
  - Sensitivity to key parameters:
    - Long-run real effective interest rate:
      - Baseline assumes convergence to 2.5 percent.
      - Alternative calibrations considered: 2.8 percent (2002-19 average) and about 2.0 percent (excluding sovereign crisis and Covid-19).
      - A 30-basis point increase in long run real interest rates implies the recommended additional annual increase in the structural primary balance would be some 0.2 percentage points higher than the baseline.
    - Medium-term growth:
      - Baseline assumes boost from RRP investment and structural reforms.
      - Alternative with long-term potential growth of ¾ percent (average 2002-19) would necessitate an additional 0.3 p.p. average increase in structural primary balance starting in 2024 over the medium-term relative to the baseline.
      - Additional risks from fiscal cliff effects at end of NGEU period could reduce long-term growth further.
    - Market sensitivity to debt:
      - Higher sensitivity of interest rate to debt level necessitates stronger consolidation over the medium-term.
- Policy conclusion:
  - Appropriate fiscal consolidation critically depends on medium-term output dynamics and market risk appetite.
  - While debt is forecast to decline under the model baseline, the model calls for more ambitious consolidation, and higher recommended fiscal effort under adverse scenarios.

*INTERNATIONAL MONETARY FUND*

### Annex I — Model details and calibrations (key highlights and parameter values)
- Key model features:
  - Two-way feedback between fiscal policy and output (fiscal tightening negatively affects output via fiscal multipliers; output affects fiscal outcomes via automatic stabilizers).
  - Macro stabilizing role of fiscal policy is constrained by high debt due to rising interest rates and risk of losing market access.
  - Hysteresis: recessions have persistent negative effects on potential output via loss of physical and human capital and lower investment.
- Calibration highlights:
  - Welfare function:
    - Discount factor, β 0.99
    - Risk aversion, σ 2
    - Labor elasticity, η 1/0.3
    - Weight of labor, ξ 1
  - Fiscal parameters:
    - Fiscal multiplier, m1 0.5
    - Fiscal multiplier sensitivity to shocks, m2 3
    - Automatic stabilizers (primary balance semi-elasticity to the gap) 0.4
    - Adjustment cost, χ 3
  - Interest rate and debt parameters:
    - Effect of debt level on the risk premium, α 2.5%
    - Effect of debt change on the risk premium, α2 0.5%
    - Debt level at which the risk to lose market access is 50%, d 150%
    - Debt limit accuracy, d1 3
    - Effect of debt change on the risk to lose market access, d2 1
    - Effect of debt change on the risk to lose market access, d3 0
  - Economy parameters:
    - Potential growth, long-term 1.3%
    - Population growth -0.4%
    - Real interest rate 2.5%
    - Shock persistence 0.77
    - Shock size 0.032
    - Hysteresis 10%
    - Hysteresis threshold -1%
  - Additional calibration notes:
    - Average fiscal multiplier of 0.5; automatic stabilizers set to 0.4; fiscal multiplier sensitivity (m2) of 3 means a negative output gap of five percent lowers the fiscal multiplier by 0.15.
    - Risk premium linear in government debt implies increase of 2.5 bps per 1 p.p. increase in debt-to-GDP ratio.
    - Parameters imply 50 percent probability of losing market access at debt-to-GDP ratio of 150 percent.
    - Potential growth at 1.3 percent reflects above-historic growth (2001-19 average 0.75%) and is about ½ p.p. below medium-term potential growth of 1.9 percent under the baseline WEO.
    - Real interest rate of 2.5 percent based on 20-year average 10-year bond yield (4.25 percent) and inflation (1.75 percent).

*INTERNATIONAL MONETARY FUND*

### Labor market and digitalization in Portugal — key findings
- Aggregate outcomes during Covid-19:
  - Aggregate employment rate declined and unemployment rate increased less during Covid-19 than in previous recessions.
  - Pattern broadly in line with median euro area (EA) country and smaller than the US, reflecting extensive job retention schemes.
  - Labor force participation rate dropped more sharply during Covid-19 than in previous two recessions, driven largely by low-skilled and young workers.
- Distributional impacts:
  - Young workers (15-29 years old): employment share in total employment fell by around 1.1 percentage points between 2020Q1 and 2020Q2.
  - Low-skilled workers (below tertiary education): employment share fell by around 1.6 percentage points over the same period.
  - Contact-intensive employment (e.g., hotels and restaurants): share declined by around 1 percentage point.
  - Non-digital employment experienced the sharpest drop in its share of total employment in Portugal, with around 1.7 percentage points decline.
  - No significant gender differential in employment changes in Portugal during the pandemic, unlike some other advanced economies.
- Digital vs non-digital classification and method:
  - Digital occupations identified using O*NET-derived distal scores (weighted averages of knowledge and work activity related to computers), mapped to ISCO08 codes.
  - Occupations above the median distal score classified as digital (50th percentile level is 53).
  - ISCO08 occupations classified as digital include managers, professionals, technicians and associate professionals, and clerical support workers.
  - Non-digital occupations include service and sales workers, agricultural/forestry/fishery workers, craft and related trade workers, plant and machine operators and assemblers, and elementary occupations.
- Notes on measurement:
  - Some decline in labor force participation may reflect statistical measurement errors (individuals who should be unemployed may have been reclassified as inactive during Covid-19).

*INTERNATIONAL MONETARY FUND*

### 4.       On the basis of this measure of digital

### 1prtea2023002 - 4.       On the basis of this measure of digital

### Digital employment dynamics during Covid-19
- Portugal experienced a sharper increase in the share of jobs in digital occupations during Covid-19 compared to the rest of the Euro Area (EA), accompanied by a falling share of non-digital jobs.
- The rise in Portugal’s digital employment share was driven by an increase in the share of the “professional” occupation.
- In Portugal, digital employment increased in absolute terms during Covid-19 while non-digital employment declined.
- The empirical comparisons use 2019 as the pre-Covid-19 base year (changes are measured relative to the same quarter q in 2019 to address seasonality).

### Regression approach and identification
- Sample: 29 European countries (list includes Austria, Belgium, Bulgaria, Croatia, Czechia, Denmark, Estonia, Finland, France, Germany, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, and United Kingdom) and the U.S.
- Timing: post-recession period indicators include 2020Q2 to 2022Q2.
- Covid-shock variable (Europe): largest drop in the average of Google mobility indicators in (i) retail and recreation areas and (ii) transit locations in 2020 relative to January 2020 for each country.
- Covid-shock variable (U.S.): Bartik shock (normalized for interpretation using the difference between the 10th and 90th percentiles of the Bartik shock’s distribution across states).
- Controls for European regressions include pre-Covid level of digital employment share to account for heterogeneity in pre-existing digital employment inclinations. U.S. regressions include additional demographic and regional controls (e.g., share with bachelor’s degree, share aged 25–44, race composition, migration in-flows, GDP per capita, JOLTs quit rates).

### Key empirical findings on Covid-19 impact
- U.S. results: significant but temporary increase in digital employment share. Both digital and non-digital employment declined in absolute levels in the U.S., but digital employment declined less; the increase in digital employment share was driven by digital and cognitive occupations rather than digitalization of manual or routine jobs.
- Europe results: the increase in the share of digital employment is small and not statistically significant at the aggregate 29-country level; results should be interpreted with caution because:
  - Cross-country sample size is 29 at the aggregate level while U.S. analysis is at state level.
  - Many European countries deployed job retention schemes that likely preserved jobs in more affected occupations and sectors (including non-digital jobs), potentially muting the observable Covid-19 effect on digital employment shares.
- Portugal stylized facts suggest a sharp persistent rise in digital employment share; regression analysis provides suggestive evidence that digital employment was shielded during Covid-19.

### Policy implications from digital employment findings
- Emphasize policies to invest in digitalization and digital skills and in higher education in Portugal to build a more resilient labor market for future shocks.
- Distributional impacts matter: young and low-skilled workers in contact-intensive and non-digital jobs were more adversely affected during the pandemic, reinforcing targeted skills and education policies.

### Household vulnerabilities and macro-financial context
- House prices: since 2018Q1 real house prices increased by 40 percent (the highest appreciation rate in Europe). Real house price growth decelerated to around 2 percent y/y in 2022Q4 (versus 9.1 percent y/y one year earlier).
- New home buyers: mortgage rates on new issuances reached 3.2 percent at end 2022, representing a 240-bps increase from end-2021. The monthly bill of buyers purchasing property in the main cities in 2022 rose by almost half relative to 2021. If interest rates were to increase by a further 300 basis points, mortgage bills would double relative to 2021.
- Household expenditures and indebtedness (as of 2022):
  - Median household spends one third of its gross income on food and energy.
  - Bottom tercile spends 56 percent of gross income on food and energy.
  - Share of households with non-mortgage loans: 14 percent in the bottom tercile, 28 percent in the second tercile, and 25 percent in the top tercile.
  - Estimated average debt service among households with debt payments is around 10.4 percent at end-2021.
- Banking sector exposures:
  - Household loans collateralized by residential real estate (RRE) account for over half of total loans to the nonfinancial private sector and amount to over 40 percent of 2022 GDP.
  - Other non-collateralized household loans represent 10 percent of total loans or 6 percent of GDP.
- Government policy response:
  - Government estimated to have spent about 1 percent of GDP on average during 2022-23 to shield households from rising food, energy, and housing costs.
  - Two mortgage relief measures: (i) measures to encourage banks to restructure loans for borrowers at risk (November 2022); (ii) an interest rate subsidy to absorb part of the rise in interest rates for financially stretched borrowers (March 2023).

### Stress-testing household balance sheets: definitions and methodology
- Financial vulnerability (default risk): household is financially vulnerable if debt service and basic living expenditures represent more than 70 percent of gross income. Basic living expenditures include essential consumption (food and utilities) and housing costs. Alternative standard measure: debt service exceeds 40 percent of gross income.
- Mortgage debt-at-risk: outstanding mortgages of households identified as financially vulnerable as a share of total mortgages outstanding.
- Consumer debt-at-risk: outstanding non-mortgage debt held by financially vulnerable households as a share of total consumer loans.
- Data: granular household-level data from EU-SILC allowing identification across income distribution and tenure status.
- Logit regressions and historical estimation use 2004–2020 for mortgage arrears relationships.

### Stress-test scenarios and shocks
- Baseline scenario: follows IMF October 2022 WEO forecast.
- Example adverse scenario (‘cost of living’): interest rate shock of 200 bps and a food and energy price shock of 20 percent relative to baseline. Annex II Table 2 (not reproduced here) shows cumulative shocks by end-2023 for Portugal and EA.
- Worst-case scenario: intensification of cost-of-living crisis with interest rates increasing by a further 200 bps relative to the baseline, and food and energy prices rising 20 percent above baseline projections.
- Time horizon: 2-year horizon for simulated paths of household income, housing cost, other basic expenses, and repayments of other loans.

### Stress-test results: vulnerability, arrears, and consumption-at-risk
- Arrears probability (Portugal):
  - When households are overburdened by basic expenditures and debt repayments, probability of being in arrears on mortgage payments increases by 70 percent (from 3.1 to 5.3 percent on average during the estimation period 2004–2020).
  - For EA (country-level regressions) the average probability of being in arrears jumps from 4.5 to 6.8 percent for vulnerable households.
  - Probability of being in arrears on other retail loans in Portugal rises from 3.6 to 5.8 percent when households are overburdened; for EA it rises from 7.3 to 10.3 percent.
- Standard vulnerability measure (DSTI ≥ 40 percent):
  - Share of mortgage borrowers with DSTI (including all debt payments) exceeding 40 percent is estimated to rise to 8.8 percent under the baseline and to 14.0 percent in the ‘tightening’ scenario in Portugal.
  - Because stressed households hold a significant portion of outstanding debt, mortgage debt-at-risk could double and reach a quarter of outstanding mortgage debt under the worst-case scenario.
- Broader vulnerability when accounting for basic living expenditure:
  - In adverse scenarios, almost half of households could struggle to afford basic expenditures in Portugal (about twice as many as before the energy crisis).
  - Share of financially vulnerable low-income families could increase to 78 percent under the baseline (from 60 percent) and reach around 90 percent under the ‘cost of living’ scenario.
  - Only between 5 and 13 percent of high-income households would be financially vulnerable depending on scenario severity.
  - In the worst-case scenario, one third of consumers could be economically vulnerable and be forced to cut back on consumption of non-essential goods, accounting for over one fourth of consumption.
  - Estimated reduction in aggregate consumption would range between 2 and 5 percent.

### Implications for banks and financial stability (preview)
- High exposure of Portuguese banks to RRE, combined with relatively weaker CET1 capital buffers (compared to EA), raises risks to financial stability from a sharp fall in house prices.
- The paper proceeds to quantify the impact on banks from changes in asset quality and to examine the effectiveness of policy measures to reduce household vulnerabilities and preserve financial stability.

*Source: IMF staff analysis as presented in the provided content unit.*

### 11.      To quantify the impact of household

### 11.      To quantify the impact of household

### Methodology for quantifying household financial stretch on banks’ capital
- Four-step procedure:
  - Estimate a range of scenarios to account for uncertainty around the outlook by end-2023.
  - Estimate the link between being financially vulnerable and the likelihood of default at the individual household level.
  - Simulate the increase in the share of financially vulnerable households to estimate the increase in probability of default.
  - Use data from EBA Risk Dashboard to project the impact of higher credit risk on banks’ capital position.
- Use estimates of house price overvaluation in Portugal to compute bank impact under a house price correction.

### Impact on banks: baseline versus house price correction
- Absence of a sharp house price correction:
  - Capital depletion would not exceed 20 basis points in Portugal (versus 15 basis points in the EA).
- Abrupt decline in house prices in Portugal (eliminating the 20 percent estimated overvaluation):
  - On aggregate, it would shed up to 100 basis points of capital in Portugal (versus 85 basis points in the EA).
  - Estimate does not consider households with credit quality deterioration requiring provisions even if DSTI falls below the estimated threshold where default rate jumps.
- Assumption for house price correction:
  - The 20 percent estimated house price overvaluation is corrected by end 2023.
  - This impacts LGD of defaulted exposures: LGD increases by 20 percent over the weighted average LGD on retail loans secured on real estate property reported by Portuguese IRB banks on non-defaulted exposures (i.e., 20.1 percent as of 2022Q4).
  - The stressed LGD is 40 percent.

### Policies to mitigate the impact of soaring food and energy prices — selected shock mitigation policies
- Government measures in 2022 included:
  - Reduced tax burden on fuel.
  - Hold on planned carbon tax increase.
  - Reduced VAT rate on electricity.
  - Exceptional income support to households.
- Simulation assumptions:
  - Reduction in the price of energy and the exceptional income support applies to all households.
  - Compute fiscal outlay (cost) of ‘selected shock mitigation policies’ under the baseline and ‘cost of living’ scenario.
  - Calculate share of households and mortgage debt at risk protected (benefit).
- Cost-effectiveness results:
  - Baseline:
    - Around 3.5 percent of households would be saved from distress.
    - Cost of 0.6 percent of GDP.
    - Reduction of risky debt: 1.7 percent.
  - ‘Cost of living’ scenario:
    - Share of households shielded: 3.8 percent.
    - Cost of 0.7 percent of GDP.
    - Reduction of share of mortgage debt at risk: 2.5 percent.

### Hypothetical interventions shielding consumers from the entire (100 percent) increase in food and energy prices (2022-23)
- Three targeting schemes simulated:
  - (i) Broad policy: all households shielded.
  - (ii) Partially targeted: poorest two thirds shielded.
  - (iii) Narrowly targeted: bottom tercile shielded.
- Narrowly targeted policy results:
  - Baseline:
    - Saves 7.9 percent of households.
    - Protects 0.8 percent of mortgage debt at risk.
    - Cost of 0.8 percent GDP.
  - ‘Cost of living’ scenario:
    - Saves 12 percent of distressed households.
    - Protects 2.5 percent of risky debt.
    - Cost of 1.5 percent of GDP.
- Note: The cost depends on wholesale market prices during 2022-23, assumed in line with the October 2022 WEO forecast.

### Policies to mitigate the impact of higher rates on mortgage borrowers
- Decree-Law No. 80-A/2022 (published November 25, 2022):
  - Eligibility: borrowers with first residence floating-rate loans of up to EUR 300,000 at acquisition where DSTI is 50 percent or higher, or DSTI exceeds 36 percent with an increase in DSTI of at least 5 percentage points in 2023.
  - Simulation: assume banks restructure eligible loans by reducing monthly installments through a reduction of interest payments (half of the increase by end-2023).
  - Estimated effects:
    - Around 0.5 to 3.2 percentage points of mortgage-debt-at-risk would be protected from distress.
    - Between 0.3 and 2.3 percent of mortgage borrowers would be protected depending on the scenario.
    - Restructuring would be applied to 7-18 percent of outstanding mortgage debt.
    - Benefit for banks (lower provisions): around 5 basis points of CET1.
    - Cost for banks (lower NII): between 10 and 20 basis points of CET1.
- Decree-Law No. 20-B/2023 (came into force March 23, 2023):
  - Support: temporary subsidy in 2023 for half of the increase in current and past benchmark rates at origination augmented by a 3-percentage point increase.
  - Eligibility: outstanding amount at origination lower than EUR 250,000; family income up to the 6th income bracket (EUR 38,632 annual income); DSTI greater than or equal to 35 percent.
  - Simulation results:
    - Under the ‘interest rate shock’ or ‘cost of living’ scenario, mortgage debt at risk would be lower by up to one percentage point under the policy.
    - Debt relief estimated subsidy: 0.46 percent on eligible debt (around 15 percent of outstanding mortgages).
    - Cost: around EUR 60 million (3 basis points of GDP).
    - Benefit for banks (lower provisions): estimated at 1 basis point of CET1.
  - Note: These are lower bound projections due to bias in reference rate at origination and exclusion of mortgage originations after 2017 HFCS.

### Key findings on household vulnerability and macro effects
- House price valuation and risk:
  - Since onset of Covid-19, house prices in Portugal have risen faster than fundamentals can account for, pointing to overvaluation of around 20 percent.
  - This implies an elevated risk of price correction.
- Vulnerability shares and debt composition:
  - Under adverse conditions, almost half of all households could become financially stretched in Portugal.
  - These households represent over 40 percent of mortgage debt and 45 percent of consumer debt.
  - Share of vulnerable low-income families could range between 78 and 90 percent.
  - Share of vulnerable high-income households could range between 5 and 13 percent, depending on severity of scenario.
- Consumption and macro impact:
  - In the worst-case scenario, one third of consumers could be forced to cut back on consumption with an estimated reduction in aggregate consumption of 7 percent.
- Capital depletion under market price correction:
  - Considering banks have adequately provisioned existing risks, capital depletion would not exceed 100 basis points under a market price correction that brings house prices back to fundamental values in Portugal.

### Policy implications and cost-effectiveness insights
- Government support measures can help maintain borrower repayment capacity; benefit measured by share of household/debt spared from financial distress.
- Under the baseline:
  - ‘Selected shock mitigation policies’ (VAT reductions and extraordinary income support) could shield around 3.5 percent of households from financial distress and 1.7 percent of mortgage debt at risk at a cost of 0.6 percent of GDP.
- Targeting implications:
  - Targeting a similar budget envelope to the bottom tercile of the income distribution would be more cost effective to reduce the share of financially stretched households.
  - Including the middle tercile in a policy package would increase financial stability support since these households are more likely to hold mortgage debt.

*Source: IMF staff analysis as presented in the provided chapter content.*

### 0.6 percent of GDP ...

### 1prtea2023002 - 0.6 percent of GDP ... 

### Shock mitigation policies: benefits, coverage, and fiscal cost
- Illustrative policy interventions include: Portugal’s announced measures (reduction in the tax burden for fuel and electricity) and three hypothetical subsidy targeting options:
  - Broad policy: all households receive a subsidy.
  - Medium targeting: the poorest two-thirds receive a subsidy.
  - Narrow targeting: the bottom tercile receive a subsidy.
- Key empirical outcomes (Portugal, as reported):
  - In the baseline: 0.6 percent of GDP (fiscal cost) ...
  - In the adverse scenario: 3.8 percent of households would be saved (benefit metric).
  - Mortgage debt-at-risk reduction reported: only 2.5 percent of mortgage debt-at-risk saved at a cost of 0.7 percent of GDP.
- Measurement and panels:
  - Top panels measure benefit as the share of households saved from distress (percent of households).
  - Bottom panels measure benefit as the decline in mortgage debt-at-risk (percent of households and percent of GDP).
  - Each country is represented by a curve; Portugal (PRT) and other governments (Croatia HVR, Cyprus CYP, Greece GRE) shown with specific symbols for announced interventions (square) and the three hypothetical interventions (circle).
- Projections are as of end 2023.
- Sources used for these policy illustrations: HFCS microdata; Eurostat; and IMF staff calculations.

### Annex I — House price overvaluation: methodology and findings
- Methodology:
  - A vector error correction model (VECM) relates observed real housing price (p) to long-run equilibrium real housing price (p*) determined by housing stock (hs), real household disposable income (di), real mortgage interest rate (R), and a macroprudential policy dummy (MacroPru) that proxies intensity of policy interventions.
  - Macroprudential dummy takes value +1 (-1) for each tool tightened (loosened) in a quarter.
  - The VECM formulation includes dynamics for changes (Δ) in p, hs, di, and R and estimates country-specific speed of adjustment.
- Key results for Portugal:
  - VECM estimates put over-valuation in 2022Q3 at around 20 percent.
  - This 20 percent lies just above the median of the distribution for selected European countries with dynamic housing markets and at the upper end of the 8-16 percent range estimated for 2021 by the European Central Bank.
  - The model indicates a gradual adjustment in housing prices, with about 20 percent of disequilibria adjustment occurring over one year in Portugal.
- Country sample for comparison: Selected countries include Austria, Germany, France, Portugal, Slovakia, Spain, and Sweden. (Text figure reports 2009Q1-2022Q4; individual VECMs extend further back depending on data availability.)

### Annex II — Technical aspects of the household vulnerability model
- Microdata and dataset construction:
  - Two microdata sources combined: 2020 EU-SILC microdata (housing costs, financial stretch, debt status since 2004) and the 2017 Household Finance and Consumption Survey (HFCS) for granular balance-sheet data.
  - HFCS data are aged forward to end-2021 using a matching procedure targeting aggregate statistics on household income, indebtedness, consumption, mortgage rates, and prices sourced from Eurostat and national central banks.
  - For Portugal: EU-SILC has around 30,000 households in 2020 (326,000 observations in 2004-20). The HFCS survey covers under 6,000 households.
  - Annex II Table 1 reports EU-SILC counts by country (example: PRTPortugal 27,695).
- Simulation approach and shocks:
  - Household-level simulations project changes in DSTI (debt service to income) and DSECTI (debt service and essential consumption to income) under scenarios j ∈ {1,...,7}.
  - Projections account for changes in interest rates (∆i), household income (∆inc), food (∆food), energy (∆energy), and inflation (∆inf). Interest payments on floating-rate loans adjust to benchmark curves; rents are indexed to inflation.
  - Income is extrapolated using cumulative growth of gross disposable income per capita; nominal household debt changes match aggregate gross debt-to-income ratio paths; consumption scaled to include durables, renovation, and insurance via HICP-linked country weights.
  - Assumptions on consumption responses: household spending on food and utilities rises with market prices; quantities remain constant over the forecasting horizon; households do not adjust consumption composition in the projection.
- Vulnerability definitions and thresholds:
  - A household is financially vulnerable if DSECTI ≥ 70 percent. This threshold is stated as the most significant threshold of mortgage default across countries.
  - Standard default-risk measure reported for benchmarking is DSTI ≥ 40 percent.
  - For macroprudential policy purposes in Portugal, a DSTI ratio of 60 percent (defined on total household disposable income, rather than gross income) is identified as the most discriminatory limit for mortgage default in Portugal.
  - To assess consumption effects, a household is economically vulnerable if DSTCTI > 1 (debt service and total consumption exceed gross income).
- Heterogeneity notes:
  - Income projection is at the aggregate country level; in 2022 income changes were heterogeneous across income classes with lower-income households experiencing relatively higher income growth due to employment pickup, increases in the minimum wage, and concentrated extraordinary support on vulnerable households.

### Empirical diagnostics and thresholds (selected figures reported)
- Overvaluation estimate:
  - Portugal house price overvaluation in 2022Q3: around 20 percent.
  - ECB 2021 estimate range: 8-16 percent.
  - Speed of disequilibria adjustment in Portugal: about 20 percent over one year.
- Vulnerability thresholds and sensitivity:
  - DSECTI vulnerability threshold emphasized: 70 percent.
  - Standard DSTI default-risk threshold for benchmarking: 40 percent.
  - Suggested DSTI policy-relevant threshold in Portugal: 60 percent (on disposable income).
- Data coverage examples:
  - EU-SILC Portugal (2020): around 30,000 households (326,000 observations in 2004-20).
  - HFCS (latest wave 2017): under 6,000 households for Portugal; simulations performed on HFCS data aged to 2021.

*Source: IMF staff analysis and calculations, HFCS microdata, EU-SILC microdata, Eurostat, and national sources as presented in the original document.*

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_Source: https://www.imf.org/-/media/files/publications/cr/2023/english/1prtea2023002.pdf_