Roma–Econ Contact

Economic modelling, causal inference and data science

Economics for policy and business decisions.

We work on macroeconomic forecasting, policy evaluation and data analysis for policy institutes and companies.

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Models
Dynamic CGE · ARDL · DiD · IV · BVAR
Stack
R · Julia · SQL

Services

How can we help you?

  1. Macroeconomic forecasting & analysis

    Forecasting and impact analysis using time-series and multi-country, multi-sector models.

    ARDL · BVAR · Dynamic CGE

  2. Policy analysis & causal inference

    Microeconomic and macroeconomic applications

    Causal analysis of policy effects on people, firms and the wider economy.

    DiD · Event studies · FE · IV · RDD · Survival · BVAR

    Scope and methods

  3. Data science & analytics

    Data preparation, modelling and reporting

    We collect, clean and harmonise data, build statistical models, and produce reproducible datasets, reports and dashboards.

    R · Julia · Python · SQL · Git

    Scope and methods

How we work

  1. Models suited to the question

    We build or adapt models to the question and data. Where appropriate, we provide the source code in Python, Julia or R.

  2. Working with imperfect data

    We work with limited, noisy or incomplete data and make the assumptions and data limitations explicit.

  3. Clear reporting

    Results are reported in briefs, reports and technical files, with the main assumptions and limitations stated clearly.

Who we work with

Public & policy

Think tanks & policy institutes

Economic analysis for regulation, public policy and long-term planning.

  • Trade & energy shocks
  • Fiscal & industrial policy
  • Labour markets
  • Population projections

Private sector

Corporates & private enterprises

Forecasting and analysis of productivity, investment, innovation and AI adoption.

  • Scenario forecasting
  • Firm productivity
  • Investment constraints
  • Predictive dashboards

Discuss a project

Tell us the question, the data you have and the output you need. We can then define the scope, method and deliverables.

Email us

Working with us

  • Initial call

    A free 30-minute call to discuss the question, available data and expected output.

  • Two-week analysis

    A fixed-price two-week impact or policy analysis, usually delivered as a short report with the supporting results.

  • A four-week study

    A fuller study with the methods, results and validation files documented for review.

  • Model handover

    Source code, scenario tools and technical documentation can be included with the results.

  • Ongoing support

    Ongoing modelling, forecasting and data support.

Projects are invoiced at three milestones: the framework, the interim findings and the final deliverables.

Macroeconomic forecasting & analysis

We use time-series and multi-country, multi-sector models for macroeconomic forecasting and impact analysis.

Typical outputs: GDP, emissions, sectoral output, energy prices, electricity penetration and employment.

Over time

Macroeconometrics & forecasting

Time-series models estimated on macroeconomic and financial data to measure short- and long-run relationships, trace shocks and produce forecasts with uncertainty.

Methods

ARDL
Time series. Short- and long-run effects estimated from cointegrated data.
BVAR · State-space
Bayesian macro-econometrics for shocks, transmission and forecasting under uncertainty.

Questions we answer

  • Where is growth heading over the next decade, and how wide is the uncertainty?
  • How do fiscal and monetary shocks pass through to the wider economy?

Deliverables

  • Macroeconometric estimates under uncertainty
  • Scenario forecasts for strategic planning and stress-testing

Computable general equilibrium models

CGE models represent linked markets across sectors and regions, allowing the effects of a policy or shock to be traced through the economy.

Models

Dynamic CGE
Proprietary. Capital accumulation drives long-run growth; used for impact analysis and forecasting, with no full-employment constraint.

Questions we answer

  • What does a tariff or trade shock do to output, prices and jobs, sector by sector?
  • How will an energy-transition or infrastructure programme ripple through regional economies?

Deliverables

  • Impact assessments by country, region and sector
  • A report explaining the main mechanisms and results

Work examples

Climate transition risk at Enel We estimate Enel's downside market-value risk and the additional effect of a carbon-price scenario to 2030. The scenario adds about €0.7 billion to an estimated one-in-twenty-year loss of €18.2 billion; over six years, parameter uncertainty contributes more to the estimated risk. Open the work example Energy prices and industrial productivity We compare 50 Italian industries over 1997–2023 to estimate how responses to energy-price increases vary with energy cost exposure. During 2022–23, each additional percentage point of energy cost share was associated with about 4 percentage points less output growth; the estimated difference fades within two to three years. Open the work example Defence spending across the UK's regions We simulate UK defence spending rising from 2.3% to 3% of GDP by 2030 in a regional CGE model of the UK. By 2030, real GDP is 0.34% and employment 0.53% above the baseline, with the largest estimated regional GRP gains in the South West, Northern Ireland and Wales. Open the work example The NHS spending settlement across the UK's regions We simulate NHS day-to-day spending growing 3% a year in real terms to 2030 in a regional CGE model of the UK. By 2030, real GDP is 0.22% and employment 0.36% above the baseline, with the largest estimated regional GRP gains in the North East, Northern Ireland and Wales. Open the work example

Where we've applied it

  • Energy & power
  • Infrastructure
  • Trade & tariffs
  • Innovation
  • Growth forecasting

Our dynamic CGE uses data from the IEA, WTO, IMF, OECD and World Bank and runs entirely in R, so clients do not need licensed modelling software to use the delivered model.

Microeconomic and macroeconomic applications

Policy analysis & causal inference

We use causal inference methods to estimate the effects of policies and shocks on people, firms and the wider economy.

Data: cross-section, panel, longitudinal, administrative, survey and firm-level.

Questions we answer

  • Did the subsidy raise productivity, or did better firms simply apply?
  • How did a reform change employment, wages or health, and for whom?
  • How do fiscal and monetary shocks pass through to the wider economy?

Methods

DiD · Event study
Treated versus untreated, before versus after. Effects that unfold over time, with pre-trend checks.
Panel · FE
Fixed effects and longitudinal methods that control for what doesn't change within people, firms or regions.
IV · RDD
Instrumental variables and regression discontinuity when take-up of a policy is not random.
Survival
Time-to-event analysis for exits, transitions and durations.
BVAR · State-space
Bayesian macro-econometrics for shocks, transmission and forecasting under uncertainty.

Deliverables

  • Policy and programme evaluations with a credible counterfactual
  • Effect sizes with uncertainty intervals and statistical diagnostics
  • Breakdowns of effects across groups and evidence on the mechanisms involved
  • Reports written for policy, management and technical audiences

Work examples

Long-term care benefit triggers In survey data for 30 countries, more than one third of expected needs-related resource loss after age 65 occurs at exactly one ADL limitation, before a typical two-limitation benefit trigger. Open the work example Income screening after accounting for care needs We compare conventional and needs-adjusted income screens in 30 countries. The additional group identified after accounting for care needs has the highest two-year death rate among the groups compared. Open the work example Macroeconomic forecasting & analysis Energy prices and industrial productivity We compare 50 Italian industries over 1997–2023 to estimate how responses to energy-price increases vary with energy cost exposure. During 2022–23, each additional percentage point of energy cost share was associated with about 4 percentage points less output growth; the estimated difference fades within two to three years. Open the work example Data science & analytics Mortality projections by health status We estimate separate mortality curves by self-reported health in the UK, the Netherlands and Italy and project them to 2050. In all three countries, the estimated modal age at death is about ten years lower for adults in poor health, while remaining life expectancy at 65 is about eight years higher for those in good health. Open the work example

Where we've applied it

  • Health & ageing
  • Labour & human capital
  • Sports economics
  • Productivity & firm dynamics
  • Investment & financial constraints
  • Fiscal, monetary & industrial policy
  • Population projections

For prediction problems, we also use forecasting and machine-learning methods.

Data preparation, modelling and reporting

Data science & analytics

We combine data from multiple sources, clean and harmonise it, build models and produce reproducible datasets, reports and dashboards.

Tools: R · Julia · Python · SQL · Git · GEMPACK

The pipeline

  1. Collect

    Administrative records, surveys, firm-level and open data combined through reproducible scripts.

  2. Clean

    Errors, gaps and duplicates handled with documented, testable rules.

  3. Harmonise

    Definitions, units and codes aligned across sources and years.

  4. Model

    Statistical and predictive models, validated out of sample.

  5. Deliver

    Dashboard-ready tables, interactive views and automated reports.

Questions we answer

  • How can we combine data from multiple systems with inconsistent definitions?
  • Can the data we already collect be used to forecast demand, risk or other outcomes?
  • Can recurring reports be rebuilt automatically from the same code?

Deliverables

  • Cleaned and harmonised datasets for analysis and dashboards
  • Statistical models and predictive analytics
  • Reproducible, version-controlled pipelines with documentation
  • Automated reports, policy briefs and visualisations

Work examples

Squad use at Juventus and Inter We combine thirteen seasons of Juventus and Inter team sheets to measure where players started, how often they changed position and how those patterns differed between the clubs. Open the work example Mortality projections by health status We estimate separate mortality curves by self-reported health in the UK, the Netherlands and Italy and project them to 2050. In all three countries, the estimated modal age at death is about ten years lower for adults in poor health, while remaining life expectancy at 65 is about eight years higher for those in good health. Open the work example Policy analysis & causal inference Income screening after accounting for care needs We compare conventional and needs-adjusted income screens in 30 countries. The additional group identified after accounting for care needs has the highest two-year death rate among the groups compared. Open the work example

Where we've applied it

  • Large administrative datasets
  • Survey data
  • Firm-level data
  • Corporate BI & dashboards
  • Automated policy briefs

Deliverables include the code and documentation, with a handover session if required, so the analysis can be rerun internally.

Work example · Serie A, 2013/14 to 2025/26

Squad use at Juventus and Inter

For clubs and leagues. We use team-sheet records to compare how Juventus and Inter used players across positions and seasons.

Juventus started a player away from his usual position in 19.8% of league starts, about two players a match. Inter did so in 11.4%, about one.

Data: Transfermarkt line-ups and market values, from a public dataset: 494 league matches per club, 9,674 starts by players with five or more starts in the season.

Circle: a position, sized by its starts. Arrow: ten or more starts away from a player's usual position.

Season by season

Until 2017/18 both clubs moved players in about 18% of starts. Since 2018/19 Inter have stayed at or near the bottom of the league's normal range for positions, at 7%, while Juventus swung from season to season, even under one coach, at 21%.

JuventusInterMiddle half of other long-standing Serie A clubs

The starting line-up

The club's average starting line-up in each season: the bigger the dot, the more players in that position per match. From 2019/20 Inter barely change shape; Juventus switch between a back four and a back three.

2013/14

Who moved where

Regular starters whose usual position changed from one season to the next. At Juventus, half of the ten are full-backs moved to wide midfield or back again, often the same wing-back role under another label; at Inter, most moves were at the back and at the base of midfield.

    In numbers

    Seven more measures, Juventus and Inter, Serie A 2013/14 to 2025/26
    MeasureJuventusInter
    Starts in a different line (defence, midfield or attack); about four in ten at Juventus and two in ten at Inter are full-backs used as wing-backs6.5%3.2%
    Utility players per season, used three or more times in each of two lines3.21.7
    Formations used in three or more matches118
    Matches in the season's main formation61%80%
    Arrivals from another club in 14 European top divisions, loan returns included, who changed their usual line (2014/15 on)7 of 6510 of 75
    Combined market value of the outfield players with five or more league starts, median season of 2013/14 to 2017/18 (euros of each season)€400m€240m
    The same, 2018/19 to 2025/26€530m€550m

    Moving and market value

    The typical change in market value from one season to the next, for regulars at the club in both seasons. Moved players lost more. Without the moves that are mostly a change of label, the fall is 20% at Juventus and 10% at Inter. A pattern, not proof of cause: at Inter the moved players were also older.

    In euros, the typical regular kept in position lost about €1.5 million of market value in a season at Juventus and €0.5 million at Inter; the typical moved player lost about €3 million at Juventus and €2 million at Inter. Before the move, Juventus' moved players were worth about as much as those kept (€25 million against €22 million); Inter's were cheaper (€12 million against €21 million), partly because more of Inter's moves came in earlier seasons, when values were lower. These are medians of each player's change, in euros of the day, not adjusted for inflation. With groups this small, the gap between moved and kept players is not precise.

    Among 32 rivalries

    Real Madrid and Barcelona are almost identical. Juventus and Inter have the second-widest gap of the 32 rivalries we compared in starts away from the usual position, just behind Juventus and Napoli.

    Full club and player results

    The results explorer provides the same measures for 443 clubs and 21,824 players across 14 European top divisions from 2013/14 to 2025/26, by season, with the underlying results available as CSV files.

    Open the results explorer
    • Overview
    • Clubs
    • Club profile
    • Rivalries
    • Players
    • Position changes
    • Method & data
    • Downloads

    Data and workflow

    1. Collect

      Every Serie A starting line-up for both clubs from 2013/14 to 2025/26, from a public dataset of Transfermarkt records, with the other clubs for comparison.

    2. Clean

      Players with five or more league starts in a season: 9,674 starts at the two clubs.

    3. Harmonise

      Transfermarkt's position labels grouped into defence, midfield and attack, the same way in every season.

    4. Model

      Each player's usual position in each season, every start compared with it, and benchmarks from the other long-standing Serie A clubs.

    5. Deliver

      Tables, a three-page report and the interactive figures on this page.

    Interpretation

    • A more positionally fixed system requires depth in individual roles, while a more flexible system places greater value on players who can cover several positions. The recruitment needs differ accordingly.
    • In this sample, players who changed position had weaker subsequent changes in market value than players kept in the same position. The comparison is descriptive rather than causal.
    • Public team-sheet data can be used to describe a club's positional stability and compare changes across seasons or coaches.

    How we measured it

    A player's usual position is where he started most often for his club that season, among players with five or more league starts; any other start counts as away from it. A line means defence, midfield or attack. Transfermarkt lists a wing-back as a full-back in a back four but as a wide midfielder in a back three, and one centre-back in a back three may appear as a sweeper; leaving such label swaps out, the gap is 15.4% against 9.5% of starts. Serie A comparisons use the 15 other clubs with eight or more seasons in the league. Arrivals and the rivalries use league matches in 14 European top divisions. Market values are Transfermarkt estimates in euros, each player's last valuation in the season, not adjusted for inflation: mostly from May or June, but from March in 2013/14 and 2014/15, April 2020 in 2019/20 and December 2025 in 2025/26, the latest available for these players. Players without a valuation in a season are left out of the combined values.

    Work example · Long-term care, 30 countries

    Long-term care benefit triggers

    For insurers and regulators assessing long-term care benefit design. We examine what is missed when benefits begin at two ADL limitations rather than one.

    Many private long-term care policies begin paying at two limitations in activities of daily living (ADLs). We estimate the resource implications of each additional limitation and use observed two-year transitions to project how much needs-related loss occurs before that trigger.

    Data: ELSA and SHARE survey microdata, 2002–2022; 531,248 individual-waves.

    The question

    • How much needs-related resource loss occurs before a two-ADL benefit trigger, and how do alternative designs compare at the same expected cost?

    What we found

    • To report the same financial strain, a person with one limitation needs 1.49 times the resources of someone with none. A second limitation takes that to 1.89, three or more to 2.09. The first step is the largest.
    • In money, a person over 65 with median resources (income plus 5% of wealth) has about £24,000 a year in England and about €24,000 across the SHARE countries taken together (2021–23 and 2021–22 prices). On the England price (1.43, 1.81 and 2.14 times), one limitation means needing about £11,000 a year more to report the same strain, two about £20,000 and three or more about £28,000. On the Europe price (1.52, 1.91 and 2.03 times) the figures are about €12,000, €22,000 and €24,000. This is what the scale implies, not a care cost.
    • Add up, over the years people can expect to live between 65 and 95, the share of their resources that limitations absorb: their needs-loss. 34.5% of a woman’s and 37.3% of a man’s falls at exactly one limitation, where a two-limitation trigger pays nothing.
    • The first limitation is often short: 53% of people aged 65–74 with one report none two years later. A quarter of women and a third of men who have a limitation between 65 and 95 are projected never to reach two.
    • Counting needs, 59% of over-65s with one limitation are poor, against 30% on resources alone.

    Needs-related loss by ADL state

    Expected needs-loss between 65 and 95, and the part of it that comes at exactly one limitation. Change the assumptions: the share stays between 29.2% and 42.2%. In money, at median resources and without discounting, a woman's expected needs-loss between 65 and 95 is about £48,000 in England and €49,000 in the SHARE countries, £16,000 and €17,000 of it at exactly one limitation; a man's is about £35,000 and €35,000, £12,000 and €14,000 of it at one. The projected years in each state are the same on both prices; only the price differs, so the share falling at one limitation is 33% in England and 36% in the SHARE countries for women (2021–23 and 2021–22 prices).

    Alternative benefit designs at equal cost

    Each design pays a cash benefit in the states it covers, scaled so that all of them cost the same per person over 65. Against the two-limitation trigger, every design that pays from the first limitation closes more of the needs-adjusted poverty gap. In money, the four budgets are about £250, £750, £1,500 and £2,500 per person over 65 a year in England, and €300, €850, €1,700 and €2,800 in the SHARE countries, taking each country's median resources of people aged 50 and over (£25,000 in England, about €28,000 on average across the SHARE countries). At the largest budget the two-limitation trigger pays each recipient their country's median: £25,000 in England, and about €26,000 a year on average in the SHARE countries; a benefit from the first limitation pays 54% of that, to more people.

    Implications for benefit design

    • The position of the trigger determines where benefit spending goes. A half benefit from the first limitation reaches more of the needs-adjusted poverty gap than the same money spent from two.
    • Benefits from one limitation would pay many short claims, so reassessment and waiting periods would shape their cost. We did not model either.
    • A first tier would change most where single-limitation cases are the largest share of the newly needs-poor: 54% in the Nordic countries, 41% in Central Europe and 36% in England and Ireland, against 28% in Southern and Eastern Europe and 17% in Israel.

    How we did it

    Pooled OLS · FE
    The price of a limitation. Reported financial strain on long-run resources (equivalised income plus 5% of net wealth, relative to the country-year median) and on counts of limitations, with survey-by-country-by-year fixed effects. 362,977 individual-waves.
    Multinomial logit
    Two-year transitions between none, one, two, three or more limitations and death, by age and sex: 243,718 transitions, 8,503 of them to death.
    Markov · Microsimulation
    The life course from 65 to 95, projected for women and men and simulated for 100,000 lives each. Intervals come from 300 draws of the price estimates, each paired with a draw of the transition estimates.
    Static frontier
    Five benefit designs at equal cost, applied to the observed population over 65, with needs-adjusted poverty measured against 60% of the country-year median.
    Money
    Pounds and euros per person per year, at the prices of ELSA wave 10 (interviews 2021–23) for England and SHARE wave 9 (2021–22) for the other countries. English resources are equivalised benefit-unit income for the year plus 5% of net non-housing wealth; SHARE household income and wealth are adjusted for household size, and other currencies are converted to euros at market exchange rates, with no adjustment for price levels. Budgets and benefits are shares of the median resources of people aged 50 and over in each country (£25,000 in England, €28,000 on average across the SHARE countries); the other figures use the median resources of people over 65, £24,000 in England and €24,000 across the SHARE countries taken together.

    Limits

    • The price is an equivalence scale anchored on reported strain, not a compensating transfer or an estimate of care costs. The money figures show what it implies at median resources; they are not care costs, benefit amounts or premiums.
    • Survey mortality is understated, so projected survival is an upper bound. With death rates 40–80% higher, the share before the trigger rises to 36–42%. About a quarter of starting interviews have no two-year follow-up and are left out of the transitions.
    • Limitations are self-reported and observed every two years. Real two-limitation policies also pay on severe cognitive impairment and use waiting periods; neither is modelled.
    • ELSA wealth excludes housing and is not equivalised, unlike SHARE’s, a known data issue under review. The design comparison ignores behaviour, take-up and claims handling.
    • On the poverty headcount, rather than the gap, the ranking depends on the budget: the two-limitation trigger prevents the most cases at 6% of median resources, and a benefit from the first limitation prevents more at the other budgets. The design comparison uses the baseline price only and carries no uncertainty intervals.

    Work example · Targeting care and support, 30 countries

    Income screening after accounting for care needs

    For ministries, regions and policy institutes targeting support to older people. We compare conventional income screens with screens that adjust resources for care needs.

    We define the income screen as the poorest fifth of each country and year, using income plus 5% of wealth. Adjusting those resources for care needs identifies an additional group that passes the conventional screen but falls below the needs-adjusted threshold. They account for 5.6% of people over 65 in the 30-country sample.

    Data: ELSA and SHARE survey microdata, 2002–2022; 531,248 individual-waves.

    The question

    • Who is missed by a conventional income screen once care needs are included, and how does a needs-adjusted screen perform instead?

    Who they are

    Among people aged 50 and over, the hidden group is on average 75 years old; 60% are women and 35% live alone. They report 2.65 limitations in daily activities and 82% rate their health fair or poor. 65% already receive some care or help, yet 22.4% report an unmet care need, the most of any group. Their share of the needs-poor grows with age. In money, in the latest wave the typical hidden person has resources of about £17,000 a year in England and €22,000 in the SHARE countries, above their country's income line; their median shortfall below the needs-adjusted line for their number of limitations is about £3,500 and €4,600 a year (2021–23 and 2021–22 prices).

    Two years later

    Their death rate is the highest of any group, even after allowing for their age. Money is a smaller part of the story: on financial difficulty they rank third of four. Of those aged 50 and over interviewed again two years on, in the waves where deaths are recorded, 32% are still hidden, 42% are flagged by neither screen and 22% by both, so a screen would need re-running each cycle.

    Comparing targeting rules

    Every rule flags the same share of over-65s in each country and year. Further right means reaching more of the deaths and new limitations of the next two years; higher means reaching more of the financial difficulty. Needs-adjusted resources, a rule with two inputs, reach more health events than the income flag with almost the same financial reach.

    20%

    Implications for targeting

    • An income screen misses a growing share of the needs-poor as people age, about a third of them over 85, and the people it misses have the highest two-year death rate of any group.
    • Counting needs costs almost nothing in financial reach and adds health reach. Flagging 20% of over-65s, it reaches 32.1% of later deaths and new limitations against 27.4%, and 33.4% of financial difficulty against 33.7%.
    • Where limitation counts are not recorded, a frailty index, priced against reported financial strain in a similar way, reaches more health events still (38.1%), at a small cost in financial reach (32.9%). We tested it on survey data, not on administrative records.

    How we did it

    Equivalence scale
    Needs-adjusted resources. Resources (equivalised income plus 5% of net wealth) divided by a scale for the number of limitations: 1.50 for one, 1.89 for two, 2.05 for three or more. It averages separate England and Europe estimates from reported financial strain (with survey-by-country-by-year fixed effects), weighted by their number of interviews in the estimation sample, four in five of them from SHARE; the long-term care example uses a single pooled estimate, which puts one limitation at 1.49.
    Quintile screens
    The poorest fifth of each country and year, on resources and on needs-adjusted resources. Hidden means flagged only by the second: 3.7% of people aged 50 and over. In England in 2021–23 the income line is about £15,000 a year; counting needs, it is about £12,000 for someone with no limitation, £18,000 with one, £22,000 with two and £24,000 with three or more. In the SHARE countries in 2021–22 the income line averages about €17,000, from €3,300 in Bulgaria to €61,000 in Luxembourg, and counting needs about €16,000, €23,000, €29,000 and €32,000.
    LPM · Cox
    Two-year outcomes by group, adjusted for five-year age band, sex and survey-by-country-by-year. Over full follow-up from each person’s first interview, the hidden group’s hazard ratio for death averages 2.36; it varies with age.
    Capture · Gradient boosting
    Targeting rules rank people aged 65 and over within their country and year (312,521 individual-waves). Capture is the share of later events that fall among the flagged; the model benchmark is cross-fitted in five folds by individual.
    Money
    Pounds and euros per person per year at the prices of ELSA wave 10 (interviews 2021–23) and SHARE wave 9 (2021–22). English resources are equivalised benefit-unit income for the year plus 5% of net non-housing wealth; SHARE household income and wealth are adjusted for household size, and other currencies are converted at market exchange rates. The English screen lines are England's own; the euro ones average each country's. The hidden person's English figures are England's median, the euro ones a median across the SHARE countries taken together. Both cover the latest wave.

    Limits

    • Outcomes are associations. They show who goes on to die or struggle, not whether outreach would change it.
    • The hidden group partly exists by construction: two bottom-fifth screens that do not overlap leave some people flagged by one only, and its size depends on the 20% cut-off.
    • The health gain comes mostly from the SHARE countries. In England the two rules are close (27.4% against 23.1% of health events).
    • New limitations share an input with the needs-adjusted rule. On deaths alone the gain holds: flagging 20% of over-65s, it reaches 36.9% of later deaths against 28.3% for the income flag.
    • Deaths are seen only in the waves where the survey records them, and in those waves a quarter to a third of each group has no two-year follow-up. ELSA wealth excludes housing and is not equivalised, unlike SHARE’s, a known data issue under review.

    Work example · Enel, 2005 to 2024

    Climate transition risk at Enel

    We use Enel as a case study to estimate downside market-value risk and examine how that risk changes under a carbon-price scenario.

    If the EU carbon price rises to €139.5 a tonne by 2030, as in the NGFS Highway to Paris scenario, and Enel absorbs the whole cost, its net income falls by 7.7%. That adds about €0.7 billion to a one-in-twenty-year loss of €18.2 billion. Over six years, uncertainty in the model's own parameters matters far more than the carbon shock.

    Data: Enel's annual reports and daily share prices, 2005–2024; its reported 2024 emissions; NGFS Phase V carbon-price scenarios and EU carbon allowance prices.

    Parameters taken as known+ their uncertainty+ carbon shockEnel can close plants

    The question

    • How much of a utility's market value is at risk in a bad year, and how much does a carbon-price path to 2030 add to that risk?

    What we found

    • Before any shock, a one-in-twenty bad year would cost Enel about 26% of its €70.0 billion market value (€18.2 billion) on the model. On Enel's own 19 annual share-price moves, it would cost 30% (€21.1 billion). A one-in-a-hundred year would cost 37–42% (€26.0–29.1 billion).
    • The carbon shock takes the EU carbon price from €68.6 to €139.5 a tonne by 2030. On the 13.1 Mt its EU plants will still emit after the coal exit, it costs Enel €541 million a year after tax and minority shareholders. If Enel absorbs all of it, net income falls by 7.7% and the one-in-twenty loss rises by €0.7 billion, to €18.8 billion. The one-in-a-hundred loss barely moves.
    • Over six years, the uncertainty in the model's own parameters matters most. Allowing for it raises the one-in-twenty loss from 11.5% to 30.4% of market value. The carbon shock adds 1.4 percentage points (about €1.0 billion) if every plant keeps running.
    • Letting Enel close plants that stop paying recovers about €0.4 billion of that. Coal already loses money at today's carbon price, so it closes at once. Gas plants have an 8% chance of closing by 2030. In the worst 1% of scenarios, the carbon hit to 2030 net income falls from €1.8 billion to €0.8 billion.

    Baseline one-year risk

    We estimate one-year downside risk in two ways. The parametric estimate uses the fitted mean-reverting process for Enel's price-to-earnings ratio, while the historical estimate uses the empirical distribution of its 19 annual share-price changes since 2006. The largest observed fall was −44% in 2008. Because observed equity returns have heavier tails than the normal distribution used in the parametric model, the model-based tail estimate is likely to be conservative.

    Carbon-price shock calculation

    1. Exposed emissions

      The 19.16 Mt Enel reported for 2024, less 2.62 Mt from coal plants that close by 2027, on the 79.3% of fossil output inside the EU carbon market: 13.1 Mt.

    2. Extra cost

      €70.9 a tonne more by 2030: €931 million a year before tax, €541 million after tax (27.8%) and Enel's ownership share (80.5%).

    3. Net income

      If Enel absorbs it all, 2024 net income of €7,016 million falls to €6,475 million, −7.7%.

    4. Valuation

      With the share price unchanged in the short run, the P/E rises from 10.0× to 10.8×. Because the P/E drifts back to 9.4×, the expected one-year return falls from +0.9% to −2.1%.

    5. Value at risk

      The one-in-twenty loss rises from 25.9% to 26.9% of market value: from €18.2 billion to €18.8 billion.

    Cost pass-through

    The share of the extra cost Enel passes on to its customers decides how much of the shock reaches profit. The 99% figure barely moves because, at a higher P/E, this version of the model also narrows the spread of outcomes slightly, which offsets the worse expected return in the far tail. The logarithmic version used over six years does not do this: there both figures rise by about 2 percentage points.

    One-year value at risk for Enel, by how much of the carbon cost is passed on to customers
    Carbon shockNet income95% VaR99% VaR
    No shock€7,016m25.9% · €18.2bn37.1% · €26.0bn
    Enel absorbs it all€6,475m (−7.7%)26.9% · €18.8bn37.2% · €26.0bn
    Half passed on€6,746m (−3.9%)26.4% · €18.5bn37.1% · €26.0bn
    All passed on€7,016m (0%)25.9% · €18.2bn37.1% · €26.0bn

    The carbon price to 2030

    The shock follows Highway to Paris, one of the NGFS short-term scenarios. The NGFS is the central banks' and supervisors' climate network, and this scenario describes an orderly tightening of carbon pricing, with prices for Italy and Spain to 2030. We add its increase over the same model's baseline to the observed end-2024 price of €68.6 a tonne. The simulation lets the price vary around that path with the EU carbon price's own volatility, 38% a year.

    Implications for climate risk assessment

    • Under this transition scenario, the carbon-price shock is small relative to the other sources of estimated risk and is concentrated in Enel's remaining gas fleet. The average effect on 2030 net income is about €150 million, around 2% of 2024 net income.
    • Parameter uncertainty is quantitatively more important than the carbon-price path in the six-year simulation. Treating the fitted parameters as known produces declining risk over time, an artefact of imposing parameter certainty.
    • Holding the generating fleet fixed produces a larger tail effect. Allowing uneconomic plants to close reduces the carbon-related effect on 2030 earnings by more than half in the worst 1% of simulations.
    • The analysis uses public annual reports, share prices and published NGFS scenarios, with the assumptions documented in the model.

    How we did it

    P/E · AR(1)
    Mean reversion in the price-to-earnings ratio. Fitted on the seven usable year-pairs between 2008 and 2021: after the Endesa purchase and the 2016 share issue, with one-off years left out. The P/E reverts towards 9.4×, closing 40% of the gap each year (R² 0.94).
    Parametric · Historical
    One-year VaR from the model's normal spread of returns, and from the empirical quantiles of Enel's 19 annual share-price changes, 2006–2024. Converted to euros at the end-2024 market value, €70.0 billion.
    Carbon shock
    Exposed 2030 emissions × the price increase × (1 − pass-through) × (1 − tax rate) × Enel's ownership share. The lower earnings raise the P/E at an unchanged share price, and the P/E process turns that into a lower expected return.
    Monte Carlo · Real options
    100,000 scenarios to 2030 on the logarithmic P/E process. They draw its parameters and Enel's earnings growth from their statistical uncertainty, the carbon price around the NGFS path, and a random share of the cost passed on. Coal and gas fleets can close when they stop paying, an option valued by least-squares Monte Carlo (Longstaff–Schwartz). Spanish island units are regulated and keep running. With all of this switched off, the simulation reproduces the one-year results.
    CES · Revenue
    Revenue from physical volumes. Enel's own data cannot tell how far generation, distribution and sales substitute for one another, because all three moved together. The elasticity is taken from a published estimate for the sector (Antoszewski, 2019).
    Data
    Each year's figures as originally reported, not later restatements. The window is split into four regimes: before and after Endesa, after the 2016 share issue, and after the 2022 energy crisis. Four one-off years (2012, 2014, 2019 and 2022, with large write-downs or the gas-price spike) are left out of the fit; the share price barely reacted to most of them.

    Limits

    • Only the cost side of carbon pricing is modelled. A higher carbon price also raises wholesale power prices, and with them the margins on Enel's renewable, hydro and nuclear output, about 70% of its generation, partly offset by fixed-price contracts and hedging. Counting that would reduce, and could reverse, the net effect.
    • Samples are small throughout: the P/E process rests on seven observations, the historical VaR on 19, and the study covers one company. Read the figures as the right order of magnitude, not a precise forecast.
    • The scenario matters. Highway to Paris adds €71 a tonne by 2030; the more abrupt NGFS Sudden Wake-Up Call adds about €85; the long-term Net Zero 2050 scenario adds €108–340, depending on the model.
    • The carbon price at which each type of plant stops paying, and decommissioning costs, are not disclosed. They are set consistently with Enel's announced strategy and tested for sensitivity: the six-year 95% figure stays between 30.8% and 31.3%.
    • Gas and oil output is held at 2024 levels, which is conservative: Enel targets a 29% cut in emission intensity between 2024 and 2030.
    • This is a case study of the method on public data. It is not investment advice or a view on Enel's shares.

    Work example · Italy, 50 industries, 1997 to 2023

    Energy prices and industrial productivity

    We compare Italian industries with different energy cost shares to estimate how productivity, output and employment respond to changes in energy prices.

    In 2022, real electricity prices for Italian businesses rose by about 70% and real gas prices more than doubled. Between 2021 and 2023, each extra percentage point of energy cost share meant about 4 points less growth in real output. The estimated effect is largest in the first year and fades within two to three years; we do not find a corresponding improvement when prices fall.

    Data: Eurostat value added and hours for 50 market industries, the 2010 input-output table and non-household electricity and gas prices, 1996–2024; ISTAT TFP as a check.

    The question

    • What do energy price shocks do to productivity, output and employment across Italian industries, and which industries bear the brunt?

    What we found

    • Energy price rises hit exposed industries harder. After a 10% real rise, a highly exposed industry (90th percentile, energy at about 3.9% of output) loses about 1.4 percentage points more productivity growth than a lightly exposed one (10th percentile, about 0.2%).
    • The estimated difference is largest after about one year, when productivity is 1.3% and output 1.6% lower in the more exposed industry. The difference closes within two to three years.
    • We do not detect a corresponding productivity gain when energy prices fall. The estimated response is therefore asymmetric between price increases and decreases.
    • The 2022–23 crisis shows the same pattern. Each extra point of energy cost share meant about 4 points less output growth between 2021 and 2023. Over 2019–21, before the crisis, there is no such pattern, and the result holds after controlling for how hard COVID hit each industry.
    • The most exposed are water supply, paper, basic metals, non-metallic minerals and chemicals, but also some service industries: personal services such as laundries, and postal and courier services.

    Energy prices, 1996–2024

    Electricity and gas prices for non-household consumers, all taxes included, deflated by consumer prices. They were broadly stable until 2021, then rose sharply in 2022, driven by the gas supply crisis. That makes 2022 a large and clearly external shock, the cleanest test available.

    Industry exposure

    Exposure is each industry's purchases of electricity, gas and steam as a share of its output, from the 2010 input-output table, fixed in advance so that it does not respond to later prices. It is highly concentrated: a handful of industries spend 3–10% of output on energy, and most spend under 1%. Several service industries rank higher than expected, so energy risk is not only a manufacturing issue.

    Dynamic response to a price increase

    The gap between a high- and a low-exposure industry after a 10% real price rise, from the year of the rise to three years on. After one year, the exposed industry has 1.3% lower productivity, 1.6% lower output and 0.4% fewer hours worked; by years two and three the productivity and output gaps have closed. The estimates are consistent with a temporary reduction in output rather than a persistent difference in productivity. The cumulative output effect can nevertheless be economically meaningful for highly exposed industries.

    Checks on the 2022–23 estimate

    • Pre-crisis placebo. Over 2019–21, before prices rose, exposed industries did not do worse (slope +1.0, p = 0.49).
    • Controlling for the COVID period. Some low-energy services were still recovering from COVID in 2021–23, but exposure is unrelated to how hard COVID hit an industry (correlation 0.08), and controlling for each industry's 2019–21 change leaves the result unchanged (−4.0, p = 0.007).
    • Influence of the most exposed industry. Excluding water supply, the most exposed, strengthens the result (−5.2, p = 0.01).
    • Measured from pre-COVID 2019 to 2023, the gap is smaller (−2.3 points per point of exposure) and not statistically significant, consistent with the damage fading over time.

    Robustness

    The estimated coefficient is negative across the main specifications, although its precision varies. The relationship is strongest for price increases, manufacturing industries, gas prices and comparisons involving the top quartile of energy exposure. Estimates are less precise when 2022–23 is excluded, a period in which the change in energy prices was much larger than in most earlier years.

    Effect of energy prices on annual productivity growth in more exposed industries, by specification
    SpecificationEstimatep-value
    Baseline: electricity and gas prices−0.0260.11
    Price rises only−0.0370.003
    Gas price only−0.0220.07
    Electricity price only−0.0280.22
    Manufacturing only−0.0290.04
    Top quartile of exposure against the rest−0.1290.01
    TFP instead of labour productivity (ISTAT, to 2022)−0.0330.09
    Excluding 2022–23−0.0180.31

    Implications for energy-price exposure

    • Industries with higher energy cost shares show larger declines in productivity and output following price increases. We do not estimate an offsetting effect following price decreases.
    • Energy exposure is concentrated in a relatively small number of industries. An intervention defined by energy cost share would therefore be concentrated in these industries rather than spread evenly across the economy.
    • The asymmetric estimates make price increases more consequential than equivalent price decreases. Contracts, hedging and own-generation arrangements may therefore affect firms' effective exposure, although the industry-level data do not allow us to estimate those mechanisms directly.
    • The estimated difference is temporary rather than permanent, with most of the response occurring during and shortly after the price increase.

    How we did it

    Panel · FE
    Industries compared with each other. Annual productivity growth on the change in the log real energy price times each industry's energy cost share, with industry and year fixed effects. Year effects absorb every national shock, including recessions, COVID and the average effect of prices; what remains is the extra effect on exposed industries. Standard errors clustered by industry and year; 50 industries, 1997–2023, 1,350 observations.
    Exposure
    Electricity, gas and steam purchases as a % of gross output, from the 2010 input-output use table, fixed in advance. The effect of a 10% rise is compared between the 90th (3.9%) and 10th (0.2%) percentile industries.
    Local projections
    The cumulative change over zero to three years, with industry and year fixed effects and the lagged change, for productivity, output and hours.
    Asymmetry
    Price rises and falls entered separately, each interacted with exposure.
    Crisis cross-section
    The change from 2021 to 2023 against energy cost share, with robust standard errors, a 2019–21 placebo, a control for the COVID change and a check without water supply.
    Design
    Written down before any results were estimated. Energy producers, finance, real estate and non-market services are left out, because their measured output moves with the shock or is imputed from inputs.

    Limits

    • Relative, not total, effects. The design measures how much more exposed industries are hurt than less exposed ones; the total effect of energy prices on the economy is absorbed by the year effects and is not estimated.
    • Exposure comes from 2010 and may have shifted since, for example through efficiency gains or electrification.
    • Prices are national business averages. Individual firms face different prices depending on contracts, hedging and consumption band.
    • Industry averages can hide large differences between firms, and some exposure figures for service industries reflect how the input-output tables allocate energy use.
    • The average effect across all years is borderline significant (p = 0.11). The robust findings concern price rises, the dynamic response and the 2022–23 crisis.

    Work example · The United Kingdom, the Netherlands and Italy

    Mortality projections by health status

    We estimate separate mortality curves for adults in good and poor self-reported health in three countries and project them to 2050.

    Across the three countries, the estimated modal age at death is about ten years lower among adults in poor self-reported health. The difference is 10.3 years in the UK, 10.6 in the Netherlands and 10.1 in Italy. At age 65, remaining life expectancy is 8.1, 8.4 and 8.3 years higher for the healthy group, respectively.

    Data: British Household Panel Survey and Understanding Society, 1991–2024; the Survey of Health, Ageing and Retirement in Europe, 2004–2022. The national life tables of each country.

    Results by country

    The United Kingdom Adults aged 20 to 89 · 1991 to 2023, projected to 2050
    British Household Panel Survey and Understanding Society     At 65 in 2023: healthy 25.0 years, unhealthy 16.9 See the results     The Netherlands People aged 50 to 89 · 2005 to 2021, projected to 2050
    Survey of Health, Ageing and Retirement in Europe     At 65 in 2021: healthy 24.5 years, unhealthy 16.0 See the results     Italy People aged 50 to 89 · 2005 to 2021, projected to 2050
    Survey of Health, Ageing and Retirement in Europe     At 65 in 2021: healthy 26.8 years, unhealthy 18.5 See the results

    The question

    • How much longer do healthy adults live than unhealthy ones, how will the two groups' mortality change to 2050, and is the difference the same from one country to another?

    What we found

    • In all three countries, estimated mortality is higher for the poor-health group at every age covered by the surveys. The modal ages are 83.5 and 93.8 for the poor- and good-health groups in the UK in 2023, 83.0 and 93.5 in the Netherlands, and 86.0 and 96.0 in Italy in 2021.
    • At 65 the healthy can expect 25.0 more years of life in the UK, 24.5 in the Netherlands and 26.8 in Italy; the unhealthy 16.9, 16.0 and 18.5.
    • The fitted mortality improvement is faster for the poor-health group in all three countries. Its modal-age parameter rises by 0.32% a year in the UK since 1991, and by 0.16% in the Netherlands and 0.10% in Italy since 2005. The Dutch and Italian drift estimates are based on seventeen fitted years and substantially smaller samples, so their projections to 2050 are less precise.
    • At 60, the death rate of the poor-health group is 5.2 times that of the good-health group in the UK, 2.6 times in the Netherlands and 3.8 times in Italy.

    How we did it

    Data
    Household surveys that follow the same people, with their self-rated health and deaths: the British Household Panel Survey and Understanding Society for adults aged 20 to 89 in the UK, 1991 to 2024, and the Survey of Health, Ageing and Retirement in Europe for people aged 50 to 89 in the Netherlands and Italy, 2004 to 2022.
    Deaths
    Calibrated to each country's national life tables. A survey records who leaves, not always who died. A respondent who leaves without a recorded death is given a death probability from the national rate for their age and year, scaled by the relative risk of their health group in the recorded deaths. The level comes from the life tables, the difference between the groups from the survey.
    Health
    Good-or-better self-rated health, the survey's own question, matched across changes in how it was asked.
    Curves
    A Gompertz–Makeham hazard for each group, in its modal-age form: a rate of ageing and a modal age for each group and a background floor shared by both, all changing each year.
    Dynamics
    A random walk with drift in the logarithm of each parameter, with both the drift and the size of the annual shocks estimated. The projection uses the same estimated parameter process.
    Estimation
    Bayesian, by Hamiltonian Monte Carlo, in Julia, one model per country. The model also estimates the yearly moves between health and work states.
    Projection
    Each posterior draw continues its own walk to 2050, with its own drift and shocks, so the bands include the uncertainty in the estimates as well as in the future.
    Scenarios
    The same draws under other assumptions: the pace of improvement, a pandemic, and the share of adults in good health, set for each country.

    Implications for longevity planning

    • A national life table averages groups whose mortality differs by a factor of up to 5 in middle age. Mortality for a population with a different health mix can therefore differ widely from the national average.
    • Changes in the health mix matter most at the ages where mortality is high. A fall in good health among younger adults, as in the UK since 2015, does little to period life expectancy.
    • Projection uncertainty is large, and larger where the survey is shorter: the central projection gives an incomplete description of the model's uncertainty.
    • The specification can be re-estimated as new survey waves and life tables become available, and can be applied to other household panels with self-rated health and mortality information.

    Limits

    • Health is self-reported, and people may rate the same health differently from one country to another, so each country's split is its own and the levels are not a common standard.
    • The projections continue each country's average improvement over its fitted years. Each country page shows how the figures change when improvement slows.
    • The UK survey covers adults of every age since 1991; the Dutch and Italian one people aged 50 and over since 2004. Each country page lists the limits of its survey.

    Mortality projections by health status · 1991 to 2050

    The United Kingdom

    Separate mortality curves for adults in good and poor self-reported health in the UK, estimated on the British Household Panel Survey and Understanding Society and projected to 2050.

    At 2023 mortality rates, remaining life expectancy at age 22.5 is 65.6 years for the good-health group and 54.1 for the poor-health group. The fitted mortality trend improves faster for the poor-health group. Under the model's continuation of those trends, the gap narrows from 11.6 years in 2023 to 8.8 in 2050.

    Data: British Household Panel Survey, 1991–2008, and Understanding Society, 2009–2024: 772,754 person-years. ONS national life tables.

    What we found

    • At every age from 20 to 90, unhealthy adults die at higher rates than healthy ones. The difference is widest around 60, where their death rate is 5.2 times as high; at 85 it is 2.5 times. The two curves do not meet at any age the data cover.
    • From 1991 to 2023, life expectancy at 22.5 rose by 5.0 years for the healthy, to 65.6, and by 7.9 years for the unhealthy, to 54.1.
    • Continuing the model's own trends, by 2050 the healthy reach 69.9 years, with a 95% interval of 61.0 to 77.3, and the unhealthy 61.1, with an interval of 53.7 to 69.7. Age-standardised adult mortality falls by 43%.
    • The share of adults in good health fell from 71% in 2015 to 63% in 2024. Most of the fall is below age 50, where few people die, so it does little to life expectancy for the population as a whole.

    Mortality by health status

    After early adulthood, the risk of dying rises almost exponentially with age, and a small background risk does not depend on age at all. We fit this shape, a Gompertz–Makeham curve, to each group separately, so each has its own rate of ageing and its own location in age. The dots are the survey's death rates, calibrated to the national life tables, which the model is fitted to. After 2023 the curves are projections. The year control shows the fitted and projected curves over time.

    2023

    Defining health status

    Health is the survey's own question: adults who rate their health good or better are counted as healthy. The wording and the answer scale changed when Understanding Society replaced the British Household Panel Survey in 2009, so we match the two scales across the change and hold the ethnic mix of the sample constant. The share classified in good health reached its highest post-2009 level in 2015. Since then it has fallen by about 8 points below age 50, and by about 3.5 points above age 70, where it is still higher than in 2010.

    Changes in the mortality parameters

    Each curve has two parameters of its own, which change from year to year. The modal-age parameter locates the curve along the age axis, and the rate of ageing sets how steeply mortality rises with age. The unhealthy curve has moved faster: its modal age has risen by 0.32% a year, against 0.18% for the healthy. The gap between the two has narrowed from 13.3 years in 1991 to 10.3 in 2023. Each parameter follows a random walk with drift, and the projection extends those estimated processes beyond 2023. The resulting uncertainty intervals widen with the projection horizon.

    Scenarios

    The baseline projection continues the estimated mortality-parameter processes from 1991 to 2023 and holds the age-specific share in good health at its 2024 level. Alternative scenarios change the pace of mortality improvement, impose a temporary pandemic shock, or alter the age-specific health distribution. Each scenario is evaluated using the same 4,000 posterior draws, so its interval retains estimation and process uncertainty. In 2050, halving the estimated pace of improvement lowers population life expectancy at age 22.5 by 2.7 years relative to the baseline projection; the better-health and worse-health scenarios change it by +0.4 and −1.0 years. A pandemic shock in 2030 lowers life expectancy in that year by 1.1 years but does not alter the 2050 projection.

    Open the scenario simulator

    Results explorer

    The results explorer contains the scenario simulator, life expectancy by age and year, the two mortality curves and their uncertainty, a life-table calculator based on the posterior draws, health and labour-market transitions, and the estimated model parameters. The underlying results are available as CSV files.

    Open the results explorer
    • Overview
    • Scenario simulator
    • Life expectancy
    • Mortality curves
    • Life-table calculator
    • Curve parameters
    • Health and work
    • Health share
    • Fit to the data
    • Estimation
    • Method & data
    • Downloads

    How we did it

    Sample
    The British Household Panel Survey linked to Understanding Society, adults aged 20 to 89, on fourteen five-year age groups and thirty-four years. Ages are given at the middle of each group, so 22.5 stands for 20 to 24.
    Deaths
    Calibrated to the ONS national life tables. A panel records who leaves, not always who died. A respondent who leaves without a recorded death is given a death probability from the national rate for their age and year, scaled by the relative risk of their health group in the confirmed deaths. The level comes from the life tables, the difference between the groups from the panel.
    Health
    Good-or-better self-rated health, matched across the 2009 change of survey by counting part of the ambiguous middle answer as healthy, with the ethnic mix held constant across years.
    Curves
    A Gompertz–Makeham hazard for each group, in its modal-age form: a rate of ageing and a modal age for each group and a background floor shared by both, all changing each year, fitted to the one-year probability of death.
    Dynamics
    A random walk with drift in the logarithm of each parameter, with both the drift and the size of the annual shocks estimated. The projection uses the same estimated parameter process.
    Estimation
    Bayesian, by Hamiltonian Monte Carlo, in Julia: four chains, largest R̂ 1.005. The model also estimates the yearly moves between health and work states.
    Projection
    Each of the 4,000 draws continues its own walk from 2023 to 2050, with its own drift and shocks. Life expectancy is computed draw by draw, so the bands include the uncertainty in the estimates as well as in the future.
    Scenarios
    The same draws under other assumptions. Each draw's drift is recovered exactly from the projection, so a scenario that changes the pace of improvement keeps that draw's own shocks. A pandemic raises both groups' death rates in proportion; a health scenario changes the share in good health at each age, which weights the two curves into the population's.
    Checks
    Against the published life tables. Across ages 23 to 87, the median ratio of the model's population mortality to the published rate lies between 0.92 and 1.14 in every fitted year, and is 1.01 pooled.

    Limits

    • Health is self-reported. At the ages where it has fallen most, answers also reflect mental health and expectations, so part of the fall may carry no mortality risk.
    • The projection continues the average improvement of 1991 to 2023. Improvement slowed after about 2010; measured on the years since then, the drift lowers life expectancy at 22.5 in 2050 by about three years for the healthy and three and a half for the unhealthy.
    • The two groups are projected separately, each with its own drift. In 18% of draws the unhealthy curve falls below the healthy one at some age by 2050, which the estimates never show; the top of the unhealthy range should be read with that in mind.
    • The modal age of the healthy, 93.8 in 2023, lies above the oldest age observed. Its level depends on the curve holding beyond the data.
    • Deaths in 2008 and 2024 cannot be calibrated, so those years are bridged by the model, and the projection starts from 2023.

    Mortality projections by health status · 2005 to 2050

    The Netherlands

    Separate mortality curves for people aged 50 and over in good and poor self-reported health in the Netherlands, estimated on the Survey of Health, Ageing and Retirement in Europe (SHARE) and projected to 2050.

    At 2021 mortality rates, remaining life expectancy at age 52.5 is 35.7 years for the good-health group and 26.2 for the poor-health group, a difference of 9.5 years. The fitted mortality improvement is faster for the poor-health group; under the model's continuation of the 2005–2021 trends, the difference falls to 7.4 years by 2050. The drift estimates are imprecise, reflecting the shorter time series and smaller survey sample.

    Data: SHARE, release 9.0.0, 2004–2022: 16,081 interviews of 6,486 people aged 50 to 89, 51,613 person-years. Life tables of Statistics Netherlands (CBS).

    What we found

    • At every age from 50 to 90, unhealthy people die at higher rates than healthy ones. At 60 their death rate is 2.6 times as high, and at 85 3.1 times.
    • From 2005 to 2021, life expectancy at 52.5 rose by 1.1 years for the healthy, to 35.7, and by 1.7 years for the unhealthy, to 26.2.
    • Continuing the model's own trends, by 2050 the healthy reach 37.5 years, with a 95% interval of 25.3 to 49.6, and the unhealthy 30.2, with an interval of 18.0 to 44.4.
    • The share of people in good health hardly moved, from 73% in 2005 to 72% in 2021. Above age 75 it rose from 58% to 68%, partly because the healthier members of an ageing panel survive, so we treat the Dutch health mix as having no trend.

    Mortality by health status

    After early adulthood, the risk of dying rises almost exponentially with age, and a small background risk does not depend on age at all. We fit this shape, a Gompertz–Makeham curve, to each group separately, so each has its own rate of ageing and its own location in age. The dots are the survey's death rates, calibrated to the national life tables, which the model is fitted to. After 2021 the curves are projections. The year control shows the fitted and projected curves over time.

    2021

    Defining health status

    Health is the survey's own question: people who rate their health good or better are counted as healthy. In the first wave half the sample answered it at the end of the health module and reported better health, so part of their "good" answers is counted as healthy to match the later waves. There were no Dutch interviews from 2014 to 2018, so those years carry the 2013 answers. The share in good health hardly moved over 2005 to 2021, from 73% to 72%. Few people in their early fifties joined the survey after 2015, so the youngest group rests on a handful of interviews in the last years.

    Changes in the mortality parameters

    Each curve has two parameters of its own, which change from year to year. The modal-age parameter locates the curve along the age axis, and the rate of ageing sets how steeply mortality rises with age. The unhealthy curve has moved faster: its modal age has risen by 0.16% a year, against 0.08% for the healthy. The gap between the two has narrowed from 11.3 years in 2005 to 10.6 in 2021. Each parameter follows a random walk with drift, and the projection extends those estimated processes beyond 2021. The resulting uncertainty intervals widen with the projection horizon. The drift estimates are imprecise: none is clearly distinguishable from zero, and the projection intervals widen quickly with the horizon.

    Scenarios

    The baseline projection continues the estimated mortality-parameter processes from 2005 to 2021 and holds the age-specific share in good health at its level in 2020 and 2021. Alternative scenarios change the pace of mortality improvement, impose a temporary pandemic shock, or alter the age-specific health distribution. Each scenario is evaluated using the same 8,000 posterior draws, so its interval retains estimation and process uncertainty. In 2050, halving the estimated pace of improvement lowers population life expectancy at age 52.5 by 0.8 years relative to the baseline projection; the better-health and worse-health scenarios change it by +0.4 and −0.3 years. A pandemic shock in 2030 lowers life expectancy in that year by 1.0 years but does not alter the 2050 projection.

    Open the scenario simulator

    Results explorer

    The results explorer contains the scenario simulator, life expectancy by age and year, the two mortality curves and their uncertainty, a life-table calculator based on the posterior draws, health and labour-market transitions, and the estimated model parameters. The underlying results are available as CSV files.

    Open the results explorer
    • Overview
    • Scenario simulator
    • Life expectancy
    • Mortality curves
    • Life-table calculator
    • Curve parameters
    • Health and work
    • Health share
    • Fit to the data
    • Estimation
    • Method & data
    • Downloads

    How we did it

    Sample
    The Survey of Health, Ageing and Retirement in Europe (SHARE), release 9.0.0, people aged 50 to 89 interviewed from 2004 to 2022, on eight five-year age groups. Interviews are two or more years apart, so each interval is cut at calendar-year boundaries into person-years. Ages are given at the middle of each group, so 52.5 stands for 50 to 54.
    Deaths
    Calibrated to the national life tables of Statistics Netherlands (CBS), cell by cell. A survey records who leaves, not always who died. A respondent who leaves without a recorded death is given a death probability from the national rate for their age and year, scaled by the relative risk of their health group in the recorded deaths; deaths are placed in their calendar year. The level comes from the life tables, the difference between the groups from the survey.
    Health
    Good-or-better self-rated health, with part of the "good" answers of the first wave, where half the sample answered at the end of the health module, counted as healthy to match the later waves.
    Curves
    A Gompertz–Makeham hazard for each group, in its modal-age form: a rate of ageing and a modal age for each group and a background floor shared by both, all changing each year, fitted to the one-year probability of death.
    Dynamics
    A random walk with drift in the logarithm of each parameter, with both the drift and the size of the annual shocks estimated. The projection uses the same estimated parameter process.
    Estimation
    Bayesian, by Hamiltonian Monte Carlo, in Julia: four chains, largest R̂ 1.004. The model also estimates the yearly moves between health and work states.
    Projection
    Each of the 8,000 draws continues its own walk from 2021 to 2050, with its own drift and shocks. Life expectancy is computed draw by draw, so the bands include the uncertainty in the estimates as well as in the future.
    Scenarios
    The same draws under other assumptions. Each draw's drift is recovered exactly from the projection, so a scenario that changes the pace of improvement keeps that draw's own shocks. A pandemic raises both groups' death rates in proportion; a health scenario changes the share in good health at each age, which weights the two curves into the population's.
    Checks
    Against the published life tables. Across ages 53 to 87, the median ratio of the model's population mortality to the published rate lies between 0.89 and 1.01 in every fitted year, and is 0.95 pooled.

    Limits

    • Health is self-reported, and people may rate the same health differently from one country to another, so the split is each country's own.
    • Seventeen fitted years of a survey of a few thousand people leave the trends poorly pinned down. The healthy group's life expectancy at 52.5 in 2050 has a 95% interval of 25.3 to 49.6 years.
    • The two groups are projected separately, each with its own drift. In 55% of draws the unhealthy curve falls below the healthy one at some age by 2050, which the estimates never show; the top of the unhealthy range should be read with that in mind.
    • Few people in their early fifties joined the survey after 2015, so every late-year figure by age rests on thin cells at the young end, and so does the health mix the projection holds.
    • There were no Dutch interviews from 2014 to 2018, and most Dutch deaths are undated, so they are spread over the interval since the last interview, which for the latest wave spans 2013 to 2020.
    • Deaths in 2004 and 2022 cannot be calibrated, since the interviews cover those years only in part, so they are bridged by the model, and the projection starts from 2021.

    Mortality projections by health status · 2005 to 2050

    Italy

    Separate mortality curves for people aged 50 and over in good and poor self-reported health in Italy, estimated on the Survey of Health, Ageing and Retirement in Europe (SHARE) and projected to 2050.

    At 2021 mortality rates, remaining life expectancy at age 52.5 is 38.4 years for the good-health group and 28.7 for the poor-health group, a difference of 9.7 years. The fitted mortality improvement is faster for the poor-health group; under the model's continuation of the 2005–2021 trends, the difference falls to 8.6 years by 2050. The drift estimates are imprecise, reflecting the shorter time series and smaller survey sample.

    Data: SHARE, release 9.0.0, 2004–2022: 28,558 interviews of 8,394 people aged 50 to 89, 58,449 person-years. Life tables of the Italian statistical institute (ISTAT).

    What we found

    • At every age from 50 to 90, unhealthy people die at higher rates than healthy ones. The difference is widest around 65, where their death rate is 3.9 times as high; at 85 it is 2.8 times.
    • From 2005 to 2021, life expectancy at 52.5 rose by 0.9 years for the healthy, to 38.4, and by 1.0 years for the unhealthy, to 28.7.
    • Continuing the model's own trends, by 2050 the healthy reach 39.4 years, with a 95% interval of 20.9 to 54.6, and the unhealthy 30.8, with an interval of 21.0 to 41.9.
    • The share of people in good health rose below age 75: from 67% to 75% between 50 and 64, and from 49% to 61% between 65 and 74, from 2005 to 2021. Above 75 it stayed near 38%, and because the panel aged, the share of all its members changed little, from 57% to 56%.

    Mortality by health status

    After early adulthood, the risk of dying rises almost exponentially with age, and a small background risk does not depend on age at all. We fit this shape, a Gompertz–Makeham curve, to each group separately, so each has its own rate of ageing and its own location in age. The dots are the survey's death rates, calibrated to the national life tables, which the model is fitted to. After 2021 the curves are projections. The year control shows the fitted and projected curves over time.

    2021

    Defining health status

    Health is the survey's own question: people who rate their health good or better are counted as healthy. In the first wave half the sample answered it at the end of the health module and reported better health, so part of their "good" answers is counted as healthy to match the later waves. The share in good health rose below age 75 over 2005 to 2021: from 67% to 75% between 50 and 64 and from 49% to 61% between 65 and 74. Above 75 it changed little.

    Changes in the mortality parameters

    Each curve has two parameters of its own, which change from year to year. The modal-age parameter locates the curve along the age axis, and the rate of ageing sets how steeply mortality rises with age. The unhealthy curve has moved faster: its modal age has risen by 0.10% a year, against 0.03% for the healthy. The gap between the two has narrowed from 10.8 years in 2005 to 10.1 in 2021. Each parameter follows a random walk with drift, and the projection extends those estimated processes beyond 2021. The resulting uncertainty intervals widen with the projection horizon. The drift estimates are imprecise: none is clearly distinguishable from zero, and the projection intervals widen quickly with the horizon.

    Scenarios

    The baseline projection continues the estimated mortality-parameter processes from 2005 to 2021 and holds the age-specific share in good health at its level in 2020 and 2021. Alternative scenarios change the pace of mortality improvement, impose a temporary pandemic shock, or alter the age-specific health distribution. Each scenario is evaluated using the same 8,000 posterior draws, so its interval retains estimation and process uncertainty. In 2050, halving the estimated pace of improvement lowers population life expectancy at age 52.5 by 0.5 years relative to the baseline projection; the better-health and worse-health scenarios change it by +0.6 and −0.3 years. A pandemic shock in 2030 lowers life expectancy in that year by 0.9 years but does not alter the 2050 projection.

    Open the scenario simulator

    Results explorer

    The results explorer contains the scenario simulator, life expectancy by age and year, the two mortality curves and their uncertainty, a life-table calculator based on the posterior draws, health and labour-market transitions, and the estimated model parameters. The underlying results are available as CSV files.

    Open the results explorer
    • Overview
    • Scenario simulator
    • Life expectancy
    • Mortality curves
    • Life-table calculator
    • Curve parameters
    • Health and work
    • Health share
    • Fit to the data
    • Estimation
    • Method & data
    • Downloads

    How we did it

    Sample
    The Survey of Health, Ageing and Retirement in Europe (SHARE), release 9.0.0, people aged 50 to 89 interviewed from 2004 to 2022, on eight five-year age groups. Interviews are two or more years apart, so each interval is cut at calendar-year boundaries into person-years. Ages are given at the middle of each group, so 52.5 stands for 50 to 54.
    Deaths
    Calibrated to the national life tables of the Italian statistical institute (ISTAT), cell by cell. A survey records who leaves, not always who died. A respondent who leaves without a recorded death is given a death probability from the national rate for their age and year, scaled by the relative risk of their health group in the recorded deaths; deaths are placed in their calendar year. The level comes from the life tables, the difference between the groups from the survey.
    Health
    Good-or-better self-rated health, with part of the "good" answers of the first wave, where half the sample answered at the end of the health module, counted as healthy to match the later waves.
    Curves
    A Gompertz–Makeham hazard for each group, in its modal-age form: a rate of ageing and a modal age for each group and a background floor shared by both, all changing each year, fitted to the one-year probability of death.
    Dynamics
    A random walk with drift in the logarithm of each parameter, with both the drift and the size of the annual shocks estimated. The projection uses the same estimated parameter process.
    Estimation
    Bayesian, by Hamiltonian Monte Carlo, in Julia: four chains, largest R̂ 1.004. The model also estimates the yearly moves between health and work states.
    Projection
    Each of the 8,000 draws continues its own walk from 2021 to 2050, with its own drift and shocks. Life expectancy is computed draw by draw, so the bands include the uncertainty in the estimates as well as in the future.
    Scenarios
    The same draws under other assumptions. Each draw's drift is recovered exactly from the projection, so a scenario that changes the pace of improvement keeps that draw's own shocks. A pandemic raises both groups' death rates in proportion; a health scenario changes the share in good health at each age, which weights the two curves into the population's.
    Checks
    Against the published life tables. Across ages 53 to 87, the median ratio of the model's population mortality to the published rate lies between 0.84 and 0.97 in every fitted year, and is 0.93 pooled.

    Limits

    • Health is self-reported, and people may rate the same health differently from one country to another, so the split is each country's own.
    • Seventeen fitted years of a survey of a few thousand people leave the trends poorly pinned down. The healthy group's life expectancy at 52.5 in 2050 has a 95% interval of 20.9 to 54.6 years.
    • The two groups are projected separately, each with its own drift. In 40% of draws the unhealthy curve falls below the healthy one at some age by 2050, which the estimates never show; the top of the unhealthy range should be read with that in mind.
    • Few people in their early fifties joined the survey after 2015, so every late-year figure by age rests on thin cells at the young end, and so does the health mix the projection holds.
    • The modal age of the healthy, 96.0 in 2021, lies above the oldest age observed. Its level depends on the curve holding beyond the data.
    • Deaths in 2004 and 2022 cannot be calibrated, since the interviews cover those years only in part, so they are bridged by the model, and the projection starts from 2021.

    Work example · United Kingdom, 13 regions, 2026 to 2030

    Defence spending across the UK's regions

    We use a regional CGE model of the UK to estimate how raising defence spending to 3% of GDP affects output, employment, prices and trade across industries and regions between 2026 and 2030.

    Raising defence spending from 2.3% of GDP in 2025 to 3% in 2030 adds £14.5 billion a year by 2030 (2017 prices) and leaves real GDP 0.34% and employment 0.53% above the baseline, about 53p of GDP for each pound spent. The South West, Northern Ireland and Wales gain most; London gains least, and offshore oil and gas loses slightly.

    Model: Regional CGE model of the UK, 72 industries, the 12 ITL1 regions and the offshore oil and gas area, with recursive dynamics, developed in-house in Python.

    The question

    • How would raising defence spending to 3% of GDP by 2030 change output, jobs, prices and trade in the UK as a whole and in each region, and which industries would supply the extra demand?

    What we found

    • As the spending difference increases, the modelled GDP difference also rises. Real GDP is 0.05% above the baseline in 2026 and 0.34% above it in 2030, when annual defence spending is £14.5 billion higher and real GDP £7.6 billion higher than in the baseline (2017 prices).
    • By 2030, the difference in real GDP is about £0.53 for each additional £1 of defence spending relative to the baseline. Export volumes are 1.08% below the baseline and import volumes 1.14% above it.
    • Employment rises more than GDP, 0.53% above the baseline by 2030, because with the real wage fixed each year the extra demand draws in more workers. Consumer prices are 0.42% higher.
    • The largest output increases are in defence and public administration (+5.4%), scientific research and development (+3.2%), shipbuilding and other transport equipment (+3.1%) and aerospace (+2.4%). Output falls in several export-oriented industries, including publishing and broadcasting (−1.1%), crude oil extraction (−0.9%) and motor vehicles (−0.8%).
    • Regional effects reflect differences in industrial composition. The largest real GRP increases are in the South West (+0.69%), Northern Ireland (+0.64%), Wales (+0.62%) and Scotland (+0.56%); the smallest is in London (+0.03%), and the offshore oil and gas area is −0.21%.

    Year by year

    Defence spending rises each year, and the gap from the baseline widens with it. Higher GDP this year raises next year's consumption, investment and government demand, and defence investment adds to the capital stock. Consumption follows the previous year's GDP, so its first-year effect is zero by construction.

    Spending and GDP

    The extra spending builds from £2.1 billion in 2026 to £14.5 billion a year in 2030 (2017 prices). Of that, 45% is equipment, which the national accounts record as investment (aircraft, ships, electronics, weapons, machinery, research and software), and 55% is personnel, operations and support. Real GDP rises by about half as much as the spending.

    Industries, 2030

    Output and employment against the baseline. Output rises in defence and several supplying industries, while it falls in some export-oriented industries as domestic costs increase. All 72 industries are in the results explorer.

    Output and employment by industry in 2030, % against the baseline: the eight largest rises and the two largest falls in output
    IndustryOutputJobs
    Defence and public administration+5.4%+6.2%
    Scientific research and development+3.2%+4.7%
    Shipbuilding and other transport equipment+3.1%+4.0%
    Aerospace+2.4%+3.9%
    Construction+0.7%+1.1%
    Cement, lime and concrete+0.6%+0.9%
    Rail transport+0.4%+0.5%
    Motor vehicle trade and repair+0.4%+0.5%
    Motor vehicles−0.8%−1.2%
    Publishing and broadcasting−1.1%−1.7%

    Results explorer

    The results explorer contains all 263 model variables by industry, region and year for both the baseline and the defence spending scenario, with the underlying results available as CSV files.

    Open the results explorer
    • Overview
    • Macro
    • Regions
    • Industries
    • Emissions
    • All variables
    • Closure & shocks
    • Model & run
    • Downloads

    Interpretation

    • The regional effects are uneven. Real GRP rises by around 0.6–0.7% in the South West, Northern Ireland, Wales and Scotland, where defence and defence industries are a larger share of the economy, against 0.2–0.35% in the Midlands and the East of England and close to zero in London.
    • The reported scenario is gross of financing: it does not include higher taxes, borrowing costs or reductions in other government spending. The net macroeconomic effect therefore depends on how the additional defence spending is financed and would require a separate financing scenario.
    • By 2030, £14.5 billion of additional annual defence spending is associated with £7.6 billion higher real GDP relative to the baseline. The model also produces higher imports and lower exports, alongside the other general-equilibrium adjustments. The reported results do not isolate a single accounting explanation for the difference between spending and GDP.
    • The model is standardised: the baseline, closure and dynamic rules are fixed, and a scenario is defined only by its shock file, so results for different policies can be compared directly. The implementation has no proprietary software dependency.

    How we did it

    Regional CGE
    72 industries and 72 commodities, domestic and imported sources, three margin services, one household, government, investment by industry, exports and 13 regions. Database built from the ONS 2017 input-output and supply-use tables, with coal, crude oil and natural gas separate and electricity produced by six generation technologies.
    Defence shock
    Defence spending from 2.3% to 3% of GDP, 2.5% by 2027. The addition is 45% equipment, investment by the defence and public administration sector in aircraft, ships, electronics, weapons, machinery, research and software, and 55% personnel, operations and support. It is added to other government spending and investment.
    Production
    Nested substitution. Intermediate inputs are CES (Armington) blends of domestic and imported goods. Labour, land and a capital–energy composite substitute with elasticity 0.5; within it, capital and energy with 0.5, and fuels, electricity and generation technologies with 1.0.
    Regions
    A top-down method. National industries' regional output follows national output, using ONS regional GVA by industry; local industries, such as construction, retail and personal services, serve regional demand, and regional consumption follows regional labour income. Offshore oil and gas is a region of its own.
    Dynamics · Closure
    Solved one year at a time. Capital follows a ledger of depreciation, by industry from ONS capital consumption and stocks, and investment; consumption, investment and government demand grow with the previous year's real GDP. Each year: capital, land, technology, the real wage, tax rates, world prices and the exchange rate are fixed.
    Solution
    204,951 linearised equations, condensed to about 4,550 unknowns and solved by sparse LU at each step, with the database updated along a Gragg multi-step path and Richardson extrapolation (4, 8 and 12 steps a year).

    Work example · United Kingdom, 13 regions, 2025 to 2030

    The NHS spending settlement across the UK's regions

    We use a regional CGE model of the UK to estimate how the 2025 Spending Review's NHS settlement, 3% real growth a year in day-to-day spending, affects output, jobs, wages and prices across industries and regions between 2025 and 2030.

    By 2030 the settlement adds £17.9 billion a year (2025 money) and leaves real GDP 0.22% and employment 0.36% above the baseline, about 37p of GDP for each pound spent. The North East, Northern Ireland, Wales and Scotland gain most; London is roughly unchanged, and output falls in offshore oil and gas and in other export-oriented industries.

    Model: Regional CGE model of the UK, 72 industries, the 12 ITL1 regions and the offshore oil and gas area, with recursive dynamics and a medium-term labour market, developed in-house in Python.

    The question

    • What does growing NHS day-to-day spending by 3% a year in real terms, rather than with the economy, do to output, jobs, wages and prices in the UK as a whole and in each region, and which industries gain or lose?

    What we found

    • As the spending difference increases, the modelled GDP difference also rises. Real GDP is 0.05% above the baseline in 2025 and 0.22% above it in 2030, when annual NHS spending is £17.9 billion higher and real GDP £6.5 billion higher than in the baseline (2025 money).
    • The ratio of the real-GDP difference to the spending difference falls from about £0.51 per additional £1 in 2025 to £0.37 in 2030. By 2030, export volumes are 1.48% below the baseline and import volumes 0.57% above it, while wages and consumer prices are also higher.
    • Employment is 0.36% above the baseline by 2030, roughly 120,000 jobs, while real take-home pay is 0.54% higher. Under the model's wage-adjustment rule, part of the labour-demand response shifts from employment to real wages over time.
    • The largest increase is in health (+8.1% output, +10.9% jobs), with smaller increases in supplying industries: pharmaceuticals (+0.7%), residential care (+0.2%) and employment services (+0.2%). Output falls in several export-oriented industries, including crude oil extraction (−1.3%), aerospace (−1.2%), iron and steel (−1.1%) and motor vehicles (−1.1%).
    • The largest regional GRP increases are in the North East (+0.64%), Northern Ireland (+0.64%), Wales (+0.52%) and Scotland (+0.50%). The South East is +0.08%, London −0.05% and the offshore oil and gas area −0.91%.

    Year by year

    The extra spending, shown under each year as a share of GDP, rises steadily and the gap from the baseline widens with it. The employment response is larger initially, while the real-wage response increases as the model's labour-market adjustment accumulates. Consumption and investment follow the previous year's GDP, so their first-year effect is zero by construction.

    Spending and GDP

    NHS spending grows 1.5 points a year faster than in the baseline, where it keeps pace with the economy. The extra spending builds from £2.9 billion in 2025 to £17.9 billion a year in 2030 (2025 money), when health spending is 9.3% above the baseline. Real GDP rises by less than half as much as the spending, and the share falls as the settlement grows.

    Industries, 2030

    Output and employment against the baseline. Output rises most in health and several supplying industries, while it falls in a number of export-oriented industries as wages and prices increase. All 72 industries are in the results explorer.

    Output and employment by industry in 2030, % against the baseline: six rises and four of the largest falls in output
    IndustryOutputJobs
    Health+8.1%+10.9%
    Pharmaceuticals+0.7%+0.9%
    Residential care and social work+0.2%+0.2%
    Employment services+0.2%+0.2%
    Construction+0.2%+0.3%
    Retail trade+0.1%+0.1%
    Motor vehicles−1.1%−1.8%
    Iron and steel−1.1%−1.5%
    Aerospace−1.2%−2.0%
    Crude oil extraction−1.3%−5.2%

    Results explorer

    The results explorer contains all 263 model variables by industry, region and year for both the baseline and the NHS spending scenario, with the underlying results available as CSV files.

    Open the results explorer
    • Overview
    • Macro
    • Regions
    • Industries
    • Emissions
    • All variables
    • Closure & shocks
    • Model & run
    • Downloads

    Interpretation

    • The largest modelled GRP increases occur in the North East, Northern Ireland, Wales and Scotland, while the effects are smaller in the South East and close to zero in London. In the model, this pattern reflects differences in the regional importance of health services and in industrial composition.
    • The modelled GDP difference is smaller than the additional NHS spending. By 2030, real GDP is £6.5 billion above the baseline against £17.9 billion of additional annual spending. The model does not value the health outcomes produced by that spending, so this ratio is not a cost-benefit measure.
    • Labour-market adjustment becomes increasingly important over the simulation. Health employment is about 11% above the baseline by 2030 and real wages rise as labour demand increases. The model does not impose explicit occupational training, recruitment or migration capacity constraints.
    • The reported scenario excludes both the financing of the additional spending and any feedback from improved health to labour supply or productivity. Neither effect is therefore included in the reported GDP and employment estimates; each would require a separate scenario.

    How we did it

    Regional CGE
    72 industries and 72 commodities, domestic and imported sources, three margin services, one household, government, investment by industry, exports and 13 regions. Database built from the ONS 2017 input-output and supply-use tables.
    NHS shock
    NHS day-to-day spending grows 3.0% a year in real terms, the Spending Review rate to 2028–29, assumed to continue in 2029–30, against a baseline in which it grows with the economy (1.5% a year). Government purchases of health services grow 1.5 points a year faster; the addition is not financed.
    Labour market
    Medium term. Real take-home wages adjust each year to the gap between employment and the baseline, so employment gains fade into wage gains over time. The speed is calibrated to the OBR's assessment that 76% of the 2025 employer National Insurance rise passes into real wages by 2029–30.
    Regions
    A top-down method. Health is a local industry, produced where it is consumed, so NHS spending lands in every region; national industries' regional output follows national output, using ONS regional GVA by industry, and regional consumption follows regional labour income.
    Dynamics
    Solved one year at a time. Capital follows a ledger of depreciation, by industry from ONS capital consumption and stocks, and investment; consumption, investment and other government demand grow with the previous year's real GDP.
    Solution
    204,951 linearised equations, condensed and solved by sparse LU at each step, with the database updated along a Gragg multi-step path and Richardson extrapolation (4, 8 and 12 steps a year); the wage rule is solved within each year by iteration.

    Who we are

    Work examples

    Macroeconomic forecasting & analysis Climate transition risk at Enel We estimate Enel's downside market-value risk and the additional effect of a carbon-price scenario to 2030. The scenario adds about €0.7 billion to an estimated one-in-twenty-year loss of €18.2 billion; over six years, parameter uncertainty contributes more to the estimated risk. Open the work example Macroeconomic forecasting & analysis Energy prices and industrial productivity We compare 50 Italian industries over 1997–2023 to estimate how responses to energy-price increases vary with energy cost exposure. During 2022–23, each additional percentage point of energy cost share was associated with about 4 percentage points less output growth; the estimated difference fades within two to three years. Open the work example Macroeconomic forecasting & analysis Defence spending across the UK's regions We simulate UK defence spending rising from 2.3% to 3% of GDP by 2030 in a regional CGE model of the UK. By 2030, real GDP is 0.34% and employment 0.53% above the baseline, with the largest estimated regional GRP gains in the South West, Northern Ireland and Wales. Open the work example Macroeconomic forecasting & analysis The NHS spending settlement across the UK's regions We simulate NHS day-to-day spending growing 3% a year in real terms to 2030 in a regional CGE model of the UK. By 2030, real GDP is 0.22% and employment 0.36% above the baseline, with the largest estimated regional GRP gains in the North East, Northern Ireland and Wales. Open the work example Data science & analytics Squad use at Juventus and Inter We combine thirteen seasons of Juventus and Inter team sheets to measure where players started, how often they changed position and how those patterns differed between the clubs. Open the work example Data science & analytics Mortality projections by health status We estimate separate mortality curves by self-reported health in the UK, the Netherlands and Italy and project them to 2050. In all three countries, the estimated modal age at death is about ten years lower for adults in poor health, while remaining life expectancy at 65 is about eight years higher for those in good health. Open the work example Policy analysis & causal inference Long-term care benefit triggers In survey data for 30 countries, more than one third of expected needs-related resource loss after age 65 occurs at exactly one ADL limitation, before a typical two-limitation benefit trigger. Open the work example Policy analysis & causal inference Income screening after accounting for care needs We compare conventional and needs-adjusted income screens in 30 countries. The additional group identified after accounting for care needs has the highest two-year death rate among the groups compared. Open the work example