On period, cohort and population life expectancy

This paper introduces Population Life Expectancy (PoLE), a new indicator representing the mean age at death of active cohorts, which reveals that actual population longevity gains over the last 150 years in Switzerland and Norway are approximately 50% higher than suggested by traditional Period Life Expectancy measures.

The Gist

The Big Idea: Measuring How Long We Actually Live

Imagine you are trying to guess how long a group of people will live. For over a century, demographers have used a standard ruler called Period Life Expectancy (PLE).

The Problem with the Old Ruler (PLE)
The old ruler works like a "time-traveler's snapshot." It asks: "If a baby born today lived their entire life under the exact same health conditions as they do right now, how long would they live?"

The catch? No one actually lives like that.

• Conditions change. Medicine gets better. Diseases get cured.
• If you are 80 years old today, you didn't live your whole life with today's medical technology. You lived through the 1950s, the 80s, and the 90s.
• Because the old ruler assumes conditions never get better, it often underestimates how long people will actually live. It's like predicting a runner's finish time by assuming they will run on a muddy track forever, even though the track is being paved with asphalt every year.

The New Solution: Population Life Expectancy (PoLE)

The authors of this paper introduced a new, smarter ruler called Population Life Expectancy (PoLE).

The Analogy: The "Real-Life" Movie vs. The "Hypothetical" Script

• The Old Way (PLE): Imagine a movie script where the main character is stuck in a time loop. They experience the same year, 2024, over and over again for 80 years. The script predicts they will die at 82.
• The New Way (PoLE): Imagine the actual movie. The character is born, grows up in the 1950s, survives the flu of the 1960s, enjoys the antibiotics of the 1980s, and benefits from the heart surgery of the 2020s. The script predicts they will live to be 90 because the "movie" gets better as it goes on.

PoLE calculates the average age at death for the real mix of people alive in a specific year. It accounts for the fact that the 80-year-old has already survived the hard parts of life, and the 30-year-old will likely benefit from future medical breakthroughs.

What Did They Find? (The Swiss and Norwegian Story)

The researchers tested this new ruler on data from Switzerland and Norway, looking back 150 years. Here is what they discovered:

1. The "Hidden" Gain
The old ruler (PLE) suggested that life expectancy doubled over the last 150 years (going from ~40 to ~80). That sounds like a 100% improvement!
The new ruler (PoLE) tells a different story. It shows that the actual population's life expectancy went from ~63 to ~90. That is a 50% improvement.

• Why the difference? In the past, many babies died very young. This dragged the "average" down heavily. But the people who survived childhood often lived very long lives. The new ruler realizes that the "average person alive today" has already survived the dangerous early years, so their future looks brighter than the old math suggested.

2. The "Crossing of the Paths"
There is a fascinating moment in history around 1950.

• Before 1950: If you were already alive (say, 40 years old), you were expected to live longer than a baby just being born. Why? Because the baby faced high risks of infant mortality, while the 40-year-old had already beaten the odds.
• After 1950: The trend flipped. A baby born today is expected to live longer than a 40-year-old alive today.
• The Meaning: This flip is a "tangible sign of human progress." It means we have finally conquered the early dangers of life so thoroughly that the future looks brighter for the newborn than the present looks for the older generation.

3. The Gap is Closing, But Still There
In 2024, the new ruler (PoLE) says a Swiss man will live to about 89.7 years, while the old ruler (PLE) says 82.4 years. That is a difference of over 7 years!
This means that if you are alive today, you are likely to live significantly longer than the "official" statistics suggest, because you will benefit from the medical advances of the next 20 or 30 years.

Why Does This Matter?

Think of Period Life Expectancy (PLE) as a weather report for today. It's great for telling you if you need an umbrella right now (it reacts quickly to crises like pandemics or heatwaves).

Think of Population Life Expectancy (PoLE) as a climate forecast for the next decade. It tells you what the actual journey will be like for the people walking through the door today, accounting for the fact that the weather is getting better (or worse) as they travel.

The Takeaway:
We are living longer than the headlines tell us. The "real" people in our society are benefiting from a steady march of progress that the old, static math fails to capture. The authors aren't saying we should stop using the old numbers, but they are asking us to add this new number to the conversation so we can see the full, brighter picture of human longevity.

Technical Summary

1. Problem Statement

The paper addresses a fundamental limitation in demographic analysis: the misinterpretation of Period Life Expectancy (PLE).

• The Issue: PLE is the most widely used longevity indicator, but it describes a hypothetical cohort that lives its entire life under the mortality conditions of a single year. It does not represent the actual life expectancy of a real population alive in that year, which consists of a mixture of "active cohorts" (people born in different years) with varying past and future mortality risks.
• The Consequence: In contexts of declining mortality (the historical norm), PLE systematically underestimates the true longevity of the living population.
• Existing Alternatives: Previous attempts to correct this, such as the Cross-sectional Average Length of life (CAL) and the Average Cohort Life Expectancy (ACLE), have proven insufficient. CAL ignores future mortality trends, while ACLE (which projects future mortality) still underestimates longevity because it relies on life expectancy at birth rather than the remaining life expectancy of individuals already alive, and often uses rigid assumptions (e.g., a fixed 0.5% annual mortality decline).

2. Methodology

The authors introduce a novel indicator, Population Life Expectancy (PoLE), and apply it to data from Switzerland (1876–2024) and Norway (1846–2024) using the Human Mortality Database (HMD).

Definition of PoLE:
PoLE is defined as the mean age at death of all individuals alive in a specific year $t$. It is calculated by averaging the expected age at death for every individual currently alive, weighted by the population's age structure.
$$PoLE_t = \frac{\sum_{x=0}^{110} N_{x,t} \cdot E[A_{x,t}]}{\sum_{x=0}^{110} N_{x,t}}$$
Where:

• $N_{x,t}$ is the population size at age $x$ in year $t$.
• $E[A_{x,t}]$ is the expected age at death for an individual of age $x$ in year $t$.
• $E[A_{x,t}] = x + e_{x, t-x}$, where $e_{x, t-x}$ is the remaining cohort life expectancy for the cohort born in year $t-x$ at age $x$.

Mortality Projection Model:
To calculate the remaining life expectancy for non-extinct cohorts (those not yet fully observed), the authors employ a log-linear Poisson regression model with age-period interaction:
$$\log(\mu_{x,t}) = \alpha_x + \beta_x \cdot t$$

• $\mu_{x,t}$: Mortality rate at age $x$ in year $t$.
• $\alpha_x$: Age-specific effect.
• $\beta_x$: Age-specific period effect (interaction), allowing mortality decline rates to vary by age.
• Technique: Natural splines are used to model these effects. This contrasts with the ACLE method (Schoen & Canudas-Romo), which assumed a uniform, age-independent mortality decline (e.g., 0.5% per year). The authors also tested a simpler age-independent model to demonstrate the superiority of the interaction model.

3. Key Contributions

1. Introduction of PoLE: A new metric that directly answers the question: "How long can the actual population alive in year $t$ expect to live?"
2. Methodological Refinement: Unlike ACLE, PoLE calculates the expected age at death based on remaining life expectancy for current ages, rather than life expectancy at birth. This avoids underestimating the longevity of older cohorts who have already survived high-risk early-life periods.
3. Advanced Projection: The use of an age-period interaction model provides more realistic long-term projections than fixed-rate decline assumptions, capturing the nuance that mortality improvements vary significantly across different ages.

4. Key Results

The study compares PoLE against PLE, Cohort Life Expectancy (CLE), and ACLE for Switzerland and Norway.

• Magnitude of Difference: PoLE is consistently and significantly higher than PLE.
  • Swiss Men (2024): PoLE = 89.7 years vs. PLE = 82.4 years (a gap of 7.3 years).
  • Swiss Women (2024): PoLE = 91.3 years vs. PLE = 85.9 years (a gap of 5.4 years).
  • Historical Context: In 1900, the gap was even wider (approx. 20 years), as PLE was heavily depressed by high infant mortality, whereas PoLE reflected the higher survival chances of those who had already reached adulthood.
• Growth Trends:
  • PLE suggests a doubling of life expectancy over 150 years (e.g., ~40 to ~80 years, +100%).
  • PoLE suggests a more moderate but realistic gain of approximately +50% (e.g., ~63 to ~90 years).
• The Crossover Phenomenon:
  • Pre-1950: PoLE > CLE. This indicates that for those alive at the time, life expectancy was higher than for newborns, largely due to high infant mortality affecting the CLE calculation.
  • Post-1950: CLE > PoLE. The curves crossed in the mid-20th century. This signifies that due to long-term mortality declines, newborns today have a higher life expectancy than those currently alive. The authors interpret this crossover as a "tangible sign of human progress."
• Model Performance: The age-period interaction model (Model 4) provided superior projections compared to the age-independent model (Model 5). The latter produced unrealistic linear increases and predicted a crossing of male/female life expectancies by 2060, which the interaction model avoided.

5. Significance and Implications

• Reframing Longevity: PoLE offers a more accurate representation of the "real" longevity of a population. It corrects the historical narrative that life expectancy has doubled; instead, it shows a substantial but less dramatic increase when accounting for the survival of existing cohorts.
• Policy and Perception: While PLE remains the best tool for measuring the immediate impact of acute crises (e.g., pandemics, heatwaves) due to its sensitivity, PoLE is superior for assessing long-term societal gains in health and longevity.
• Demographic Insight: The crossover of PoLE and CLE provides a new metric for identifying the phase of the demographic transition where improvements in mortality begin to favor future generations over current ones.
• Future Research: The authors suggest extending PoLE calculations to countries with different demographic profiles to study the relationship between the PoLE/CLE crossover and specific phases of demographic transition.

In conclusion, the paper argues that while PLE is useful for specific conjunctural analyses, PoLE is the necessary indicator for understanding the true life expectancy of a living population, revealing that humanity has achieved greater longevity gains than standard metrics suggest, particularly for those who have already survived early-life risks.