Projection Methods
How the population projection on the Projections page works – and why methods produce different results.
The Projections page offers five methods for population projection. They often produce very different results – this is not an error, but reflects fundamentally different assumptions. All methods are based on historical data from 2002–2024.
Linear trend extrapolation
Constant annual increase (or decrease)
Principle
The average annual population change (positive or negative) is extrapolated constantly into the future.
Calculation
- OLS regression slope over all data years (2002–2024)
- P(t) = P_base + Δ × Schritte
- Base year age structure is scaled proportionally
Strengths
- ✓ Simple and transparent
- ✓ Stable against fluctuations
- ✓ Easy to understand
Weaknesses
- ✗ No age structure dynamics
- ✗ Ignores birth rate decline
- ✗ Can produce negative values
Exponential extrapolation
Constant growth rate in % instead of absolute increase
Principle
The same OLS slope as the linear method, but applied as a constant growth rate (%).
Calculation
r = Δ / P_base
P(t) = P_base × (1 + r)^Schritte
Why ≈ Linear?
For small growth rates (|r| < 1 %/year):
(1 + r)ⁿ ≈ 1 + r·n
Norsjö shrinks ~0.7 %/year → barely any difference to linear over 76 years.
Strengths
- ✓ More realistic for growth
- ✓ No negative result possible
Weaknesses
- ✗ No age structure dynamics
- ✗ For decline ≈ linear
Cohort shift
Detailed age model with freely selectable parameters
Principle
Each individual age cohort (0–100) ages by exactly 1 year per simulation step. TFR, life expectancy and migration are freely configurable.
Algorithm per year
- Cohort shift: cohort[i] → cohort[i+1]
- Mortality: age-specific death rates
- Births: Women(15–49) × TFR / 35
- Migration: clusters distributed across cohorts
Adjustable parameters
| TFR | Children/woman; replacement level = 2.10 |
| Life expectancy | Constant / Optimistic / Increasing |
| Migration | Clusters: 0–19 / 20–39 / 40–59 / 60+ |
Component method
Historical TFR and migration – fully automatic from data
Principle
Like the cohort shift, but all parameters are automatically derived from historical data (2002–2024). No manual override.
TFR estimate from DB
TFR ≈ Ø_Geburten / (Ø_Pop × 0,15) × 35
Demographic collapse effect
For Norsjö, TFR ≈ 1.3. This leads to a self-reinforcing spiral:
few women → few children
→ in 25 years even fewer mothers
→ even fewer children → …
Example scenarios
| Method | Pop. 2100 |
|---|---|
| Component method | ~661 |
| Linear extrapolation | ~1.765 |
| Exponential extrap. | ~2.278 |
Component + Migration ★ New
Historical TFR – freely configurable migration age groups
Principle
TFR and mortality are automatically derived from data as in the component method. The migration clusters (youth, work, family, seniors) are freely configurable – ideal for realistically simulating municipal recruitment scenarios.
Example scenarios
- → +50 young families/year (20–39 yrs): 0–4 cohort grows, but TFR remains historically low (≈ 1.3)
- → +100 seniors/year: 60+ groups strengthen, no effect on births
- → Mixed profile: most realistic representation of an active recruitment policy
Parameter comparison
| Parameter | Component | Comp.+Mig. |
|---|---|---|
| TFR | DB avg. | DB avg. |
| Mortality | DB avg. | DB avg. |
| Life expectancy | selectable | selectable |
| Migration | DB avg. | free |
PDE Scenario (IIASA) ★ New
Full control over all parameters – TFR, life expectancy, migration, SRB
Principle
A single-state cohort component model based on the IIASA PDE approach (Population-Development-Environment). The user defines all demographic assumptions: fertility, mortality, immigration, emigration, and the sex ratio at birth.
Algorithm per year
- Expand age distribution into single years (base year)
- Linearly interpolate TFR and e₀ from base to target value
- Per simulation step: apply births (via TFR), deaths (via e₀), migration
- Re-aggregate result into 5-year age groups
Linear Scenario Interpolation
All parameters are linearly interpolated from the historical base value to the user-defined target value – no abrupt jump, but a smooth transition over the entire projection period.
r(t) = r(t₀) + (t−t₀)/(t₁−t₀) × [r(t₁) − r(t₀)]
Adjustable parameters
| TFR | Total fertility rate (0.5 – 5.0) |
| e₀ | Life expectancy at birth (60 – 95 years) |
| Immigration | Annual immigration (absolute) |
| Emigration | Annual emigration (absolute) |
| SRB | Sex ratio at birth (1.00 – 1.10) |
Strengths
- Full control over all assumptions
- Smooth interpolation instead of jumps
- Scientifically grounded (IIASA methodology)
Weaknesses
- Requires demographic expertise
- Unrealistic inputs possible
When which method?
| Purpose | Recommended method |
|---|---|
| Rough short-term estimate (≤ 10 years) | Linear or Exponential |
| Medium-term with age structure (10–25 years) | Component method |
| Long-term (> 25 years) | Component method |
| "What-if" scenarios (TFR, Migration) | Cohort shift |
| Municipal recruitment scenarios | Component + Migration ★ |
| Custom scenario assumptions (TFR, e₀, migration) | PDE Scenario (IIASA) ★ |
Note: The component method and "Component + Migration" ignore the TFR slider in the UI – they always use the historically calculated TFR from the DB data (2002–2024). The TFR slider only affects the Cohort method.