Changing Patterns of Fertility in Sweden: A Time Series Analysis of Structural Breaks and Sequential Detection, 1950–2025

Abstract

Sweden has experienced pronounced long-run fluctuations in fertility since the mid-twentieth century, alongside persistent within-year seasonality in births. While many fertility movements can be interpreted ex post in relation to economic conditions, cohort size, and institutional reforms, a central practical challenge is ex ante: when does an emerging decline become statistically detectable as the change unfolds, rather than being mistaken for an ordinary cycle?
Using monthly live births in Sweden from 1900–2024 and annual fertility indicators from 1950 onward, sourced from Statistics Sweden (SCB) (2026) and the Human Fertility Database, this thesis evaluates the prospective detectability of gradual fertility declines using the CUSUM algorithm. Because standard CUSUM procedures target mean shifts, slope changes in the original series are transformed into approximate mean shifts by detrending and deseasonalising a reference regime, computing residuals, and differencing. Decision thresholds are calibrated via Monte Carlo simulation from the estimated reference-period AR(1) model to control the false alarm rate under serial dependence.
The framework is applied to three historical episodes: the diffusion of oral contraceptives (1965), the Swedish economic crisis (1991), and the post-2010 fertility decline. Detectability is compared across fertility indicators, including monthly births, Total Fertility Rate (TFR), tempo-adjusted TFR, and age-specific fertility rates. Three patterns emerge consistently. First, observed TFR is the most reliable
early-warning indicator, detecting in all three episodes with delays of one to three years, while monthly births detect promptly only once aggregated to the annual level. Second, tempo-adjusted indicators detect later than their observed counterparts or not at all, providing a structured statistical lens on the tempo–quantum distinction central to demographic theory. Third, the age-group pattern of detection delays distinguishes broad economic shocks (uniform delays across age groups) from postponement-driven declines (rapid detection at peak childbearing ages but long delays at younger ages). Cross-validation with offline structural break methods (Bai–Perron, slope change test, Chow test) indicates that breaks confirmed in hindsight may have been statistically indistinguishable from ordinary fluctuation for several years after the underlying change occurred, quantifying a surveillance lag with direct implications for the design of demographic early warning systems.

Popular Abstract

When Does a Fertility Change Become Visible? Sweden 1950–2025
Sweden's fertility has fallen to its lowest level in postwar history. But how long does it take before such a decline actually shows up in the statistics? We did the math, and the answer depends dramatically on which number you're looking at.
In 2024, Sweden recorded its lowest fertility rate since the postwar era: 1.43 children per woman. All five Nordic countries reached similar historic lows. But the decline began as early as 2010, meaning more than a decade passed before anyone realised something fundamental had changed. Why did it take so long?
The problem: Decisions about preschools, schools, hospitals, pensions, and housing all depend on knowing how many children will be born in the coming years. When the trend shifts, society needs to react quickly. But fertility data is noisy, and a real change can look just like an ordinary fluctuation for a long time. Our thesis asks a question that demographic research rarely poses directly: not why fertility falls, but when such a change first becomes statistically visible while it is happening.
What we did: We analysed Swedish fertility data from 1900 to 2024 and applied a method called CUSUM, originally developed in the 1950s for industrial quality control and later adapted for disease outbreak surveillance. The method continuously compares incoming data to a baseline and raises an "alarm" when enough evidence has accumulated that a real change is occurring. We tested it on three major episodes in Swedish history: the arrival of the contraceptive pill in the 1960s, the 1990s economic crisis, and the ongoing decline since 2010.
What we found: The results surprised us. Despite having monthly birth data going back to 1900, the method failed to detect any of the three declines from monthly birth counts. The noise in monthly data is simply too large. Annual fertility rates worked excellently and triggered alarms within 1 to 3 years for all three episodes. The conclusion is counterintuitive: more detailed data is not always better. Filtering out short-term noise often beats high temporal resolution.
We also found something striking when we looked at different age groups. During the 1990s crisis, fertility dropped simultaneously across all ages, the fingerprint of a broad economic shock. After 2010, the pattern is completely different: among women aged 30 to 34, the decline was detected within a year, while for women in their early and mid twenties it took 10 to 12 years, and among teenagers it was not detected at all. This suggests that the current decline is largely about women postponing childbearing, but with a worrying nuance: at ages 30 to 34, where there is little room left for further postponement, a real reduction is visible.
Why it matters: Our analysis shows that a structural change can remain statistically invisible for 2 to 15 years after it has actually occurred, depending on which indicator is monitored. That is a surprisingly long lag. The concrete recommendation is to build future demographic early-warning systems on annual fertility rates broken down by age group, not on raw birth counts. Society could then react several years faster than today. The thesis also shows that statistical methods from one field, like quality control or epidemic monitoring, can yield fresh insight when borrowed for another.

• author: von Ahnen, Lisa and Kraft, Nora
• supervisor: Andreas Jakobsson
• organization: Mathematical Statistics
• alternative title: Förändrade fertilitetsmönster i Sverige: En tidsserieanalys av strukturella brott och sekventiell detektion, 1950–2025
• course: FMSM01 20261
• year: 2026
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• keywords: CUSUM, sequential change detection, structural breaks, Bai–Perron, Total Fertility Rate (TFR), tempo adjustment, Bongaarts–Feeney, postponement, Swedish fertility, demographic surveillance, time-series analysis, detection delay, Chow test, slope change test, age-specific fertility rates (ASFR), tempo–quantum distinction, Second Demographic Transition (SDT), AR(1) pre-whitening, Monte Carlo calibration, early warning systems, Nordic fertility, minimum detectable change (MDC), fertility decline, Sweden, tempo-adjusted TFR, monthly births, oral contraceptives, Swedish economic crisis, post-2010 fertility decline, quantum fertility
• publication/series: Master's Theses in Mathematical Sciences
• report number: LUTFMS-3556-2026
• ISSN: 1404-6342
• other publication id: 2026:E57
• language: English
• id: 9234569
• date added to LUP: 2026-06-17 14:26:43
• date last changed: 2026-06-17 14:26:43