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

Sammanfattning

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.