1. Introduction

Unit labour cost (ULC) is a compact measure of cost-pressures from wages relative to productivity. When ULC rises, each unit of output requires more labour cost; when it falls, firms can produce the same output with cheaper effective labour. In an export-exposed sector such as Serbian industry, persistent ULC increases can erode competitiveness, while declines can signal efficiency gains or wage restraint. The attached figures follow Serbia’s industrial ULC at monthly frequency from 2008 to late-2025 (index 2024=100), including seasonally adjusted versions and decompositions using STL, plus diagnostics on seasonal behaviour.

Several broad forces frame this period. The series spans the aftershocks of the Global Financial Crisis (GFC), EU-adjacent supply-chain integration, the sudden COVID-19 stop-start cycle, and the inflation-tightening phase of 2022–2023. Read against that backdrop, the figures allow us to separate underlying trend movements from recurring seasonal patterns and short-lived shocks, and to see whether recent readings look elevated, benign, or reverting toward trend.

A top-line preview is as follows. The log-level ULC moves in multi-year waves rather than a single monotonic trend. Seasonality is present but not dominant, and its amplitude appears reasonably stable over the sample. The COVID-19 shock registers as a sharp but transitory disturbance; subsequent volatility eases as the economy normalises, although shorter bursts reappear around inflation and energy-price episodes. Through 2024–2025 the adjusted series sits near its longer-run path, pointing to a cooling in month-to-month volatility relative to the pandemic period.

2. Description of the time series and components

2.1 Overall patterns in levels and adjusted series

The original monthly ULC displays visible jaggedness typical of administrative and production calendars. The seasonally adjusted curve smooths these regular swings and clarifies the medium-term narrative: an upswing in the immediate post-GFC years, intermittent plateaus, and a sharp pandemic-era disturbance in 2020 followed by normalisation. In the last two years, the adjusted line oscillates in a narrower band, suggesting that the surge in month-to-month cost pressures has moderated.

The gap between the raw and adjusted paths is informative: it widens in months with strong seasonal effects (for example, inventory run-downs or year-end wage payments), but those gaps are largely symmetric across the year, indicating a stable seasonal cycle rather than creeping seasonal drift.

2.2 Trend, seasonal, and irregular components

The STL trend isolates the multi-year path of ULC. It rises in the early 2010s, flattens intermittently, and then shows a brief but pronounced kink at the onset of COVID-19 before reverting toward a gentler slope. This pattern is consistent with wage and productivity dynamics that alternately amplify and offset each other: periods of faster nominal wage growth not fully matched by productivity gains will lift ULC; spurts in productivity, sometimes linked to capital deepening or shifts in product mix, pull the trend down.

The seasonal component is clearly present but of moderate amplitude. Monthly signatures, visible in both the decomposition and the separate seasonal diagnostics, align with industrial schedules, bonus/payroll timing, and maintenance downtime. Importantly, the amplitude does not appear to trend upward over the sample, which means that the seasonal filter is not masking a growing seasonal bias. The remainder component is bursty: the pandemic period shows outsized residuals, while the subsequent years revert to smaller, more evenly distributed shocks. Occasional spikes outside 2020 likely reflect idiosyncratic events (temporary closures, regulation changes, or data revisions).

2.3 Differences of the log series and their decompositions

When the log series is first-differenced and seasonally differenced, the resulting growth-rate-like measure becomes mean-reverting around zero. In the “Original vs Seasonally Adjusted” view for these differences, one sees sharp spikes around the pandemic’s onset, with rapid reversion thereafter; the adjusted line removes a clear annual echo, making the short-run impulses cleaner to read.

The STL of these differenced data splits the volatility into a small, regular seasonal pulse and an irregular component that dominates during shock months but otherwise remains compact. This is consistent with a process where most of the predictable structure is yearly repetition, and where large deviations are episodic rather than persistent.

The variance shares implied by the STL output point to a trend-dominated series with seasonality playing a secondary, regular role. That configuration is typical for a cost index built from wages and productivity: structural shifts in either input drive the medium-term story, while seasonality reflects production rhythm rather than regime change. The irregular share spikes in 2020 and then recedes, which is exactly what one would expect if the shock was large, temporary, and followed by mechanical catch-up.

2.4 Seasonal diagnostics and detailed patterns

Seasonal plots and subseries charts confirm the calendar regularities. Certain months cluster systematically above or below the annual mean in the log scale, and the spread within each month’s box remains fairly stable across years.

Lag plots suggest short-run persistence, nearby months are positively related, together with an annual echo at the seasonal lag, which is what one expects when wages adjust in scheduled steps and production cycles repeat yearly.

The TSstudio seasonal plots, especially the boxplots, visualise this succinctly: medians are well-centred and interquartile ranges are not widening over time, arguing against a creeping seasonal change.

3. Economic outlook

What do these time-series features imply for the near-term narrative? First, the underlying trend has not accelerated materially in the most recent window. After the pandemic disturbances, the adjusted ULC oscillates near its longer-run path rather than trending away. That is good news for competitiveness: it implies that nominal wage growth and productivity have been broadly aligned on average, even if not month by month.

Second, the regular seasonal cycle remains contained. Because the amplitude is predictable and stable, firms and policymakers can discount it when interpreting monthly releases. Where attention is warranted is in the remainder: occasional single-month jumps still appear, but they are not clustering, which argues against a new regime of persistent shocks.

Third, the context matters. The inflation-tightening period of 2022–2023 likely pushed up nominal wages and altered energy-intensive cost structures; productivity dynamics, including process upgrades and supply-chain reshoring, likely offset some of that pressure. If the figures’ latest segment is any guide, ULC in industry has resumed behaving like a normal, trend-plus-seasonal series rather than a shock-dominated one, leaving the competitiveness picture broadly stable going into 2025.

4. Methodological appendix

The analysis uses STL (Seasonal-Trend decomposition by Loess) on the log of the ULC index and its first and seasonal differences. STL views the observed series as the sum of a smooth trend-cycle, a recurring seasonal pattern, and an irregular remainder. It alternates robust local regressions to estimate the seasonal and trend components, allowing the method to adapt when the seasonal pattern is not perfectly constant and to down-weight outliers. The seasonal adjustment shown in the figures simply subtracts the estimated seasonal component from the original series; differenced versions highlight short-run changes by removing low-frequency drift. Diagnostics, seasonal plots, subseries charts and lag plots, are used to cross-check that the recurring monthly pattern is stable and that shocks are not being mistaken for seasonality. References include Cleveland et al. (1990) for STL and Hyndman & Athanasopoulos (2021) for practical guidance.

5. Conclusion

Serbia’s industrial unit labour costs over 2008–2025 exhibit a familiar structure: a trend that moves in waves as wages and productivity take turns leading, a stable seasonal cycle tied to production calendars, and sporadic irregular shocks. The pandemic period is the clear outlier, but it is followed by reversion, not a new plateau. In the most recent observations the series looks neither overheated nor unusually depressed relative to its trend; rather, it has settled into a steady rhythm with moderate, predictable seasonality and fewer outsized surprises.

For policymakers, the key message is to keep the wage–productivity balance aligned so the trend does not drift upward; for firms, the message is to discount the seasonal noise and focus on medium-term efficiency. As fresh monthly data arrive, the same toolkit, STL on log levels and on differences, read alongside seasonal diagnostics, will continue to provide an interpretable lens for separating signal from seasonal and shock noise.

References

Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I. (1990). STL: A seasonal-trend decomposition procedure based on loess. Journal of Official Statistics, 6(1), 3–73.

Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and practice (3rd ed.). OTexts. (Open textbook).