Quarterly data confirm the channel. They also insist on breaks, lags, and humility.

1. The big takeaway: Croatia has an Okun relationship, but not a single “Okun number”

If you came here hoping for one crisp coefficient that turns GDP into jobs like a vending machine, insert growth, receive employment, you will be disappointed. If you came hoping for something more realistic, evidence that output and unemployment are meaningfully linked, that the link has timing, and that shocks can bend the relationship, you will leave with the report largely on your side.

Across the full quarterly workflow, the report’s message is consistent: Croatia’s data are broadly in line with Okun’s Law, especially when the relationship is expressed in business-cycle terms (output gap versus unemployment gap) and when the models allow for dynamics rather than demanding immediate, contemporaneous obedience. Yet the same evidence also makes it hard to believe in a stable, all-period, one-slope story. Structural change, crisis episodes, and asymmetries matter. The “law” behaves like a rule of thumb with a changing grip.

The report’s contribution is not that it “finds Okun.” Most serious analysts would expect some inverse relationship between activity and unemployment. The contribution is that it shows, with quarterly granularity, where Croatia’s Okun channel looks sturdy, where it looks state-dependent, and where the modelling choices determine whether you are measuring a signal or a mirage.

2. What the combined evidence actually says

The results, taken together, form a coherent narrative, provided you read them as a package rather than as a menu of isolated tests.

Start with the foundations. The level series (log GDP per capita and the unemployment rate) behave like variables with persistence, non-stationary under standard testing, and therefore require careful treatment to avoid spurious regression. The gap variables, constructed using the Hodrick–Prescott filter, behave more like stationary cyclical measures, which is exactly what a slack-focused Okun story wants. Put plainly: the report finds it easier to tell a clean Okun story in the language of deviations from trend than in the language of levels.

Then come breaks. The report’s break-aware testing repeatedly points to structural change around major episodes, including the global financial crisis and the COVID shock, with breakpoints appearing around the late-2000s and around 2020 in different specifications. This matters because it makes a full-sample “average” relationship suspicious. If the labour market’s response mechanism changes across regimes, then one coefficient is an average across different economies, not just different quarters. The report’s break framework (drawing on multiple-break logic in the spirit of Bai and Perron) effectively formalises what the charts already hinted: Croatia does not move along a single Okun curve; it redraws the curve when history intervenes. (Bai & Perron.)

Cointegration then separates the story into two tracks. In levels, evidence is mixed and method-sensitive. In the gap framework, evidence of a long-run relationship is considerably stronger and more consistent across approaches, including combined-test logic (Bayer & Hanck) and break-aware cointegration ideas (Gregory & Hansen). The economic interpretation is straightforward: cyclical slack in output and cyclical slack in unemployment appear tied together in a way that makes error-correction modelling meaningful. In contrast, insisting on a single long-run equilibrium in levels over a period with major breaks is harder to justify without additional structure and careful diagnostics. (Engle & Granger; Gregory & Hansen; Johansen; Bayer & Hanck.)

ARDL and NARDL estimation is where this becomes policy-relevant. In the preferred gap-based models, the report finds a negative long-run relationship between output slack and unemployment slack, and, crucially, an error-correction mechanism that implies gradual adjustment rather than immediate translation. Output gaps can close faster than unemployment gaps, consistent with the intuition that labour markets are inertial objects: hiring, separation, and matching do not reset instantly every quarter. The models make that inertia measurable through the speed of adjustment, and they do so in a way that fits the macro story of lagged labour-market response. The framework is recognisably ARDL-bounds logic (Pesaran, Shin & Smith), with asymmetry explored via the nonlinear ARDL approach (Shin, Yu & Greenwood-Nimmo). (Pesaran, Shin & Smith; Shin, Yu & Greenwood-Nimmo.)

Finally, causality, interpreted carefully as predictability rather than metaphysical cause, tilts the narrative strongly in one direction: output (and especially the output gap) helps predict unemployment outcomes more convincingly than the reverse. The report reinforces this with time-varying evidence: the strength of predictive direction is not constant across the sample, but the dominant pattern is output leading labour-market slack rather than unemployment leading output. This is as close as the report gets to a simple headline: if you want to anticipate unemployment in Croatia, watch the output side and the cyclical stance, not merely the unemployment rate itself.

3. Where the channel looks strongest, and where it leaks

The simplest way to interpret the evidence is to treat Croatia’s Okun relationship as a two-layer mechanism.

Layer one is cyclical slack. When output runs below potential, unemployment tends to run above its trend (or “natural”) counterpart. The gap framework is where the report finds the most consistent long-run linkage and the most interpretable adjustment dynamics. This is not an abstract win for filtering. It is an economic win for the concept of slack: the relationship is clearer when both sides are expressed as “how far from normal?” rather than “what level are we at?” (Hodrick & Prescott.)

Layer two is regime dependence. Crisis episodes, particularly the global financial crisis and the pandemic, do not simply move Croatia along a stable curve. They appear to change the curve’s slope or stability, or at least to change the data-generating environment enough that break-aware testing becomes necessary. That is why the report spends so much time on structural breaks and on models that tolerate changing regimes and nonlinearity rather than insisting on one timeless mapping. (Bai & Perron; Zivot & Andrews; Clemente, Montañés & Reyes; Gregory & Hansen.)

Where does the mechanism “leak”? The report highlights three leakage points that are best understood economically, not technically.

First, timing leakage: unemployment responds with lags. The quarterly evidence repeatedly implies that growth can return before joblessness falls meaningfully. That is not a failure of Okun’s Law; it is a reminder that labour markets adjust through contracts, expectations, and matching processes, not through instantaneous arithmetic.

Second, asymmetry leakage: the report’s nonlinear models show that downturns can have sharper short-run labour-market effects than upturns have in reverse. In the difference-based nonlinear framework, short-run asymmetry is detected even when long-run asymmetry is not. That has a recognisable policy meaning: job destruction can be swift, job creation can be slower and more conditional. Yet in the gap-based nonlinear models, asymmetry is not strongly supported, suggesting that the cyclical slack relationship itself is more symmetric than the short-run quarterly changes might imply. This is a subtle result, and it matters. It suggests that the labour market may behave asymmetrically in the turbulence of quarter-to-quarter movements, even if the broader cyclical adjustment relationship is more balanced when viewed in slack terms. (Shin, Yu & Greenwood-Nimmo.)

Third, stability leakage: some specifications that pass “headline” tests still fail diagnostics related to distributional assumptions or coefficient stability. The report is blunt on this: evidence of cointegration is not a licence to trust any model you can fit. In policy terms, this is a warning against “model shopping”, picking the specification that gives the prettiest coefficient and ignoring the signs that the relationship is unstable in parts of the sample.

4. The euro in 2023: Regime change and credibility anchor, not a free lunch

Croatia’s euro adoption in 2023 matters here mostly as institutional context. It can be treated as a regime change in the macro policy environment, a credibility anchor and a constraint that changes how stabilisation is conducted and how shocks are absorbed. But it is not a magic wand that rewrites labour-market dynamics overnight. The report’s results suggest that Croatia’s Okun mechanism is shaped as much by cyclical slack, structural breaks, and adjustment speeds as by the nominal framework under which policy operates.

In practical terms, the euro environment tends to sharpen the importance of internal adjustment, productivity, wages, and labour-market institutions, because exchange-rate adjustment is no longer the domestic lever. That does not “break” Okun’s Law; it can, however, change the way output shocks translate into labour outcomes and the way policy can respond. In a world of constrained monetary autonomy, the labour market’s responsiveness, and the speed at which unemployment slack closes, becomes even more consequential.

The report does not claim that the euro causes any particular coefficient change. Its contribution is more disciplined: it provides a framework for thinking about labour-market adjustment in a Croatia that has crossed a new institutional threshold. If the Okun channel is stable in slack terms but state-dependent around crises, then the policy aim should be to reduce the frequency and severity of those break-creating episodes, and to make labour-market adjustment less costly when they occur.

5. Practical takeaways

The report’s evidence points to a policy stance that is less glamorous than the usual debate, but more useful. It implies that Croatia’s labour market responds to output conditions, but does so with inertia and with sensitivity to regime shifts. That yields a few actionable conclusions.

• Slack is the language that travels best. The output-gap / unemployment-gap relationship appears empirically stronger and more interpretable than purely level-based relationships. When policymakers argue about “overheating” or “slack,” they are speaking the language the data seem most willing to support.
• Timing is a policy variable. If unemployment slack adjusts slowly, policy evaluation should not assume instant labour-market payoffs from growth rebounds; lags are part of the mechanism.
• Crisis management is labour-market policy. Breaks and regime shifts are not just macro events; they reshape the growth-jobs link and can leave unemployment slack persistent even when output stabilises.

If you want the same points in a tighter “results-to-implications” form, the report effectively suggests:

• For stabilisation: focus on reducing the amplitude of output gaps, because cyclical output conditions predict labour-market slack more reliably than the reverse.
• For labour-market policy: reduce inertia, improve matching, flexibility, and adaptation, so that unemployment slack closes more quickly when output returns toward potential.
• For forecasting and surveillance: treat output and output-gap indicators as leading signals for labour outcomes; unemployment is more of a lagging symptom than a leading guide.

6. What to watch next

A good “leader column” ending does not pretend the story is complete. It tells readers what would change the conclusion. The report implicitly points to three “watch items” that matter for the next cycle.

• Watch whether post-shock recoveries close unemployment slack faster than before. If the speed of adjustment rises, it would suggest improved labour-market responsiveness or different policy transmission in the newer institutional regime.
• Watch for new breakpoints. The report’s emphasis on structural breaks implies that the next large shock could change the relationship again, especially if it affects labour-market functioning rather than merely output levels.
• Watch asymmetry in the next downturn. Short-run asymmetry detected in difference-based nonlinear models implies that recessions can carry disproportionate labour-market pain. If that persists, policy should treat downturn prevention and rapid stabilisation as employment policy, not just GDP policy.

The cleanest summary is this: Croatia’s quarterly data do not undermine Okun’s Law; they rescue it from oversimplification. The relationship works, but it works through slack, lags, and regimes, not through a single coefficient etched into stone. That is inconvenient for slogans. It is also exactly what policy needs.

7. References

Bai, J., & Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 66(1), 47–78. DOI: https://doi.org/10.2307/2998540

Bayer, C., & Hanck, C. (2013). Combining non-cointegration tests. Journal of Time Series Analysis, 34(1), 83–95. DOI: https://doi.org/10.1111/j.1467-9892.2012.00814.x

Clemente, J., Montañés, A.,& Reyes, M. (1998). Testing for a unit root in variables with a double change in the mean. Economics Letters, 59(2), 175–182. DOI: https://doi.org/10.1016/S0165-1765(98)00052-4

Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276. DOI: https://doi.org/10.2307/1913236

Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99–126. DOI: https://doi.org/10.1016/0304-4076(69)41685-7

Hodrick, R. J., & Prescott, E. C. (1997). Postwar U.S. business cycles: An empirical investigation. Journal of Money, Credit, and Banking, 29(1), 1–16. DOI: https://doi.org/10.2307/2953682

Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica, 59(6), 1551–1580. DOI: https://doi.org/10.2307/2938278

Okun, A. M. (1962). Potential GNP: Its measurement and significance. American Statistical Association, Proceedings of the Business and Economic Statistics Section, 98–104.

Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics, 16(3), 289–326. DOI: https://doi.org/10.1002/jae.616

Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In Festschrift in Honor of Peter Schmidt (pp. 281–314). Springer. DOI: https://doi.org/10.1007/978-1-4899-8008-3_9

Zivot, E., & Andrews, D. W. K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 10(3), 251–270. DOI: https://doi.org/10.1080/07350015.1992.10509904