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When counties move together, your econometrics must admit it. When they don’t, your policy slogans shouldn’t either.

1. From pictures to proof: Why the panel tests come next

Part I let the county charts speak first. They did what good charts usually do: they hinted at an Okun relationship, especially in gap form, while also showing enough county heterogeneity to make any one-size-fits-all conclusion look risky. Part II is where the report stops admiring the scenery and checks whether the road is actually paved.

The logic is sequential and practical. Before estimating an Okun coefficient, before arguing that output slack maps into labour-market slack, you need to know what kind of data you are sitting on. Are the series drifting with persistent trends? Are they stationary cycles around a stable mean? Do counties share common shocks that make them move as a bloc? And are county “slopes” plausibly similar, or is Croatia really a bundle of different Okun channels wearing one flag?

The report’s Part II answers those questions in the same order. It begins with panel unit root tests (stationarity), moves to cross-sectional dependence (whether counties are interlinked), checks slope homogeneity (whether coefficients are common), then asks whether a long-run relationship exists (cointegration), estimates long-run effects and short-run dynamics (FMOLS/DOLS/MG/PMG and ARDL/NARDL), and ends with causality tests (direction of predictive content). The purpose is not to impress readers with test acronyms. It is to avoid the classic mistake: “estimating relationships” that are really just shared trends, common shocks, or mis-specified dynamics.

2. First, don’t trip over stationarity: What the panel unit root results imply

Okun-type work is always tempted by an easy regression: unemployment on output (or gaps on gaps), add a constant, interpret a slope, call it a law. The report insists on a basic discipline first: check whether the variables behave like stable, mean-reverting processes or like persistent series that can generate spurious correlations.

A minimalist way to phrase the problem is this: if a variable behaves like a unit root process, shocks don’t die out quickly, they accumulate. In “template” form, that’s the familiar random-walk intuition:

If you regress one drifting series on another drifting series without a valid long-run structure, you can get impressive-looking slopes that are essentially decorative. That is why the report starts with six first-generation panel unit root tests, Levin–Lin–Chu, Breitung, Im–Pesaran–Shin, ADF–Fisher, PP–Fisher, and Hadri, applied to the key county series (LGDP, unemployment rate, output gap, unemployment gap, and their first differences).

The results are clean in their broad classification. The report finds that LGDP and the unemployment rate (UR) are non-stationary in levels but stationary in first differences across the county panel—an I(1) pattern that fits the macro intuition of trending output and persistent labour-market rates. By contrast, output and unemployment gaps appear stationary in levels, which is what the gap construction is designed to deliver: cyclical deviations from trend rather than trend itself.

The economic meaning is immediate. In levels, Croatia’s county GDP and unemployment rates contain long-run drift; in gaps, the series are closer to “slack indicators” that fluctuate around zero. That matters for Okun interpretation. If your goal is to talk about cyclical stabilization, booms, busts, overheating, slack, the gap model is structurally better aligned with the data properties the report finds. If your goal is to make long-run claims in levels, you must move into cointegration territory: if these level variables are I(1), then any stable long-run relationship must be demonstrated rather than assumed.

But the report also flags an important limitation of these first-generation tests: they assume cross-sectional independence. In county panels, that is a heroic assumption. Croatia does not run twenty separate macro policies. National shocks do not ask for county passports.

3. When counties move together: Cross-sectional dependence and why it changes the toolkit

The report’s next step is a sober admission: county economies are connected. Labour mobility, fiscal policy, nationally shared crises, and integrated markets mean counties likely share common factors. In econometric terms, residuals may be correlated across counties. If you ignore this, you can underestimate standard errors and overstate confidence, turning “plausible” into “proven” by statistical sleight of hand.

The report therefore applies a battery of cross-sectional dependence (CSD) tests, presented as four complementary lenses: Pesaran’s CD test, Juodis & Reese’s CDw test, a power-enhanced CDw+ (with Fan et al.’s enhancement), and Pesaran & Xie’s CD* test using principal components. The null across these tests is, in essence, “no strong cross-sectional dependence.” The report’s overall impression is clear: strong cross-sectional dependence is present for the key variables in levels and in differences, consistent with the idea that counties share common shocks and structural interlinkages.

There is nuance, some tests reject more strongly than others, and CD* appears more conservative in parts of the panel. The report interprets that discrepancy as partly a power issue in shorter panels and partly the cost of adjusting for latent factors. But it does not let nuance dilute the main implication: assuming county independence would be inappropriate.

Economically, this is a reminder that county differences do not live in isolation. When the global financial crisis hits, it doesn’t choose one county at a time. When a national policy shifts, it shifts for all. That is why the report treats CSD as more than a technical hurdle. It is a description of Croatia’s economic reality: counties are distinct, but they are not separate worlds.

Methodologically, this step forces the toolkit to evolve. Once CSD is present, the report argues for using second-generation unit root and cointegration tests that explicitly allow for cross-sectional dependence, rather than relying on first-generation results as if counties were unrelated laboratory samples.

4. One Croatia or many Croatias: Slope homogeneity and the danger of “average Croatia”

If CSD asks whether counties move together, slope homogeneity asks whether they move together in the same way. Okun’s Law in a panel often tempts analysts into a single national coefficient: one β for all counties, neatly summarising the country. The report tests whether that is defensible.

Using Pesaran–Yamagata slope homogeneity logic, the report tests four key Okun-related specifications: LGDP as a function of UR, UR as a function of LGDP, output gap as a function of unemployment gap, and unemployment gap as a function of output gap. The results are described as mixed depending on whether one uses standard versions of the test or HAC-corrected variants. Standard tests often reject homogeneity, suggesting heterogeneity in county slopes; HAC corrections sometimes soften that verdict for particular specifications.

The report does not pretend this yields one clean yes/no answer. Instead it treats the mixed results as guidance: heterogeneity is not an afterthought. For several specifications there is meaningful evidence that counties differ in how unemployment and output relate. That is economically intuitive. A county anchored in different industries, with different labour-market frictions, may display a different unemployment response to the same output movement.

The report even draws a policy implication from this testing: if slopes are heterogeneous, then a “uniform national response” may not fit all counties equally well. This is not an argument for twenty separate macro policies. It is an argument for respecting the limits of a single narrative. If the Okun channel differs by county, then a national average coefficient can be a useful summary, but it is also a mask.

5. Second-generation unit roots: When dependence and breaks are part of the story

Having established CSD, the report upgrades its stationarity testing. It applies Pesaran’s CIPS test, designed for heterogeneous panels with cross-sectional dependence. Here the report makes an interesting finding: under CIPS, LGDP and the output gap are found stationary in levels, while UR and the unemployment gap remain non-stationary in levels but become stationary after differencing. The report interprets this as broadly consistent with macro intuition: unemployment measures are persistent; output measures can appear more stationary once common factors are controlled via cross-sectional averages.

The practical implication for Okun modelling is that not all variables behave the same way, even within the same conceptual family. In the report’s reading, dynamic modelling should respect that: UR and unemployment gap may need differencing or cointegration handling, while LGDP and output gap can sometimes enter in levels depending on the chosen framework and the way common factors are treated.

But the report doesn’t stop at dependence. It turns to structural breaks, which are not just a nuisance but a feature of the 2000–2023 period. Using multiple-break logic (Bai & Perron) and the Ditzen–Karavias–Westerlund procedure, the report finds strong evidence of breaks in the relationships. For LGDP on UR it detects multiple breakpoints (including around 2009 and near the COVID period); for the reverse regression fewer breaks; for the gap model also breaks; and for the reverse gap regression more ambiguous break evidence.

The report’s synthesis is blunt: there is robust structural instability in these relationships, with break dates clustering around major disruptions. If you estimate one Okun coefficient over the entire period without acknowledging breaks, you risk treating regime changes as “noise.”

To deepen this, the report uses the Karavias–Tzavalis panel unit root test with structural breaks and highlights a striking sensitivity: when breaks are estimated endogenously (unknown breaks), the test rejects unit roots strongly (suggesting stationarity with breaks); when breaks are imposed as “known” at 2009 and 2020, the test fails to reject unit roots. The report reads this as evidence that stationarity conclusions can depend heavily on how breaks are modelled: if imposed break dates don’t match the true break dynamics, test power falls.

Economically, this is a caution against simplistic crisis labelling. Everyone knows 2009 and 2020 were big shocks. But local economies can break earlier, later, or in multiple steps. Counties don’t all pivot on the same quarter.

Methodologically, the conclusion is clear: if you want credible inference in county Okun panels, you must allow for structural change, not merely mention it.

6. Cointegration: Do output and unemployment share a long-run tether across counties?

Once you’ve established that some variables are I(1), that counties share shocks, and that breaks matter, cointegration becomes the central question. Cointegration is simply the idea that even if two series drift in levels, they may drift together, sharing a stable long-run relationship.

In “template” terms, if unemployment and output share a long-run equilibrium, then short-run deviations should correct over time. That logic can be expressed in an error-correction form:

If (), deviations from equilibrium shrink; the system pulls back.

The report applies three families of panel cointegration tests: Pedroni, Kao, and Westerlund, each with different assumptions and strengths, and each offering a slightly different lens on heterogeneity and adjustment.

The report’s own comparative reading is the important part. It describes the Pedroni results as particularly strong for the gap model (output gap and unemployment gap), where both within-dimension and between-dimension statistics generally support cointegration. The Kao test, more restrictive because it assumes a common cointegrating vector, produces more mixed outcomes, which the report interprets as a warning that the “one long-run slope for all counties” assumption may be too tight in a heterogeneous regional economy. Westerlund, grounded in an error-correction paradigm and well-suited to short panels, offers what the report treats as a more reliable picture: strong and consistent evidence of cointegration in the gap model, and more nuanced evidence in the first-difference/levels model depending on trends and dependent-variable choice.

Put in economic language, the report is saying this: Croatia’s counties appear to share a long-run relationship between cyclical slack in output and cyclical slack in unemployment more clearly than they share a single, stable relationship in levels. That is aligned with the intuition that regional labour markets respond to national cycles in broadly similar ways, even if their levels differ.

The report also stresses a structural point: across tests, the gap model behaves better. That doesn’t prove the gap model is “true,” but it does suggest it is empirically coherent for the kind of policy questions readers care about: slack, overheating, stabilisation, and recovery dynamics.

7. Estimating the long run: What the coefficients imply, and why estimator choice matters

Cointegration tests tell you whether a long-run relationship exists; they don’t give you the best estimate of its size. The report therefore turns to long-run estimation using four approaches: FMOLS, DOLS, Mean Group (MG), and PMG/ARDL logic, with estimates produced in different software implementations and compared for robustness.

The report’s overall conclusion is not coy: the evidence supports the long-run validity of Okun’s Law across counties, and the estimated magnitudes are economically meaningful. It reports that long-run elasticities imply (depending on specification and trend inclusion) sizeable effects: unemployment increases are associated with lower output, and higher output is associated with lower unemployment, with FMOLS/DOLS/MG showing consistent negative long-run relationships.

But the report also highlights an important difference across estimators. FMOLS, DOLS, and MG are described as the most reliable long-run coefficients under the dataset conditions because they are consistent with the time-series properties, robust under heterogeneity, and aligned with theoretical expectations. PMG/ARDL, by contrast, assumes long-run slope homogeneity and can perform poorly in small panels with structural breaks, showing unstable or near-zero long-run coefficients in some configurations. The report treats PMG/ARDL as informative for dynamics but less stable as a long-run anchor here.

This matters economically because it guards against false precision. A reader might ask, “What is Croatia’s county Okun coefficient?” The report’s answer is effectively: you can estimate it, but don’t pretend there is a single number that survives all assumptions. Robust long-run estimates are those that tolerate heterogeneity and structural change rather than assuming them away.

8. Short-run dynamics: ARDL models and how fast counties “correct”

Long-run relationships are comforting; policy crises happen in the short run. The report therefore estimates ARDL models (via the ARDL/NARDL framework) to separate short-run movements from long-run adjustment.

For the first ARDL model (unemployment rate as dependent variable, LGDP as explanatory), the report finds a negative long-run coefficient on LGDP: higher GDP is associated with lower unemployment in the long run, consistent with Okun. It also emphasises the error-correction mechanism: the coefficient on the lagged level of unemployment is negative and significant, implying that deviations from the long-run path correct gradually. The report interprets the adjustment speed as modest but consistent, unemployment doesn’t snap back; it drifts back.

In the short run, the report finds an immediate negative effect of GDP changes on unemployment changes, but it also notes that lagged GDP differences can turn positive and significant—suggesting partial rebound or short-run reversal dynamics. The report offers intuitive economic interpretations: adjustment costs, labour-market rigidities, and transitional rebalancing after acceleration. Unemployment dynamics also show inertia: lagged unemployment changes matter, consistent with persistence or hysteresis-type behaviour.

The report then estimates an ARDL gap model (unemployment gap as dependent variable, output gap as explanatory) and finds again a negative long-run relationship consistent with Okun. The error-correction term indicates a moderate adjustment speed. Short-run changes in output gap reduce unemployment gap contemporaneously, which is exactly the “cyclical slack” interpretation: when activity rises relative to potential, labour-market slack narrows. The report also notes some lagged compensatory effects, again suggesting that quarterly/annual labour-market adjustment can overshoot and then correct.

The report’s diagnostic discussion is practical rather than triumphalist: most standard checks look fine; non-normality shows up; one specification flags possible misspecification via RESET. The key point is that the core Okun signs and the adjustment mechanism remain interpretable, but the models shouldn’t be treated as flawless machines.

9. When the labour market is asymmetric: NARDL and the recession/recovery imbalance

Okun’s Law is often accused of being too linear: it assumes expansions “undo” recessions in symmetric fashion. The report tests that assumption explicitly using NARDL, which separates positive and negative changes in the explanatory variable to detect asymmetric responses.

In the first NARDL model (UR on LGDP decomposed into positive and negative changes), the report finds statistically significant short-run and long-run asymmetry tests. The interpretation is the one policymakers recognise instinctively: recessions tend to raise unemployment quickly and strongly; expansions don’t always reduce it with equal speed or magnitude.

The report describes oscillating short-run effects and highlights that negative GDP changes have strong immediate impacts on unemployment. It frames this as evidence that downturns can have stronger and more immediate labour-market consequences than upturns have in reverse, an asymmetric Okun channel.

In the gap-based NARDL model (unemployment gap on output gap decomposed into positive and negative components), the report again finds strong evidence of asymmetry in both short and long run. It interprets the results as showing that negative output shocks widen unemployment slack sharply and persistently, while positive output shocks reduce slack more gradually and with mixed dynamics. The report explicitly links this to labour-market frictions, hysteresis, and capacity adjustment lags: even when output recovers, unemployment slack may take longer to close.

From an economic perspective, this is the most policy-relevant message in the dynamic modelling block. It suggests that “grow your way out” can work, but not mechanically. Growth needs to be sustained and sufficiently inclusive to overcome frictions that slow labour-market repair. And it implies a classic stabilisation lesson: preventing deep downturns may do more for employment than relying on symmetric recoveries after the fact.

10. Causality: Who leads whom, and what it suggests for county-level policy thinking

The report finishes Part II with panel Granger causality tests. It is careful about prerequisites: causality testing should be consistent with stationarity/cointegration status, use differences when variables are not cointegrated, and use levels within an error-correction framework when cointegration is present.

The report applies two approaches: the Dumitrescu–Hurlin panel Granger non-causality test and an “improved” Granger panel causality test by Juodis, Karavias & Sarafidis, suited to panels with fixed time dimensions and relatively large cross sections, conditions the report says apply here.

The conclusions are described as robust and consistent across methods, directions, and specifications. In the first-difference model, causality from unemployment changes to output changes is not significant, whereas causality from output changes to unemployment changes is strongly supported. That is the classic Okun direction: output leads labour-market outcomes in the short run.

In the gap model, the report finds strong bidirectional causality between output and unemployment gaps. That does not necessarily mean “two-way structural causation” in a deep sense; it means the cyclical components contain predictive content for each other, plausible in an interconnected macro system where slack feeds back through demand, confidence, and adjustment processes.

The report also tempers this with methodological caution: the panel has a short time dimension (2000–2023), structural breaks exist, and these features can affect inference. Yet it emphasises convergence: different causality methods tell broadly the same story, and that story is consistent with the broader cointegration evidence.

Economically, the causality block strengthens the report’s overall narrative about counties. The Okun channel is not merely a static slope; it is a dynamic system. Output movements tend to precede unemployment adjustments in change terms; in gap terms, slack measures interact more tightly. For policy, this suggests that monitoring and stabilising output conditions, especially cyclical slack, can be a meaningful lever for labour-market outcomes, while also recognising feedback loops once slack is present.

11. Bridge: What Part III will do next

Part II’s formal results do not reduce Croatia’s counties to a single Okun coefficient, and that is the point. They show that the relationship is empirically grounded, methodologically defensible only when dependence and breaks are acknowledged, and economically richer when dynamics and asymmetry are allowed. Part III will integrate Parts I and II into one synthesis: what the county heterogeneity means for labour-market policy, stabilisation choices, and the constraints, and opportunities, of Croatia’s EU and euro-era framework, as the report itself frames them.