Reading Time: 9 minutes

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

In Part I we let the charts do the talking. Here, we make them swear an oath.

Once you move from a single country to a panel of six economies, Bosnia and Herzegovina, Croatia, Montenegro, North Macedonia, Serbia and Slovenia, your statistical life gets both easier and harder. Easier, because you gain variation and you can ask “regional” questions with more authority. Harder, because countries do not behave like identically trained lab mice. They share shocks, they diverge in institutions, and they occasionally decide to trend in ways that make economists reach for aspirin.

So the workflow in the report becomes deliberately sequential: first establish what kind of data-generating creature you’re dealing with (stationary or drifting), then ask whether output and unemployment share a long-run anchor (cointegration), then estimate that anchor with methods designed for non-stationary panels, and only then talk about dynamics and predictive direction (causality). That is not econometric fussiness. It is basic hygiene.

2. Are these series “well-behaved”? Panel unit root results and meaning

The report begins this formal stage by confronting an awkward truth: macro panels are rarely collections of independent stories. They are more like a family dinner, everyone insists they’re doing their own thing, while reacting to the same news in real time.

That matters because many “first-generation” panel unit root tests assume cross-sectional independence. If countries share common shocks or spillovers, those tests can become overconfident. That is why the report first checks cross-sectional dependence, using the M. Hashem Pesaran CD test. The finding is blunt: cross-sectional dependence is “statistically significant for most variables,” so the independence assumption is not a safe comfort blanket.

The report also tests whether slope parameters can reasonably be treated as homogeneous across countries, using the Pesaran and Yamagata approach, and finds evidence against homogeneity “in all model settings.” Translation: do not pretend these economies share one single Okun coefficient by divine decree.

Only then do we walk into the unit-root room, first with standard tests (the familiar cast: Andrew Levin–Chien-Fu Lin–Chia-Shang James Chu; Kyung So Im–M. Hashem Pesaran–Yongcheol Shin), and then with “second-generation” tests designed for cross-sectional dependence, especially Pesaran’s CIPS.

The economics of this step is simple: if GDP and unemployment drift over time (are non-stationary in levels), regressions in levels can be misleading unless a true long-run relationship ties them together. If the gap measures (output gap, unemployment gap) are stationary, they behave more like cyclical deviations that mean-revert, exactly what a “gap” concept is supposed to do.

The report’s reading of the evidence is that cross-sectional dependence pushes us toward the second-generation tests, and that the results support treating level variables with caution while recognising that gap-based variables often behave more “cycle-like.” The point is not to fetishise a p-value; it is to decide what kind of modelling is legitimate next.

A further complication is structural change. This region has not enjoyed the luxury of stable regimes and gentle trends. The report therefore also considers unit-root testing with structural breaks, citing Yiannis Karavias and Elias Tzavalis, precisely because ignoring breaks can make a series look more “unit-root-ish” than it truly is. Again, this is not statistical ornamentation: it is a recognition that “trend plus shocks plus reforms” is a common macro cocktail in post-socialist data.

3. Do they share a long-run relationship? Panel cointegration results

Unit roots are only the first gate. The next question is more interesting: even if output and unemployment drift, do they drift together? That is what panel cointegration tests ask.

The report applies three families of tests, Peter Pedroni, Chihwa Kao, and Joakim Westerlund, to both Okun specifications, with and without deterministic trends. The reason for the trio is not indecision; it is triangulation. The tests differ in assumptions and power, especially in small samples and heterogeneous panels, so convergence of evidence matters.

3.1 Pedroni: the fork in the road between “levels” and “gaps”

The Pedroni results provide a clear narrative contrast. For the first-difference/levels-style relationship between LGDP and the unemployment rate, the results are “broadly inconclusive or reject cointegration,” particularly without trend; only one statistic under a trend specification hints at cointegration, and that hint is not supported by the rest.

For the gap specification, output gap with unemployment gap, the Pedroni statistics “strongly reject the null of no cointegration” across most deterministic assumptions and regardless of variable ordering. The report’s conclusion is unambiguous: the gap model shows strong evidence of cointegration.

That difference matters economically. If the gap variables are cointegrated, then deviations from the long-run relationship are mean-reverting: slack is not just a poetic metaphor, it behaves like something that gets corrected. The report spells this out: disequilibria in the gap model are “mean-reverting,” consistent with the structural validity of Okun’s gap form.

3.2 What cointegration buys you

Cointegration is not merely permission to run regressions in levels. It changes what you can claim. It makes error-correction logic coherent: short-run shocks push the system away from equilibrium, and adjustment mechanisms pull it back. In practice, it also disciplines interpretation: if a relationship is not cointegrated, then long-run coefficients are, at best, fragile stories told with too much confidence.

The report leans into that discipline when it says the modelling strategy should “rely on error correction models (ECM) or asymmetric NARDL models applied to the gap specification,” while the first-difference model “lacks cointegration support,” meaning an ECM framing is not appropriate there. In other words, the data are nudging the researcher toward a particular specification, not because it is fashionable, but because it is statistically coherent.

4. Estimating Okun in a panel: What the coefficients imply

Once cointegration is on the table, especially for gaps, the next step is to estimate the long-run relationship in a way that respects non-stationarity, potential endogeneity, and heterogeneity. The report uses FMOLS, DOLS, and MG estimators, and it does so symmetrically in both directions (output → unemployment and unemployment → output), under constant-only and constant-plus-trend specifications.

This is where the analysis starts producing numbers with economic bite.

4.1 Levels: unemployment is expensive; growth is helpful but modest

Across FMOLS, DOLS and MG, the report finds “a negative long-run relationship between GDP and unemployment,” consistent with Okun’s Law.

In the direction UR → LGDP, the constant-only specifications imply that a one-percentage-point increase in unemployment is associated with a reduction in log GDP on the order of about 2.5 to 3.5 percentage points. The report calls this “substantial” and emphasises its economic meaning: unemployment is not just a social statistic; it maps to real output losses.

But then comes the twist economists know too well: add a linear trend, and the relationship weakens dramatically, sometimes losing significance, sometimes even flipping sign (in one software implementation). The report treats this as a warning label: deterministic trends can absorb co-movement and reveal how sensitive long-run elasticities are to specification choices.

In the reverse direction LGDP → UR (still in long-run terms), the coefficients are negative and significant in constant-only models, implying that a 1% increase in real GDP reduces unemployment by about 0.13 to 0.16 percentage points in the long run, “modest but meaningful,” and described as within typical magnitudes in the broader literature (without needing to turn this into a literature review).

The asymmetric feel between directions is important for interpretation. Output growth helps unemployment; but unemployment also carries a large output penalty. That is not contradictory. It simply reminds the reader that macro relationships are not symmetric mirrors: the path from slack to output can look different from the path from output to slack.

4.2 Gaps: slack matters, but the map is more delicate

When the report shifts from levels to gaps, it keeps the Okun logic but finds smaller magnitudes and greater sensitivity to modelling choices. In the direction unemployment gap → output gap, the constant-only results imply that a one-point widening in the unemployment gap is associated with an output gap decline of roughly two points, interpreted as meaningful slack translating into lost output potential.

In the reverse direction output gap → unemployment gap, the implied effect is smaller: a one-point improvement in the output gap narrows the unemployment gap by around 0.08 to 0.36 points depending on estimator and specification, still broadly consistent with Okun’s Law, but more volatile across methods.

The report also notes a tension in PMG/ARDL estimates for one gap direction (unemployment gap → output gap): the long-run relationship is negative but statistically insignificant in both constant and trend models in that specific setup, underscoring that “gap” does not automatically mean “easy.”

4.3 The big caveat: Trends are not innocent

As shown in Table 1 across the long-run estimators, a repeated theme emerges: including trends often “dramatically” attenuates coefficients or makes them insignificant, suggesting either over-specification or structural change that weakens stable long-run co-movement. The report therefore argues that constant-only FMOLS and MG results should be treated as more reliable in this small panel setting, especially given heterogeneity and sample limitations.

That is not a claim that trends are “wrong.” It is a claim that, in these data, trends are powerful enough to change the story, and therefore the story must be told with humility.

Table 1: Summary of panel regression models for former Yugoslav republics (Long-run coefficients)

Estimation method	First difference model				Gap model
	1	2	3	4	5	6	7	8
FMOLS (Stata)	-2.95	-0.64	-0.18	-0.03	-2.31	-2.12	-0.07	-0.1
	(<.01)	-0.05	(<.01)	(>.05)	(<.01)	(<.01)	(<.01)	(<.01)
FMOLS (EViews)	-3.54	0.28	-0.13	0.35	-2.07	-1.95	-0.13	0.07
	(<.01)	-0.44	(<.01)	-0.05	(<.01)	(<.01)	(<.01)	-0.07
DOLS (Stata)	-2.53	-0.58	-0.23	-0.01	-1.47	-1.6	-0.29	-0.36
	(<.01)	(<.01)	(<.01)	(<.01)	<.01)	(<.01)	(<.01)	(<.01)
DOLS (EViews)	-2.66	-0.02	-0.15	-0.03	-0.87	-1.02	-0.09	-0.08
	(<.01)	-0.93	(<.01)	-0.72	-0.17	-0.08	(<.01)	(<.01)
MG (Stata)	-2.9	-0.57	-0.14	0.04	-2	-2.02	-0.08	-0.09
	(<.01)	-0.19	(<.01)	-0.77	-0.01	(<.01)	(<.01)	(<.01)
PMG/ARDL (EViews)	-3.22	0.39	-0.15	0.04	-0.41	-0.47	-0.12	-0.08
	(<.01)	-0.24	(<.01)	-0.5	-0.19	-0.34	(<.01)	(<.01)

Note: (1): LGDP = f(UR) with constant; (2) LGDP = f(UR) with trend; (3) UR = f(LGDP) with constant; (4) UR = f(LGDP) with trend; (5) Output gap = f(Unemployment gap) with constant; (6) Output gap = f(Unemployment gap) with trend; (7) Unemployment gap = f(Output gap) with constant; (8) Unemployment gap = f(Output gap) with trend. FMOLS and DOLS specification: panel method – pooled estimation; cointegrating equation deterministic: constant only (trend specification: constant (level)), Long-run covariance estimates: prewhitening with lags from SIC, Bartlett kernel, Newey-West automatic bandwidth, NW automatic lag length. For long-run variance Bartlett kernel with Newey-West automatic bandwidth was used. Automatic leads and lags specification was based on SIC criterion. P-value in parenthesis.

5. Short-run dynamics and adjustment: What moves, what returns, what bites

Long-run coefficients tell you where the system wants to be. Short-run dynamics tell you how messy the journey is.

Here the report’s PMG/ARDL estimates become useful because they combine long-run relationships with short-run adjustment and an error-correction term. The headline is reassuring: “error-correction terms are negative and significant,” validating cointegration and implying convergence back to equilibrium after shocks.

In plainer English, the system does not wander forever. When output and unemployment deviate from their longer-run relationship, particularly in the preferred gap frameworks, the dynamics include a pull back toward balance. That is exactly what makes Okun’s Law valuable for policy narratives: it is not only about correlation, but about adjustment.

The report also notes that short-run changes in unemployment or output gaps generally show expected signs and significance in these models, evidence that the Okun channel is not only a long-run abstraction, but also a meaningful short-run mechanism, at least in parts of the specification space the diagnostics allow.

There is also a nod to asymmetry. The report’s synthesis later emphasises that some nonlinear models find short-run asymmetry, expansions and contractions do not have identical labour-market effects, while not finding strong evidence of long-run asymmetry. This matters because it suggests that “recoveries” and “recessions” may operate through different labour-market plumbing in the short run, even if the longer-run relationship remains broadly Okun-like.

The key interpretive lesson: the long-run Okun anchor may exist (especially in gaps), but the short run can still be lopsided, an economy can shed jobs quickly and regain them slowly, or vice versa, without violating the existence of a long-run relationship.

6. Causality results: Who leads whom, and what that suggests

Finally we arrive at the question that readers tend to ask first, and economists insist on asking last: does growth “cause” unemployment to fall, or does unemployment “cause” growth to disappoint?

The report answers this using two panel Granger non-causality tests: the Elena-Ivona Dumitrescu–Christophe Hurlin test and the Arvid Juodis–Yiannis Karavias–Vasilis Sarafidis approach with Half-Panel Jackknife correction, explicitly motivated by the panel’s short time dimension (T ≈ 26) and small N.

6.1 Levels: GDP predicts unemployment; feedback depends on the test

In levels, the Dumitrescu–Hurlin results suggest no causality from unemployment to GDP, but strong evidence that GDP Granger-causes unemployment, supporting a unidirectional story: output movements help predict unemployment changes.

But the Juodis–Karavias–Sarafidis test, with bias correction, finds bidirectional causality in levels at the 1% level. The report interprets this as evidence of “a more complex feedback process,” in which unemployment can also inform future output changes, perhaps reflecting endogenous labour-market adjustment and expectations effects in these economies.

Economically, the safe reading is not “we have discovered deep causation.” The safe reading is: output is consistently useful for predicting unemployment, and depending on the test (and its small-sample corrections), unemployment may also carry predictive content for output. That is entirely compatible with the earlier results: long-run linkages exist (especially in gaps), and dynamics can run both ways.

6.2 Gaps: A stronger cyclical signal, but not perfectly symmetric

As shown in Table 2 in the gap specifications, the Dumitrescu–Hurlin test supports bidirectional causality: the output gap Granger-causes the unemployment gap, and the unemployment gap also Granger-causes the output gap, though the former is “substantially higher” in strength.

That asymmetry is intuitive even without invoking extra theory: cyclical output shortfalls show up in labour-market slack, but labour-market slack can also signal and propagate cyclical weakness.

Table 2: Dumitrescu and Hurlin Granger panel causality test

	Test statistic (p-value)
Null hypothesis	W¯	Z¯	Z˜	Causality
UR does not Granger-cause LGDP	0.67	-0.58 (.56)	-0.63 (.53)	No
LGDP does not Granger-cause UR	4.34	5.79 (<.01)	4.77 (<.01)	Yes
DUR does not Granger-cause DLGDP	1.41	0.72 (.47)	0.46 (.65)	No
DLGDP does not Granger-cause DUR	1.33	0.57 (.57)	0.33 (.74)	No
Unemployment gap does not Granger-cause Output gap	2.66	2.87 (<.01)	2.29 (.02)	Yes
Output gap does not Granger-cause Unemployment gap	7.51	11.27 (<.01)	9.42 (<.01)	Yes
DUnemployment gap does not Granger-cause DOutput gap	1.8	1.39 (.16)	1.03 (.31)	No
DOutput gap does not Granger-cause DUnemployment gap	4.15	5.46 (<.01)	4.45 (<.01)	Yes

7. Bridge: What Part III will do next

By the end of Part II, the report has done something valuable and unfashionable: it has earned the right to interpret.

The tests do not deliver a single, universal Okun coefficient carved into stone. They deliver a structured set of claims: cross-country interdependence is real; heterogeneity is non-trivial; cointegration is far stronger in the gap specification than in the levels/first-difference framing; long-run coefficients are economically meaningful but sensitive to deterministic trends; adjustment mechanisms exist in dynamic models; and predictive direction generally runs from output to unemployment, with some evidence of feedback depending on the causality test and small-sample correction. Part III will take these blocks of evidence and do what readers actually care about: integrate them into a coherent regional interpretation and a cautious policy narrative, without pretending that “EU-stage context” can substitute for econometric evidence, but also without pretending that econometric evidence lives in a vacuum.