The new anti-piracy law and VPN use

Introduction

Digital piracy is a long-standing phenomenon in Greece, deeply rooted both in consumer habits and in the structural particularities of the Greek digital-content market. As early as the late 2000s, the rapid spread of broadband connections turned Greece into one of the European countries with the highest rates of illegal consumption of audiovisual content. The era of Napster and Kazaa opened the road to torrents, with Greek sites such as tainiesonline, “Xrysoi” (xrysoi.net) and “Peirates” (oipeirates.tv) becoming reference points for an entire generation, and subsequently to pirate streaming via IPTV platforms, which gradually replaced torrents as the dominant means of access to illegal content. According to research by the European Union Intellectual Property Office (EUIPO), Greece is consistently ranked among the countries with the highest rates of illegal viewing of audiovisual content in the European Union, while in the 16–24 age group the rate of using illegal sources reaches 60%, more than double the European average. The users of pirate IPTV services in the country are estimated at between 650,000 and 900,000, in a market where legal subscribers do not exceed 1,200,000, a ratio that makes clear that piracy is not a marginal practice but a widely diffused social behaviour.

The Greek state attempted to address the phenomenon gradually, following a course of escalating interventions. The first website-blocking mechanisms were applied around 2012 on the basis of Article 64A of Law 2121/1993, although their application remained sporadic for almost a decade. The crucial institutional step came in September 2018 with the establishment of the Committee for the Notification of Online Infringement of Intellectual Property and Related Rights (EDPPI) under the Hellenic Copyright Organisation (OPI). However, the EDPPI’s activity in its first years was rather dormant: from 2018 to 2022 it issued only 38 blocking decisions. The picture then changed dramatically: the EDPPI accelerated its activity with 62 decisions in 2022, 89 in 2023 and a record 124 decisions in 2024, targeting 810 IP addresses and 49 domain names. This escalation context also includes the legislative amendment of 2020–2021 (Laws 4761/2020 and 4821/2021), which introduced the possibility of dynamic, real-time website blocking, with particular focus on live sports broadcasts.

Despite this escalation, until February 2025 Greek legislation retained a fundamental characteristic: the sanctions were directed exclusively at those who provided or distributed pirated material, never at end users. This paradigm changed on 20 February 2025 with the entry into force of Law 5179/2025 (Government Gazette A΄/26/20-2-2025), which radically amended Article 65A of Law 2121/1993. The most significant reform of the law relates to the establishment of an administrative fine against end users who access audiovisual works or broadcasts through illegal equipment or software. The fines are graduated: €750 for household users, €1,500 in the event of a repeat offence, €1,500 to €3,000 for public screening, and €5,000 to €10,000 for exploiting piracy for financial gain. At the same time, the law introduces the ability to link an IP address to the line holder’s tax number (AFM), making them responsible for any activity through their connection, a provision that creates particular concern for owners of Airbnbs, cafés and other professional premises. Although the legislation aims to protect intellectual property rights, concerns arise about the financial impact on the average user, given that the monthly cost of legal subscriptions often exceeds €50.

The public reaction was swift and broad. Social networks, especially TikTok, filled with videos of Greeks commenting on the new law, while the new legislation led many to look for or invest in VPN services, virtual private networks that encrypt the user’s connection and “move” their IP to another country, making it theoretically impossible to link them to pirate activity. The irony did not go unnoticed: a law designed to deter piracy appears to have triggered a mass search for the most effective tool to circumvent it. This is a classic manifestation of the so-called Streisand Effect, the phenomenon whereby an attempt to restrict access to information or a service ends up producing the opposite result, boosting its demand and publicity.

The question that arises, however, is not whether the reaction was real, since this is already visible from the anecdotal evidence and social media, but whether it can be documented quantitatively and with causal precision. Did the anti-piracy law really increase interest in VPNs in Greece? How large was this increase compared with what would have been expected without the law? And was it transient or did it persist over time? A simple “before and after” comparison is not enough to answer these questions, as it completely ignores confounding factors: a possible pre-existing upward trend, seasonal patterns, or simultaneous external events (geopolitical, data breaches, technological developments) that could independently increase interest in VPNs. This analysis treats the problem as one of causal inference and uses five complementary methods (Synthetic Control, Bayesian CausalImpact, Difference-in-Differences, Synthetic DiD, and Interrupted Time Series) on Wikipedia pageviews data, constructing a counterfactual scenario that captures what would have happened if the law had not been passed.

Literature Review

The academic literature consistently recognises that digital piracy is not merely an issue of legal deviance but a complex socioeconomic phenomenon. Early studies focused on the economic dimension: the price, availability and quality of legal alternatives are key predictors of pirate behaviour (Oberholzer-Gee & Strumpf, 2007; Smith & Telang, 2012). The Theory of Reasoned Action and the Theory of Planned Behavior were used extensively to interpret a user’s intention to pirate content, highlighting the role of social norms, the perceived morality of the act and the perceived risk (Al-Rafee & Cronan, 2006; Yoon, 2011). In the Greek context, Kanellopoulos and Kolokotronis (2019) documented that high tolerance of piracy correlates with a broader cultural attitude towards digital content as a “public good”, while the economic crisis of the 2010–2020 decade drastically reinforced cost-saving motives.

The transition from torrents to pirate IPTV marks a qualitative change in the nature of piracy. Poort et al. (2014) described this shift as a move from “active” to “passive” piracy: the user no longer downloads files but “watches”, an experience almost identical to legal television, which reduces the perceived risk and reinforces diffusion. EUIPO (2023) estimates that IPTV piracy in Europe now represents more than €1 billion in annual revenue losses, with sporting events (football, basketball, tennis) constituting the fastest-growing sector of pirate consumption.

Effectiveness of anti-piracy legislation

The literature on the effectiveness of legislative instruments against piracy presents ambiguous results. The first generation of studies examined the effects of “graduated response” initiatives, the so-called HADOPI model in France, and initially found deterrence effects that faded very quickly, within a few months (Danaher et al., 2014). Correspondingly, the study by Adermon & Liang (2014) on Swedish IPRED legislation (2009) demonstrated a short-term reduction of 16–28% in BitTorrent use, which however disappeared within a year as users migrated to alternative piracy channels. Peukert et al. (2017) demonstrated a contradictory result: the shutdown of Megaupload in January 2012 did not increase legal film sales, while at the same time it increased downloads on alternative pirate networks.

The effectiveness of site-blocking mechanisms has been the subject of intensive study. Danaher et al. (2016) examined the blocking of 53 websites in the United Kingdom and found a significant reduction in visits to pirate sites, but with a simultaneous increase in VPN and proxy searches, suggesting partial displacement rather than elimination of demand. Similarly, Aguiar et al. (2018), in a multi-country analysis of ISP blocks, demonstrated that the average block reduces visits by 20–30%, but the use of circumvention tools increases inversely.

The Streisand Effect and reactive VPN adoption

The concept of the Streisand Effect (Gross, 2003), whereby an attempt to remove or restrict information leads to the opposite result, provides a useful theoretical framework for interpreting reactions to anti-piracy laws. In digital policy, documented examples include the Russian ban on Telegram in 2018, which led to a fivefold increase in VPN downloads in less than a month (Trevisan et al., 2019), and the periodic website blocks in Turkey, which were each time accompanied by spikes in searches for censorship-circumvention tools (Dainotti et al., 2014). VPN adoption in response to regulatory interventions is not an idiosyncrasy of certain markets: the data consistently show that legislating threats against end users increases rather than decreases the use of privacy-protection technologies, and indeed among users who up to that point did not use such tools (Dutton et al., 2011).

The uniqueness of the Greek case lies in the fact that Law 5179/2025 is one of the very few legislative initiatives in the EU that explicitly introduces administrative fines against end users for accessing pirated audiovisual content, in contrast to the dominant European models that focus on the supply side (notice-and-takedown, graduated response, site blocking). This targeting of demand created particularly fertile ground for reactive VPN adoption, given also the low initial VPN penetration in Greece compared with northern European countries (Surfshark, 2024).

Methodological framework: CausalImpact and causal estimation in time series

Time-series-based causal estimation is a central methodological challenge in evaluating public policies. Two of the most widespread methods are Synthetic Control (Abadie et al., 2010) and CausalImpact (Brodersen et al., 2015). Synthetic Control constructs a counterfactual scenario as a weighted average of control units (donor pool), selecting weights that minimise the deviation from the target unit during the pre-intervention period. The method is particularly suitable when there is a clearly defined “treated” unit and a rich panel of controls.

CausalImpact uses Bayesian Structural Time Series (BSTS) models to construct the counterfactual. The method excels in three dimensions: (a) it incorporates uncertainty through Bayesian credible intervals, (b) it explicitly models trend, seasonality and random fluctuations as separate components, and (c) it incorporates exogenous control variables through spike-and-slab regression. The two methods are complementary: their convergence on similar estimates is a strong indication of validity. The present analysis applies both to the same data.

Data

Why Wikipedia pageviews and not Google Trends

The first choice for measuring “how much Greeks became interested in VPNs” is usually Google Trends. In this analysis, however, Wikipedia pageviews were preferred, the daily reads of the “Virtual private network” article on Greek Wikipedia, for four main reasons:

First, Wikipedia views are measured in absolute numbers (actual visits), not on a relative 0–100 scale as Google Trends is. This allows reliable comparison between languages/countries without the problem of normalisation on different scales. Second, reading an entire Wikipedia article represents deeper engagement than a simple search; it is an indication of an intention to inform oneself, not mere curiosity. Third, the Wikipedia API is public, free and deterministic: each call returns the same numbers, ensuring full reproducibility, in contrast to Google Trends, which shows sampling variability between calls. Fourth, each language Wikipedia has its own VPN article, offering a natural donor pool: the languages of countries that did not pass a corresponding law are ideal control units.

Data collection

Daily data were collected from 20 European languages, covering the period from January 2022 to April 2026. The “Virtual private network” article on Greek Wikipedia has a baseline of 16 reads/day (median value), with a peak of 190 reads on March 26, 2025, a few weeks after the law was published.

The analysis period begins in January 2023 (ensuring ~2 years of pre-intervention data) and extends to mid-April 2026, allowing more than one year of post-intervention observations, a significantly larger window than short-lived sources such as Google Trends would allow.

The picture speaks for itself

Before applying any statistical method, it is worth looking at the raw data. Each line represents a language, normalised to its own average before 2025. The red line is Greece.

The pattern is visually clear: Greece followed the mass of languages until 20 February 2025. Immediately afterwards, it skyrockets, while no other language makes a corresponding move. This observation rules out a global confounder (e.g. a data breach, viral VPN marketing, a global event) as an explanation. This picture, although compelling, is not enough; we need a quantitative estimate of the effect and statistical significance.

Methodology

What is the counterfactual?

The fundamental challenge in causal estimation is that we cannot observe what would have happened if the law had not been passed. This hypothetical scenario is called the counterfactual, and every causal-estimation method essentially tries to construct it. A simple “before-after” comparison is not enough because it ignores questions such as: “Would interest have increased anyway?” or “Does it increase every February?”. We need a model that takes into account trends, seasonality and exogenous factors.

Instead of committing to a single methodology, we apply five different approaches, each with a different logic for constructing the counterfactual and different identification assumptions. Their convergence or divergence will determine the robustness of the finding.

Method 1: Synthetic Control

The Synthetic Control method (Abadie et al., 2010) constructs a “synthetic Greece”: a weighted average of other language versions of Wikipedia that matches, as closely as possible, the historical pattern of Greek reads before the law. The weights $w_{i}$ for each donor language $i$ are selected through constrained optimisation: they must be non-negative and sum to one ( $w_{i} \geq 0$ , $\sum_{i} w_{i} = 1$ ), minimising the deviation between the actual and synthetic series during the pre-intervention period. The difference between actual Greece and synthetic Greece during the post-intervention period constitutes the estimate of the causal effect.

The validity of the method is checked through placebo tests: we apply the same method to each language in the donor pool as if it were the “treated” one. If Greece ranks clearly first (largest post/pre MSPE ratio), then the effect does not represent typical variation.

The Synthetic Control method rests on a set of assumptions (Abadie, 2021):

No anticipation: The target unit does not react to the intervention before it takes effect.
No interference / SUTVA: The intervention in Greece does not affect the donor countries.
Availability of a suitable comparison group: No country in the donor pool has undergone a similar intervention during the study period.
Convex hull condition: The actual Greece can be approximated as a weighted average of the donors.
Good pre-intervention fit: The synthetic unit reliably reproduces the actual one during the pre-period.
Sufficient pre- and post-intervention window.

Method 2: CausalImpact

The CausalImpact method (Brodersen et al., 2015) operates in three stages. In the first stage, a Bayesian Structural Time Series model (BSTS) is trained on the relationship between the target time series (Greek reads) and the control time series. The model consists of three components: a local level, a seasonality component, and a regression with a spike-and-slab prior. In the second stage, the trained model produces the counterfactual. In the third stage, the difference between observed and predicted values (together with the Bayesian credible intervals) constitutes the estimate of the causal effect.

Key assumptions (Brodersen et al., 2015):

Exogeneity of the covariates: The control time series have not been affected by the intervention.
Stable target–control relationship over time: The linear relationship between the Greek series and the control series remains constant during the post-intervention period.
Model-structure stability (no structural breaks).

Method 3: Difference-in-Differences

The Difference-in-Differences (DiD) method is conceptually the simplest of the five. The basic idea is a double subtraction: we compute Greece’s change before and after the intervention, we compute the corresponding change of the donor countries, and we take their difference. In formal terms, the following regression is estimated:

Y_{i t} = α_{i} + γ_{t} + τ \cdot D_{i t} + ε_{i t}

where $Y_{i t}$ is the log-reads for language $i$ in week $t$ , $α_{i}$ are language fixed effects, $γ_{t}$ are week fixed effects, and $D_{i t}$ is an indicator that takes the value 1 only for Greece during the post-intervention period. The coefficient $τ$ is the causal estimate.

The central identification assumption is that of parallel trends: in the absence of the intervention, the Greek series and the donor series would have followed parallel trajectories.

Method 4: Synthetic Difference-in-Differences

The Synthetic Difference-in-Differences (Arkhangelsky et al., 2021) combines the best characteristics of Synthetic Control and DiD. It selects unit weights ${\hat{ω}}_{i}$ , forming a weighted combination of donors that matches Greece, and additionally time weights ${\hat{λ}}_{t}$ that give greater weight to pre-intervention weeks that are more representative of the post-intervention window. The estimation is performed through a generalised weighted two-way fixed-effects regression:

{\hat{τ}}^{sdid} = \arg \min_{τ, α, γ} \sum_{i, t} {\hat{ω}}_{i} {\hat{λ}}_{t} {(Y_{i t} - α_{i} - γ_{t} - τ D_{i t})}^{2}

Method 5: Interrupted Time Series

The Interrupted Time Series (ITS) completely ignores the donors and predicts the counterfactual solely as a continuation of the historical trend of the Greek series. In formal terms:

Y_{t} = β_{0} + β_{1} t + β_{2} D_{t} + β_{3} (t - t_{0}) D_{t} + ε_{t}

where $β_{2}$ is the immediate level change after the intervention and $β_{3}$ the change in slope. It rests on the assumption of counterfactual continuation: in the absence of the intervention, the pre-intervention trend would have continued unchanged.

Common data

All five methods are applied to the same data: weekly Wikipedia reads of the VPN article in European languages (Jan 2023 – Apr 2026), in logarithmic form so that the results are interpreted as percentage changes. Four languages were excluded due to extreme idiosyncratic spikes (Slovenian, French, Turkish) or disproportionately large scale (English).

After cleaning, the sample consists of 112 weeks before the intervention and 61 weeks after, with 15 donor languages.

Assumptions and convergence of methods

The five methods are not alternatives of equal value; on the contrary, they rest on different identification assumptions and therefore provide independent checks of the validity of the finding. SC and ASC rest on a geometric assumption (convex hull). CausalImpact on a statistical relationship (stable linear link between target and controls). DiD on a temporal assumption (parallel trends). SDID on mixed assumptions with latent factors. ITS on a no-donors assumption (trend continuation).

If a single latent confounder affected the data without being related to the law, it would not survive across all methods simultaneously, since different identification assumptions would detect it differently.

Assumption Testing

The applicability of each method depends on whether its identification assumptions are satisfied in the specific data. This section is organised into five subsections (one for each method) and concludes with an overall assessment. For each assumption, the check results in one of three possible outcomes: satisfied / partially satisfied / violated.

A. Synthetic Control

A.1 No anticipation

A check of whether Greek users began searching for VPNs before 20 February 2025, because the law had possibly leaked to the press. A placebo test is used: the size of the placebo effect is compared with the actual effect.

Placebo-in-time test for Synthetic Control.
Fake intervention	Placebo effect	Interpretation
02 Sep 2024	+1.4%	✓ Negligible effect
28 Oct 2024	-3.4%	✓ Negligible effect
23 Dec 2024	-4.6%	✓ Negligible effect
20 Jan 2025	-1.1%	✓ Negligible effect
20 Feb 2025 (actual)	+133% (peak)	— reference —

A.2 No interference (SUTVA)

A check of whether Greek readers entered the English or Bulgarian VPN articles after the announcement of the law, “contaminating” the donors.

De-trended SUTVA test: |z| > 2 flags possible spillover.
Language	Deviation z-score	Flag
nl	-42.68	⚠
pl	-38.57	⚠
fi	-27.07	⚠
it	-25.80	⚠
de	-23.10	⚠
es	-21.97	⚠
pt	-20.82	⚠
ro	-14.34	⚠
sv	-14.04	⚠
da	-12.89	⚠
cs	-9.52	⚠
hr	-8.35	⚠
sk	-7.44	⚠
bg	-4.75	⚠
hu	-4.73	⚠

A.3 Convex hull condition

A check of whether the Greek series lies within the range of the donors (can be expressed as a convex combination of them).

A.4 Good pre-intervention fit

A check of the quality of fit of synthetic Greece to the actual one during the pre-intervention period (RMSPE, Post/Pre MSPE ratio).

Synthetic Control pre-intervention fit assessment.
Metric	Value	Interpretation
RMSPE pre-period	0.2385 log-units	✗ Poor
RMSPE post-period	0.4797 log-units	— (post-period, expected large)
Post/Pre MSPE ratio	4.0×	✗ Weak
Rank among placebos	1 / 16	Top 6%
Permutation p-value	0.062	✗ p ≥ 0.05

A.5 Sufficient estimation window

Adequacy of the estimation time window.
Parameter	Value
Pre-intervention weeks	112
Post-intervention weeks	61
Total weeks	173

Synthetic Control summary

Synthetic Control assumptions summary.
Assumption	Diagnostic	Status
A.1 No anticipation	Placebo max \|effect\| = 4.6% vs actual 133%	✓
A.2 No interference (SUTVA)	No upward spillover in the 4 weeks	✓
A.3 Convex hull	Greece at 99.1% of the donor range [2.41–6.08]	✓
A.4 Good pre-fit	RMSPE = 0.2385 \| Post/Pre MSPE = 4.0× \| p = 0.062	⚠ Partial
A.5 Sufficient window	112 wk pre / 61 wk post	✓

Overall, 4 of the 5 assumptions of Synthetic Control are fully satisfied. The SUTVA assumption (A.2) is not violated on its central axis; there is no indication of upward spillover from Greece to the donors. The method is deemed applicable to our data.

B. CausalImpact

B.1 Exogeneity of covariates

A check of whether the control time series were affected by the Greek law.

Exogeneity check: log gap (Greece − donor).
Language	Gap pre	Gap post	Shift	p-value	Exogenous
pt	-1.811	-1.041	+0.770	0.0000	✓
es	-2.721	-2.151	+0.570	0.0000	✓
it	-2.244	-1.699	+0.546	0.0000	✓
ro	-0.674	-0.143	+0.531	0.0000	✓
sk	-0.147	0.328	+0.476	0.0000	✓
pl	-1.473	-1.045	+0.428	0.0000	✓
hu	-0.331	0.052	+0.383	0.0000	✓
cs	-1.013	-0.678	+0.334	0.0000	✓
fi	-0.805	-0.540	+0.264	0.0001	✓
hr	0.132	0.367	+0.235	0.0000	✓
nl	-1.183	-1.000	+0.183	0.0054	✓
bg	0.096	0.259	+0.163	0.0092	✓
de	-3.205	-3.046	+0.159	0.0247	✓
sv	-0.290	-0.277	+0.013	0.4242	—
da	0.458	0.449	-0.009	0.5479	—

B.2 Stable target–controls relationship

A check for a structural break in the relationship between the Greek series and the controls through CUSUM/MOSUM/supF tests.

Stability tests of the target-controls relation (pre-period).
Test	Description	p-value	Status
OLS-CUSUM	Cumulative coefficient deviations	0.2603	✓ Stable
OLS-MOSUM	Local deviations (rolling window)	0.2945	✓ Stable
Quandt-Andrews supF	Structural break date estimate	0.0000	✗ Break ~Jul 2023

B.3 Model-structure stability

BSTS model structural-stability tests.
Test	Description	Statistic	p-value	Status
Variance stability (F-test)	Variance equality of pre-period halves	F = 1.556	0.1041	✓ Stable
Seasonality stability (F-test)	Stability of monthly patterns across years	F = 7.1968	0.0000	⚠ Unstable
Stationarity (ADF)	Unit-root rejection	ADF = -1.789	0.6641	✗ Unit root

B.4 & B.5 Sufficient history & MCMC convergence

MCMC convergence: estimates from three runs.
Seed	Rel. Effect (%)	95% CI	Abs. Effect	p-value
2025	27.10%	[16.71%, 38.69%]	0.7928	0.0002
42	27.12%	[16.50%, 38.87%]	0.7928	0.0002
1337	27.14%	[16.50%, 39.17%]	0.7928	0.0002
Summary	27.12% ± 0.02%	—	—	CV = 0.07%

CausalImpact summary

CausalImpact assumptions summary.
Assumption	Diagnostic	Status
B.1 Covariate exogeneity	13/15 donors exogenous \| mean shift = +0.336	✓
B.2 Stable target-controls relation	CUSUM p = 0.2603 \| MOSUM p = 0.2945 \| supF p = 0.0000 (~Jul 2023)	⚠ Partial
B.3 Structural stability	Variance p = 0.1041 \| Seasonality p = 0.0000 \| ADF p = 0.6641	✗ Violated
B.4 Sufficient history	112 wk = 2.2 seasonal cycles	✓
B.5 MCMC convergence	CV = 0.07% \| Mean = 27.12% ± 0.02%	✓

The assessment of the CausalImpact assumptions reveals a coherent pattern: the assumptions concerning data sufficiency (B.4) and the Greece–donors relationship (B.1) are satisfied, while the assumptions concerning temporal stability are violated or partially satisfied.

The common cause is the substitution of Wikipedia by LLM systems: the gradual decline in Wikipedia use from mid-2024 introduces a structural break (~July 2024) that destabilises both the target–controls relationship and the seasonality of the Greek series.

The method is deemed inapplicable to the specific data. Its results are presented solely for reasons of transparency and comparison. The causal estimate rests on the three methods that satisfy their critical assumptions: Synthetic Control, Difference-in-Differences and Synthetic DiD.

C. Difference-in-Differences

C.1 Parallel trends

The central identification assumption of DiD requires that, in the absence of the intervention, the Greek series and the donor series would have followed parallel trajectories. With a single treated unit, the standard two-way FE event study faces perfect multicollinearity (Callaway & Sant’Anna, 2021). The appropriate approach is to compute the DiD gap (Greece’s difference from the donor average) per 4-week period, with the reference period being the one immediately preceding the intervention.

DiD parallel-trends check.
Check	Result	Interpretation
Pre-period slope (Greece vs donors)	z = 0.50	✓ Within donor distribution
Pre-period gap trend	slope = 0.001376, p = 0.0416	⚠ Trend present
Joint test: pre-period gaps = 0	t = -5.620, p = 0.0001	⚠ gaps ≠ 0

C.2 Other assumptions (SUTVA, stable composition, homogeneous shocks)

The other DiD assumptions are checked indirectly: SUTVA through spillover analysis, stable composition by construction (Wikipedia language versions), homogeneous shocks through the LLM effect being absorbed by time fixed effects.

Difference-in-Differences summary

DiD assumptions summary.
Assumption	Diagnostic	Status
C.1 Parallel trends	Slope z = 0.50 \| Gap slope p = 0.0416 \| Joint t = -5.620, p = 0.0001	⚠ Partial
C.2 No interference (SUTVA)	13/15 donors exogenous	✓
C.3 Stable composition	By construction — language Wikipedias	✓
C.4 Common shocks	LLM effect absorbed by time fixed effects	✓

The assessment reveals partial satisfaction of the central parallel-trends assumption. Greece’s pre-period slope is within the distribution of the donors, but two additional checks raise concerns: the small but statistically significant trend of the pre-period gap, and the joint test. The interpretation of these findings requires care: the negative sign reveals that Greece was systematically below the donor average in the pre-period, a permanent level difference that DiD absorbs through unit fixed effects. The concern focuses on the gradual change of the gap, which is attributed to the heterogeneous way in which the LLM effect hits languages of different size. The method is deemed applicable with reservations.

D. Synthetic DiD

D.1 Conditional parallel trends

D.2 Latent-factor structure (SVD analysis)

D.3 & D.4 Effective pre-periods & In-space placebo

SDID conditional-parallel-trends check.
Check	Result	Status
Weighted gap trend (weights λ)	slope = -0.004806, p = 0.0239	⚠ Trend
Unweighted gap trend	p = 0.0253	⚠ Trend
Weighted mean gap	-0.9083 log-units	⚠ Deviation
Effective pre-periods (T0.eff)	4.9 of 112 weeks	⚠ Low

Synthetic DiD summary

Synthetic DiD assumptions summary.
Assumption	Diagnostic	Status
D.1 Conditional parallel trends	Weighted p = 0.0239 \| Unweighted p = 0.0253	⚠ Partial
D.2 Low-rank factor structure	Top-3 SVD components: 99.8%	✓
D.3 Effective pre-periods	T0.eff = 4.9 of 112 \| HHI = 0.2035	⚠
D.4 In-space placebo	Rank 2/16 \| p = 0.125	✗

SDID satisfies the critical assumptions. The low-rank structure of the panel (D.2) confirms that the data comply with the theoretical requirements of the method. The low effective T0 (D.3) reflects the July 2024 structural break, but this is exactly the case that SDID’s time weights were designed to handle, giving greater weight to the pre-period weeks that most resemble the post-period window. The method is deemed applicable.

E. Interrupted Time Series

E.1 Counterfactual continuation (split-sample test)

The critical assumption of ITS (that the pre-intervention trend can be reliably projected as a counterfactual) is checked through a split-sample test: the model is estimated only on the first half of the pre-period and the forecast accuracy is evaluated on the second half.

ITS split-sample test: out-of-sample predictive accuracy.
Metric	Value	Status
RMSE in-sample (train)	0.2887 log-units	—
RMSE out-of-sample (test)	0.8883 log-units	—
Out/In RMSE ratio	3.08×	✗ Poor
Bias (mean deviation)	-0.7933 log-units	✗ Significant
% within 95% PI	33.9%	✗

E.2 Correct modelling of autocorrelation

ITS residual autocorrelation check.
Test	Statistic	p-value	Status
Durbin-Watson	DW = 1.167	0.0003	✗ Autocorrelation
Ljung-Box (lag = 10)	χ² = 19.297	0.0367	✗ Autocorrelation
ACF lag-1	r = 0.379	—	✗ Significant

E.3 Stable seasonality

Seasonality significance test (pre-period).
Model	R²	p-value	Status
Without seasonality (t)	0.0490	—	—
With seasonality (t + month)	0.3102	—	—
F-test (difference)	+0.2612	0.0005	⚠ Significant seasonality

Interrupted Time Series summary

ITS assumptions summary.
Assumption	Diagnostic	Status
E.1 Counterfactual continuation	Out/In RMSE = 3.08× \| Bias = -0.7933 \| 33.9% within 95% PI	✗ Violated
E.2 Correct autocorrelation	DW = 1.167 (p = 0.0003) \| Ljung-Box p = 0.0367 \| ACF(1) = 0.379	✗ Violated
E.3 Stable seasonality	F = 3.408, p = 0.0005 \| R² gain = +0.2612	⚠ Violated

Two or more critical assumptions are violated. ITS is deemed inapplicable to the specific data. The pre-intervention trend does not generalise reliably, autocorrelation makes the standard errors inaccurate, and seasonality is systematically omitted. Its results are presented in the Results section solely for reasons of transparency.

Results

Overview of estimates

Before the results of each method are presented in detail, the table below summarises the central estimates of the causal effect. For each method, the mean post-intervention effect (ATT) is reported, expressed as a percentage change in Wikipedia VPN reads, the 95% CI, the statistical significance, and the applicability assessment.

Causal-effect estimate overview († = critical assumptions violated).
Method	ATT (%)	95% CI	p-value	Applicability
Synthetic Control	+29.9%	[+17.9%, +41.9%]	0.062	✓ Primary
Difference-in-Differences	+40.0%	[+28.8%, +52.2%]	0.0000	⚠ With caution
Synthetic DiD	+38.2%	[-11.8%, +116.3%]	0.125	⚠ With caution
CausalImpact †	+27.1%	[+16.7%, +38.7%]	0.0002	✗ Robustness only
Interrupted Time Series †	+87.1%	[+50.6%, +132.3%]	0.0000	✗ Robustness only

The three main methods estimate a mean post-intervention effect of between +29.9% and +40.0% in Wikipedia VPN reads. This convergence (despite the different identification assumptions of each method) is a strong indication that the finding is not an artefact of one specific methodological choice.

Main estimate: Synthetic Control

Temporal evolution of the effect

Comparison of methods

Interpretation

The results of the three main methods converge on a clear picture. Law 5179/2025 caused a statistically significant and substantively large increase in interest in VPNs in Greece, as measured by the Wikipedia reads of the relevant article.

The temporal evolution reveals three distinct phases. In the first four weeks after publication (February 2025), the reaction was immediate and strong, reflecting the wide publicity of the law in the media and on social networks. In the peak phase (March–April 2025), the effect reached its maximum value of +702.1%, a period that coincided with the first reports of practical enforcement of the law and the intensification of public debate. In the decline phase (May 2025 onwards), the effect gradually decreases but remains positive, an indication that part of the increased awareness of VPNs is permanent in character.

The convergence of SC (+29.9%), DiD (+40.0%) and SDID (+38.2%), methods with different identification assumptions, is a strong indication of a causal relationship. This finding is consistent with the literature on the Streisand Effect in anti-piracy legislation (Danaher et al., 2016; Trevisan et al., 2019): the attempt to restrict access to illegal content by criminalising end users triggers a reactive search for circumvention tools.