Age Verification and Public Adaptation: A Pre-Registered Synthetic Control Multiverse

Abstract

Starting in January 2023, Louisiana and more than 20 other states passed laws requiring age verification for websites with substantial adult content. Using Google Trends data and a synthetic control design, we examine how these laws affect the public’s digital behavior across four dimensions: searches for compliant websites, non-compliant websites, VPNs, and adult content. Three months after the laws were passed, results show a 51% decrease in searches for the main compliant platform, while searches increased for both non-compliant platform (48.1%) and VPN services (23.6%). Through multiverse analyses, we demonstrate the robustness of these findings to numerous model specifications. Our findings reveal that while regulations reduce traffic to compliant sites and likely decrease overall consumption, users adapt by shifting to providers without verification requirements. This approach provides valuable insights for policymakers around the world considering similar legislative measures of digital content regulation. Our methodology also offers a framework for real-time policy evaluation in contexts with staggered implementation.

Keywords

internet regulation age verification synthetic control google trends multiverse analysis policy evaluation digital behavior

1. Introduction

The internet has transformed the way individuals access and consume content, presenting challenges for regulators. While internet regulation has existed since the technology’s earliest days, recent years have witnessed a shift toward stricter rules about what content people can access and how, particularly regarding age-restricted material such as online pornography. The regulation of online adult content represents a complex policy challenge at the intersection of privacy rights, child protection, and digital governance.

Proponents of content regulation argue that age verification on pornographic websites is essential to protect minors (Marsden, 2023), citing evidence that early exposure to such content through digital platforms can lead to detrimental psychosocial outcomes (Flood, 2009; Owens et al., 2022). Critics of these verification requirements contend that such measures are ineffective, compromise user privacy, and could drive users toward less regulated platforms (Blake, 2019; Electronic Frontier Foundation, 2024).

State-level policy interventions bring these debates into focus and provide an opportunity for empirically rigorous evaluation. Louisiana’s implementation of age verification requirements in January 2023 marked a change in the way states approach online content regulation, with other states quickly introducing similar legislation (Act no. 440, 2022); see Table 1). These laws require online platforms hosting adult content to implement age verification systems using government-issued identification or other verifiable credentials, with substantial penalties for non-compliance. The constitutionality of such requirements have come under scrutiny in Free Speech Coalition, Inc. v. Paxton, in which the Supreme Court allowed Texas to enforce its law requiring pornography sites to verify the age of their users before providing access (Free Speech Coalition, Inc. v. Paxton, 2025).

Table 1.

State Age Verification Laws and Implementation Dates

Title	Law passage	Law effective
Louisiana HB 142 (2022)	2022-06-15	2023-01-01
Utah SB 287	2023-03-14	2023-05-03
Mississippi SB 2346	2023-04-18	2023-07-01
Arkansas SB 66/Act 612	2023-04-11	2023-07-31
Virginia SB 1515	2023-05-12	2023-07-01
Montana SB 544	2023-05-22	2024-01-01
Texas HB 1181	2023-06-12	2023-09-19
North Carolina HB 8	2023-09-29	2024-01-01
Indiana SB 17	2024-03-13	2024-08-16
Idaho H 498	2024-03-20	2024-07-01
Florida HB 3	2024-03-25	2025-01-01
Kentucky HB 278	2024-04-05	2024-07-15
Nebraska LB 1092 (Online Age Verification Liability Act)	2024-04-16	2024-07-19
Georgia SB 351	2024-04-23	2025-07-01
Alabama HB 164	2024-04-18	2024-10-01
Kansas HB2592/SB394	2024-04-25	2024-07-01
Oklahoma SB 1959	2024-04-26	2024-11-01
South Carolina H 3424	2024-05-21	2025-01-01
Tennessee SB 1792	2024-05-28	2025-01-01

Source: Adapted from Free Speech Coalition Action Center

The legal decision, however, is silent on the policy’s effects on user behavior. Whether these laws work as intended or produce unintended behavioral shifts remains a fundamental question for empirical study. Two such shifts are of particular concern: substitution and circumvention. Given that many adult content sites are based outside the U.S. (The Age Verification Providers Association, 2025), users may easily substitute compliant platforms with non-compliant ones that exist outside of jurisdictions for enforcement. Alternatively, users can circumvent the laws by employing tools like virtual private networks (VPNs) to mask their location (Roach, 2025). If these laws incentivize such workarounds, they risk not only undermining their own efficacy but also pushing users toward less regulated and potentially more harmful online environments.

This paper examines the effects of state-level age verification requirements for adult content websites in the United States, contributing to our understanding of the effect of digital regulation on user adaptation. This paper leverages the staggered timing of state-level age verification laws to evaluate their effectiveness in modifying user behavior. Our analysis uses Google Trends data aggregated at the state level, providing high-frequency measures of search interest. This approach allows us to capture immediate behavioral responses to policy implementation while addressing traditional challenges in measuring adult content consumption patterns. Our research design builds on recent methodological advances in policy evaluation with synthetic control designs (Ben-Michael et al., 2022). We mirror approaches of pre-registered synthetic controls and other policy evaluation papers surrounding the COVID-19 vaccine lotteries (e.g. (Barber & West, 2022; Lang et al., 2023)). This method is valuable for evaluating age verification laws, as evidence from early adopter states can inform decisions in states still considering such policies. We use synthetic controls in combination with a multiverse analysis to address concerns about researcher degrees of freedom (Silberzahn et al., 2018; Steegen et al., 2016).

In the three months after the laws were passed, we find a 51% decrease in searches for the most popular adult content platform in the U.S. (Pornhub), which complied with state age verification laws. At the same time, searches for the second most popular adult content platform (XVideos), which did not comply with state laws, increased 48.1%, while searches for VPN services increased 23.6%. Through multiverse analyses, we show the robustness of our findings. Together, these findings provide evidence of large substitution and circumvention effects, raising important questions for the design of age verification policies.

2. Related Literature

2.1. Online Adult Content and the Challenge of Regulation

The proliferation of adult content on the internet has created a complex regulatory challenge, prompting lawmakers to implement policies aimed at protecting minors (Marsden, 2023). Proponents of these regulations, such as age verification mandates, point to a body of research associating adolescent exposure to pornography with negative psychosocial outcomes, including depressive symptoms, body image concerns, and the acceptance of aggressive sexual scripts (Löfgren-Mårtenson & Månsson, 2010; Owens et al., 2022; Peter & Valkenburg, 2016; Tsitsika et al., 2009; Ybarra & Mitchell, 2005). However, this research is largely correlational, making it difficult to disentangle whether exposure causes these outcomes or if pre-existing vulnerabilities drive content consumption. The potential for harm is also moderated by factors like parental communication and comprehensive sex education, which can mitigate negative effects (Owens et al., 2022; Peter & Valkenburg, 2016; Wright et al., 2021).

While the policy debate is often framed around harm mitigation, the efficacy of age verification laws is contingent on the realities of the digital environment. Online platforms are the dominant mode of adult content consumption, with a majority of adults reporting monthly use (Solano et al., 2020), often via mobile devices (Morichetta et al., 2019). This market, though highly concentrated among a few top platforms, is notoriously fluid; regulatory pressure on dominant sites often redirects users toward smaller, non-compliant alternatives (Happ et al., 2024). This dynamic gives rise to two predictable user adaptation strategies: substitution and circumvention. First, the global nature of the internet means many non-compliant sites are hosted abroad, making them largely immune to domestic enforcement and easy substitutes for regulated platforms (Novicoff, 2025). Second, users can employ technical workarounds, such as virtual private networks (VPNs), to mask their location and evade restrictions (Roach, 2025). With nearly half of American adults already using VPNs (Milden, 2025), this form of circumvention presents a low-friction path for users to bypass verification, fundamentally challenging the efficacy of state-level mandates.

2.2. Measuring Behavioral Responses to Internet Regulation

The study of internet regulation has evolved from early descriptive work into a field defined by rigorous empirical evaluation. Seminal work by Deibert and Rohozinski (2010a) established a taxonomy of first-generation controls, documenting how governments mandated and implemented technical barriers to restrict online access and how users developed circumvention tools in response. As they observed, “No matter how restrictive the regulations or how severe the repercussions, communities around the world have exhibited enormous creativity in sidestepping constraints on technology in order to exercise their freedoms” (Deibert & Rohozinski, 2010b, p. 43). These early studies revealed consistent patterns of user adaptation, where technical barriers often led to rapid development and adoption of workaround solutions. Later research examined more complex regulatory frameworks targeting platform liability, noting that a policy’s success often depended on cooperation from private intermediaries and the reach of jurisdictional authority (Zittrain & Palfrey, 2008). Together, this work research established a foundational dynamic in the study of digital regulation in the context of a global internet: users consistently develop workarounds to technical restrictions, demonstrating that policy efficacy cannot be separated from behavioral adaptation.

Recent studies leverage new methods of data collection approaches and statistical methods to isolate the causal effects of digital regulation. For instance, Goldberg et al. (2024) used a synthetic control design to evaluate the GDPR, finding that the privacy regulation reduced website traffic and revenue. Similarly, studies of cookie consent rules have revealed their complex and sometimes unintended impacts on advertising and user engagement (Peukert et al., 2022). Research on platform bans shows that users often migrate to alternative services (M. E. Roberts, 2018; M. E. Roberts, 2020), while studies of national firewalls find a corresponding rise in the use of circumvention tools like VPNs (Chen & Yang, 2019). This body of evidence makes clear that evaluating digital regulation requires measuring not only direct compliance but also the displacement effects that occur across the broader ecosystem.

However, measuring these behavioral shifts presents significant methodological challenges, primarily due to the nature of digital trace data. While sources like search queries provide powerful, real-time measures of organic online activity (Lazer et al., 2009), they have key limitations. Population-level data from Google Trends, for example, is reported on a relative scale, which can obscure the true magnitude of a behavioral change (Choi & Varian, 2012; Kristoufek et al., 2016). Furthermore, its aggregated and anonymized nature prevents the demographic analysis needed to assess whether age-targeted policies are affecting the intended population. User adaptation creates further measurement error. The widespread use of privacy tools like VPNs can mask a user’s location and distort traffic data, making it difficult to observe the true effect of a geographically-specific law (Ikram et al., 2016; Khan et al., 2018; Ramesh et al., 2023). These challenges in data interpretation and causal identification require careful methodological design to credibly estimate the real-world impact of internet regulations.

3. Policy Implementation Details

3.1. Louisiana Implementation & Follow on States

Louisiana Act 440 was the first state law to require age verification law for adult content providers, mandating that websites containing a “substantial portion” (i.e., more than 33.33%) of adult content must verify users’ ages through government-issued identification or commercial age verification services. Key features of the Louisiana implementation include:

Specific technical requirements for verification providers

Clear definitions of covered content and websites

Substantial penalties (not to exceed $5,000 for each day of violation; not to exceed $10,000 for failure to perform reasonable age-verification)

Of the states that passed these laws, Louisiana was unique in that it was the only state that implemented age verification in a manner that plausibly preserved a user’s anonymity while verifying age (Davidson, 2024). The age verification process was disintermediated by the state and its associated vendors such that only a coarse measure of a person’s age was provided (i.e. over 18). In response to this law, compliant websites, such as Pornhub, enacted age verification protocols in accordance with the new regulation. However, noncompliant websites, such as XVideos, did not enact such protocols, leaving the user experience of accessing adult content unchanged.

In subsequently adopting states, the methods of age verification tended to be stricter, either requiring uploads of an individual’s government identification, providing PII data, or even presenting biometric data (face scans). While these laws have provisions to require the deletion of the data, collection of such data could have additional chilling effects. In all additional 17 states except one (Georgia), Pornhub has exited the market entirely given the more invasive verification process, preventing access from any IP addresses located in those states. Similar to Louisiana, XVideos did not comply with subsequent age verification laws. A timeline of state laws can be found in Table 1.

3.2. Platform Responses

This staggered implementation and the varied industry response created a natural experiment to evaluate the law’s behavioral effects. Following the implementation of these laws, major adult content providers adopted divergent compliance strategies. Two firms, Pornhub and XVideos, which together accounted for approximately 40% of U.S. adult content traffic, took contrasting approaches (Figure 1) (Semrush, 2025). Pornhub (and its parent company, Aylo) either complied with age verification requirements in states with less invasive methods or exited regulated markets entirely where verification was more stringent. In contrast, the Czech-based XVideos remained accessible in all regulated states without requiring verification or technological workarounds. We hypothesize that enforcement actions against the Czech-based entity would face greater administrative barriers despite both companies being recognized as conducting business in the U.S. XVideos’ market share and contrasting regulatory response provides an effective comparison point for analyzing how these laws affect user behavior. This differential response provides an effective setup for analyzing how age verification laws impact user behavior, creating clear incentives for users of regulated platforms to either substitute to non-compliant alternatives or circumvent restrictions through VPNs.

Figure 1.

SEMRush: Top websites in the United States

4. Pre-registered Research Question and Hypotheses

Our research question and hypotheses stem from pre-registration analysis available at https://osf.io/vp9z6/?view_only=f6695912a1c5487ca8a0f088ae0dc569 and https://github.com/davidnathanlang/internet_regulation_synth_project). The divergent compliance strategies adopted by major adult content platforms in response to state laws provide a clear empirical framework for testing theories of user adaptation to regulation. The decision by Pornhub, a market leader, to either implement age verification or exit a state market introduces a significant friction for users, in the form of privacy costs, inconvenience, or access denial. In contrast, the continued, unrestricted availability of a major competitor, XVideos, creates a readily accessible substitute. This policy-induced shift in the market structure generates a strong expectation of behavioral change, as users are incentivized to seek lower-cost methods of access, either through substituting for non-compliant websites or circumventing through the usage of VPNs. We also analyze generic searches for “porn,” as users may substitute toward a more diffuse set of smaller platforms to avoid regulation. Taken together, these dynamics lead to the following pre-registered hypotheses.

4.1. RQ1

Research Question 1: Do online age-restriction policies cause shifts in internet behavior?

4.2. H1

The average treatment effect (ATT) of state-level age verification laws will be negative on Google Trends search volume for compliant adult content platform (Pornhub) in treated states relative to synthetic control states.

We speculate that the additional friction of age verification and readily available substitute sites will lead users towards other sites.

4.3. H2

The ATT of state-level age verification laws will be positive on Google Trends search volume for non-compliant adult content platform (XVideos) in treated states relative to synthetic control states.

Based on our first hypothesis, we believed non-compliant firms, which remained active and without any additional friction for access, would gain market share and new users.

4.4. H3

The ATT of state-level age verification laws will be positive on Google Trends search volume for virtual private networks (VPNs) in treated states relative to synthetic control states.

We speculate that users will begin searching for this technology in order to spoof their location so that they can access compliant content platforms without age verification and that the presence of age verification laws will raise the saliency of privacy-enhancing technology.

4.5. H4

The ATT of state-level age verification laws will be positive on Google Trends search volume for generic adult content searches (”porn”) in treated states relative to synthetic control states.

We speculate that due to the 33.33% content clause of many of these regulations to trigger age verification, individuals may search for pornographic content on more diffuse and less concentrated platforms that are not as impacted by these laws.

5. Data

Our analysis relies on Google Trends, a publicly available dataset that provides high-frequency and geographically disaggregated data on search behavior. Google Trends track the relative search volume for a given term on a normalized 0–100 scale, where 100 represents the peak search interest for that term in a specific region and time period. These data are well-suited for our study as they allow us to observe immediate, state-level behavioral responses to policy implementation. The utility as a reliable indicator for social and economic trends has been validated in prior academic research (Goldsmith-Pinkham & Sojourner, 2020; Jun et al., 2018; Mavragani et al., 2018; Mellon, 2013).

Despite its strengths, Google Trends data has known limitations, including the use of a relative rather than absolute scale, a non-transparent sampling methodology, and an inability to disaggregate search data by user demographics (Hölzl et al., 2025). A primary concern is one of construct validity: in our case, whether search interest is an adequate proxy for browsing behavior. To address this and align with best practices recommending ex post validation of keywords (Hölzl et al., 2025), we conducted a validation analysis comparing Google Trends data with actual web traffic (see Appendix A). The analysis confirms a strong and positive correlation between search interest and browsing volume for both the compliant (r = 0.84) and non-compliant (r = 0.81) platforms. This analysis supports the construct validity of using search behavior as a proxy for user activity in this context.¹

Figure 2.

Google Trends data for pornhub 2022-01-01 to 2024-10-31

We provide an example of Google Trends data in Figure 2. While not a causal test, we would expect that searches for the main compliant site, Pornhub, would drop in a state that implemented an age verification law, while remaining relatively constant in states to did not implement a similar law. The red line shows pre-implementation data, while the blue line shows post-implementation data.² Almost all states show precipitous drops in search activity after law implementation. Texas is the one exception, as the court initially stayed enforcement of the state law; once the law was enforced, a similar pattern emerged.

These data should provide an intuitive understanding of Google Trends data. With an understanding of the regulatory implementation, platform responses, and behavioral data, we now turn to an explanation of our methodological approach to measuring the impact of state laws on user adaptations.

6. Methodology

We use a synthetic control methodology to analyze the impact of age verification requirements on digital behavior. Synthetic control is a technique that allows individuals to calculate their counterfactual estimate prior to seeing any outcome data (Abadie, 2021).³ This technique is particularly well-suited for cases where a single aggregated unit, such as a state, receives a treatment (Abadie et al., 2010). Direct comparison to other states is often ill-advised as comparator states may differ in many important characteristics and may not mirror the pre-intervention trends of the focal treated state. However, it is possible to construct a composite comparator state that mirrors the pre-treatment trends of the treated state. The synthetic control method allows us to construct a synthetic version of the treated state using a convex combination of other states (the donor pool) based on pre-treatment outcomes and relevant covariates. In short, we make a set of faux states that consists of states that did not adopt age verification laws but matched the pre-adoption paths of states that adopted these laws.

To build intuition around the method, we first discuss the case of a single state—in our case, Louisiana. We construct our synthetic control by minimizing the Mean Squared Predicted Error of our outcome variable in the pre-treatment period using the following expression:

\underset{w_{j}}{minimize} \sum_{m = 1}^{T_{0}} v_{m} {(Y_{1 m} - \sum_{j = 2}^{J + 1} w_{j} Y_{j m})}^{2}

(1a)

subject to \sum_{j = 2}^{J + 1} w_{j} = 1

(1b)

w_{j} \geq 0

(1c)

where Y₁ corresponds to our vector of pre-treatment outcomes (search behavior metrics) for Louisiana, Y_j corresponds to the pre-treatment outcomes and associated indices of other states in the donor pool, w_j corresponds to the unit weights (the associated weighting of each state in our synthetic construction), and v_m corresponds to a variable importance weight of the pre-treatment outcomes at time m, until the end of the pre-treatment period T₀. We minimize this expression subject to the constraints that both our unit weights and variable weights are non-negative and sum to unity. Once the counterfactual w_j weights are derived, estimating the counterfactual the Average Treatment on the Treated (ATT) would consist of taking the average difference between Louisiana after it adopted the policy and its counterfactual state across the evaluation period:

ATT = \frac{1}{T_{n} - T_{0} + 1} \sum_{t = T_{0}}^{T_{n}} (Y_{1 t}^{obs} - \sum_{j = 2}^{J + 1} w_{j} Y_{j t})

(2)

To estimate treatment effects when treatment timing is staggered and there are multiple treated states, we utilize a technique known as generalized synthetic control (Xu, 2017). This technique is quite similar in intuition to classical synthetic control; however, the mechanism used to generate counterfactual outcomes are quite different.

The formula for ATT using the Generalized Synthetic Control (GSC) method is:

A T T_{t}^{GSC} = \frac{1}{N_{t}^{r}} \sum_{i \in T} [Y_{i t} (1) - {\hat{Y}}_{i t}^{GSC} (0)]

(3)

where:

$N_{t}^{r}$ is the number of treated units,

Y_it(1) is the observed outcome for treated unit i at time t,

${\hat{Y}}_{i t}^{GSC} (0)$ is the GSC-estimated counterfactual outcome for treated unit i at time t.

The counterfactual outcome is estimated as:

{\hat{Y}}_{i t}^{GSC} (0) = X_{i t} \hat{β} + {\hat{λ}}_{i}^{⊤} {\hat{f}}_{t}

(4)

where:

X_it represents observed covariates,

$\hat{β}$ is the estimated coefficient vector from the control group,

${\hat{λ}}_{i}$ is the estimated factor loading for treated unit i,

${\hat{f}}_{t}$ is the estimated time-varying factor.

By using this approach to estimate counterfactual-outcomes, it is no longer the case that weights are restricted to be non-negative or to sum to unity. Relaxing the convex hull assumption allows negative weights through the factor model approach, which improves pre-treatment fit for treated units that would otherwise be poorly approximated by a convex combination of control states. We examined the distribution of treated states relative to the control donor pool and found no obvious outliers. Louisiana and several other Southern states with similar demographic and internet usage profiles are well-represented among potential donors. Our multiverse analysis also includes augmented synthetic control estimates, which similarly relax strict convexity requirements while maintaining interpretable weights.

Our pre-registered inference approach relies on a parametric bootstrap estimate. We use 1,000 iterations implemented in the gsynth package to compute standard errors. We collect a short-term and longer-term measure at one and three months of our estimates using the cumuEff function in the gsynth package. Following Ferman et al. (2020), we rely exclusively on pre-treatment outcomes for constructing the synthetic control as a safeguard against specification searching. This is a concern we share given the many researcher degrees of freedom in synthetic control applications. In our multiverse, we also use augmented synthetic control estimates, which allow for more traditional synthetic control weights while accommodating multiple treated units with staggered adoption times.

In Appendix Section B, we further elaborate how to interpret results for the single-treated state of Louisiana where we trained our synthetic control model on the 52 weeks preceding the law’s implementation using data starting in 2022. This analysis motivated our pre-registration and subsequent evaluation efforts.

While synthetic control methods have been widely used to evaluate various policy interventions, their application to digital behavior analysis represents a novel contribution to both the methodological literature and our understanding of internet regulation effectiveness. Given concerns about researcher degrees of freedom in synthetic control methodologies (Ferman et al., 2020), we pre-registered the specification for our synthetic comparison group using data starting in January 2022. We further elaborate on deviations from our protocol in Appendix Section C.

We rely exclusively on pre-treatment outcome data to estimate our counterfactual. (Kaul et al., 2022) notes that this approach shrinks non-outcome variable importance weights to zero. As part of our multiverse analysis detailed in Section 8, we test the robustness of our results to the inclusion of additional covariates, including demographic variables.

7. Pre-registered Findings

We use the Generalized Synthetic Control (GSC) model to estimate treatment effects. This approach employs a latent factor model and uses cross-validation to select model parameters, optimizing the mean-squared prediction error of counterfactual outcomes. Instead of having an explicit linear combinations of weights, the generalized synthetic control estimates counterfactual outcomes using a latent factor model with time-varying factor loadings and unit-specific intercepts.

Our analysis found support for all four of our hypotheses, as highlighted in Table 2 and Figure 3. Table 2 contains the results for each search term as well as the absolute pre-treatment difference between the proposed synthetic control and the adopting states prior to enactment of age verification. In general, these models had good pre-treatment fit with the mean absolute error (MAE) being at most 2.3 Google scale points across the four terms.⁴ The ATT is measured as the average of the twelve weeks after treatment has been implemented. We report standard 95% confidence intervals with their associated lower and upper bounds. Standard errors were derived from bootstrap estimations and reflect sampling uncertainty rather than measurement uncertainty. The negative ATT estimate (−33.8) for the compliant platform (i.e. Pornhub) in states with age verification laws showed a decrease in usage compared to synthetic control states, supporting our first hypothesis (H1). In support of our second hypothesis (H2), we found a positive ATT estimate (27.9) indicating that users switched from compliant platforms to noncompliant alternatives (i.e. XVideos). We also found support for our third hypothesis, with Google Trends showing increased search interest for “VPN” in treated states relative to synthetic control states (ATT = 13.3). Lastly, our fourth hypothesis (H4) was supported, with significant findings (ATT = 3.5) indicating an overall increase in Google search interest for “porn” in treated states relative to synthetic control states. We note that the pre-registered effects are statistically significant. However, their sign and magnitude vary with the length of the evaluation window. This sensitivity is especially pronounced for the VPN and porn results. The apparent reversion for VPN and porn searches over longer time horizons suggests these may be transitory responses. Users initially search for workarounds but then either adopt them (reducing future search need) or abandon efforts. Examining outcomes outside of our specified three-month period would require a new pre-registration to avoid concerns about post-hoc specification searching. We encourage future research to examine effect persistence.

Table 2.

Pre-registered Hypotheses by Keyword

Search term	MAE	ATT	CI.lower	CI.upper
pornhub	0.70	−33.84	−34.97	−32.64
xvideos	1.17	27.85	26.83	30.43
vpn	2.29	13.33	10.00	16.73
porn	0.76	3.48	2.80	4.58

Figure 3.

Change in Google Trends relative to synthetic control. The figure shows the comparison of trends for Pornhub, Xvideos, VPN, and Porn

Carrying forward our pre-registered specification, we see largely similar effects across all states that adopted age verification laws as we saw in Louisiana (Appendix B). In Figure 3, we plot the generalized synthetic control results for the overall treatment population. Each panel corresponds to one of the four search terms we use and its corresponding hypothesis. The horizontal dotted line corresponds to the average treatment effect over the three month period following a law’s implementation. Overall, the effects closely mirror what we see in Louisiana, with one notable exception: the search patterns for pornographic material (H4) are slightly larger relative to trend following launch.

Given that Google Trends scale points are somewhat opaque, we offer an easier-to-interpret framing of these effects. In Figure 4, we report the one month and three month Cumulative Average Treatment Effects (CATT) along with their standard errors. As a reminder, a Google Trends score of 100 would correspond to the week with the most search traffic for a given search term within the specified time period (2022-01-01 to 2024-10-31). Thus, a week with a Google Trends value of 50 would reflect a 50% decrease in search traffic for that term relative to the peak traffic week. If we were to report a 200 scale point CATT, that would correspond to a search term gaining an additional two weeks of its highest relative search volume. In the one-month period following an age verification law becoming effective, we saw that the compliant firm (Pornhub) effectively lost 139.7 points, or more than a week of peak search traffic. The noncompliant firm (XVideos) gained a roughly equal magnitude increase in their search volume of 137 points, or more than a week of search traffic. Searches for “vpn” also spiked during this month by 94.8 points, yielding almost an additional week of search traffic. Searches for the term ”porn” saw the smallest spike over the specified time period, gaining only 30 points over the one-month time period, representing substantially less than a week of peak search traffic. Over a three-month evaluation period, we saw these effects continue to accumulate for the focal compliant firm and non-compliant firm. Pornhub lost more than a month of relative search volume (−439.9), and XVideos gained more than three weeks of peak relative search volume (362.1). The effects for VPN (173.3) and porn (45.3) searches accumulated in the same direction but not with the same level of magnitude.

Figure 4.

One month and three month cumulative average treatment effects for pornhub, Xvideos, VPN, and porn

As an alternative interpretation of these effects, we also annotate Figure 4 with the percentage change relative to the Google Trends counterfactual estimate. This interpretation makes it clear that Pornhub and XVideos saw larger percentage changes in relative search volume compared to the other search terms examined. Over the three months after the age verification law was passed, the focal compliant firm lost more than half their search traffic (51%). The focal noncompliant firm saw relatively large magnitude gains in their search volume (48.1%). While we still see large gains in search traffic for VPN (23.6%) and porn (4.3%), these estimates are smaller in magnitude. Both framings help provide different senses of the magnitude of the change in more quantifiable ways than Google Trends points on their own.

Market dynamics provide important context for interpreting these effects. Figure 5 presents a sensitivity analysis illustrating the potential magnitude of changes in firm-specific and net search behavior at a national scale. Using 2022 U.S. Google Trends data as a baseline—prior to any state adopting age verification laws—we retrieved the average search volume for each firm-specific term. Querying all terms together in Google Trends places them on a comparable scale, allowing for direct comparison across platforms (Appendix E).5 The blue bars in Figure 5 represent these baseline 2022 averages.

Figure 5.

Estimated nationwide effect

Our analysis focuses on the two dominant platforms in the U.S. adult content market. The compliant firm (Pornhub) historically commanded approximately three times the search volume of the non-compliant firm (XVideos), reflecting its position as the market leader. We then apply our estimated treatment effects from the synthetic control analysis to this baseline data to project what nationwide adoption of age verification laws might yield. For Pornhub, the 2022 average search volume was 34.89 points on the Google Trends scale. Applying the estimated 51% reduction yields approximately 17.09 points post-treatment—a decrease of 17.79 points. For XVideos, the baseline search volume was 12.72 points. Applying the estimated 48.1% increase yields approximately 18.83 points post-treatment—an increase of 6.12 points. The green bars in Figure 5 display these projected post-treatment values, while the red bars show the net change: a combined reduction of 11.68 points across both platforms.

This analysis, while crude and non-exhaustive given the many other platforms and search terms users might employ, highlights two key findings. First, ignoring substitution effects substantially overstates the law’s impact on overall adult content consumption. The net reduction in firm-specific adult content searches (11.68 points) is approximately two-thirds of what one would estimate by examining only the compliant platform (17.79 points). Researchers or policymakers who focus solely on traffic declines to regulated sites would miss this offsetting increase to unregulated alternatives. Second, applying these treatment effects to 2022 baseline data would reverse the rank ordering of market dominance—the non-compliant firm (XVideos) would surpass the compliant firm (Pornhub) in relative search volume, with 18.83 points compared to 17.09 points. These dynamics underscore a complex policy trade-off: while age verification laws successfully reduced traffic to regulated platforms, they may have inadvertently strengthened the market position of non-compliant alternatives operating outside the reach of domestic enforcement.

8. Multiverse Analysis

While we recognize that we chose an extremely parsimonious specification for our pre-registration, there are a number of additional paths we may have taken as researchers (Huntington-KleinPörtner et al., 2025). We utilize a multiverse analysis where we cross many of the steps and decisions we have taken as researchers with other plausibly valid approaches. The choices that we examined are summarized in Table 3.

Table 3.

Summary of Methodological Choices

Category	Description
Start date	Start date: 2022-01-01 (alternative: 2019-01-01). Google Trends data at monthly frequency to capture staggered adoption. Trade-off between pre-treatment fit and overfitting to high-frequency noise (Sun et al., 2024).
Treatment date	Defined as either (1) when laws took effect or (2) when laws were passed, to account for anticipatory behavior or skepticism about enforcement.
Identity verification	Treatment groups re-estimated based on state verification methods: Government ID, Digitized ID, Transaction data, Business/Government Database, or any method.
Covariates	Primary specification excludes non-pre-treatment outcomes. Control variables include state demographics, income, and internet/technology access from the 2020 Census.
Evaluation window	Effects assessed over one-month and three-month post-implementation windows to capture immediate adaptation and persistent behavioral changes.
Identification Technique	Compared two synthetic control extensions: (1) Generalized Synthetic Control (Xu, 2017), allowing heterogeneous treatment effects via interactive fixed effects; (2) Augmented Synthetic Control (Ben-Michael et al., 2022), balancing fit between individual treated units and pooled treatment effects.

While our multiverse is not fully crossed, in total for each keyword we generate 800 point estimates. We plot these point estimates in the violin plot in Figure 6. The red filled charts correspond to synthetic controls generated with gsynth, and the blue correspond to synthetic controls generated with the augmented synthetic control methods. The points correspond to either the minimum mean squared predicted error (MSPE) in the pre-treatment (blue) or the minimum cross-validation error in gsynth models. Looking only at the sign estimates of this multiverse, our results comply with H1 98% of the time, H2 complies 98.6% of the time, H3 complies 80.9% of the time, and H4 complies 100% of the time. We note that we saw no deviations from our pre-registered hypotheses when we defined our treatment date as the day the age verifications laws became effective. The only times we generated point estimates that were not consistent with our hypotheses was when we defined the treatment date as when the law was first passed.

Figure 6.

Multiverse estimates

9. Discussion

Our analysis reveals several key insights about the effectiveness of state-level age verification requirements for adult content websites. The results demonstrate a 51% reduction in searches for the largest compliant platform, accompanied by increases in searches for the largest non-compliant platform (48.1%), VPN services (23.6%), and porn (4.3%). Subsequent researchers using distinct econometric approaches have also found qualitatively similar results (Guo & Peng, 2025; Spencer, 2025). These findings suggest that while age verification laws may successfully reduce search traffic to regulated platforms, they also appear to drive users to search for potentially less regulated alternatives. These results contribute to ongoing debates about the efficacy of digital content regulation. While proponents of age verification requirements argue that such measures are essential for protecting minors, our findings indicate that these policies may primarily shift user behavior rather than fundamentally alter access patterns. The observed increase in VPN-related searches suggests that users are actively seeking ways to circumvent these restrictions, potentially undermining the policies’ intended protective effects. Anecdotal data from other states with different age verification regimes, such as Texas, have suggested similar circumvention behaviors (Fung, 2024). In light of concerns that synthetic control estimates can be “cherry-picked,” our pre-registered design provides a crucial safeguard against specification searching. Moreover, the extensive multiverse analysis confirms that these core findings are not artifacts of our analytical choices, but are robust across a wide range of plausible models.

Our work connects to broader research on digital regulation effectiveness, including content moderation policies (S. T. Roberts, 2019; Madio et al., 2025), platform-specific restrictions (Gorwa et al., 2020; Horta Ribeiro et al., 2021), and privacy regulations (Goldberg et al., 2024), which consistently show substantial user adaptation. Our results align with this literature while providing specific insights into responses to age-based access controls. With multiple states and countries pending implementation of similar age verification laws (Ramkumar & Bobrowsky, 2025), understanding these behavioral responses is increasingly urgent. For researchers, our work demonstrates the value of combining pre-registered analyses with high-frequency behavioral data for real-time policy evaluation. We encourage future work to build on our approach while incorporating additional data sources for more nuanced insights.

Our analysis faces several important limitations. First, Google Trends data captures search behavior rather than actual web traffic, creating a construct validity challenge. While we observe search pattern changes, compliant firms have reported actual traffic decreases of 80% or more (Iovine, 2023), suggesting our methodology may underestimate real effects. We rely on Google Trends to ensure our analysis adheres to principles of open science, intentionally avoiding the opaque, ‘black box’ methodologies of proprietary traffic vendors. While we prioritize the transparency and reproducibility of search data, we acknowledge that this comes at the cost of not capturing the full fidelity of direct traffic, and our confidence intervals should be interpreted with this distinction in mind. Second, users may access sites through direct URLs, bookmarks, or other non-search methods, potentially causing us to miss important behavioral adaptations. Third, the Stable Unit Treatment Value Assumption (SUTVA) may not hold perfectly as users in control states could change their search behavior in response to nearby states’ laws, particularly in border regions. Similarly, users in treated states may subsequently use their VPNs to spoof their geolocation in either control states or regions outside of the US. This could potentially inflate our treatment estimates. Finally, and most importantly for this study, Google Trends data are aggregated and anonymized, preventing us from differentiating users by age—a crucial limitation given that protecting minors is the primary policy objective. We cannot directly determine the extent to which observed changes reflect behavioral shifts among minors or across all age groups.

While our analysis cannot definitively resolve debates about protecting minors online, it provides crucial empirical evidence about user responses to current regulatory strategies. The substantial adaptation effects suggest that age verification requirements, while potentially valuable as part of a broader strategy, may have limited efficacy as a standalone policy tool, pushing the public into less regulated corners of the internet. Future research should address several key questions. Studies using more granular data could determine whether behavioral changes vary by age group, illuminating the policies’ effectiveness at protecting minors specifically. Comparative analysis of different implementation approaches could identify which verification methods best balance access restriction with privacy concerns. Longer-term studies will be crucial for understanding whether initial adaptation patterns persist as users and platforms adjust to the regulatory environment. Our results point to a fundamental tension for policymakers: attempts to regulate online content through access restrictions risk displacing users to less-regulated corners of the internet. Effectively governing the digital sphere will require confronting this trade-off between visible enforcement and its unintended consequences.

Footnotes

Acknowledgements

We are grateful for the valuable comments and feedback from participants at the NYU Center for Social Media and Politics. We also thank Andrew Baker, Thomas Dee, Ben Domingue, Rexx Douglas, Scott Cunningham, Lief Esbenshade, David Ginsburg, Jonathan Huck, Klint Kanopka, Saurabh Khanna, Nick Huntington-Klein, Maxim Massenkoff, Hirotaka Miura, Amarita Natt, and Robb Willer for their insightful feedback on the manuscript. We also appreciate thoughtful comments from the editor and two anonymous reviewers. We also wish to thank the Free Speech Coalition for providing information on policy adoption and implementation details. Additionally, we appreciate the guidance of Eli Ben-Michael, Avi Feller, and Jesse Rothstein on the use of the augsynth package. We also extend our thanks to Philippe Massicotte for developing the gtrendsr package, which facilitated this research.

ORCID iD

David Lang

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

All data used in this study are publicly accessible through the Google Trends API via the gTrendsR package. For reproducibility purposes, both the raw data and analysis code are available in the project’s GitHub repository. Researchers interested in replicating or extending our findings can access all materials necessary to reproduce the analyses presented in this paper.*

Notes

Appendix

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