Robustness and Diagnostics
A potential concern is that including both the DESI and its underlying components may introduce post-treatment bias (‘bad controls’). To address this, we estimated four alternative specifications: (i) DESI only; (ii) components only; (iii) DESI residualized against the business components; and (iv) a two-factor PCA decomposition of DESI and its components. Across these approaches, the negative coefficient of DESI on exports persists in the baseline (non-EU β ≈ −0.115,
p ≈ 0.048; intra-EU β ≈ −0.121,
p ≈ 0.044). However, when using residualized DESI, the coefficient attenuates toward zero, consistent with the interpretation that the paradox partly reflects over-control by including components alongside the index Results are presented in
Table 2 and
Figure 1.
In terms of cross-sectional dependence, re-estimating the baseline two-way FE models with Driscoll–Kraay SEs leaves our conclusions unchanged: the DESI–exports coefficient remains negative and statistically significant. Applying CCE [
28] yields qualitatively similar results, indicating that unobserved common shocks do not explain the paradox. Regarding serial correlation and heteroskedasticity, a Wooldridge test on first-differenced residuals indicates serial correlation and groupwise heteroskedasticity is also present. Our main tables therefore use country-clustered SEs, and DK SEs are reported as a robustness check, with inferences materially unchanged. In terms of within-country macro controls, because year FE absorbs year-only regressors, Brent and EUR/USD levels are not identified. We therefore allow heterogeneous exposure examining Brent and EUR/USD interactions with energy intensity. The interaction terms are insignificant, suggesting that oil or FX shocks are not the driver of the DESI–exports relationship.
Table 3 shows that the negative DESI coefficient remains significant under both covariance estimators. This confirms that the “DESI paradox” is robust to serial correlation and cross-sectional dependence. Other digitalization components retain their expected signs but are not consistently significant.
To further account for potential cross-sectional dependence, we estimated the model using the Common Correlated Effects (CCE) estimator [
28], which augments the regression with cross-sectional dependent and explanatory variable averages. As shown in
Table 4, the DESI coefficient remains negative and significant (β ≈ −0.115,
p ≈ 0.031), while other digital indicators remain statistically insignificant. This indicates that the paradox is robust to unobserved common shocks, such as EU-wide policy changes or global demand fluctuations.
Figure 2 shows the DESI score vs. GBARD share.
We also conducted a Wooldridge AR(1) test for serial correlation in panel data. The estimated coefficient on the lagged residual was −0.146 (p ≈ 0.08), suggesting mild first-order serial correlation. Given the presence of both serial correlation and heteroskedasticity, we report country-clustered SEs in the main tables and provide Driscoll–Kraay SEs as a robustness check, with inferences remaining unchanged.
The chart reveals a clear positive trend between a nation’s commitment to public Research and Development, measured as a share of the government budget, and its overall digital competitiveness. This relationship suggests that strategic government investment in R&D is a powerful driver of innovation and technological advancement, which are critical components of a thriving digital economy.
Figure 3 highlights the link between economic prosperity and digital maturity. The upward trend of the regression line indicates that countries with a higher logged GDP per capita consistently achieve higher DESI scores. This underscores the importance of a robust economy as a foundation for building a competitive digital society and suggests that policies aimed at economic growth can have a synergistic effect on digitalization.
Table 5 provides summary statistics for the key variables used in the analysis and their pairwise correlation matrix. The correlation matrix offers a first glimpse into the relationships within the data. For example, DESI10 exhibits strong positive correlations with its underlying components, such as Cloud_Share (0.80) and Social_Media_Use (0.74). This high degree of correlation foreshadows the potential for “over-control” issues in regression models that simultaneously include both the composite index and its specific components, a point that becomes central to interpreting the baseline results. Raw correlations between the digital variables and economic outcomes are generally positive but modest in size.
Using the previously described two-way fixed effects model, the initial analysis examines the contemporaneous relationship between the various digitalization and innovation predictors and the three economic outcomes. The results are presented in
Table 6.
The most striking and counter-intuitive result from the baseline models is the coefficient on DESI10. For both non- and intra-EU exports, the overall digital maturity index has a statistically significant negative association. Specifically, holding other factors constant, a 10-point increase in a country’s DESI score is associated with an approximately 11.5% decrease in non-EU exports and a 12.1% decrease in intra-EU exports. In the model for logged GDP per capita, no predictor achieves statistical significance at the 5% level.
This DESI paradox appears to contradict the widely held belief, and the foundational premise of the Digital Decade policy, that greater digital maturity should enhance economic performance, including trade. However, this result should not be interpreted as evidence that digitalization is detrimental to exports. Instead, it is more likely a statistical artifact arising from the specific nature of the fixed effects model and the inclusion of multiple, related digital indicators.
The fixed effects specification isolates the effect of within-country changes over time. The model asks the following question: when a country’s DESI score increases more than its typical trend (and more than the EU average trend for that year), what happens to its exports, conditional on the changes in its specific business digitalization levers (like Cloud_Share and Ecomm_Sales)? The DESI is a broad composite index that includes many components not directly related to merchandise exports, such as the digitalization of public services, consumer internet usage, and human capital. When the model explicitly controls for the business-oriented digital tools that are most likely to directly impact export activity, the DESI10 variable captures the effect of the residual components of digital maturity. It is plausible that a within-country increase in these other components (e.g., a shift towards a more digitally enabled service economy or greater consumer connectivity) could coincide with a structural shift away from merchandise-heavy production, thus negatively correlating with goods exports.
Figure 4 shows the evolution of DESI by country. This phenomenon of “over-control” suggests that composite indices can be misleading in conducting a granular analysis of specific outcomes like trade. The key lesson is not that DESI is bad, but that, for targeted policy, one must look at specific levers and not just the aggregate score.
To explore whether the impact of digitalization is conditional based on other factors, we introduce interaction terms into the model, addressing the hypotheses under RQ2. Our analysis focuses on interactions between digital levers and both the national innovation capacity (GBARD_Share) and overall digital ecosystem maturity (DESI10). The results for non-EU exports are presented in
Table 7.
The most significant and policy-relevant finding from this model is the interaction between cloud adoption and public R&D spending. The main effect of Cloud_Share is now positive and statistically significant (β ≈ +1.40), suggesting that, on average, increasing cloud adoption is associated with higher non-EU exports. However, this effect is powerfully moderated by GBARD_Share. The interaction term, Cloud_x_GBARD, is negative and statistically significant (β ≈ −78.17, p = 0.041).
This negative interaction term refutes the initial hypothesis of complementarity (H2a) and instead points to a substitution effect. The marginal effect of cloud adoption on non-EU exports is not constant and depends on the level of public R&D investment. The total marginal effect can be expressed as ∂(Cloud_Share)∂(log Non-EU Exports) = 1.402 − 78.172 × GBARD_Share, a relationship visualized in
Figure 5, which plots the estimated marginal effect of cloud share across the observed GBARD share range.
Interpretating this interaction leads to profound conclusions. In countries with a low share of government spending on R&D (low GBARD_Share), the adoption of cloud computing provides a large, significant boost to non-EU export performance. In these contexts, the cloud likely acts as a crucial gateway to advanced technologies, scalable infrastructure, and global markets that firms would otherwise lack access to, providing an effective substitute for a weaker domestic public innovation ecosystem. Conversely, in countries that already have a high level of public R&D investment (high GBARD_Share, e.g., Germany, Sweden), firms are likely already embedded in a rich innovation ecosystem. For these firms, the additional or marginal benefit of adopting standard cloud services for the purpose of exporting is much smaller and statistically indistinguishable from zero. The two channels for accessing innovation appear to be substitutes, not complements. This finding has direct policy implications: promoting basic cloud adoption may be a highly effective industrial policy for enhancing global competitiveness in countries with less developed national innovation systems, while innovation leaders may need to focus on fostering more advanced or bespoke digital technologies. Other interaction terms, including those with DESI10, were found to be not robustly significant, suggesting no clear, systematic complementarity between firm-level digitalization and national digital maturity once other factors are controlled for.
To assess the temporal dynamics of these relationships and check the robustness of the contemporaneous findings, a model using one-year lags of all predictors was estimated. The results of this lagged model were revealing in their general lack of statistical significance. Across all three outcome variables, none of the lagged predictors were significant at the conventional 5% level. The only marginally significant effect was a positive association between lagged e-commerce sales and logged GDP per capita (p = 0.089).
The absence of strong lagged effects suggests that the economic impacts of these specific forms of digital adoption are realized relatively quickly, largely within the same year. This challenges narratives that posit long and variable lags in the economic benefits of technology materializing. For the types of digital tools analyzed here—primarily operational and market-facing (e.g., e-commerce, cloud services)—the connection to performance appears to be more immediate than for deep, structural investments. This finding lends confidence to our primary contemporaneous models, which seem to effectively capture these fast-moving operational channels.
The very high R2 values (0.995–0.998) in our FE regressions reflect the fact that most of the variance is explained by country and year fixed effects, leaving limited within-country movement in the digital adoption indicators. Variance decomposition shows that approximately 35% of the variance in Cloud adoption, 22% in e-commerce use, and 24% in social media use occurs within countries over time, with the remainder absorbed by country averages and common year shocks.
To probe sensitivity, we re-estimated the models with country-specific linear time trends and in terms of first differences. In both cases, the main coefficients retain their sign and approximate magnitude, but with reduced statistical significance, reflecting the smaller pool of within-country variation being exploited.
These results highlight two implications. First, the paradoxical DESI–exports relationship is not simply driven by time trends or spurious cross-sectional patterns. Second, because measurement error is more consequential when variation is limited, our coefficients should be seen as conservative lower-bound estimates of the true causal impact of digital adoption on exports.
A potential concern is that digital adoption may itself respond to trade performance, creating reverse causality. We address this issue in three complementary ways.
Dynamic specifications.
We extend the baseline two-way fixed effects model to include distributed lags of digital adoption variables:
Exportsit = αi + γt + β0Dit + β1Di,t−1 + β2Di,t−2 + θ′Xit + εit, where Dit denotes adoption (cloud, e-commerce, social media). Across specifications, the contemporaneous coefficient β0 remains stable and significant, while lagged coefficients β1, β2 are small and statistically weak. In terms of magnitude, the cumulative effect β0 + β1 + β2 is close to the contemporaneous estimate. These results indicate that the impact of adoption on exports is fast-moving, while feedback from trade performance into adoption over one- to two-year horizons is limited.
COVID-19 event study.
We further probe short-run dynamics by implementing an event study centered on 2020. We interact adoption measures with event–time dummies (t − 2020 = −2, −1, 0, +1, +2). Estimates show no significant pre-trend, and the pandemic shock does not overturn the negative DESI–exports relationship. The absence of anticipatory effects strengthens our claim that contemporaneous adoption influences exports rather than the reverse.
IV and control–function considerations.
We discuss three plausibly exogenous sources of variation in adoption: the staggered rollout of cloud regions, cross-border backbone infrastructure expansions, and the formula-based allocation of EU digital grants. These supply-side shifters affect the cost and availability of adoption but are orthogonal to idiosyncratic export shocks. While harmonizing these data across EU-27 is beyond the scope of the present study, we outline a control–function approach as a roadmap for future work.
Identification summary.
Together, the dynamic specifications, the COVID-19 event study, and a discussion of exogenous shifters support a contemporaneous interpretation: digital adoption exerts rapid effects on exports, while reverse causality appears limited.
Table 8 reports distributed-lag models with up to two digital adoption lags. Across cloud, e-commerce, and social media, the contemporaneous coefficient remains the main driver, while lagged terms are small and imprecise; the cumulative effect β
0 + β
1 + β
2 is close to zero. These dynamics indicate limited reverse causality from exports to adoption over one- to two-year horizons, consistent with the fast-moving impacts of adoption on export performance. Results are estimated with two-way fixed effects and country-clustered standard errors, while inference is unchanged when using Driscoll–Kraay SEs.
We next explore whether the impact of cloud adoption on exports depends on public R&D intensity (GBARD). To do so, we estimate an interaction model of cloud adoption with GBARD, controlling for DESI and country and year fixed effects.
Figure 6 plots the average marginal effect (AME) of cloud across the empirical GBARD range, together with 95% confidence intervals. The AME is positive and statistically significant at low GBARD levels, but decreases monotonically as GBARD rises, approaching zero in high-GBARD countries. This pattern suggests that cloud adoption is most beneficial for trade in environments with weaker public R&D intensity, while the marginal contribution of cloud diminishes when such resources are abundant.
Table 9 reports the marginal effects at representative GBARD percentiles (25th, 50th, 75th). At the 25th percentile of GBARD, cloud adoption is associated with a significant positive increase in exports. At the median, the effect remains positive but smaller in magnitude, while at the 75th percentile the effect is close to zero and not statistically significant.
The declining marginal effect of cloud adoption as GBARD rises is consistent with a substitution mechanism: when public R&D intensity is low, firms appear to rely more heavily on cloud services as a substitute for missing research infrastructure, which translates into higher export gains. Conversely, in high-GBARD environments, cloud’s marginal payoff is reduced, as public R&D capabilities provide complementary innovation channels. This indicates that cloud adoption and public R&D can act as substitutes at low GBARD levels and as complements in more advanced, R&D-intensive settings.
While, ideally, one would employ deflated trade volumes and a full split between goods and services exports, our robustness checks indicate that the main findings are not sensitive to outcome scaling, to intra- versus extra-EU distinctions, or to the inclusion of COVID years. This provides reassurance that the estimated link between digital adoption and export performance reflects a structural relationship, rather than artifacts of measurement or temporary shocks.
To illustrate the economic significance of our results, we translate the estimated coefficients into export effects. At the 25th percentile of GBARD, a 10-percentage-point increase in Cloud adoption raises extra-EU exports by +2.5%; at the median the effect is +1.2%; and at the 75th percentile the effect is close to zero and statistically insignificant.
This heterogeneity implies a simple decision rule for policymakers:
Low-GBARD countries: prioritize measures that facilitate SME cloud adoption (e.g., subsidized access, digital infrastructure support), as the marginal export payoff is high.
High-GBARD countries: focus on complementarities, ensuring cloud adoption is integrated with advanced R&D programs, rather than treated as a standalone lever.
These translations demonstrate that digital adoption policies can have tangible trade benefits, but their effectiveness depends on the broader innovation environment.