4.1. Coverage
The panel holds 270 country-year cells, of which 268 carry both a consumer adoption and an SME participation value. Two are incomplete: Greece has no SME e-sales figure for 2019, and France has no household purchasing figure for 2020. Neither series was interpolated, and both gaps are carried as missing through every model. The three-month consumer adoption series, added as a robustness measure, covers 269 cells across the full window. Three sample sizes recur below and are worth fixing here: 270 is the full country-year grid (27 × 10); 269 is either single series on its own, missing one cell; and 268 is the count with both series present, which is the base for every model that uses the two together and for the alignment gap. First-difference models drop one further year per country and so run on 239.
Consumer adoption carries five break flags and SME participation three; the enterprise series also carries one low-reliability flag. All flags are retained in dedicated variables and documented in the metadata audit; no flagged observation is recoded or removed from the primary analysis. In total, 9 of the 270 country-years carry a break (b) or low-reliability (u) flag on one of the two indicators: breaks for Germany (2021), Ireland (2021), Latvia (2016), Luxembourg (2018) and Sweden (2016) on the consumer series and for France (2021), the Netherlands (2024) and Sweden (2022) on the enterprise series, together with the low-reliability flag for Greece (2019). Excluding all nine leaves the main levels coefficient essentially unchanged (0.111 versus 0.116,
p = 0.175), so the finding does not rest on flagged observations.
Table 1 lists the concepts and sources;
Table 2 reports coverage and descriptive statistics.
4.2. Development of the Two Series (RQ1)
The two series grew at very different rates (
Figure 1a;
Table 3). Consumer online purchasing rose from a cross-country mean of 47.1% in 2015 to 72.1% in 2024, representing a gain of 25 percentage points. SME e-sales participation moved from 16.0% to 22.1% over the same decade, a gain of 6 percentage points. The two figures rest on different populations and denominators and are not directly comparable as magnitudes.
The dispersion of the two series moved in opposite directions, and this is the more telling pattern. Cross-country variation in consumer adoption collapsed: its standard deviation fell from 19.08 to 11.91, a decline of 0.91 points per year that a simple time trend fits almost perfectly (
p < 0.001, R
2 = 0.96). Member states that lagged in 2015—Romania at 22%, Bulgaria at 31%—closed much of the distance to the leaders, so the household distribution tightened year after year. SME participation did not show comparable convergence. Its cross-country standard deviation rose slightly, from 6.75 to 7.37 (+0.13 per year), though this upward drift was not significant under the country-clustered bootstrap (
Table A3); no statistically reliable convergence in SME participation was evident, and if anything, dispersion drifted upward. Member states are becoming more alike in the share of consumers purchasing online. They are not becoming similarly alike in the share of SMEs participating in e-sales. Škare et al. [
32], linking DESI to the joint European Commission–ECB enterprise survey, identify managerial capability and the supply of skilled labour—resources that develop slowly and remain unevenly distributed across member states—as constraints on the firm side. Constraints of that kind may help to explain why the SME participation distribution stays wide while the consumer adoption one closes.
The convergence in consumer adoption we observe is consistent with Stângaciu et al. [
33], who report that the pandemic-era expansion of EU e-commerce coincided with a narrowing of disparities among member states. Their territorial convergence finding is told with consumer indicators; the value of separating the two measures is that the observed convergence is confined to consumer adoption and has no clear counterpart on the firm side.
Pooled across all country-years, consumer adoption and SME participation correlate at 0.55 (Spearman 0.51, N = 268). This is a moderate pooled association, and it frames the two questions the rest of the analysis turns on: whether it reflects the two sides moving together within countries over time and whether it is stable across the decade.
4.3. Within-Country Association (RQ2)
Table 4 reports the primary levels specification alongside the first-difference sensitivity check. Both isolate within-country variation, and both return a small positive coefficient that falls short of conventional significance. Because the co-development question is conceptually symmetric whereas the fixed-effects specification is directional, we also estimated the reverse specification, with consumer adoption as the dependent variable. The coefficient is 0.364 (
p = 0.151), leading to the same substantive conclusion of a positive but imprecisely estimated within-country association. As direction-neutral summaries, the two-way within-country correlation is 0.205, and the correlation of consecutive-year within-country changes is 0.15. The weak within-country co-movement therefore does not depend materially on which indicator is designated as the dependent variable.
In levels, with country and year fixed effects, a one-point rise in consumer adoption is associated with a 0.116-point change in SME e-sales participation (SE 0.073, 95% CI [−0.027, 0.259], p = 0.11). The confidence interval spans zero. In first differences, where the year-to-year change in SME e-sales participation is regressed on the corresponding change in consumer adoption, the coefficient is 0.091 (SE 0.047, 95% CI [−0.002, 0.184], p = 0.055)—the same sign, the same rough magnitude, and again an interval whose lower bound touches zero.
The contrast with the pooled correlation of 0.55 is the point. A substantial part of that pooled association reflects persistent differences between countries: countries that rank high on consumer adoption also rank high on SME e-sales participation, because both track a country’s broader digital and economic development. Once that between-country ranking is absorbed by the fixed effects, the estimated within-country association is small and imprecisely estimated. The estimate is sensitive, however, to the weighting assigned to member states. Because the unweighted specification treats each member state as one observation—appropriate for a question about convergence across jurisdictions, each of which sets policy independently—it gives Luxembourg the same weight as Germany. Weighting instead toward larger economies, by national population aged 15–74 or by the number of enterprises with 10–249 persons employed, raises the levels association to 0.248 (
p = 0.002) and 0.260 (
p < 0.001), respectively (
Table A3). The first-difference association remains small and non-significant under every weighting. Weighting changes the estimand rather than testing a mechanism: it allows a few large economies to dominate, so the larger weighted coefficient does not by itself establish that the association is stronger in bigger member states. We therefore report the weighted models only as sensitivity analyses and do not interpret the contrast as evidence of heterogeneity by economy size; the unweighted specification, which treats each member state as one jurisdiction, remains the primary one. On this evidence, consumer adoption is not robustly associated with contemporaneous changes in SME e-sales participation. The two specifications agree, which matters more than either
p-value: a result that survives first-differencing but stays marginal in levels, or vice versa, would invite a specification-dependent reading. Here neither model provides statistically precise evidence of a within-country association, and both point the same way.
Inference rests on country-clustered robust standard errors from a GEE with an independent working correlation. With 27 clusters, conventional robust covariance estimates may provide imperfect finite-sample inference [
30], so we supplement the Wald tests with two small-sample corrections: the bias-reduced CR2 variance with a t(26) reference and a wild cluster bootstrap-t that imposes the null with Rademacher weights over 9999 replications. Both are reported in
Table A2. These procedures differ in their variance estimators and reference distributions and therefore need not yield identical
p-values; the primary GEE sandwich inference in
Table 4 remains the reference, with CR2 and the bootstrap reported as small-sample robustness checks. They confirm and, if anything, strengthen the baseline reading: the levels’
p-value is 0.145 under CR2 and 0.218 under the bootstrap, and the first-difference
p-value rises from 0.055 to 0.097. The GEE sandwich
p-value of 0.112 in
Table 4 and the 0.148 obtained under conventional cluster-robust (CR1) standard errors in
Table A2 apply to the identical point estimate of 0.116 and differ only in the variance estimator; the small-sample corrections (CR2, wild cluster bootstrap) are the appropriate reference for finite-sample inference with 27 clusters. Two single-country exclusions that came closest to significance under conventional inference are also non-significant under the bootstrap. Two one-sided tests (TOSTs) for equivalence further support equivalence within ±0.5 and ±0.3 percentage-point bounds (
p < 0.001 and
p = 0.015, respectively). The equivalence tests use country-clustered standard errors (HC1) with a t(26) reference. These bounds are anchored to the SME participation scale rather than chosen arbitrarily: a coefficient of 0.3 to 0.5 would imply a 3-to-5-percentage-point change in SME participation for a 10-point change in consumer adoption, equivalent to roughly 15 to 26% of the pooled SME participation mean of 19.6%.
4.4. Configurations and Persistence (RQ3)
Classifying each country-year by its alignment gap makes the imbalance concrete. Under the ±0.25 SD band, 117 of 268 observations (43.7%) are SME-leading—the firm side relatively ahead—and 99 (36.9%) are consumer-leading, with only 52 (19.4%) falling inside the aligned band. Four observations in five sit off-centre. Widening the band to ±0.50 SD moves more cases into the aligned category, as it must, but the picture holds: 32.1% are SME-leading, 29.5% consumer-leading, and 38.4% aligned. The split between the two leading directions stays near-symmetric under both bands, so both directional categories remain substantial under the wider tolerance band.
The substantive pattern is not materially sensitive to the particular standardisation used. Reconstructing it from within-year percentile ranks or from robust standardized scores using the median and the median absolute deviation reproduces almost exactly the same series (correlations of 0.97 and 0.98 with the z-score gap). The three-category configuration is correspondingly stable: the same country-year is assigned the same category in 83–87% of cases across constructions (Cohen’s κ = 0.74 and 0.79). The main levels coefficient is also not driven by extreme values; trimming the most extreme 5% of gaps leaves it small and non-significant (0.08, p = 0.31).
One caution on reading these labels: the gap is relative, standardised within each year across the 27 states, so “SME-leading” does not mean a country’s firms sell more than its consumers buy. The two percentages have different populations and different denominators—individuals aged 16–74 on one side and enterprises with 10–249 persons employed on the other—and cannot be compared as magnitudes at all. The label means only that the country’s SME side stands higher against the EU distribution than its consumer side does. A country can shift category because its neighbours moved, not because it did.
Persistence is high. Year-on-year, 200 of 239 transitions (83.7%) stay in the same configuration, against 36.5% expected from the marginal distributions alone; Cohen’s κ of 0.74 places this in the range conventionally read as substantial agreement beyond chance, with a 95% country-clustered bootstrap interval of [0.60, 0.83] that stays well clear of zero. Because slow-moving national indicators can generate high year-to-year retention mechanically, we benchmarked the observed persistence using joint circular shifts of the panel. The same temporal offset was applied to every country, preserving the cross-sectional configuration within each shifted year while changing the temporal cut point. Across the nine non-trivial rotations, retention averages 0.793 (range 0.782–0.799) and κ averages 0.673 (range 0.657–0.685). The observed values (0.837 and 0.743) are the largest among the ten admissible temporal rotations. Because only ten joint temporal rotations are possible, the exact randomisation
p-value is 0.10 for both statistics. The configuration persistence is thus somewhat greater than a null preserving both temporal and cross-sectional structure would typically produce, but the margin is modest, and much of the observed stability reflects the joint inertia of the two slow-moving series rather than a distinct and durable cross-country ordering. This persistence does not depend on the ±0.25 SD threshold: across bands from 0.10 to 1.00 SD, κ remains between 0.68 and 0.74 (
Table A4, Panel B), and it is equally visible in threshold-free measures. The within-country first-order autocorrelation of the gap is 0.46, the between-country share of its variance is 0.85, and the year-to-year rank correlation of countries on the gap is 0.93 (
Table A4, Panel A). The temporal ordering of the two series can also be read descriptively. Upon pooling the within-country demeaned series, the cross-correlation between consumer adoption at year t and SME participation at year t + k peaks at k = 0 (r = 0.68), with near-symmetric values one year on either side (0.66 at k = −1, 0.58 at k = +1); a distributed-lag specification tells the same story, with the contemporaneous term significant (0.13,
p = 0.04) and the one-year lag not (−0.03,
p = 0.68). At annual frequency, the co-movement is therefore essentially contemporaneous, with no detectable lead of one dimension over the other. This is exploratory description, not a causal-ordering test. Broken out by state, the two imbalanced configurations are the most stable (
Table 5): an SME-leading country-year is followed by another SME-leading year 90.3% of the time (country-clustered bootstrap 95% CI 83.3–95.7%) and a consumer-leading year by another consumer-leading year 90.8% of the time (95% CI 81.2–96.7%). Direct transitions between the two extremes number 3 in 239 (1.3%). Relative alignment shows the lowest retention: 57.1% of aligned years are followed by another aligned year (95% CI 41.9–69.2%), an interval that does not overlap those of the two outer categories. This difference should not be over-read, because the classification geometry works against the middle category; the aligned band is bounded on both sides and sits at the centre of the distribution, so its members are closer to a boundary than those of the two open-ended outer categories and have more ways to leave it.
Grouping countries according to the configuration implied by their mean alignment gap yields three classes, and this grouping is not a new construction; it applies the same ±0.25 SD bands set in
Section 3.7, evaluated on each country’s mean gap. Thirteen member states fall on the SME-leading side (Lithuania, Croatia, Ireland, Portugal, Malta, Romania, Spain, Belgium, Cyprus, Bulgaria, Greece, Denmark, Czechia), nine on the consumer-leading side (Latvia, Finland, Poland, Estonia, Germany, Slovakia, the Netherlands, France, Luxembourg), and five sit inside the aligned band (Sweden, Italy, Slovenia, Hungary, Austria). No separation test is reported for these classes: they are defined by cutting the mean gap at the pre-set bands, so testing whether the resulting groups differ on the mean gap would be circular. What can be checked independently is agreement with a different criterion, and the mean-gap classification matches the unique modal annual configuration wherever one exists, resolving the ties for Czechia (5/0/5) and Sweden (4/4/2).
Figure 2 displays the underlying country-year pattern.
These are classes read off the pre-specified bands at country level, not groups recovered by a clustering procedure, and nothing in what follows depends on their boundaries.
Table 6 gives the full country picture, and it shows how unevenly the positions are held. Nine member states never leave one configuration across the whole decade; Croatia, Cyprus, Lithuania and Portugal are SME-leading in all ten years, while Estonia, Luxembourg, the Netherlands, Poland and Slovakia are consumer-leading in all ten. France is consumer-leading in all nine of its observed years. Romania and Spain are SME-leading in nine years of ten, and Germany is consumer-leading in eight. Others are far less settled: Sweden splits into four SME-leading years, four aligned, and two consumer-leading, and Czechia divides evenly between the two extremes. Hungary and Italy sit mostly in the aligned band. Therefore, the persistence reported above is not uniform across states—a minority of countries account for most of the stability, and a handful move repeatedly.
Romania’s position illustrates how the relative measure must be read and is worth spelling out because it inverts the intuitive picture. Romanian consumers rank near the bottom of the EU adoption distribution, and Romanian SMEs also rank low on e-sales participation; the classification is SME-leading because the consumer side sits further below the EU norm than the firm side does. It is a statement about relative standing within the EU distribution, not about either side being strong in absolute terms. The same caution applies to every label in the table.
4.5. Dispersion and Co-Alignment (RQ4)
Because the gap is standardised within year on complete cases, its cross-country dispersion is governed exactly by the annual correlation between the two sides: SD(gap) = √(2(1 − ρ)). The two are the same fact viewed from two angles, and reporting them together keeps the convergence question honest.
The annual correlation fell over the decade from 0.539 in 2015 to 0.415 in 2024 (
Figure 1c). A linear trend on the 10 annual values has a negative slope (−0.016 per year), but inference on 10 annual points estimated from 27 countries is fragile: a country-clustered bootstrap that re-estimates each year’s correlation places the 95% interval on the slope at [−0.049, 0.013], so the decline is not statistically distinguishable from no trend (
Table A3). By the identity, the dispersion of the gap rose in step, from 0.96 to 1.08, and carries the same uncertainty. The point estimate is robust to which year is dropped (leave-one-year-out slopes range from −0.020 to −0.024), so the direction is stable even though it is imprecisely estimated. The decline is a trend rather than a monotonic slide;
Table 3 shows the correlation dropping in 2019, recovering through 2020 and 2021, then falling again. The pattern is not confined to a single pandemic-year change; the downward trend includes interruptions and partial recoveries.
Set beside the raw-series trends from
Section 4.2, three separate facts line up. Cross-country dispersion in consumer adoption fell sharply and significantly (−0.91 per year, R
2 = 0.96; bootstrap 95% CI [−1.25, −0.51]). Dispersion in SME e-sales participation drifted upward, but only slightly and not significantly (+0.13 per year; bootstrap 95% CI [−0.06, +0.33]). Moreover, independently of both, the annual correlation between the series edged down without reaching significance. The first two do not mathematically imply the third: a correlation is invariant to separate rescaling of its components, so both dispersions could have moved exactly as they did while the correlation held constant. What ties the third fact to the gap is construction rather than causation—because the gap is a difference in within-year standardised scores, its dispersion rises precisely as the correlation falls. Taken together and read at the level of statistical confidence each trend supports, the three describe consumers growing significantly more alike in their online buying, firms showing no significant change in the spread of whether they sell online, and a co-alignment between the two that edges down but not decisively. Only the consumer-side convergence is firmly established; the other two are directional descriptions consistent with it. The convergence observed over the Digital Single Market period is, on these data, a convergence in consumer adoption with no counterpart in SME participation. Whether the single-market programme caused the household convergence is beyond what a descriptive panel can establish; what the data show is that the observed convergence is confined to consumer adoption and has no clear counterpart on the firm side.
This reading sits within a small recent study on digital convergence in Europe. Aumeboonsuke [
34], applying sigma and beta convergence to five composite digital indices, which finds the EU converging more consistently than comparator regions across the 2010–2024 window (a demand-and-infrastructure convergence that our household series echoes). What that single-index work cannot register is that the convergence is one-sided; pairing the two constructs, as we do, exposes a divergence inside a single economy that composite-index convergence studies are built not to see. Bruno et al. [
35] make the complementary point at finer resolution, showing that national digital aggregates mask substantial within-country divides. Their caution reinforces ours (
Section 3.5): a country-level correlation is a statement about national distributions, not about the firms and consumers inside any one country.
4.6. Robustness
Table 7 collects the robustness programme. The question it addresses is narrow: is the weak, marginal within-country association of
Section 4.3 sensitive to the definition of consumer adoption, to functional form, to sample or to specification? Across the reported specifications, the estimate remains small and positive and does not reach conventional significance. The separate-period estimates reported below are descriptive checks of temporal stability, interpreted through the interaction test rather than through differences in their individual
p-values.
The country-specific trend specification remains positive (0.126, p = 0.09); the coefficient does not reach the 0.05 threshold, so the substantive interpretation is unchanged, although the association is better described as consistently weak than as a clean zero. Across the specifications measured in percentage points, the estimate stays between 0.05 and 0.14; that stability, not any single row, is the result. The three-month consumer adoption measure returns the weakest coefficient of all (0.048, p = 0.59); defining consumer adoption by recent rather than annual purchasing does not strengthen the link to SME e-sales participation, which warns against any reading in which the null is an artifact of the twelve-month window. The source–period interaction, testing whether the association differs between the pre-2020 and 2020-onwards household series, is itself insignificant (interaction coefficient 0.03, p = 0.45), so we find no evidence that the estimated association differs across the two source periods; this test does not, however, establish full metric comparability across the series break. The three selected-country exclusions move the coefficient between 0.08 (without Germany) and 0.14 (without Romania) without crossing into significance. These are illustrative checks on contrasting states, not the full leave-one-country-out series over all 27 members. A more direct pre-/post-pandemic test addresses whether the consumer–SME relationship itself shifted around COVID-19, rather than merely across the data-source break. Adding an interaction between consumer adoption and a post-2020 indicator to the two-way fixed-effects specification leaves the interaction insignificant (−0.03, p = 0.50), and estimating the association separately on the two sub-periods gives 0.176 (p = 0.08) for 2015–2019 and 0.121 (p = 0.01) for 2020–2024, both small and close to one another. We therefore find no evidence that the within-country relationship changed across the pandemic break; the data do not support a distinct pandemic-era regime. A further check addresses the survey-year to reference-year realignment of the enterprise series. Re-estimating the baseline with each enterprise value kept at its original published survey year, rather than shifted to the reference year it describes, gives a within-country association of 0.128 (p = 0.12), which is close to the 0.116 of the aligned specification. This result is therefore not an artefact of the temporal realignment.
Two further properties hold by construction rather than by test and are noted for completeness. Both directional configurations remain substantial under the ±0.25 and ±0.50 SD bands, although the category shares change as expected when the tolerance band is widened: the ±0.25 and ±0.50 SD bands give the same qualitative split (
Section 4.4). The alignment measure is scaled so that its annual mean is exactly zero and the correlation–dispersion identity of Equation (3) holds to machine precision, which no estimation choice can disturb.