Operating Model or Financial Structure? Profitability in Italian SMEs

1. Introduction

Why some firms earn more than others has been answered, in the literature on small and medium enterprises, almost entirely in financial terms. Capital structure is the organising variable: Adair and Adaskou (2015), Balios et al. (2016), Dalci (2018), D’Amato (2019), Bui et al. (2021), Boshnak (2023) and Arhinful et al. (2025) estimate the association between leverage and profitability across national panels and report with remarkable consistency that the two move in opposite directions. Recent work extends the covariate set—Agliardi et al. (2024), Gutiérrez-Ponce (2024), Abdalla et al. (2025)—without reopening the question of whether financial structure is the right organising variable.

It may not be. Return on assets is a joint product of how a firm is financed and how it operates, and the operating side—the share of value added absorbed by labour, the intensity of bought-in production, the reliance on leased rather than owned assets—has been left almost entirely outside the discussion. Cost structure is studied at sectoral or macroeconomic level, where Canarella et al. (2013), Grau and Reig (2021) and Bradfield et al. (2023) locate it, and enters firm-level models as an unexamined control if at all. The two explanations have never been placed in competition inside a single specification. That is the gap, and the research question follows from it: when financial structure and operating model are estimated jointly on the same firms, which determines profitability, and how much of the answer survives the choice of estimator?

Posing the question this way exposes a second problem. The equity ratio and return on assets share a component: net worth contains current-year profit, and return on assets is computed on that same profit, so part of any contemporaneous association is an accounting identity. Campello (2006) recognised the joint determination of financing and performance, and a substantial literature—Bharati and Jia (2018), Iqbal et al. (2022), Adem and Dsouza (2024), Dsouza et al. (2025)—addresses endogeneity through system GMM or lagged instruments. But endogeneity is treated as a nuisance corrected in a robustness column, not as a threat to whether the parameter is recoverable at all.

A third literature, developed in parallel without contact with the other two, completes the argument. Firm profits are persistent and mean-reverting: Glen et al. (2001), Goddard et al. (2006), Bartoloni and Baussola (2009), Maury (2018) and Eklund and Lappi (2019) establish the regularity across settings. Its implication for identification has not been drawn. If profitability at t is substantially predicted by profitability at t−2, any lagged financial ratio embedding past profit is correlated with the current error, and the internal instruments the endogeneity literature relies on are invalid by construction.

The setting is the Italian population of certified innovative firms with a matched control group of conventional SMEs: 14,913 firms observed between 2014 and 2025. Decree-law 179/2012 created certified innovative start-ups with a statutory life of sixty months; Decree-law 3/2015 added innovative SMEs as an intermediate category. Evaluations by Caselli et al. (2019), Biancalani et al. (2022), Aiello et al. (2024) and Albanese and Bronzini (2026) estimate average effects while presuming the mechanism through which certification operates—a relaxed financial constraint—without measuring it. Three populations drawn from one accounting framework differ in the financial instruments available to them.

The originality lies in estimating it three times over, by methods answering different questions. Panel estimation asks what the average association is and whether it survives the estimator. Unsupervised partitioning asks whether one coefficient vector describes every firm and, unlike the taxonomy work of Chu et al. (2014), Ayadi et al. (2021) and Uddin et al. (2024), re-estimates the relationship inside each group. Machine-learning regression asks whether the linear form is adequate and, unlike the prediction-oriented work of Jones (2023), D’Amato et al. (2024) and Mekelburg and Strauss (2024), uses the same firm-demeaned data as the panel estimator, so the comparison is like-for-like and the residual gap can be decomposed. Convergence among methods with different assumptions is what makes the conclusion durable.

The contribution is fourfold: it measures the relative weight of financial and operating determinants within one specification; it shows that the capitalisation coefficient is not identified by accounting data of this kind and diagnoses why the instruments fail; it establishes that the structure of profitability determination differs across regulatory populations, which bears on the premise of the certification scheme; and it demonstrates a diagnostic rather than competitive use of machine learning.

The article continues as follows. Section 2 reviews the four literatures the paper draws on—capital structure and small-firm performance, endogeneity and identification, profit persistence, and the evaluation of certification schemes—and locates the gap the study addresses. Section 3 describes the data, the construction of the variables and the three estimation strategies. Section 4 reports the panel estimates and the specifications through which the capitalisation coefficient is traced. Section 5 partitions firms on the variables of the equation and re-estimates it within each group. Section 6 tests the adequacy of the linear functional form by machine-learning regression. Section 7 positions the findings relative to the existing literature, Section 8 draws the policy implications, Section 9 sets out the limitations, and Section 10 concludes. Four appendices report the full estimation tables, the instrumental-variable attempts, the clustering battery and the machine-learning diagnostics.

2. Literature Review

Capital structure and profitability in small firms. Whether the way a firm is financed shapes what it earns is among the most heavily worked questions in the empirical literature on small and medium enterprises, and its central result is unusually stable across settings: leverage and profitability are negatively associated. Adair and Adaskou (2015) establish the pattern for French SMEs, Balios et al. (2016) for Greek firms under crisis conditions, Banga and Gupta (2017) and Gnanaprasuna et al. (2025) for Indian samples, Dalci (2018) for Chinese manufacturers, D’Amato (2019) for Italian SMEs, Agyei et al. (2020) for Ghanaian banks and Bui et al. (2021) for Vietnam. Boshnak (2023), Mansour et al. (2023), Mahmood et al. (2023), Kambi and Kasoga (2024) and Arhinful et al. (2025) extend the finding to further national panels, while more recent work enlarges the covariate set rather than reopening the question: Agliardi et al. (2024) introduce dynamic optimisation, Gutiérrez-Ponce (2024) sustainability reporting, Abdalla et al. (2025) family ownership and Marozva (2026) macro-financial conditions. The consistency of the sign conceals a real disagreement about why it holds. Under pecking-order reasoning, profitable firms accumulate retained earnings and borrow less, so causality runs from performance to structure and the negative coefficient describes financing behaviour rather than its consequences. Under trade-off and agency reasoning, leverage disciplines managers and lowers the cost of capital, and the negative sign becomes a puzzle to be resolved by appeal to distress costs. Kenourgios et al. (2020), Amini et al. (2021) and Duppati et al. (2023) each report evidence compatible with more than one mechanism, and the designs employed cannot separate them, because a single contemporaneous correlation is consistent with all of them. A smaller set of studies reports the opposite sign or a conditional one, typically in samples of young or capital-constrained firms, and the divergence is generally attributed to institutional differences or sample composition rather than to specification. Three features of this literature bear on what follows. The modal design is a national panel of a few hundred to a few thousand firms observed over five to ten years, estimated by fixed effects or system GMM with contemporaneous regressors. The equity or debt ratio is almost always the focal variable, and cost-structure variables, where they appear at all, enter as controls without discussion. And the mechanical relationship between dependent variable and focal regressor is rarely acknowledged: net worth contains current-year profit, and return on assets is computed on that same profit, so part of any contemporaneous association is an accounting identity rather than an economic relationship. Campello (2006) is among the few to treat financing and performance as jointly determined, and that position has not become standard practice in the work that followed.

Endogeneity and what identification is used for. A methodologically self-aware body of work addresses the problem directly. Bharati and Jia (2018), Canarella and Miller (2018), Ahmed et al. (2022), Iqbal et al. (2022), Adem and Dsouza (2024), Chauhan et al. (2024), Choi et al. (2024), Dsouza et al. (2025), Li et al. (2025), Essel (2025, 2026), Alwadeai and Abideen (2026) and Islam et al. (2026) all confront endogeneity explicitly, typically through system GMM or lagged internal instruments, while Camuffo and Poletto (2024) move towards experimental identification. Yet endogeneity is generally treated as a nuisance to be corrected rather than as evidence in its own right, and the correction appears as a robustness column beside a preferred estimate. What is almost never done is to trace the focal coefficient across the full range of estimators and treat disagreement among them as the substantive finding. Where instruments fail—as internal lags must whenever the dependent variable is persistent—the failure tends not to be reported. The tools are present in this literature; they are used to defend an estimate rather than to test whether any estimate is defensible.

Profit persistence. A separate and theoretically mature line of work establishes that firm profits are persistent and mean-reverting. Glen et al. (2001) document the pattern in emerging markets, Goddard et al. (2006) in European manufacturing, Bartoloni and Baussola (2009) in Italy, Hirsch and Gschwandtner (2013) and Hirsch and Hartmann (2014) in food processing, and Eklund and Lappi (2019) across European regions. Maury (2018) and Wibbens (2019) connect persistence to competitive advantage, Hirsch et al. (2021), Jaisinghani and Sekhon (2022) and Opstad et al. (2022) extend it to more recent samples, Fairfield et al. (2009) tie it to accounting measurement and Agliardi et al. (2026) to refinancing decisions. The implication for the two preceding literatures is direct and largely unexploited. If profitability at t is substantially predicted by profitability at t−2, then any lagged financial ratio embedding past profit is correlated with the current error through persistence alone. Persistence therefore does not merely complicate estimation: it invalidates the internal instruments on which identification routinely relies. Each literature is well developed, and each cites the other rarely.

Innovative firms and public support. Public support for innovative and young firms has generated a dense empirical literature, and the Italian case is among the most closely studied. Decree-law 179/2012 created a certified category of innovative start-ups with a statutory life of sixty months, granting tax relief, free access to a public credit guarantee, exemption from ordinary insolvency procedures and relief from company-law rules on capital maintenance; Decree-law 3/2015 added innovative SMEs as an intermediate category, with eligibility thresholds on research spending, graduate employment and intellectual property. Caselli et al. (2019), Antonietti and Gambarotto (2020), Barboza and Capocchi (2020), Cavallo et al. (2020, 2021), Accetturo (2022), Biancalani et al. (2022), Colombelli et al. (2023), Agstner (2024), Aiello et al. (2024), Banfi et al. (2024), Bottai et al. (2024), Anderloni and Harasheh (2025), Barboza and Braga (2025), Colombelli and Tubiana (2025) and Albanese and Bronzini (2026) between them examine financing, employment, survival, location and innovation output. Two limitations recur. Evaluations estimate average treatment effects on outcomes while treating the mechanism as given: certification is presumed to operate by relaxing a financial constraint, and the constraint itself is not measured. And the comparison is almost always between certified firms and a matched control, leaving the internal heterogeneity of the certified population unexamined, even though that population contains firms at very different stages of operational development. The setting is well suited to addressing both, since the scheme defines three populations drawn from a single national accounting framework, which makes a comparison of coefficient structure across them meaningful in a way cross-country comparisons are not.

Firm taxonomies and machine learning. Two methodological literatures complete the picture. Work on firm taxonomies partitions firms by financial or business-model characteristics: Chu et al. (2014) in design industries, Musile Tanzi et al. (2018), Ayadi et al. (2021) and Zarutska et al. (2022, 2024) in banking, Pieroni et al. (2020) in circular-economy models, and Panchal and Krishnamoorthy (2020), Shpak et al. (2023), Siddiqui and Rivera (2024), Uddin et al. (2024), Amit et al. (2025) and Antunes Marante et al. (2025) in more recent applications. The recurring weakness is selection: partitions are chosen on a single validity index, most often silhouette, which rewards isolating a few extreme observations; stability under resampling is seldom tested; and the partition is rarely used to re-estimate the substantive model within groups. Applications of machine learning to firm-level financial data have expanded rapidly. Manogna and Mishra (2021), Jones (2023), D’Amato et al. (2024), Mekelburg and Strauss (2024), Lin and Lin (2025), Romero Martínez et al. (2025) and Xu et al. (2025) apply ensemble learners to distress prediction, valuation and rating, and a substantial recent cohort extends the approach further. Almost all frame the exercise as prediction and evaluate it on accuracy. Few use flexible learners diagnostically—to ask whether the linear form imposed by a companion econometric model is adequate, which variables carry information under the same fixed-effects transformation, and whether any shortfall can be repaired parametrically. Where comparisons with linear models appear, they frequently set a levels-based machine-learning R² beside a within-transformed econometric R², which is not a like-for-like comparison. Neither literature has been used for the purpose adopted here: taxonomies describe groups without re-estimating a structural relationship inside them, and machine learning measures predictive superiority without characterising the shortfall of the parametric model it displaces.

The gap. Cost structure has been left almost entirely outside this discussion. Canarella et al. (2013), Grau and Reig (2021), Bradfield et al. (2023) and Akgün and Günay (2026) are among the few firm-level treatments. The labour share of value added, the intensity of purchased services and reliance on leased rather than owned assets are studied at sectoral or macroeconomic level, and enter firm-level profitability models as controls if they enter at all. The literature on SME profitability has organised itself around financing, and the operating model has not been posed as its competitor within a single specification. This study places both blocks in one equation and measures their relative weight by three independent routes on the same sample. It treats the instability of the capitalisation coefficient across estimators as the finding rather than concealing it, and diagnoses why the instruments fail rather than omitting them. It selects a partition of firms on a composite of eleven validity indices with bootstrap stability testing and re-estimates the equation within each group. And it applies machine learning to the same firm-demeaned data as the panel estimator, so that the comparison is like-for-like, then asks how far parametric enrichment closes the remaining gap. Two boundaries apply throughout: no design available identifies a causal effect, since there is no exogenous variation in financial structure and the regulatory populations are self-selecting; and the cost ratios are fragile for firms whose production approaches zero, a problem addressed by sample restriction rather than by rescaling on total assets, which would place them in an accounting identity with the dependent variable. See Table 1.

All figures in the final column refer to the estimating sample of 91,756 firm-year observations on 14,913 firms described in Section 3. Full bibliographic details for the studies cited are given in the reference list.

3. Data and Methodology

The panel is assembled from thirty-one AIDA extractions covering the universe of Italian certified innovative start-ups and innovative SMEs, together with a matched set of conventional small and medium enterprises. AIDA reports harmonised statutory accounts for Italian companies and has been the standard source for firm-level work on this population, including Caselli et al. (2019), Biancalani et al. (2022), Aiello et al. (2024) and Anderloni and Harasheh (2025). Each extraction contains 137 distinct accounting variables replicated over ten financial years; the reference year of each column is reconstructed from the balance-sheet closing date, which is serialised differently across extractions and requires format-specific conversion. Regulatory status and sector codes are merged from the business register maintained by the Ministry of Enterprise, matched on fiscal code.

The estimating sample comprises 91,756 firm-year observations on 14,913 firms between 2014 and 2025. It is identical across all three methods and all four appendices: the same observations enter the panel estimates, the firm-level partitioning and the machine-learning comparison, so that differences between the three sets of results are attributable to method rather than to sample. See Table 2.

The panel is unbalanced in a way correlated with regulatory status: start-ups file meaningful accounts in roughly one year in three against more than nine in ten for conventional SMEs, a pattern consistent with the reporting behaviour documented by Bottai et al. (2024). Conventional SMEs therefore contribute close to two thirds of the observations while accounting for under half the firms, and the weighting schemes reported in Appendix A establish how much this matters.

The dependent variable is return on assets. The regressors are organised into two blocks. The financial block comprises the equity ratio, the liquidity ratio, capital turnover and the logarithm of total assets—the variables around which the small-firm literature of Adair and Adaskou (2015), Dalci (2018) and Boshnak (2023) is organised. The operating block comprises the labour cost share of value added, purchased services and materials as proportions of the value of production, and payments for leased assets on the same basis. All continuous variables are winsorised at the first and ninety-ninth percentiles within year.

Two measurement decisions require justification, and both determine the sample. Cost ratios expressed against the value of production become uninformative where production approaches zero: before restriction, purchased services reach 92,344 per cent of output at the ninety-ninth percentile. The sample is therefore confined to observations with positive value of production, positive value added, and value of production of at least one per cent of total assets. The restriction removes 8.8 per cent of observations, but it is not neutral across populations—29.3 per cent of start-up observations against 1.0 per cent of conventional SME observations—because pre-operating firms are concentrated among the certified. The estimates consequently describe firms with genuine operating activity, a limitation returned to in Section 9.

Rescaling the cost ratios on total assets is not an alternative, because return on assets carries assets in its denominator and the rescaled ratios would stand in an accounting identity with it: regressing ROA on turnover and the four asset-scaled ratios in levels yields an R² of 0.488 with all four coefficients between −0.48 and −0.64, against 0.088 for the output-scaled versions. And no ratio constructed from depreciation enters as a regressor, since the operating result is computed net of depreciation.

The equation is estimated three times, by methods that interrogate different assumptions. Panel estimation establishes the average conditional association and tests whether it survives the estimator: pooled OLS, between, one-way and two-way fixed effects, random effects with Hausman and Breusch–Pagan tests, weighted least squares under two weighting schemes, and a dynamic specification following Anderson and Hsiao. Five instrument sets are examined and reported with first-stage and overidentification diagnostics, in the spirit of the endogeneity treatments of Bharati and Jia (2018), Iqbal et al. (2022) and Dsouza et al. (2025), but with failures reported rather than omitted. Standard errors are clustered by firm throughout. The lagged and dynamic specifications necessarily lose observations at the start of each firm’s series, reducing the sample to 76,261 and 64,031 respectively; all other panel specifications use the full 91,756.

Unsupervised partitioning tests whether one coefficient vector describes every firm. The 14,913 firms are summarised by decade medians of the nine variables, standardised, and thirty-one configurations across six algorithm families are scored on eleven validity criteria. Selection is by composite rank rather than by any single index, avoiding the reliance on silhouette alone that characterises the taxonomies of Chu et al. (2014), Ayadi et al. (2021) and Uddin et al. (2024); stability is verified across fifty bootstrap resamples. The equation is then re-estimated within each group on the same observations, and equality of coefficient vectors tested pairwise.

Machine-learning regression tests the adequacy of the linear form. Thirteen algorithms are fitted to the same 91,756 observations with five-fold cross-validation grouped by firm, so that no firm appears in both training and test partitions. Unlike the prediction-oriented applications of Jones (2023), D’Amato et al. (2024) and Mekelburg and Strauss (2024), the learners are applied to the same firm-demeaned data as the fixed-effects estimator, making the comparison like-for-like, and the residual gap is decomposed by parametric enrichment, permutation importance and partial dependence to establish what kind of structure the linear form omits. See Figure 1.

4. Panel Estimation Results

The F test on the null that individual effects are jointly zero equals 5.60 and rejects beyond any conventional threshold, so pooled OLS is inconsistent. The Breusch–Pagan multiplier, at 25,011.2, confirms through a different route that the variance of the individual component is non-zero, and the Hausman statistic of 117.01 on eight degrees of freedom rejects the consistency of random effects. Two-way fixed effects is the reference specification. See Table 3.

All eight regressors are significant at the one per cent level, and the within R² of 0.4232 indicates that the specification accounts for a substantial share of the variation in profitability that occurs inside firms over time. Because the regressors are measured on incompatible scales, Figure 2 rescales every coefficient to the effect of a one-standard-deviation increase, which is the only way to compare them directly. See Figure 2.

Capital turnover dominates under every estimator, and the labour share follows. Rescaled, a one-standard-deviation increase in turnover is worth roughly four points of ROA and a comparable increase in the labour share costs close to four; capitalisation is worth about three; purchased services, materials and leased assets between one and two points each. Liquidity is negligible throughout. The two blocks therefore contribute on the same order of magnitude, which the unrescaled coefficients conceal. See Figure 3.

Comparing the between and within estimators is more informative than any single coefficient, and it is the diagnostic least often reported. On the labour share and on purchased services the two agree closely, indicating relationships that hold both cross-sectionally and over time. On size they diverge sharply, so within-firm asset growth operates differently from the advantage of being structurally large. Capitalisation is higher within than between, which is consistent with the accounting identity discussed below rather than with a stronger structural effect.

The positive capitalisation coefficient faces an elementary objection: net worth contains current-year profit and ROA is computed on the same profit, so part of the correlation is an accounting identity. Lagging every regressor by one year reverses the sign, from +0.177 to −0.068. Modelling persistence instead—Anderson and Hsiao in first differences, with ROA(t−2) instrumenting the lagged difference, an autoregressive coefficient of 0.271 and a first-stage F of 18,230—returns it to positive and larger, at +0.228. Five instrument sets were then tried, and all five produce negative estimates. See Figure 4.

The figure is the finding. Static estimators cluster between +0.10 and +0.20; lagging moves the coefficient below zero; the dynamic specification moves it back to +0.23; every instrumental-variable specification places it between −0.12 and −0.28. These are not overlapping confidence intervals but qualitatively different answers. The instruments themselves fail: specification (2), which uses the second and third lags, rejects the Hansen test with a statistic of 77.18, and the mechanism is identifiable—with ROA persistent at 0.271, the equity ratio at t−2 mechanically embeds profit at t−2, which predicts profit at t through persistence alone. The instrument with a defensible exclusion restriction, net external equity injections, has a within-firm correlation with the regressor of 0.103, so any violation of exclusion is amplified roughly tenfold (Appendix B).

The sign of the capitalisation coefficient is therefore not identified by these data, and that instability is itself the result. It bears on a literature that routinely reports a positive contemporaneous association between capitalisation and SME profitability without addressing the accounting identity that generates much of it. The operating coefficients, by contrast, keep their sign and rough magnitude across every specification in Figure 4 and Appendix A: the labour share ranges only between −0.115 and −0.141 across seven of the eight estimators.

The panel is unbalanced in a way correlated with regulatory status. Weighting each firm equally rather than each observation raises capitalisation from 0.177 to 0.199 and size from 0.646 to 0.855, so the relationship is somewhat stronger among firms observed briefly. Weighting by total assets instead, to recover the effect relevant for the economic aggregate rather than the median firm, halves capitalisation to 0.099 while raising capital turnover from 5.29 to 6.89 and materials from −0.114 to −0.149. In large firms, which carry the aggregate, the operating model matters more and financial structure less. The two answers address different questions, which is why both are reported. See Figure 5.

Wald tests reject equality of the coefficient vectors: 87.18 between start-ups and innovative SMEs, 181.94 between start-ups and ordinary SMEs, and 138.08 between the two SME categories, all with p below 10⁻⁴ on eight degrees of freedom. This is not a difference in the level of profitability, which fixed effects absorb, but in the structure of determination. Certification schemes rest on the premise that innovative firms face tighter financial constraints; evaluations customarily measure average effects on growth or employment while treating the constraint as given. The evidence here shows the constraint is measurable, varies across the very populations the schemes distinguish, and survives every specification attempted.

5. Unsupervised Structure

The panel estimates impose a restriction the data have not been asked to confirm: that one coefficient vector describes every firm. The restriction can be tested without leaving the equation, by partitioning firms on its own variables and re-estimating within each partition. The exercise identifies no causal effect. It bears on whether the pooled coefficients mean what they appear to mean, or whether they average structures that differ.

Each firm is summarised by the decade median of the nine variables entering the equation, standardised, on the same sample as Section 4. Regulatory status is withheld from the procedure and used only afterwards as an external check. Thirty-one configurations were evaluated—k-means, Ward agglomerative, Gaussian mixture and fuzzy c-means for k between two and seven, density-based clustering across a grid of radii, and random-forest proximity clustering—each scored on eleven validity criteria reported in Appendix C.

Selecting on a single index misleads, and the direction of the error is systematic. Silhouette falls monotonically in k for every partitional method, so on that criterion alone the two-cluster solution always wins; Calinski–Harabasz behaves the same way, while partition R² and the Dunn index move in the opposite direction. The two density-based solutions attain the highest silhouette values in the whole battery while classifying between four and thirty-three per cent of firms as noise. Averaging ranks across all nine directional indices selects k-means at k = 4, which places first on partition R² among balanced solutions and keeps its smallest group at 14.9 per cent of firms. Fifty bootstrap resamples at eighty per cent give a mean adjusted Rand index of 0.9375, with a minimum of 0.6167. The neighbouring three-cluster solution ranks close behind and was verified to leave the coefficient pattern of Table 4 qualitatively intact. See Figure 6.

Cluster 0, a third of firms, is labour-intensive: a labour share of 89.6 per cent of value added, the lowest capitalisation at 17.3 per cent, and a median return of 3.03. Cluster 1, twenty-seven per cent, is materials-intensive and largest in scale, with materials at 47.4 per cent of output and median log assets of 9.75. Cluster 2, twenty-four per cent, comprises micro service firms: purchased services at 57.4 per cent of output, a labour share of 0.63 per cent, the smallest scale, and a median return of 7.36. Cluster 3, fifteen per cent, is the only group defined financially rather than operationally, with capitalisation of 70.1 per cent, a liquidity ratio of 3.70, the lowest turnover and the highest median return at 10.23. See Table 4.

Two features of the separation matter. The variables that distinguish the groups most sharply are the labour share, scale and capital turnover; liquidity separates them least. And capitalisation, although it defines Cluster 3, contributes less to the overall separation than the labour share—0.70 of a standard deviation between the extreme groups against 1.44. Financial structure characterises one archetype; it does not organise the partition. See Figure 7.

Compared afterwards with regulatory status, partition and register correspond strongly without coinciding, with Cramér’s V of 0.4780. Ordinary SMEs concentrate in the two established operating archetypes, 46.0 and 46.9 per cent, with only 7.1 per cent elsewhere. Innovative start-ups distribute almost inversely, 53.1 per cent in the micro-service group and 24.2 per cent in the capitalised one. Innovative SMEs spread across all four, consistent with a category reached either by graduation from start-up status or by direct entry from conventional activity.

Pairwise Wald tests reject equality of the coefficient vectors for all six pairs, with statistics between 84.45 and 374.34 on eight degrees of freedom. See Table 5.

Capital turnover carries 3.09 in the labour-intensive group and 13.16 in the capitalised one, a fourfold range. Leased assets range from −0.191 to −0.494 and purchased services from −0.098 to −0.285. The equity ratio varies less, between 0.102 and 0.231, and its ordering is informative: weakest in the materials-intensive group of larger firms, strongest in the labour-intensive group of smaller ones, which is the pattern a financing-constraint interpretation predicts.

Two further features distinguish this partition from the pooled estimate. The labour-share coefficient is stable across all four groups, between −0.132 and −0.140, so it is the one relationship the pooled specification represents faithfully. And liquidity is insignificant in three of four groups, confirming from an independent direction the inertness already visible in Section 4. The implication is specific: the pooled vector is an adequate summary in two of eight dimensions and a poor one in the remaining six.

6. Machine-Learning Regression

The second assumption of the panel specification is that each regressor enters linearly and additively. Testing it requires a comparison frequently made incorrectly. The fixed-effects estimator explains variation within firms, after removing firm means; a learner fitted to raw levels also has the between-firm variation available, so setting a within R² against a levels R² attributes to functional form what mostly reflects a different variance decomposition. Cross-validation is five-fold and grouped by firm, so no firm contributes to both training and testing. See Table 6.

The three rows answer the same question under three different treatments of between-firm variation, and reading them together is what makes the comparison interpretable. The first row gives the learner access to differences between firms as well as within them; the second removes firm means, replicating exactly what the fixed-effects estimator does; the third restores the between-firm information to the linear model in the form of firm means, following Mundlak. Comparing the first and third rows isolates how much of the linear model’s disadvantage on levels is simply unmodelled firm heterogeneity, and comparing the second with either isolates what remains attributable to functional form. Figure 8 plots the three side by side.

On raw levels the non-linear model is 1.69 times more accurate; on firm-demeaned data, which is what the fixed-effects estimator uses, the ratio falls to 1.29 and the absolute gap from 0.325 to 0.121. The linear specification recovers 0.415 of within-firm variance against 0.536 attainable. Supplying the linear model with firm means in the manner of Mundlak raises it only from 0.473 to 0.480. See Figure 9.

The figure shows the ordering; the table gives the quantities behind it and adds two columns the plot cannot carry. The first is the number of terms, which turns each specification into a price: sixteen terms buy 13.7 per cent of the gap, forty-four buy 20.6, and one hundred and sixty-four buy nothing at all. The second is the cross-fold standard deviation, which explains why the cubic expansion fails rather than merely recording that it does. Reading the two together converts a ranking of fits into a statement about the kind of structure the linear specification omits, which is the point of the exercise. See Table 7.

Partly, but not mostly. Squared terms recover 13.7 per cent of the gap, pairwise interactions 16.7, and both together 20.6. A full cubic expansion in 164 terms performs worse than the original eight-regressor model, with a cross-fold standard deviation of 0.189 against 0.013, because it overfits the tails of a heavy-tailed dependent variable. Roughly four fifths of what the learner captures is therefore not polynomial: it is local structure—thresholds, saturation, regions where a variable matters and regions where it does not. Friedman H-statistics are correspondingly small, the strongest pair reaching 0.042, so the residual structure is univariate curvature rather than pairwise interaction. See Table 8.

The labour share alone accounts for 63.5 per cent of predictive content, capital turnover for 13.3 and purchased services for 9.6: the operating block carries roughly ninety per cent of the information against 6.5 per cent for the equity ratio and 1.1 for liquidity. This is a sharper hierarchy than the panel coefficients suggest, and it corroborates the clustering result that the labour share is the variable whose relationship with profitability is both strongest and most stable. See Figure 10.

The shapes explain the residual parametric failure. The labour share declines steeply and then flattens; capital turnover rises and saturates; purchased services are flat over most of their range before bending. The equity ratio is close to monotone and mild, consistent with the modest positive fixed-effects coefficient rather than with the negative instrumental-variable estimates of Section 4.2. See Figure 11.

In the bottom decile of demeaned ROA, where the realised mean is −16.5 points, the linear model predicts −7.9; in the top decile, realised at +16.6, it predicts +6.6. The linear model compresses the distribution towards its centre by roughly a factor of two at the extremes, and gradient boosting by a factor of 1.8. In the middle six deciles both are well calibrated, with biases below 1.7 points, so essentially the whole difference arises in the tails.

Two conclusions follow for the panel section. Its coefficients are local linear approximations to a mildly curved surface and should be described as average slopes rather than constant marginal effects. And the ranking of variables they imply is corroborated rather than overturned by an independent measure of predictive content: both place the operating block first, and the machine-learning measure does so by a wider margin.

7. Discussion

Read against the literature, the results divide into three groups: those that confirm what is already established, those that contradict a widely held presumption, and those that address a question the literature has not posed.

The confirmatory group is the smallest but it anchors the rest. The static fixed-effects estimate reproduces the negative leverage–profitability association reported by Adair and Adaskou (2015), Balios et al. (2016), Dalci (2018), D’Amato (2019), Bui et al. (2021) and Boshnak (2023) across a wide range of national settings. The autoregressive coefficient of 0.271 sits within the range documented by Goddard et al. (2006), Bartoloni and Baussola (2009) and Eklund and Lappi (2019), and confirms that the mean-reverting behaviour those studies establish for larger or older firms extends to a population dominated by young and certified enterprises, where the shorter operating history might have been expected to produce faster reversion. That the estimates behave as expected where the literature is settled is what licenses the weight placed on the results where it is not.

The contradictory group concerns not a coefficient but its stability. The literature summarised in Section 2 reports the capitalisation coefficient as a parameter to be estimated, with attention devoted to controls and sample rather than to whether the parameter is recoverable at all. Estimated here under thirteen specifications, it moves from +0.18 under static fixed effects to −0.07 with lagged regressors, back to +0.23 once persistence is modelled, and to between −0.12 and −0.28 across five instrument sets. Campello (2006) anticipated the joint determination of financing and performance, but the practice that followed treats endogeneity as a correction rather than as a threat to identification. The finding is that the sign is not identified by observational accounting data of this kind, which is a stronger and less comfortable claim than the conditional or heterogeneous effects reported by Kenourgios et al. (2020) and Duppati et al. (2023). Its force comes from the contrast with the operating coefficients, which hold their sign and magnitude throughout: the labour share ranges only between −0.115 and −0.147 across the same thirteen specifications.

A second contradiction concerns policy evaluation. Studies of the Italian scheme by Caselli et al. (2019), Biancalani et al. (2022), Aiello et al. (2024), Anderloni and Harasheh (2025) and Albanese and Bronzini (2026) estimate average effects while presuming a financial-constraint mechanism common to certified firms. Wald tests reject a common coefficient vector across the three regulatory populations, with statistics of 87.18, 181.94 and 138.08 on eight degrees of freedom, and pairwise tests reject it again for all six pairs of the four clusters recovered without reference to the register, with statistics between 84.45 and 374.34. The presumed mechanism is not shared by the population it is presumed to govern.

The third group is where the contribution lies. Placing financial structure and operating model in one specification, three independent methods converge on the labour share of value added: a coefficient of −0.137 stable across specifications, between −0.132 and −0.140 across all four clusters, and 63.5 per cent of out-of-sample predictive content against 6.5 per cent for capitalisation. The invariance is the striking part. Every other coefficient varies substantially across the partition—capital turnover by a factor of four, leased assets by a factor of two and a half—while the labour share does not, which is what a structural rather than compositional relationship would look like. The literature on cost structure—Canarella et al. (2013), Grau and Reig (2021), Bradfield et al. (2023), Akgün and Günay (2026)—has not been brought into contact with the financing literature, and the comparison has not previously been made inside one equation.

Two methodological results follow the same pattern. Diagnosing instrument failure through profit persistence connects two literatures—Glen et al. (2001), Maury (2018), Wibbens (2019) on one side, Bharati and Jia (2018), Iqbal et al. (2022), Dsouza et al. (2025) on the other—that have developed in parallel without citation: persistence at 0.271 implies that the equity ratio at t−2 embeds profit at t−2, and therefore correlates with the current error by construction. And applying machine learning to the same firm-demeaned data as the panel estimator yields a like-for-like ratio of 1.29, against 1.69 on levels; since squared terms recover 13.7 per cent of the residual gap and pairwise interactions 16.7, with both together reaching only 20.6, the shortfall is local rather than polynomial, which the prediction-oriented applications of Jones (2023), D’Amato et al. (2024) and Mekelburg and Strauss (2024) do not measure. See Table 9.

8. Policy Implications

Italy’s productive structure is dominated by firms that do not grow. The size distribution is compressed towards the bottom, the share of employment in firms above the small-enterprise threshold is among the lowest in western Europe, and the number of firms that make the transition from micro to medium scale in any given decade is small. This is not a recent development and it is not primarily a financing phenomenon, although it is habitually treated as one. The evidence assembled here bears on that diagnosis directly, and its implications run against the design of the instruments currently in use.

The first implication concerns what certification schemes are for. Italy’s Start-up Act, like most European equivalents, is built on the premise that innovative firms are constrained by access to capital, and it responds with tax relief on equity investment, free access to a public credit guarantee, and relief from company-law rules on capital maintenance. Evaluations by Caselli et al. (2019), Biancalani et al. (2022), Aiello et al. (2024) and Albanese and Bronzini (2026) confirm that these instruments reach their targets and improve financing outcomes. What the present results add is that the constraint they relieve is not the binding one. Capitalisation accounts for a small and non-identified share of the variation in profitability, while the operating model—and above all the share of value added absorbed by labour—accounts for the large majority of it. A firm whose cost structure leaves it no margin does not become profitable because equity is cheaper.

The second implication concerns the sixty-month horizon. Certification expires by statute five years after incorporation, which presumes that firms reach a stable operating configuration within that window. The taxonomy recovered here suggests otherwise: a substantial fraction of certified start-ups remain in a micro-service configuration with almost no employment and negligible turnover of invested capital, and the coefficient structure governing their profitability differs sharply from that of operating firms. A fixed horizon applied to a heterogeneous population withdraws support from firms at very different stages of development. Bottai et al. (2024) and Anderloni and Harasheh (2025) document that certified firms take longer to reach profitability than their conventional peers; the implication is that the instrument’s duration is calibrated to a trajectory most of its recipients do not follow.

The third implication concerns listing and the supply of external equity. Italian firms remain overwhelmingly bank-financed and rarely access public markets, and the policy response has been to lower the cost of equity through fiscal channels—the notional-interest deduction for corporate equity, tax credits for investors in innovative firms, and simplified crowdfunding regimes. These instruments operate on the price of external capital. If profitability is determined predominantly by operating structure, the price of capital is not the margin on which the listing decision turns: firms do not list because they lack the scale and the earnings trajectory that public markets require, and neither is produced by cheaper equity. Antonietti and Gambarotto (2020) and Colombelli and Tubiana (2025) reach compatible conclusions from the innovation side.

The fourth implication concerns research and development. Eligibility is established through thresholds on research spending, graduate employment or intellectual property, which makes qualification a matter of input accounting rather than of capability. Firms with almost no operating activity satisfy these thresholds readily, since the ratios have small denominators. The certified population is therefore shaped by the measurement of eligibility as much as by innovative intent.

Taken together these results argue for reweighting rather than for withdrawal. Instruments that act on the cost of capital should be complemented by instruments that act on operating capability—managerial capacity, workforce composition, and the productivity of labour employed—since it is there that the variation in performance is concentrated. And eligibility criteria expressed as ratios to output should be reconsidered for firms whose output is negligible, because at that margin the criterion measures the denominator rather than the activity it is intended to capture.

9. Limitations

The most consequential limitation is that none of the designs employed identifies a causal effect. There is no exogenous variation in financial structure in these data: firms choose their capitalisation, and the regulatory populations compared are self-selected, since certification is voluntary and conditional on criteria correlated with unobserved characteristics. Lagging the regressors, modelling persistence and instrumenting all attenuate simultaneity without removing it, and Section 4 shows that instrumentation performs worse than the estimator it is meant to correct. The results should be read as conditional associations that survive or fail specification, not as magnitudes with a causal interpretation. The literature reviewed in Section 2 shares this limitation, but that is a reason for caution rather than an excuse, and the appropriate response is the one adopted by Manaresi and Menon in related work: to seek institutional discontinuities rather than statistical corrections.

A second limitation concerns sample composition. Innovative start-ups file meaningful accounts in roughly one year in three, against more than nine in ten for ordinary SMEs, and the restriction imposed to obtain interpretable cost ratios removes a further 29.3 per cent of start-up observations against 1.0 per cent of ordinary SME observations. Both selections are correlated with treatment status, and both remove firms at the pre-operating end of the distribution. The estimates therefore describe firms with genuine operating activity and are silent about the population the certification scheme most distinctively contains. Modelling that selection, whether through a Heckman-type correction or through bounds of the kind Manski proposes, remains to be done.

Third, sector controls are incomplete. Sector codes are available from the business register for the certified populations but for only one per cent of the control group, so the specifications with sector-by-year fixed effects rest on a subsample composed almost entirely of certified firms. The coefficients are stable across those specifications, which is reassuring, but the test is not conducted on the full sample and the possibility that operating coefficients partly capture sectoral composition in the control group cannot be excluded. Obtaining sector codes for ordinary SMEs would settle the question.

Fourth, the measurement of cost intensity remains imperfect. Ratios to the value of production are fragile where production approaches zero, and rescaling on total assets is not an alternative because it places the cost ratios in an accounting identity with the dependent variable. Sample restriction addresses the problem but does not eliminate the underlying issue, which is that firm-level accounting data measure operating structure with error concentrated in exactly the firms of greatest policy interest. The sectoral literature on the labour share—Canarella et al. (2013), Grau and Reig (2021)—avoids this by aggregating, at the cost of the heterogeneity this study exploits.

Fifth, standard errors are clustered by firm alone. Work on profit persistence documents cross-sectional dependence in firm profitability, and two-way or spatially corrected inference might widen the intervals reported here, though it would be unlikely to alter conclusions resting on statistics several orders of magnitude above conventional thresholds. Finally, the analysis is confined to a single country and a single certification regime, and the extent to which the dominance of operating structure over financial structure generalises to economies with different firm-size distributions and financing systems is an open question.

A further caveat applies to the unsupervised results. The partition is descriptive: it establishes that regulatory groups occupy distinguishable regions of the accounting space and that the boundaries are stable to resampling, but not why firms occupy the region they do. A firm may sit in the micro-service archetype because certification placed it there, because it was already there before certifying, or because both reflect an unobserved third factor. The composite selection procedure also involves discretion—the weighting of validity indices and the five per cent floor on cluster size are defensible but not unique—and the neighbouring three-cluster solution, although it leaves the coefficient pattern intact, is close enough in composite rank to warrant reporting.

10. Conclusions

This study asked which of two explanations of firm profitability carries more weight when both are placed in the same specification: the way a firm is financed, or the way it operates. The question was put to a panel of Italian firms spanning three regulatory regimes and answered three times over, by panel estimation, by unsupervised partitioning and by machine-learning regression applied to the same variables and the same sample. The three methods answer different questions about the equation—what the average conditional association is, whether one coefficient vector describes every firm, and whether the linear form is adequate—and their agreement is what makes the conclusion durable.

The answer is that the operating model dominates. The share of value added absorbed by labour carries a coefficient that is stable across estimators, essentially invariant across four otherwise heterogeneous groups of firms, and responsible for the large majority of out-of-sample predictive content. Capitalisation, the variable around which the small-firm finance literature is organised, contributes little and contributes it unreliably.

That unreliability is the study’s second conclusion, and it is a negative result stated deliberately. The coefficient on capitalisation changes sign depending on whether regressors enter contemporaneously or with a lag, changes sign again when persistence is modelled, and takes large negative values under every instrument that can be constructed from these data. The instruments themselves fail, and they fail for a reason that can be identified rather than merely suspected: profitability is persistent, so any lagged financial ratio embedding past profit is correlated with the current error. A literature that reports this coefficient as a stable parameter is reporting, in substantial part, an accounting identity between a numerator and a denominator that share the same profit figure.

The third conclusion concerns heterogeneity. The three regulatory populations do not merely differ in the level of their performance; they differ in the structure that determines it, and tests reject a common coefficient vector in every pairwise comparison. A partition built from accounting data alone, without any reference to the register, recovers four operating archetypes and reproduces the regulatory classification closely, and the equation estimated within each archetype differs again. Policy instruments premised on a single mechanism operating uniformly across certified firms are premised on something the data do not support.

Methodologically, the study makes a narrower point that may be of wider use. Comparisons between econometric and machine-learning models are frequently made on incompatible variance decompositions, setting a levels-based fit against a within-transformed one; correcting the comparison substantially reduces the apparent superiority of flexible learners. And when the remaining gap is decomposed, most of it proves irreducible by polynomial terms, which identifies the shortfall of the linear model as local rather than global structure. Used this way, machine learning becomes a diagnostic instrument for specification rather than a competitor to it.

What the study cannot claim is causality. No exogenous variation in financial structure exists in these data, and the comparison across regimes is between self-selected groups. The natural continuation is to seek that variation in the institutional features of the regime itself—the statutory expiry of certification, the eligibility thresholds, and the fiscal instruments whose rates have changed repeatedly by legislation. Those discontinuities would allow the associations documented here to be given the causal interpretation that the present design must withhold.