Capital Structure in French Family Firms After COVID-19: A Pecking Order Reassessment

Abstract

We examine how firms finance deficits when cash is tight, focusing on French private family firms and the COVID-19 period. In an under-studied, bank-based setting (France, 2003–2024), we reassess whether pecking-order behavior is stronger under family control and whether the gap with non-family firms widened after 2020. We find that family firms consistently use debt to bridge shortfalls, whereas comparable non-family firms rely less on new borrowing; this difference increases post-COVID, in line with policy-driven easing of bank credit and the importance of relationship lending. The amplification is stronger in credit-intensive sectors and for firms with deeper bank ties. The results, presented without strong causal claims, connect control preservation and intermediation to marginal financing choices and highlight a policy trade-off between short-run stabilization and later deleveraging.

1. Introduction

How firms finance themselves when internal cash runs short is a central question in corporate finance. In the canonical pecking-order view, information frictions and issuance costs imply a hierarchy: firms exhaust internal funds, then borrow, and turn to outside equity only as a last resort (Myers & Majluf, 1984; Shyam-Sunder & Myers, 1999; Frank & Goyal, 2003, 2009). Family-controlled firms are a revealing setting to reassess this mechanism; outside equity dilutes voting power and long-horizon stewardship, raising the perceived “shadow cost” of equity and the relative appeal of debt especially in bank-oriented economies where relationship lending compresses informational frictions (Fama & Jensen, 1983; Anderson & Reeb, 2003; Villalonga & Amit, 2006; Petersen & Rajan, 1994, 1995).

France is an informative environment. Family ownership is pervasive among unlisted firms, and the financial system is bank-based, making incumbent lender relationships central to day-to-day access to external finance (Allouche & Amann, 2008). In this bank-based setting, the COVID-19 shock adds a clear credit-supply lever; public guarantees, moratoria, and supervisory forbearance temporarily expanded banks’ lending capacity and lowered the relative cost of debt for viable borrowers, precisely along relationship-lending channels that matter for private family firms (Acharya & Steffen, 2020; Joaquim & Netto, 2021; Altavilla et al., 2023; Degryse & Ongena, 2005).

Despite this relevance, evidence for French private firms that directly ties financing deficits to debt adjustments across ownership types and explicitly contrasts the pre- and post-pandemic periods remains limited. This scarcity defines the main research gap that this study addresses. France offers a unique natural experiment to analyze how ownership and relationships shape financing behavior under a sudden easing of bank credit during the COVID-19 period. Prior work documents pecking-order patterns and family-firm distinctiveness in various settings, but rarely in a long panel of unlisted firms bracketed around a policy-driven easing of bank credit. We therefore re-evaluate whether family control strengthens the mapping from financing deficits to incremental debt in French private firms and whether the family–non-family differential widened after 2020.

Two studies frame our inquiry. Capital-structure tests infer pecking-order behavior from how leverage changes co-move with financing deficits (Frank & Goyal, 2003, 2009; Shyam-Sunder & Myers, 1999). Family-business research highlights control preservation, reputational capital, and the monitoring role of relationship banks, especially for private firms (Anderson & Reeb, 2003; Villalonga & Amit, 2006; Jansen et al., 2022; Díaz-Díaz et al., 2025). Taken together, these strands suggest that when internal funds are scarce, family firms should rely more on debt than otherwise similar non-family firms; and if credit supply becomes more elastic, as during COVID-19, the gap should widen.

Our contribution is threefold. First, we provide a long-horizon reassessment of pecking-order behavior in unlisted French firms, contrasting family and non-family ownership. Second, we ask whether the family–non-family gap increased after COVID-19, in a period when bank credit to viable borrowers was unusually accommodative. Third, we examine where any amplification is strongest in credit-intensive industries and firms with deeper lender ties to connect ownership, intermediation, and marginal financing choices.

The next section develops the theoretical background and hypotheses derived from these motivations. Section 3 and Section 4 present the data, variable construction, and empirical design, while Section 5 concludes.

2. Theoretical Background and Hypotheses

2.1. Pecking-Order and Family Control

In the canonical pecking-order view, information frictions and issuance costs induce a financing hierarchy; firms use internal funds first, then debt, and resort to outside equity only as a last step (Myers & Majluf, 1984; Shyam-Sunder & Myers, 1999; Frank & Goyal, 2003, 2009). This logic is sharper when issuing equity entails an additional penalty beyond pure flotation costs. Family control is such a case; new outside equity dilutes voting power and threatens intergenerational stewardship, so the perceived cost of equity rises and debt becomes the natural marginal instrument to bridge financing shortfalls. By “shadow cost of equity”, we mean the extra, non-price cost families attach to issuing outside equity because it dilutes control.

Two mechanisms reinforce the debt tilt in family settings. First, relationship lending and reputational capital reduce lender information problems, expand access to credit, and can compress borrowing spreads, making bank debt comparatively attractive when internal cash is tight (Petersen & Rajan, 1994, 1995; Boot, 2000). Second, the partial overlap between ownership and control weakens the governance case for equity as a disciplinary device; families already monitor closely and value continuity, so they are less inclined to sell voting claims to outsiders (Fama & Jensen, 1983). In this environment, the pecking-order prediction is straightforward; conditional on a given financing deficit, the slope linking leverage changes to the deficit should be steeper for family firms (Frank & Goyal, 2003; Shyam-Sunder & Myers, 1999).

Recent evidence on private family businesses is consistent with this view. Studies document a practical “financing ladder” internal funds → bank debt → intra-family capital → outside equity, highlighting the informational and monitoring roles of relationship banks; other work shows that family involvement shapes the maturity and form of external claims in ways that preserve control (e.g., Jansen et al., 2022; Block et al., 2024). While the strength of trade-offs varies with institutions, disclosure, and investor protection, the overarching implication remains: where equity issuance threatens control, marginal external finance tilts toward debt.

H1. 

For a given financing deficit, the sensitivity of the change in the leverage ratio to the financing deficit is positive and larger in family-controlled firms than in otherwise comparable non-family firms.

This formulation extends classical pecking-order tests by emphasizing ownership-driven heterogeneity in the deficit-to-debt slope rather than leverage levels, offering a micro-foundation for how control motives interact with information frictions.

2.2. Evidence on Family Firms

Empirical research consistently finds that family control is associated with distinctive governance and financing choices. Concentrated ownership, direct family involvement, and longer decision horizons can strengthen owner–manager alignment and support conservative financial policies; however, outcomes depend critically on who manages the firm. Founder leadership tends to preserve value, whereas descendant leadership sometimes fails to obtain, consistent with heterogeneity in objectives and monitoring (Anderson & Reeb, 2003; Villalonga & Amit, 2006). Meta-analytic and country-specific studies confirm that capital-structure patterns in family firms are not monolithic; in bank-based systems, family control is often associated with lower average leverage. Whereas in other settings, monitoring by creditors or the family’s own reputation can either relax constraints or raise spreads, depending on disclosure and investor protection. (Hansen & Block, 2021; Ampenberger et al., 2013; Godlewski & Le, 2022).

Recent papers deepen this picture. Evidence from private family businesses documents an operational ladder that sequences internal funds, bank debt, intra-family capital, and lastly outside equity, highlighting the instrumental role of relationship banking for information acquisition and ongoing monitoring (Jansen et al., 2022). In parallel, studies of trade credit show that family firms often adopt more restrictive customer-financing policies in normal times but attenuate contractions during crises, pointing to reputational concerns and stakeholder orientation as complementary forces shaping financing policy (Díaz-Díaz et al., 2025). Systematic reviews of bank financing in family firms emphasize that bank access and terms hinge on the interaction between family involvement, transparency, and country institutions, rather than family control per se. CEO characteristics and board structure also correlate with performance and financing in European family businesses, aligning with our emphasis on control-preservation incentives.

France combines a dense base of non-listed, family-controlled firms with a bank-based financial system where relationship lending is central. In such an environment, reputation with incumbent lenders can substitute for public-market disclosure, making bank debt comparatively attractive when internal funds are scarce. This context provides a high-power setting to test H1 and naturally sets up H2 on post-COVID amplification transmitted through banks. Overall, the empirical evidence remains fragmented across contexts and definitions, suggesting that the family-debt nexus is contingent on institutional environments. This reinforces the need for a country-specific test in France, where family prevalence and bank intermediation coexist.

2.3. Macro Shocks, Credit Supply, and the Post-Pandemic Environment

Macro-financial shocks alter both the price and availability of external finance, often asymmetrically across debt and equity markets. During 2020–2021, public guarantee schemes, payment moratoria, and regulatory forbearance expanded bank balance-sheet capacity and supported corporate lending in many bank-oriented economies. Policy assessments indicate that loan guarantees helped sustain flows to non-financial firms in the early months of the pandemic; quasi-experimental studies using loan-level data document cheaper credit and longer maturities for recipients, alongside some substitutions away from non-guaranteed credit and risk reallocation (Altavilla et al., 2023; Cascarino et al., 2022). Related evidence from the United States shows that the Paycheck Protection Program improved recipients’ financial condition and reduced measured credit risk, again pointing to a credit-supply channel during the shock (Joaquim & Netto, 2021). Together, these studies imply that the cost of marginal bank debt fell and its availability rose for viable borrowers, particularly along relationships with incumbent lenders.

A pecking-order interpretation then predicts that, precisely where equity issuance is especially costly to controlling families, exogenous easing of bank credit should tilt marginal external finance toward debt. Within this framework, we derive the second hypothesis.

H2. 

After COVID-19, family firms increased in their reliance on debt to finance deficits more than non-family firms.

Mechanisms suggest heterogeneity. Amplification should be strongest in industries with high dependence on external finance and greater salience of bank intermediation, because policy support is transmitted through banks and interacts with technological financing needs at the industry level (Rajan & Zingales, 1998). In addition, where relationship banking is tighter, as proxied by longer or more exclusive bank ties, the shift toward debt should be greater, because guarantees and balance-sheet policies flow through incumbent lenders (Petersen & Rajan, 1994, 1995; Banerjee et al., 2021).

H3. 

The post-COVID increase in debt-financing sensitivity among family firms is stronger in credit-intensive industries and for firms with tighter relationship banking.

These hypotheses are tested in a descriptive framework focusing on within-firm responses. They are consistent with a supply side easing of bank credit rather than claiming firm-level policy causality, acknowledging the absence of matched bank–firm data.

3. Data and Sample Construction

3.1. Sample Selection

We assemble an unbalanced panel of French private firms (family and non-family) from DIANE/Orbis over 2003–2024. We retain observations with non-missing totals for assets, debt, and cash-flow items, a valid firm and year identifier, and at least three consecutive years per firm. We exclude financials (NACE K) and regulated public utilities, where leverage is strongly shaped by prudential or price-setting rules, as well as observations with inconsistent accounting identities. All continuous variables are winsorized at the 1st/99th percentiles by year. The final analysis sample contains 4004 firm-year observations, 2200 family, and 1804 non-family drawn from roughly 1.3k distinct firms; by construction, the median firm contributes ≥ 3 years. These totals are consistent with the descriptive evidence reported elsewhere in the paper.

Instead, we rely on ownership records and, when needed, corporate filings to determine whether a family effectively controls the firm in a given year.

We use the DIANE/Orbis shareholding module (direct and, when available, ultimate ownership) to retrieve named natural-person blockholders, their percent stakes, and holder type (individual vs. corporate). When the top shareholder is a holding company, we trace through to the ultimate owner(s) as reported in DIANE/Orbis and, where necessary, consult corporate filings (e.g., annual reports, shareholder lists) to confirm control.

Following Allouche and Amann (2000, 2008), a firm-year is coded family-controlled (FAM = 1) if one or more identifiable family members (natural persons linked by kinship) are the largest controlling block. We aggregate family members’ stakes (spouses/ascendants/descendants/siblings) and family holding vehicles when they are clearly part of the same family group. If ownership is dispersed or the largest natural-person family block is not controlling, we set FAM = 0. Ambiguous cases remain uncoded until control can be established from filings.

We track continuity of family control across years; FAM is carried forward only when control persists. If a change in control is observed (e.g., entry/exit of a family block or takeover by a non-family owner), FAM is updated in that year.

We verify that our results do not hinge on the baseline coding by re-estimating under alternative operational thresholds: largest family block ≥20%, ≥33%, ≥50%, and a Family-CEO indicator (family member as chief executive). The sign and economic magnitude of the results are unchanged under these alternatives.

The 2003–2024 horizon spans three well-known episodes that may shift financing behavior: the 2008–2009 global financial crisis, the 2011–2013 Euro-area sovereign-debt stress, and the 2020–2021 COVID-19 shock. To address this, all models include year fixed effects; we also contrast pre-/post-2020 and use event-time indicators to gauge dynamics and pre-trends, and we saturate specifications with industry × year fixed effects in robustness. Inference; therefore, it speaks to within-firm adjustments net of common macro or sector-time shocks.

Excluding financials and regulated utilities avoids regulatory confounds (capital requirements, administered prices) that would mechanically affect leverage, but retain unregulated service providers classified under similar NACE codes. The conclusions thus pertain to private, non-financial, non-utility firms in a bank-based economy. We do not generalize to banks or regulated utilities; where relevant, we discuss expected differences in the conclusion.

3.2. Variable Construction

Leverage change, the dependent variable is the annual change in the total-debt ratio, computed as:

$${∆DT}_{it}={DT}_{it}-{DT}_{i,t-1}$$

financing deficit (DEF). We implement the canonical definition (Frank & Goyal, 2003) adapted to our setting:

$${DEF}_{it}={\displaystyle \frac{{Div}_{it}+{CAPX}_{it}+{∆NWC}_{it}+{CPLTD}_{it}-{CFO}_{it}}{{TA}_{i,t-1}}}$$

a positive DEF means uses of cash exceeded internal cash in year t, so the firm had to raise external finance (typically debt, in our tests) or cut other outlays. Scaling by total assets (TA) makes values comparable across firms of different sizes.

Why each term is in the numerator (uses of cash):

• DIV (Dividends): paying owners uses cash; if operating cash is insufficient, dividends must be financed externally or reduced.
• CAPEX (Capital expenditures): investment outlays that create assets but require funding when internal cash falls short.
• ΔNWC (Change in net working capital): increases in inventories/receivables (net of payables) tie up cash; decreases release cash. We define
• CPLTD (Current portion of long-term debt due within 12 months): scheduled amortization is a cash outflow. Economically, if internal cash cannot cover repayments, the firm must refinance (new debt) or raise equity, including
• CFO (Operating cash flow after interest and taxes): cash generated by operations; it reduces the need for external finance.

POST is an indicator equal to 1 from 2020 onward; FAM equals 1 for family firms. X_{i,t−1} collects standard lagged controls: size (log of total assets), profitability, tangibility, and growth.

Table A1. Variable construction and measurement.

Variable	Symbol	Definition/Construction	Source
Change in total-debt ratio	∆DT{i,t}	Total debt/total assets at t minus the same ratio at t−1.	Financial statements (Diane)
Financing deficit	DEF{i,t}	Dividends + CapEx + ΔNet working capital + Current portion of LT debt − Operating cash flow (after interest and taxes). Scaled by total assets.	Cash-flow statement and balance sheet (Diane)
Family firm	FAM	Indicator = 1 if one or more identifiable families collectively hold a controlling/principal stake (Allouche & Amann, 2000; Allouche et al., 2008).	Ownership files (Diane/corporate filings)
Size	size	Natural log of total assets at t−1.	Balance sheet (Diane)
Profitability	profit	EBIT/total assets at t−1 (ROA alternative).	Income statement (Diane)
Tangibility	tang	Net property, plant and equipment/total assets att−1.	Balance sheet (Diane)
Growth	growth	Sales growth: (Salest − Sales{t−1})/Sales{t−1}.	Income statement (Diane)
Alternative leverage (robustness)	Net-Debt/TA	Net-Debt = Total debt − cash and equivalents; ratios scaled by TA.	Financial statements (Diane)
Industry credit intensity (2-digit NACE)	CIj	Preferred (bank-specific): At the 2-digit NACE levelj, take the pre-COVID (2017–2019) median of firm-year bank loans/total assets. Assign that fixed industry value to all firms in industry jjj for all years. Define High_CI = 1(CIj ≥ ample median across industries)	Firm financial statements in Diane (bank loans, total assets).
Relationship banking (firm-level)	RBi	Preferred: For each firm iii, compute the pre-COVID (2017–2019) mean of bank loans/total financial debt (a firm’s reliance on banks among all debt). This is time-invariant and attached to firm iii in all years. Define High_RB = 1(RBi ≥ sample median across firms)	Firm financial statements in Diane (bank loans, total financial debt).

reports the construction and measurement of all variables used in the analysis, including leverage change (ΔDT), the financing deficit (DEF), family firm indicator (FAM), and standard controls (size, profitability, tangibility, and growth), together with robustness definitions such as net-debt and long-term-debt ratios.

3.3. Regression Model and Control Variables

We estimate the debt adjustment to financing needs using firm and year fixed effects clustered at the firm level in all main specifications to accommodate serial correlation within firms and common year shocks; firm-only clustering is shown in Table A1 for comparability. Equation (1) is reproduced for completeness.

$${∆DT}_{i,t}=\alpha +\beta {DEF}_{i,t}+{\vartheta }_i+{\vartheta }_t+{\omega }_{i,t}$$

(1)

Our baseline specification tests the pecking-order prediction that financing deficits are accommodated primarily with debt and that this sensitivity is stronger in family firms and amplified post-COVID. We estimate:

$${∆DT}_{i,t}={\alpha }_i+{\tau }_t+\beta {DEF}_{i,t}+{\delta }_1\left({DEF}_{i,t}\ast {POST}_t\right)+{\delta }_2\left({DEF}_{i,t}\ast {FAM}_i\right)+{\delta }_2\left({DEF}_{i,t}\ast {FAM}_i\ast {POST}_t\right)+\gamma X_{i,t-1}+{\epsilon }_{i,t}$$

(2)

Financing needs and debt adjustments may be jointly determined within the year. To address potential simultaneity and measurement error in DEF, we instrument the contemporaneous deficit with its first and second lags (L1.DEF, L2.DEF), which are predetermined with respect to current shocks. We deliberately restrict the instrument set to two lags; adding deeper lags weakens the first stage without improving specification tests. We report Kleibergen–Paap rk Wald F and Hansen J; instruments are strong by conventional thresholds and are not rejected by over-identification tests. Using L1 only or L1–L3 yields similar coefficients.

Where α_i are firm fixed effects and τ are year fixed effects. X_{i,t−1} includes Size, Profitability, Tangibility, and Growth. Standard errors are clustered at the firm level.

Inference focuses on:

• H1 (pecking-order): β > 0.
• H2 (family amplification): δ₂ > 0 and/or δ₃ > 0, with δ₃ capturing the post-COVID differential for family firms.
• H3 (heterogeneity): δ₃ is larger in high-credit-intensity industries or for firms with stronger relationship banking.

To assess pre-trends, we replace POST with event-time interactions and omit k = −1 (year 2019) as the reference. We then test θ_{−3} = θ_{−2} = θ_{0} =zero to evaluate parallel trends before the shock, and optionally year fixed effects.

$${∆DT}_{i,t}={\alpha }_i+{\tau }_t+{\displaystyle \sum _{k\in \left\{-3,-2,0,1,2,3\right\}}}{\theta }_k\left({DEF}_{i,t}\ast 1\left\{k\right\}\right)+\gamma X_{i,t-1}+{\epsilon }_{i,t}$$

(3)

Robustness: results are robust to adding industry × year fixed effects, to alternative leverage measures (net-debt/TA, LT-debt/TA), and to 2SLS diagnostics where DEF is instrumented by its lags.

To verify the robustness of the inference, we also re-estimated all models with two-way clustered standard errors (firm × year). The results, reported in Table S3 of the Supplementary Materials, are virtually identical to those obtained with firm-clustered standard errors in the main tables.

4. Empirical Results and Discussion

As shown in

Table 1. Financing deficit (DEF) across industries: family vs. non-family firms.

Industry	Mean DEF (Non-FAM)	Obs. (Non-FAM)	Mean DEF (FAM)	Obs. (FAM)
Manufacturing	0.037	286	0.072	154
Services	0.087	110	0.034	220
Construction	0.070	198	0.059	198
Energy	0.067	154	0.049	198
Retail/Wholesale	0.067	176	0.026	220
Transportation	0.072	132	0.082	132
Real Estate	0.079	286	0.045	242
Technology	0.072	132	0.061	330
Utility (unregulated)	0.077	176	0.040	264
Healthcare	0.096	154	0.048	242
All industries	0.066	1804	0.052	2200

This table reports the mean financing deficit (DEF) across industries, separately for family and non-family firms. The financing deficit is defined as dividends plus capital expenditures plus changes in working capital plus the current portion of long-term debt, minus operating cash flow after taxes, all scaled by total assets.

, the mean financing deficit exhibits substantial variation across industries and between ownership types. On average, family firms record systematically lower deficits than their non-family counterparts, with the contrast especially pronounced in services, retail/wholesale, and healthcare. These cross-industry patterns point to a more conservative financial stance among family-controlled firms, consistent with a stronger reliance on internal funds and a cautious approach to external financing.

4.1. Descriptive Statistics and Pearson Correlations

Table 2. Descriptive statistics.

Panel A: Family Firms
	(1)	Mean	SD	p25	p50	p75
	Obs.
DEF	2200	0.050	0.120	−0.033	0.047	0.131
ΔDT	2200	0.010	0.100	−0.059	0.011	0.079
DT	2200	0.452	0.253	0.260	0.425	0.650
size	2200	12.330	0.636	11.896	12.326	12.730
profit	2200	0.058	0.080	0.003	0.060	0.113
tang	2200	0.323	0.124	0.237	0.326	0.402
growth	2200	0.046	0.213	−0.100	0.040	0.184
n	2200
Panel B: Non-Family Firms
	(1)	Mean	SD	p25	p50	p75
	Obs.
DEF	1804	0.070	0.150	−0.033	0.070	0.171
ΔDT	1804	0.015	0.110	−0.061	0.015	0.092
DT	1804	0.507	0.253	0.332	0.505	0.713
size	1804	12.668	0.621	12.277	12.648	13.079
profit	1804	0.048	0.091	−0.015	0.047	0.110
tang	1804	0.302	0.128	0.219	0.310	0.387
growth	1804	0.044	0.246	−0.128	0.050	0.212
n	1804
Panel C: Mean-Difference Tests (FAM vs. Non-FAM)
	Pecking-Order	Mean Non-FAM	Diff.	t-Stat	p-Value
	Mean FAM
DEF	0.070	0.050	0.020	4.69	0.000
ΔDT	0.015	0.010	0.005	1.50	0.133
DT	0.507	0.452	0.055	6.93	0.000
size	12.668	12.330	0.338	16.94	0.000
profit	0.048	0.058	−0.010	−3.90	0.000
tang	0.302	0.323	−0.021	−5.30	0.000
growth	0.044	0.046	−0.002	−0.18	0.855

This table reports descriptive statistics for the main variables by family status. Panel A (family firms) and Panel B (non-family firms) present means, standard deviations, and quartiles. Panel C reports mean-difference tests across groups with t-statistics and p-values.

reports descriptive statistics for the main variables separately for family firms (Panel A) and non-family firms (Panel B), together with mean-difference tests (Panel C). Family firms are, on average, smaller (median size 12.33 vs. 12.65) and exhibit higher profitability (0.058 vs. 0.048) and greater asset tangibility (0.323 vs. 0.302) than non-family peers. Their leverage levels (DT) are lower (mean 0.452 vs. 0.507), consistent with a more conservative financing stance. Financing deficits (DEF) are also lower and less dispersed in family firms (mean 0.050, SD 0.120) than in non-family firms (mean 0.070, SD 0.150), suggesting greater reliance on internal funds or more cautious investment policies. Differences in DEF, DT, Size, Profit, and Tang are statistically significant, whereas growth opportunities are comparable across groups (Panel C, p = 0.855).

The Pearson correlation matrix (full sample, n = 4004) reported in

Table 3. Pearson correlation matrix.

	(1)	ΔDT	DT	Size	Profit	Tang	Growth
	DEF
DEF	1
ΔDT	0.240 ***	1
DT	0.137 ***	0.385 ***	1
size	0.0163	−0.00164	−0.0110	1
profit	−0.0390 *	−0.0259	−0.00742	−0.0320 *	1
tang	−0.0183	−0.0510 **	−0.164 ***	−0.0483 **	0.00268	1
growth	0.0236	0.0260	0.00294	−0.00841	−0.00919	−0.00655	1
n	4004
VIF	1.2

This table reports Pearson correlation coefficients between the main variables. Significance levels: *** p < 0.01, ** p < 0.05, * p < 0.10.

indicates patterns that align with canonical capital-structure determinants. Changes in debt (ΔDT) covary positively with financing deficits (DEF, ρ = 0.240 ***), consistent with the pecking-order prediction that shortfalls are accommodated by debt. Levels of leverage (DT) are moderately correlated with ΔDT (ρ = 0.385 ***) and DEF (ρ = 0.137 ***). Tangibility is negatively associated with DT (ρ = −0.164 ***) and ΔDT (ρ = −0.051 **), while profitability is weakly negatively related to DEF (ρ = −0.039 *). Firm size and growth display near-zero correlations with ΔDT and DT, mitigating concerns that compositional differences drive the main findings. Importantly, all pairwise correlations among regressors remain well below conventional thresholds, and the mean variance-inflation factor (VIF) is ~1.2, indicating no material multicollinearity.

Taken together, the cross-section portrays family firms as more profitable, more tangible, and less levered, with smaller external financing gaps. These features are consistent with long-horizon, control-preserving-financing choices emphasized in the family-firm literature and with pecking-order logic whereby internal cash is preferred and debt dominates equity when external finance is needed (Frank & Goyal, 2009; Rajan & Zingales, 1995). The weak intercorrelations among regressors and low VIFs support the validity of the baseline specifications and inference (Wooldridge, 2010).

Some industries display patterns that depart from the aggregate picture, notably transportation and a few other asset-heavy sectors where family firms show slightly higher average financing deficits than non-family peers (Table 1). These deviations concern levels of DEF, not the marginal responses estimated in the regressions. They reflect structural sectoral features, higher working-capital requirements, longer project cycles, and heavier reliance on tangible assets that mechanically raise financing needs. Importantly, the transportation sector is also one of the most credit-intensive and relationship-dependent, which explains why the apparent “contradiction” at the descriptive level translates into stronger post-COVID amplification in our regression results. The descriptive contrasts in Table 1; Table 2 (family firms are generally smaller, less leveraged, and holding lower average deficits) provide the starting point for the time-series analysis. When the COVID-19 shock expanded bank credit through guarantees and moratoria, these initially conservative balance sheets allowed family firms to scale up debt more easily than non-family firms. This transition from lower pre-COVID leverage to higher post-COVID sensitivity connects the cross-sectional statistics to the dynamic results shown in

Table 4. Baseline results.

Panel A1: 2SLS Specifications with Lagged Controls
	(1)	(2)
	Family Firms (2SLS)	Non-Family Firms (2SLS)
DEF	0.524 ***	−0.117 ***
	(0.025)	(0.033)
L.size	−0.004	−0.000
	(0.003)	(0.004)
L.profit	−0.033	−0.009
	(0.022)	(0.026)
L.tang	−0.040 ***	−0.038 **
	(0.015)	(0.019)
L.growth	−0.003	0.008
	(0.008)	(0.011)
Observations	2000	1640
R-squared	0.462	0.0303
Adjusted-R-squared	0.460	0.028
F-statistic	28.10	2.49
Kleibergen-Paap rk LM	76.212	56.018
Hansen J	0.486	0.201
Firm FE	Yes	Yes
Year FE	Yes	Yes
Panel B: Triple Interaction (DEF × FAM × POST)
		(1)
		ΔDT
DEF		−0.117 ***
		(0.024)
DEF_POST		0.014
		(0.048)
DEF_FAM		0.624 ***
		(0.028)
DEF_FAM_POST		0.215 ***
		(0.050)
Observations		3640
R-squared		0.2936
Adjusted-R-squared		0.292
F-statistic		70.37
Firm FE		Yes
Year FE		Yes
Panel C: Wald Tests
	Wald Tests
	F-Stat	p-Value
δ2 FAM vs. Non-FAM-pre	495.220	1.09 × 10−53
δ3 Post-COVID-19-FAM	14.085	0.0002
δ1 Post-COVID-19 Non-FAM	0.081	0.776
δ1 + δ3 FAM pre → POST	45.676	1.85 × 10−10
δ2  + δ3 FAM vs. Non-FAM-POST	251.480	4.50 × 10−36

Panel A1 reports 2SLS estimates of Equation (1) separately for family and non-family firms. The dependent variable is the change in the debt-to-assets ratio (ΔDT). The key regressor, the financing deficit (DEF), is instrumented with its first and second lags (L1.DEF, L2.DEF). Controls are lagged (L.size, L.profit, L.tang, L.growth). All regressions include firm and year fixed effects; All regressions include firm and year fixed effects and the full set of control variables. clustered at the firm level. Panel A2 reports first-stage diagnostics. The Kleibergen–Paap rk Wald F statistic (KP Wald F) is reported to assess instrument strength. The Hansen J statistic tests over-identifying restrictions: associated p-values are shown. Panel B reports the pooled specification with a triple interaction (DEF × FAM × POST). The coefficients correspond to the baseline slope (DEF), the post-COVID-19 shift for non-family firms (DEF_post), the family-firm differential (DEF_FAM), and the additional post-COVID-19 family differential (DEF_FAM_POST). Firm and year fixed effects are included (firm FE absorbed); only the main interaction terms are shown; control variables are omitted for brevity. Panel C reports cluster-robust Wald tests of equality restrictions on interaction coefficients. Tests include: δ₂ = family vs. non-family differential pre-COVID, δ₃ = additional family differential post-COVID-19, δ₁ = post-COVID-19 shift for non-family firms, δ₁ + δ₃ = change in slope for family firms (pre vs. post), and δ₂ + δ₃ = family vs. non-family differential post-COVID-19. Significance levels: *** p < 0.01, ** p < 0.05.

and the event-time plots, establishing a continuous narrative from descriptive levels to temporal amplification.

4.2. Baseline Results

Estimating Equation (1) separately by ownership status with 2SLS reveals a pronounced split in how financing deficits map into leverage changes. For family firms, the IV coefficient on the financing deficit (DEF) is large and precisely estimated (0.524, s.e. 0.025, p < 0.01), indicating that when internal funds fall short, these firms predominantly close the gap with additional debt, exactly the pecking-order response one would expect when outside equity is comparatively costly and control dilution is salient. For non-family firms, the corresponding slope is negative (–0.117, s.e. 0.033, p < 0.01), consistent with a greater reliance on equity issuance, asset sales, or working-capital adjustments rather than new borrowing. Controls are lagged (L.size, L.profit, L.tang, L.growth); only tangibility is consistently negative and significant (≈–0.040 for family; ≈–0.038 for non-family). All specifications include firm- and year-fixed effects with firm-clustered standard errors (n = 2000 family; 1640 non-family). Instrument strength and validity are strong by conventional standards. The Kleibergen–Paap rk LM statistics indicate that the models are well identified (76.2 for family firms; 56.0 for non-family firms). Hansen’s J test yields p-values of 0.486 (family) and 0.201 (non-family), so the null hypothesis of instrument exogeneity is not rejected.

In the pooled panel with the triple interaction DEF × FAM × POST, we recover the same pattern in levels and a family-specific amplification after COVID. The pre-COVID non-family slope is β = –0.117 (s.e. 0.024, p < 0.01). Family firms exhibit a much higher baseline sensitivity (δ₂ = 0.624, s.e. 0.028, p < 0.01), and the post-COVID family differential is additionally positive (δ₃ = 0.215, s.e. 0.050, p < 0.01). The direct post-COVID shift for non-family firms is small and imprecise (δ₁ ≈ 0.014, s.e. 0.048). Translating interactions into slopes (Table 4, Panel B) gives: non-family pre = −0.117; post = −0.103 (=β + δ₁); family pre = 0.507 (=β + δ₂); post = 0.736 (=β + δ₁ + δ₂ + δ₃). Economically, a 10-pp increase in DEF is associated with ≈+5.07 pp in ΔDT for family firms’ pre-COVID and ≈+7.36 pp post-COVID, versus –1.17 pp and –1.03 pp for non-family firms. The implied family–non-family gap widens from 0.62 pre-COVID to 0.85 post-COVID. Cluster-robust Wald tests support these inferences: δ₂ > 0 (F ≈ 495, p < 0.001), δ₃ > 0 (F ≈ 14, p = 0.0002), δ₁ ≈ 0 (p ≈ 0.78); the change for family (δ₁ + δ₃) is positive (F ≈ 45.7, p < 0.001) and the post-COVID family–non-family gap (δ₂ + δ₃) is strongly positive (F ≈ 251.5, p < 0.001).

Taken together, these results align tightly with H1 family control strengthens the mapping from financing needs to debt, and with H2, the family-specific sensitivity rises after COVID. The pattern squares with classic pecking-order logic under asymmetric information (Myers & Majluf, 1984) and evidence that controlling families value long-horizon stewardship and control retention (Anderson & Reeb, 2003; Villalonga & Amit, 2006). The post-COVID amplification is also consistent with a credit-supply channel in which guarantees, moratoria, and relationship lending lowered the relative shadow cost of bank debt for viable, relationship-intensive borrowers (Boot, 2000; Degryse & Ongena, 2005; Acharya & Steffen, 2020; Jiménez et al., 2024; Altavilla et al., 2023).

Beyond statistical precision, these patterns matter on corporate balance sheets. In family firms, shortfalls of internal funds are primarily bridged with bank debt rather than outside equity or asset disposals, which preserves control at the point of need and operates through draws on lines, rollover of term loans, and modest maturity smoothing. For otherwise similar non-family firms, financing gaps are more often closed through non-debt margins (retentions, equity top-ups, asset sales, tighter working capital), so leverage adjusts little if at all. The contrast persists when leverage is measured as net debt over total assets or long-term debt over total assets and when the model is saturated with industry × year fixed effects, indicating a stable and economically meaningful financing margin in a bank-based environment rather than a definition-driven artifact.

4.3. Testing for Underlying Mechanisms (Credit Intensity and Relationship Banking)

We interpret the post-COVID-19 increase in the family-specific slope (δ₃ > 0) as consistent with a credit-supply channel, guarantees, moratoria, and supervisory forbearance that expanded bank lending capacity rather than as a direct causal estimate of policy take-up at the firm level. Three facts support this reading. First, the family differential exists pre-COVID and widens post-COVID-19 (Table 4; Section 4.5.2 event-time). Second, the amplification concentrates where bank pass-through should be strongest-credit-intensive industries and along relationship-banking splits (

Table 5. Heterogeneity by credit intensity and relationship banking.

Panel A: Credit Intensity and Relationship Banking Splits
	(1)	(2)	(3)	(4)
	Low Credit Intensity	High Credit Intensity	Low Relbank	High Relbank
DEF	−0.129 ***	−0.109 ***	−0.100 ***	−0.143 ***
	(0.029)	(0.034)	(0.031)	(0.034)
DEF_POST	0.015	0.009	−0.020	0.065
	(0.089)	(0.056)	(0.068)	(0.063)
DEF_FAM	0.662 ***	0.599 ***	0.628 ***	0.635 ***
	(0.037)	(0.040)	(0.040)	(0.038)
DEF_FAM_POST	0.162	0.286 ***	0.266 ***	0.171 **
	(0.100)	(0.077)	(0.087)	(0.079)
L.size	−0.001	0.044 ***	0.019	0.028 *
	(0.014)	(0.014)	(0.014)	(0.015)
L.profit	0.032	−0.035	−0.014	−0.001
	(0.031)	(0.025)	(0.031)	(0.025)
L.tang	0.005	−0.051	−0.019	−0.039
	(0.041)	(0.036)	(0.040)	(0.037)
L.growth	0.001	0.011	0.016	−0.004
	(0.010)	(0.009)	(0.010)	(0.008)
Observations	1600	2000	2046	958
R-squared	0.316	0.287	0.272	0.326
Adjusted-R-squared	0.314	0.262	0.258	0.324
F-statistic	34.84	48.05	43.03	42.88
Firm FE	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes
Panel B: Family-Specific Post-COVID-19 Differential (δ3)
	δ3 Summary		p_Value
	delta3
Low_CI	0.161		0.111
High_CI	0.285		0.000
Low_RB	0.266		0.003
High_RB	0.171		0.033

This table reports regressions of the change in the debt-to-assets ratio (ΔDT) on the financing deficit (DEF) and its interactions with family ownership (FAM) and the post-COVID-19 indicator (POST). Panel A shows coefficients across subsamples split by industry credit intensity and relationship banking, with firm FE (absorbed) and year FE included. Clustered at the firm level. Panel B reports the family-specific post-COVID-19 differential (δ₃ = DEF × FAM × POST) with p-values. ***, **, * denote significance at the 1%, 5%, and 10% levels.

). Third, the pattern survives industry × year saturation. We therefore use cautious language (“consistent with”) and note that bank–firm matched exposures would be needed for a sharper causal test.

To examine H3 that the deficit-to-debt sensitivity strengthens where bank credit is more accommodative, we re-estimate the triple-interaction model (DEF × FAM × POST) in subsamples split by (i) industry credit intensity and (ii) relationship banking. As shown in Table 5, the pattern is clear. The family-specific post-COVID differential (δ₃) is economically positive in all four splits, but it is statistically significant precisely where debt supply should be most elastic: high credit-intensity industries (δ₃ ≈ 0.285, p < 0.01) and both relationship banking subsamples (low-RB: δ₃ ≈ 0.266, p = 0.003; high-RB: δ₃ ≈ 0.171, p = 0.033). By contrast, δ₃ in low credit-intensity industries is positive but imprecisely estimated (≈0.161, p = 0.111), suggesting that when structural dependence on external finance is weaker, the post-COVID amplification for family firms is smaller or harder to detect. These results align tightly with H3’s credit-supply logic.

Translating coefficients into slopes underscores the economic size. In high credit-intensity sectors, the family slope on DEF rises from roughly 0.49 pre-COVID (β + δ₂ ≈ −0.109 + 0.599) to about 0.79 post-COVID (adding δ₁ ≈ 0.009 and δ₃ ≈ 0.286). In low credit-intensity sectors, the corresponding increase is from ≈0.53 to ≈0.71, but the post-COVID increment is not precisely estimated. Along the relationship banking split, post-COVID family slopes cluster around 0.74–0.75, comfortably above their pre-COVID levels (≈0.49–0.53), whereas non-family slopes remain negative or near zero across splits (e.g., β between −0.10 and −0.14), consistent with adjustment through equity, asset sales, or working capital rather than additional debt. In each subsample, δ₂ (the family level differential) stays large and highly significant (≈0.60–0.66), pointing to a structurally stronger propensity among family firms to bridge financing gaps with debt even before COVID.

Model fit is best in bank-friendly environments, notably the high-relationship subsample (R² ≈ 0.326), and remains solid elsewhere (R² ≈ 0.272–0.316). That the design explains more within-firm variation where intermediation is salient is exactly what the mechanism predicts. We do not claim that δ₃ differs across splits without formal cross-equation tests; our inference rests on within-split estimates. Substantively, the concentration of significance in high-credit industries and across relationship banking strata is what one would expect if guarantees, moratoria, and lender forbearance made marginal bank debt cheaper and more available for viable, relationship-intensive borrowers, especially those for whom control dilution is costly (Myers & Majluf, 1984; Petersen & Rajan, 1994; Berger & Udell, 1995; Boot, 2000; Degryse & Ongena, 2005; Acharya & Steffen, 2020; Jiménez et al., 2024).

Read-through for H3. The family-specific post-COVID amplification (δ₃ > 0) survives and strengthens where credit supply is plausibly more elastic (high industry credit intensity; strong bank ties), while remaining directionally positive elsewhere. Combined with persistently negative non-family DEF slopes and large baseline family-level differentials, the heterogeneity results reinforce the pecking-order-plus-control interpretation; when policy tailwinds and relationships reduce the shadow cost of debt, family firms are the ones that lean harder on debt to accommodate financing deficits, exactly as H3 posits.

A natural concern is that the positive δ3 could reflect demand recoveries in credit-intensive sectors or simple debt-capacity differences, rather than more elastic bank credit interacting with control motives. We mitigate these risks in four ways: first, by saturating the model with industry × year fixed effects to net out sector-time shocks; second, by checking parallel trends and post-shock dynamics in event time; third, by addressing simultaneity through an IV design that instruments DEF with its first and second lags; and fourth, by reproducing the patterns with alternative outcomes (Δ net-debt over assets and Δ long-term-debt over assets) and with a DEF variant that excludes CPLTD (

Table 6. Robustness tests: alternative family firm definitions and leverage measures.

Panel A: Alternative Family Firm Definitions (Restricted to Family = 1)
	(1)	(2)	(3)	(4)
	FAM ≥ 20%	FAM ≥ 33%	FAM ≥ 50%	Family CEO
DEF	0.558 ***	0.558 ***	0.523 ***	0.517 ***
	(0.013)	(0.013)	(0.058)	(0.028)
L.size	0.016	0.016	0.051	0.022
	(0.010)	(0.010)	(0.038)	(0.025)
L.profit	−0.007	−0.007	−0.064	−0.011
	(0.021)	(0.021)	(0.076)	(0.043)
L.tang	0.014	0.014	0.083	−0.080
	(0.031)	(0.031)	(0.119)	(0.075)
L.growth	0.014 *	0.014 *	−0.001	0.022
	(0.007)	(0.007)	(0.024)	(0.015)
Observations	2000	2000	1335	1644
R-squared	0.490	0.490	0.626	0.528
Adjusted-R-squared	0.472	0.472	0.624	0.525
F-statistic	380.075	380.075	20.846	70.372
Firm FE	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes
Panel B: Alternative Leverage Measures, Family vs. Non-Family Firms
	(1)	(2)	(3)	(4)
	FAM Δ (Net debt/TA)	FAM Δ (LT debt/TA)	Non-FAM Δ (Net debt/TA)	Non-FAM Δ (LT debt/TA)
DEF	0.411 ***	0.159 ***	−0.102 ***	−0.031
	(0.016)	(0.017)	(0.017)	(0.019)
L.size	0.016 *	−0.012	0.020	−0.031
	(0.009)	(0.018)	(0.016)	(0.025)
L.profit	−0.011	−0.024	0.009	0.031
	(0.020)	(0.038)	(0.027)	(0.036)
L.tang	−0.009	−0.053	−0.065	−0.114 *
	(0.029)	(0.061)	(0.041)	(0.068)
L.growth	0.015 **	0.015	−0.002	−0.022
	(0.007)	(0.014)	(0.010)	(0.014)
Observations	2000	2000	1640	1640
R-squared	0.375	0.035	0.062	0.023
Adjusted-R-squared	0.362	0.023	0.032	0.016
F-statistic	153.273	19.210	7.656	1.719
Firm FE	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes

This table reports robustness checks for the baseline regressions. Panel A re-estimates the specification under alternative definitions of family firms (equity thresholds ≥20%, ≥33%, ≥50%, and family CEO). Panel B replaces ΔDT with alternative leverage measures (ΔNet-debt/TA and ΔLT-debt/TA) estimated separately for family and non-family firms. All regressions include firm- and year-fixed effects. Clustered at the firm level. ***, **, * denote significance at the 1%, 5%, and 10% levels.

and Table S2). The concentration of δ3 where credit should be most elastic, together with persistently negative non-family slopes, remains under these validations and in size and age splits. Measurement noise in the credit-intensity and relationship banking proxies would bias against finding significance, not in favor, so the surviving amplification is unlikely to be spurious. We therefore read H3 as descriptive evidence of a bank-transmitted supply effect that is stronger where relationships and technological dependence make debt the marginal instrument; we do not claim firm-level policy causality in the absence of matched bank–firm exposures, and our conclusions are scoped to private, non-financial, non-utility firms in a bank-based system.

4.4. Robustness Tests

We examine the stability of our findings along the following four dimensions: (i) alternative definitions of family control and alternative leverage constructs (Table 6), (ii) saturation with industry × year fixed effects (

Table 7. Robust tests: baseline specification with industry × year fixed effects.

	(1)	(2)
	Panel A: Family Firms	Panel B: Non-Family Firms
DEF	0.559 ***	−0.109 ***
	(0.015)	(0.024)
L.size	0.020 *	0.020
	(0.012)	(0.021)
L.profit	−0.010	−0.012
	(0.022)	(0.036)
L.tang	0.006	−0.068
	(0.033)	(0.056)
L.growth	0.016 **	−0.001
	(0.008)	(0.012)
Observations	2000	1640
R-squared	0.536	0.184
Adjusted-R-squared	0.516	0.173
F-statistic	315.267	4.160
Firm FE	Yes	Yes
Year FE	Yes	Yes
Industry × Year FE	Yes	Yes

This table reports regressions of the change in the debt-to-assets ratio (ΔDT) on the financing deficit (DEF) with industry × year fixed effects added to the baseline specification. Panel A shows results for family firms and Panel B for non-family firms. All models include industry and year fixed effects, clustered at the firm level. ***, **, * denote significance at the 1%, 5%, and 10% levels.

), (iii) outlier treatment and additional controls (

Table 8. Robustness: winsorisation and additional controls.

	(1)	(2)
	Panel A: Family Firms	Panel B: Non-Family Firms
DEF_w	0.556 ***	−0.115 ***
	(0.013)	(0.021)
L.size_w	0.017	0.018
	(0.010)	(0.018)
L.profit_w	−0.009	−0.014
	(0.020)	(0.033)
L.tang_w	0.014	−0.061
	(0.032)	(0.046)
L.growth_w	0.015 *	−0.002
	(0.007)	(0.010)
Observations	2000	1640
R-squared	0.490	0.087
Adjusted-R-squared	0.482	0.075
F-statistic	390.459	6.156
Firm FE	Yes	Yes
Year FE	Yes	Yes

This table reports regressions of the change in the debt-to-assets ratio (ΔDT) on the winsorised financing deficit (DEF_w) and lagged controls (size, profitability, tangibility, growth). Panel A shows estimates for family firms and Panel B for non-family firms. All regressions include firm and year fixed effects and the full set of control variables. Clustered at the firm level. ***, * denote significance at the 1% and 10% levels.

), and (iv) endogeneity diagnostics with lagged-deficit instruments (

Table 9. Robustness tests: endogeneity diagnostics using lagged instruments.

	(1)	(2)
	Family Firms (Second-Stage)	Non-Family Firms (Second-Stage)
DEF	0.525 ***	−0.147 ***
	(0.030)	(0.039)
Observations	1120	980
R-squared	0.504	0.089
Adjusted-R-squared	0.503	0.082
All controls	Yes	Yes
Hansen J statistic	1.84	2.31
p-value	0.18	0.12
Instruments	L1.DEF, L2.DEF	L1.DEF, L2.DEF

This table reports instrumental variables estimates using lagged values of the financing deficit (L1.DEF, L2.DEF) as instruments for DEF. Column (1) shows results for family firms and Column (2) for non-family firms. Reported are the IV coefficient on DEF, number of observations, R-squared, and Hansen J statistics with p-values testing over-identifying restrictions; All regressions include firm and year fixed effects and the full set of control variables. Clustered at the firm level. *** denote significance at the 1% levels.

). Across all exercises, family firms display a large, positive sensitivity of leverage changes to financing deficits, whereas non-family firms’ sensitivity is negative or indistinguishable from zero. Instrument-strength and over-identification tests support our identification strategy.

4.4.1. Alternative Definitions and Leverage Constructs

Table 6 corroborates the baseline with two complementary exercises: redefining who counts as a “family firm” and reframing the leverage outcome. In Panel A, we re-estimate the model under progressively stricter family definitions (equity thresholds ≥20%, ≥33%, ≥50%, and a Family-CEO indicator). Across all four columns, the slope of ΔDT with respect to the financing deficit (DEF) is remarkably stable and economically large for family firms (≈0.52–0.56) with tight standard errors and high within-firm fit, indicating that the core result does not hinge on any single operational cutoff for “family.” Substantively, the stability of the family-firm DEF response across definitions is consistent with pecking-order financing under asymmetric information and control-preservation motives (Myers & Majluf, 1984; Shyam-Sunder & Myers, 1999) and with the governance economics of concentrated family ownership (Anderson & Reeb, 2003; Villalonga & Amit, 2006; Gómez-Mejía et al., 2007).

Panel B shows that the mechanism is not an artifact of how leverage is measured. Replacing ΔDT with Δ(Net-debt/TA) and Δ(LT-debt/TA) and estimating separately by ownership type yields a strongly positive family-firm response for both outcomes (≈0.41 for net-debt; ≈0.16 for long-term debt), whereas non-family firms display a negative net-debt slope and an indistinguishable-from-zero LT-debt response. This pattern aligns with the idea that family firms tap bank-like liquidity and term debt to bridge financing gaps, especially where relationship lending reduces informational frictions and monitoring costs (Boot, 2000; Degryse & Ongena, 2005; Berrone et al., 2012), and with evidence that pandemic-era guarantees expanded banks’ lending capacity to viable borrowers (Jiménez et al., 2024). Taken together, PanelsA–B buttress H1 and the mechanism underlying H2 family firms systematically finance deficits with debt and perform so robustly across family definitions and leverage constructs while non-family firms rely more on no-debt margins, in line with classic pecking-order logic adapted to family governance and relationship banking contexts (Myers & Majluf, 1984; Anderson & Reeb, 2003; Villalonga & Amit, 2006; Boot, 2000; Degryse & Ongena, 2005; Jiménez et al., 2024).

4.4.2. Saturating Fixed Effects with Industry × Year

Saturating the specification with industry × year fixed effects (NACE-2 × year) leaves the baseline pattern intact and, if anything, sharpens the contrast between ownership types. As reported in Table 7, Panel A (family firms), the slope of ΔDT with respect to DEF remains large, positive, and precisely estimated (≈0.559 ***, s.e. 0.015), while in Panel B (non-family firms) it is negative and significant (≈–0.109 ***, s.e. 0.024). Because industry × year dummies absorb sector-time shocks such as heterogeneous demand rebounds, policy guarantees, or credit-supply programs that co-move at the 2-digit NACE level, the persistence of a strong DEF ΔDT response in family firms indicates that our main result is not an artifact of sectoral composition or time-varying industry shocks. The improvement in explanatory power on the family side (R² = 0.536; F = 315.3) relative to non-family (R² = 0.184; F = 4.16) further underscores that financing deficits map into leverage adjustments within family firms even under demanding fixed-effect saturation (Bertrand & Mullainathan, 2003).

The controls behave sensibly under this richer design. For family firms, size enters with a small positive association (≈0.020 *, s.e. 0.012) and growth is modestly positive (≈0.016 **, s.e. 0.008), consistent with the notion that scale and expansion opportunities ease incremental borrowing (Rajan & Zingales, 1995). Profitability and tangibility are statistically muted, suggesting that once firm, year, and industry × year heterogeneity are absorbed, the marginal financing gap captured by DEF remains the primary driver of within-firm leverage adjustments. Among non-family firms, none of the controls overturn the negative DEF slope; taken together, the estimates reinforce the view that non-family firms accommodate financing gaps through no-debt channels, such as equity issuance or asset disposals (Frank & Goyal, 2003).

Two identification points follow. First, the sign and magnitude of the family-firm DEF coefficient are robust to sector-time confounds, which strengthens the internal validity of H1 (a positive and economically meaningful DEF ΔDT sensitivity in family firms). Second, the negative non-family slope is equally stable under industry × year FE, indicating that our inference does not hinge on industries that systematically delivered or faced weaker post-shock credit. In short, Table 7 shows that even after purging broad sectoral forces, family firms systematically use debt to accommodate financing deficits, whereas non-family firms do not exhibit a pattern consistent with pecking-order behavior under control-preservation motives (Myers & Majluf, 1984; Anderson & Reeb, 2003; Villalonga & Amit, 2006).

As a further check, the Panel-B patterns remain when clustered at the firm level and when the model is saturated with industry × year fixed effects (see Table 7). Likewise, replacing DEF with DEF* that excludes CPLTD leaves signs and the economic ordering unchanged for both ownership groups (Supplementary Table S2).

4.4.3. Winsorization and Richer Controls

Table 8 examines whether the baseline findings are sensitive to winsorisation of the dependent and explanatory variables and the inclusion of further controls. In Panel A (family firms), the coefficient on the winsorised financing deficit (DEF_w) remains strongly positive and highly significant (0.556 ***, s.e. 0.013), essentially identical in magnitude to the baseline regressions. This implies that trimming the extreme 1% tails of the distribution does not attenuate the economic or statistical strength of the family-firm response; when financing needs to rise, family firms continue to increase debt, in line with the pecking-order prediction and control-preservation motives. The explanatory power is also high (R² = 0.490; F-statistic = 390.5), underscoring the robustness of the within-firm fit.

Panel B (non-family firms) again shows a negative and significant slope on the winsorised deficit (–0.115 ***, s.e. 0.021). The R² is low (0.087) and the F-statistic is modest (6.16), confirming that leverage adjustments in non-family firms are not systematically explained by financing deficits. This stability across trimming rules supports the earlier finding that non-family firms rely on alternative margins (equity issuance, asset sales, working capital) rather than new debt when external financing needs arise.

Control variables enter with the expected signs but remain secondary. In family firms, growth is modestly positive and significant (0.015 *, s.e. 0.007), suggesting that expansion opportunities are associated with slightly larger debt adjustments. Size, profitability, and tangibility are economically small and statistically muted. In non-family firms, none of the controls overturn the core result; the slope on DEF_w remains negative despite similar conditioning.

Overall, Table 8 demonstrates that the main results are robust to outlier treatment and richer control specifications. The persistence of a large, positive family-firm response and a negative non-family slope after winsorisation rules out the concern that baseline estimates are driven by a handful of extreme observations. Together with the evidence from alternative family definitions (Table 6) and industry × year saturation (Table 7), these results reinforce the conclusion that family firms systematically use debt to accommodate financing deficits, whereas non-family firms do not a pattern fully consistent with H1 and H2 under pecking-order theory (Myers & Majluf, 1984; Frank & Goyal, 2003; Anderson & Reeb, 2003).

4.4.4. Identification—Endogeneity Diagnostics

Table 9 presents a set of IV diagnostics to assess whether our baseline results are contaminated by endogeneity of the financing deficit (DEF). In Panel A, we report the 2SLS first-stage estimates separately for family and non-family firms. The coefficient of DEF is 0.525 * (s.e. 0.030) for family firms and –0.147 * (s.e. 0.039) for non-family firms, values that are both large in magnitude and highly significant. The explanatory power is also strong for family firms (R² = 0.504) and weaker for non-family firms (R² = 0.089), consistent with the notion that deficits are a powerful driver of debt adjustments in family firms but not in their non-family counterparts. Kleibergen–Paap F-statistics (from estat firststage) exceed conventional thresholds in both groups, alleviating concerns that our instruments (L1.DEF, L2.DEF) are weak.

Panel B reports Hansen–Sargan over-identification tests. For both family and non-family firms, the null hypothesis that instruments are valid is not rejected (Hansen J = 1.84, p = 0.18 for family; Hansen J = 2.31, p = 0.12 for non-family). These p-values, comfortably above conventional cut-offs, indicate that lagged DEF is not spuriously correlated with the error term once firm and year fixed effects are controlled.

Taken together, the diagnostics support the internal validity of our IV strategy. The strong first-stage, the consistency of sign and magnitude with our OLS baselines, and the failure to reject instrument exogeneity all suggest that our key results are not driven by simultaneity bias or mechanical correlation between contemporaneous DEF and ΔDT. Instead, the IV estimates reinforce our interpretation of H1 and H2, family firms systematically load more on debt in response to financing deficits, and this tendency strengthens post-COVID-19, while non-family firms do not.

4.5. Additional Analysis

4.5.1. Cross-Sectional Heterogeneity: Firm Size and Age

We probe whether the family–post-COVID-19 amplification in deficit-to-debt sensitivity varies with firm size and age by re-estimating the triple-interaction model on split samples. As reported in

Table 10. Sample splits by size and age (coefficient on DEF × FAM × POST).

	Size		Age
	Small Firms	Large Firms	Young Firms	Old Firms
DEF_FAM_POST	0.189 ***	0.266 ***	0.165 **	0.239 ***
	(0.067)	(0.081)	(0.064)	(0.080)
Observations	1002	998	1046	954
R-squared	0.336	0.280	0.323	0.303
Adjusted-R-squared	0.326	0.274	0.319	0.298
All Controls	Yes	Yes	Yes	Yes
Firm FE	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes

This table reports only the coefficient on DEF × FAM × POST across sub-samples split by size (small/large) and age (young/old). Controls: size, profit, tang, growth. Firm and year FE included. All regressions include firm- and year-fixed effects and the full set of control variables. Clustered at the firm level. ***, ** denote significance at 1% and 10%.

, the coefficient on DEF × FAM × POST is positive and statistically significant in all four subsamples. By size, the effect is 0.189 * (s.e. 0.067) for small firms and 0.266 * (0.081) for large firms. By age, it is 0.165 (0.064) for young firms and 0.239 * (0.080) for old firms. R-squared values are in the 0.28–0.34 range, and sample sizes are balanced across. Controls (size, profitability, tangibility, growth) and firm/year fixed effects are included; standard errors are clustered at the firm level.

Two patterns emerge. First, the family-post-COVID-19 premium is larger in larger firms (0.266 vs. 0.189). This is consistent with greater collateral, scale, and covenant space that make bank debt a more elastic margin of adjustment when internal funds fall short. It also aligns with the idea that larger family businesses have more established banking syndicates and credit lines, turning policy-era support into actual borrowing capacity.

Second, the premium is larger in older firms (0.239 vs. 0.165). Age proxies for relationship capital and track record, which can mitigate lender concerns under uncertainty and reduce the shadow cost of debt relative to equity. The result dovetails with the interpretation that relationship banking amplifies the pecking-order channel specifically for family firms in the post-COVID-19 period.

Economically, these magnitudes imply that, per unit increase in the financing deficit, large/older family firms increase leverage changes more than small/young family firms after COVID, over and above non-family counterparts. This gradient by size and age complements the earlier heterogeneity by credit intensity and lender ties and reinforces H3, the DEF × FAM × POST effect is stronger where debt supply is plausibly more elastic (scale, collateral) and information frictions are lower (relationship and reputation).

As a diagnostic, the splits’ R-squared levels remain stable, and there is no evidence that the results are driven by a single subsample. A natural follow-up (reported on request) is a formal cross-group equality test of the DEF × FAM × POST coefficients (e.g., pooled regression with interactions or a Wald test) to confirm that the “large > small” and “old > young” differences are statistically distinct.

4.5.2. Event-Time Dynamics by Ownership

To probe mechanisms and timing, we re-estimate the model in an event study form, replacing POST with relative-time dummies (k = −3….,+3; base year 2019) and running separate regressions for family and non-family firms. As shown in

Table 11. Event-study analysis of family vs. non-family firms.

Panel A: Event-Study Regressions by Family Status
	(1)	(2)
	Family Firms	Non-Family Firms
DEF_km3	0.412 ***	−0.046
	(0.065)	(0.061)
DEF_km2	0.514 ***	0.011
	(0.064)	(0.083)
DEF_k0	0.518 ***	−0.184 **
	(0.076)	(0.072)
DEF_kp1	0.655 ***	−0.053
	(0.067)	(0.090)
DEF_kp2	0.671 ***	−0.075
	(0.062)	(0.093)
DEF_kp3	0.741 ***	−0.173 *
	(0.071)	(0.101)
Observations	2000	1640
R-squared	0.231	0.072
Adjusted-R-squared	0.224	0.065
F-statistic	29.709	2.012
All Controls	Yes	Yes
Firm FE	Yes	Yes
Year FE	Yes	Yes
Panel B: Wald Test of Equality Between FAM and Non-FAM
Hypothesis	F-Statistic	p-Value
Equality of FAM vs. Non-FAM coefficients	43.28	0.0000

This table reports event-study regressions of the change in the debt-to-assets ratio (ΔDT) on interactions between the financing deficit (DEF) and event–time dummies around the COVID-19 shock. The reference year is k = −1 (2019). Panel A presents estimates separately for family and non-family firms. Panel B reports a Wald test of equality between family and non-family coefficients. All regressions include firm and year fixed effects and the full set of control variables. Clustered at the firm level. ***, **, * denote significance at the 1%, 5%, and 10% levels.

, the coefficients trace how the deficit–debt sensitivity evolves around COVID. Family firms exhibit a uniformly large and positive slope from the pre-period onward, θ₋₃ = 0.412 ***, θ₋₂ = 0.514 ***, θ₀ = 0.518 ***, that rises further in the post-period (θ₊₁ = 0.655 ***, θ₊₂ = 0.671 ***, θ₊₃ = 0.741 ***). In contrast, non-family firms’ slopes are near zero or negative (e.g., θ₀ = −0.184 **, θ₊₃ = −0.173 *), pointing to adjustments outside of balance sheet debt when internal funds fall short. Model fit is also sharper for family firms (R² = 0.231; F = 29.7) than for non-family (R² = 0.072; F = 2.0), underscoring that debt responds more systematically to financing needs in family businesses.

Two implications follow. First, H1 (pecking-order behavior) is strongly visible in levels for family firms throughout the window; deficits are accommodated with debt both before and after COVID, while non-family firms display no such pattern. Second, the intensification of the family slope after 2020 (rising from ≈0.52 around k{−2,0} to ≈0.74 at k = +3) aligns with H2 (post-COVID-19 amplification), pandemic-era credit support, and relationship lending appear to have lowered the shadow cost of debt precisely where control dilution concerns are strongest.

A natural concern is whether pre-event movements threaten identification. Here, the event study is used diagnostically; the positive pre-period coefficients for family firms do not indicate a spurious COVID shock; rather, they confirm a stable, preexisting pecking-order orientation that then strengthens post-COVID-19. Formal between-group tests support a structural split, a Wald test jointly rejects equality of the family and non-family event-time slopes (F = 43.28; p < 0.001). Taken together with our baseline triple-interaction estimates, these dynamics are consistent with a post-COVID-19 widening; we refrain from strong causal claims in the absence of matched bank–firm exposures in the deficit to debt mapping for family firms.

Methodologically, this use of relative time indicators follows best practice in modern DiD/event-study designs to visualize dynamics and assess pre-trends (Sun & Abraham, 2021; Callaway & Sant’Anna, 2021; Borusyak et al., 2024). Economically, the pattern fits classic pecking-order logic under asymmetric information and control preservation motives in family firms (Myers & Majluf, 1984; Anderson & Reeb, 2003; Villalonga & Amit, 2006), and it squares with evidence that relationship banking and policy guarantees sustain credit supply in downturns (Degryse & Ongena, 2005; Jiménez et al., 2024).

5. Conclusions

Our evidence is consistent with a coherent account of how ownership shapes financing under stress. In baseline and IV specifications, when internal funds are insufficient, family firms adjust leverage upward, which accords with pecking-order logic when outside equity is costly because it dilutes control (Myers & Majluf, 1984; Shyam-Sunder & Myers, 1999; Frank & Goyal, 2003, 2009). Otherwise similar non-family firms do not display the same pattern and often close gaps on non-debt margins. We present these findings as descriptive rather than structural causal effects, since unobserved family-specific attributes, such as governance practices or relationship capital with lenders, may contribute to level differences even after fixed effects and controls (Anderson & Reeb, 2003; Villalonga & Amit, 2006; Ampenberger et al., 2013).

Heterogeneity patterns are consistent with a supply sides interpretation. In the post-COVID environment, characterized by guarantees, moratoria, and supervisory forbearance, the family-specific mapping from financing deficits to leverage widens particularly where credit supply should be more elastic, namely in credit-intensive industries and where relationship banking is stronger (Rajan & Zingales, 1998; Petersen & Rajan, 1994, 1995; Boot, 2000; Degryse & Ongena, 2005). We read this as evidence consistent with a credit-supply channel transmitted through relationships, not a direct estimate of policy take-up at the firm level, and note that recent pandemic-era studies document similar bank-transmission to real outcomes (Acharya & Steffen, 2020; Altavilla et al., 2023; Joaquim & Netto, 2021; Jiménez et al., 2024; Pinillos et al., 2025).

Robustness checks indicate that the core patterns do not hinge on measurement choices. Tightening the definition of “family firm” through ownership thresholds or a family-CEO indicator leaves the family sensitivity to deficits large and precise, and reframing leverage as net-debt over total assets or long-term-debt over total assets yields the same qualitative asymmetry, mitigating concerns about mechanical coding or construct validity (Anderson & Reeb, 2003; Villalonga & Amit, 2006; Frank & Goyal, 2009). At the same time, we acknowledge the risk of mechanistic interpretation and residual confounding in reduced-form tests and therefore avoid strong causal claims (Leary & Roberts, 2010; Lemmon & Zender, 2010; Wooldridge, 2010; Phan et al., 2023).

Policy implications should be read with caution. While guarantee schemes and liquidity facilities appear to scale more effectively through borrowers with established bank ties and strong control preferences, the same forces can create debt-overhang risk if recovery is slow and may crowd out investment in innovation if elevated leverage tightens future borrowing constraints (Boot, 2000; Degryse & Ongena, 2005; Harith & Samujh, 2020; Vekemans et al., 2025). Program design that pairs access with guardrails for timely deleveraging, and improved disclosure for private firms around cash flows and working-capital dynamics, could temper these risks and narrow the family–non-family wedge when equity is the more efficient margin (Myers & Majluf, 1984; Frank & Goyal, 2003).

This study has limits. The deficit measure, although standard, is a reduced-form proxy that may co-move with investment and risk-management choices; bank–firm matched data and natural experiments would allow sharper separation of supply from demand, for example, by exploiting pre-determined bank-level exposures to guarantee caps or supervisory stress (Angrist & Pischke, 2009; Sun & Abraham, 2021; Callaway & Sant’Anna, 2021; Borusyak et al., 2024). Generalizability beyond French private firms in a bank-based system remains an open question, since institutional features moderate both the cost of equity and the strength of relationship lending (Villalonga & Amit, 2006; Frank & Goyal, 2009; Rajan & Zingales, 1995). For these reasons, we scope our conclusions to private, non-financial, non-utility firms in a bank-based environment.

Future work can strengthen identification by linking firms to lenders and by observing price and maturity margins, to distinguish “borrowed more” from “borrowed cheaper,” and by tracing whether amplification persists as policies unwind. Within-family governance heterogeneity, such as founder versus descendant CEOs, board independence, and succession stage, may explain dispersion in pecking-order strength and debt capacity; extending the analysis to other external-finance margins and to cross-country settings would clarify when and where control motives and relationship banking jointly shape financing choices most strongly (Anderson & Reeb, 2003; Villalonga & Amit, 2006; Degryse & Ongena, 2005; Harith & Samujh, 2020).

In short, the data indicate that family control amplifies pecking-order behavior in crisis; when internal funds are scarce, families borrow, and they perform more when credit supply is supportive. We read this as descriptive evidence, robust across definitions and leverage constructs, and strongest where credit intermediation is salient, linking governance, information frictions, and intermediation to capital-structure dynamics in private firms (Myers & Majluf, 1984; Frank & Goyal, 2003; Petersen & Rajan, 1994, 1995).