Pay structure and firm technological innovation: comparative research based on three pay gaps

Income inequality has narrowed relatively but widened absolutely in China, prompting policy actions such as repeated pay cap regulations for SOE executives. Globally, research links inequality to technological change and education, and examines consequences for innovation. Within firms, behavior responds to relative as well as absolute pay, motivating study of pay gaps: within top management (CEO–manager), within firms (management–employees), and external (relative to highest-paying industry peers). Two theories dominate: tournament theory (larger gaps motivate effort/innovation) and social comparison theory (large gaps breed perceived unfairness and hinder innovation). This study questions whether simply enlarging pay gaps universally boosts innovation and whether different pay gap types have heterogeneous effects. It proposes that both tournament and social comparison effects coexist, yielding nonlinear (inverted U-shaped) relationships whose position and slope differ across pay gap types. The study also differentiates innovation output quality (via patent citations), explores moderating firm/industry factors, and introduces fsQCA to identify context-specific pay system configurations that achieve high innovation performance.

Prior work clusters into three streams: (1) Pay gaps within top management: some find larger CEO–manager gaps enhance innovation and efficiency, though they can intensify negative effects of CEO underpayment. (2) Internal firm pay gaps (management–employees): many studies support tournament theory, showing positive links to innovation quantity and inventor participation, in China and abroad. (3) External/industry pay gaps: industry tournament incentives correlate with performance, risk, and innovation, especially where CEO mobility is likely, though some evidence shows promotion of incremental but inhibition of radical innovation. A competing view posits nonlinearity: when gaps are small, widening can help; when large, fairness concerns dominate, harming innovation; similar inverted U-shapes appear within top teams. Recent trends deepen concepts (regional/geographic pay tournaments; pay-role inversions) and better capture innovation quality (citations; breakthrough vs incremental). Limitations in prior research include focus on single pay gaps, linear assumptions, limited attention to innovation quality, and lack of holistic, context-aware analysis incorporating employee perceptions and multiple pay gaps.

Data and sample: Panel of all non-financial China A-share listed firms from 2009–2019; patent citations observed through 2022. Patent data from the China National Intellectual Property Patent Database; financials and governance from CSMAR and WIND. Cleaning steps: exclude financials; winsorize continuous variables at 1%/99%; remove ST/PT firms and missing key data. Final panel: 18,670 firm-year observations. Analyses run in Stata 17.

Variables:

• Pay gap measures (scaled by 1/10 of logs for comparability): • Internal pay gap among top management (FMPG): ln[(avg pay top-3 managers – avg pay other managers)]/10. • Internal firm pay gap (FIPG): ln(AMP – AEP)/10, with AMP = average pay of directors/supervisors/managers; AEP = average employee pay excluding managerial compensation. • External pay gap (FOPG): ln(1 + AMP_max – AMP)/10, where AMP_max is industry maximum AMP. Robustness also uses ratio forms (e.g., AMP_max/AMP).
• Innovation outputs: • Patent: ln(1 + total patent applications) as main outcome. • Patent_high: ln(1 + count of patents in top 5% of citations within same industry-year) to capture high-quality innovation. • Patent_low: ln(1 + (total patents – high-quality patents)). Also a binary Bs indicating presence of high-quality patents.
• Controls: firm size (ln assets), leverage, ROA, tangibility, age, sales growth, SOE ownership, CEO-chair duality, independent director ratio, managerial shareholding, Tobin’s Q, HHI (and HHI^2), CEO age, CEO tenure; industry and year fixed effects. Moderation uses Lerner index (FLerner) as firm competitive position.

Models:

• Baseline OLS with industry and year fixed effects: Patent_it = α + β·FPG_it + γ·Controls_it + FE_year + FE_industry + ε_it. Nonlinearities tested with quadratic terms for FMPG, FIPG, FOPG.
• Relative importance: variables standardized to compare effect magnitudes across pay gaps; multicollinearity checks (avg VIF 2.28; all VIF<10; correlations <0.65).
• Endogeneity/causality: 2SLS with instruments. For internal gaps (FMPG, FIPG): differences between firm and industry average lagged 2- and 3-year pay gaps of peers (L2.AFMPG, L3.AFMPG; L2.AFIPG, L3.AFIPG). For FOPG: ln(AMP_total) at industry level and its lag as instruments. First-stage shows strong correlations; overidentification tests support exogeneity; second-stage coefficients remain significant and directionally consistent with OLS.
• Heterogeneity: split by innovation orientation (Bs=1 vs 0), ownership (SOE vs non-SOE), and innovation quality (Patent_high vs Patent_low). Moderation by FLerner with interaction terms.
• fsQCA: To identify configurations yielding high innovation performance, select non-SOE manufacturing samples pre-2019; primary year 2017 with robustness in 2016 and 2018; split by firm size; 70 listed firms per size group. Direct calibration: for most variables, 95th percentile = full membership, 5th = no membership, 50th = crossover; for Board and Mshare, 95th/15th/50th used. Necessity analysis indicates no single necessary condition (except simple Board structure necessary for small firms). Truth table analysis with frequency threshold 1, consistency ≥0.8, PRI≥0.70 yields three small-firm and six large-firm high-innovation configurations with solution consistencies >0.9.

• Baseline relationships (Table 3; N≈17,546): • FMPG positively associated with Patent: coef 0.697 (t=4.76, p<0.01); quadratic FMPG^2 = −0.793 (t=−2.14, p<0.05) but turning point beyond data range (left-half of inverted U). • FIPG positively associated: coef 1.011 (t=9.62, p<0.01); quadratic FIPG^2 = −0.867 (t=−2.95, p<0.01); turning point beyond data range (left-half of inverted U). • FOPG negatively associated linearly: −0.160 (t=−2.77, p<0.01); with quadratic, FOPG^2 = −0.351 (t=−2.71, p<0.01), indicating a complete inverted U with turning point within data. • Controls: larger Size, higher Leverage, higher ROA, lower Tangibility, younger Age, higher TobinQ, and higher managerial shareholding (Mshare) increase Patent. SOEs show higher Patent output; HHI exhibits an inverted U with peak around HHI≈0.395.

• Relative importance after standardization (Table 4): • When FMPG and FIPG enter together, a 1 SD increase in FMPG reduces fitted Patent by ~0.044 SD (−3.03% of Patent’s SD), while a 1 SD increase in FIPG increases Patent by ~0.054 SD (+3.71%). • With all three gaps, FIPG remains the most influential positive driver; FMPG turns negative when controlling other gaps; FOPG’s impact varies with its percentile (positive at low percentiles, negative at high percentiles).

• Causality (2SLS, Table 5): First-stage instruments are strong; second-stage confirms positive effects of FMPG and FIPG on Patent (p<0.01) and inverted U for FOPG (quadratic p<0.05), consistent with OLS, supporting causal interpretation.

• Innovation quality heterogeneity (Table 6): • FMPG has stronger effects on high-quality innovation: Patent_high coef 0.669 (t=6.34) vs Patent_low 0.625 (t=4.63). • FIPG more strongly boosts low-quality innovation: Patent_high 0.565 (t=7.73); Patent_low 0.880 (t=9.19). • FOPG displays inverted U for high-quality innovation (FOPG 0.609, t=3.98; FOPG^2 −0.522, t=−5.44; inflection ~0.583). For low-quality, FOPG linear term is ns (0.270) with significant negative quadratic (−0.292, t=−2.39; inflection ~0.462).

• Innovation orientation heterogeneity (Table 7): Effects of FMPG, FIPG, and FOPG (and its quadratic) are larger and more significant for innovation-oriented firms than for non-innovation-oriented firms, supporting H2b.

• Ownership heterogeneity (Table 8): Non-SOEs show stronger positive effects of FMPG (0.818, t=4.80) and FIPG (1.133, t=8.90) than SOEs; FOPG’s inverted U is more pronounced in non-SOEs (FOPG 0.516, t=2.09; FOPG^2 −0.495, t=−3.11; inflection ~0.521) than SOEs (inflection ~0.594), supporting H2c–H2d.

• Moderation by competitive position (FLerner) (Table 9): • FMPGFLerner = −4.035 (t=−3.54, p<0.01) and FIPGFLerner = −2.304 (t=−3.01, p<0.01): higher competitive position weakens/turns negative the motivational effect of internal gaps (H3a, H3b). • For FOPG, FOPGFLerner = 2.241 (t=2.23, p<0.10) and FOPG^2FLerner = −1.360 (t=−2.50, p<0.10): increasing competitiveness shifts the inverted U rightward/downward, weakening early positive motivation and strengthening later inhibition (H3c).

• fsQCA pathways to high innovation performance (Table 10): • Small firms: three valid configurations (consistency ≥0.911). Illustrative cores: S1 (absence of Growth, HHI, Mshare, FOPG); S2 (presence of FMPG; absence of FIPG and FOPG); S3 (presence of managerial shareholding; absence of Growth, Age, HHI) with pay gaps as contributing conditions. • Large firms: six configurations (consistency 0.917–0.960). Types include: L1 (managerial equity incentives with complex boards and higher FOPG), L2 (low management pay vs peers with wide internal gaps in younger firms), L3 (wide internal gaps plus managerial equity, low external gap, prioritizing R&D over growth).

Overall, internal gaps (especially FIPG) are the strongest positive drivers of innovation quantity; FMPG supports high-quality innovation but can become detrimental alongside other gaps; external gaps follow an inverted U and often suppress innovation at higher levels.

The study integrates tournament and social comparison theories to explain how pay gaps affect firm innovation. It shows that both forces coexist, producing inverted U-shaped net effects whose position depends on the reference group and perceived advancement probability (expectancy theory). Internal gaps (especially management–employee) have strong motivational effects for innovation when moderate, while excessive gaps elevate unfairness perceptions and reduce innovation. External gaps motivate only up to a point and then broadly inhibit innovation. These effects are contingent on firm strategy (innovation orientation), ownership (non-SOEs more responsive than SOEs), and competitive position (higher competitiveness attenuates or reverses motivational effects). Differentiating innovation by quality reveals managerial pay structures are more tightly linked to high-quality outputs, whereas internal firm-wide gaps stimulate lower-quality, faster outputs. The findings highlight the importance of nuanced, context-aligned compensation design rather than one-size-fits-all pay gap policies.

This paper establishes that pay gaps and innovation are related nonlinearly: internal management and firm-wide gaps operate on the left half of an inverted U, while external gaps show a full inverted U with overall inhibitory tendencies at higher levels. Internal firm-wide gaps (FIPG) are the most influential positive drivers of innovation quantity; management gaps (FMPG) are more tied to high-quality outputs but can become detrimental when other gaps are considered; external gaps (FOPG) motivate only at low levels. The impacts are stronger in innovation-oriented and nonstate-owned firms and are dampened by stronger competitive positions. Using fsQCA, the study identifies multiple, size-contingent compensation configurations leading to high innovation performance, demonstrating that firms can reach high innovation through different combinations of pay gaps, equity incentives, organizational complexity, and competitive context. Future research should refine measures of within-firm inequality (e.g., R&D-specific pay structures), develop stronger instruments addressing endogeneity, and examine long-term and sustainable innovation under employee mobility.

• Data and variable limitations: Employee-level perceptions (motivation, fairness), education and experience, and detailed salary structures (e.g., R&D-specific pay gaps) are not observed; hidden payments/benefits may offset perceived inequities but are unmeasured, potentially biasing estimates.
• Endogeneity concerns: Although multiple IVs and 2SLS are employed, stronger instruments exogenous to innovation outcomes are still needed; reverse causality (innovation affecting pay gaps) may persist.
• Omitted contextual factors: Industry maturity, growth opportunities, and policy support are hard to measure precisely and may affect both pay gaps and innovation despite fixed effects and controls.
• Generalizability: Findings are based on Chinese A-share firms; external validity to other institutional contexts may be limited. Future work could build richer inequality metrics, focus on specific employee groups (e.g., R&D), and assess long-term/sustainable innovation effects under labor mobility.