Main Article Content
Abstract
The relationship between pay gap and corporate innovation has been the focus of significant theoretical discussion, with tournament theory and social comparison theory generating contrasting predictions. Traditional linear methods are ill-suited to capturing the nonlinear nature of the relationship. This study proposes an XGBoost-SHAP approach to predict innovation performance using a sample of 26,815 firm-year observations from Chinese A-share-listed firms from 2010 to 2023. The results show that the XGBoost model achieves an R2 of 0.382, which is 65.4% higher than OLS (R2=0.231). The SHAP value analysis indicates that the vertical pay gap ranks as the third most important factor, following firm size and firm age. The SHAP dependence plot shows an inverted U-shaped relationship between the vertical pay gap and innovation performance, with a turning point at approximately 8.7 times. The heterogeneity analysis indicates that state-owned enterprises attain their turning point earlier (7.2 times) than non-state-owned enterprises (10.1 times), suggesting that employees are more responsive to pay inequality. These findings provide practical insights that may guide managers in designing their firms’ compensation schemes. Firms that fall below the threshold may consider expanding their pay gaps, while those that fall above may consider compressing their pay gaps. This XGBoost-SHAP approach translates statistical evidence into practical diagnostic tools that managers may use to assess the optimality of their firms’ compensation schemes in supporting innovation.
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Article Details
References
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- S. Athey and G. Imbens, "Recursive partitioning for heterogeneous causal effects," Proceedings of the National Academy of Sciences, vol. 113, no. 27, pp. 7353-7360, 2016. DOI: https://doi.org/10.1073/pnas.1510489113.
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References
AFL-CIO, "Executive Paywatch 2025," AFL-CIO, Washington, DC, 2025. [Online]. Available: https://aflcio.org/paywatch.
S. Anderson, "Executive Excess 2025: CEO Pay at America's 100 Largest Low-Wage Employers," Institute for Policy Studies, Washington, DC, 2025. [Online]. Available: https://ips-dc.org/release-executive-excess-2025/.
E. P. Lazear and S. Rosen, "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, vol. 89, no. 5, pp. 841-864, 1981. DOI: https://doi.org/10.1086/261010.
L. Festinger, "A theory of social comparison processes," Human Relations, vol. 7, no. 2, pp. 117-140, 1954. DOI: https://doi.org/10.1177/001872675400700202.
J. S. Adams, "Inequity In Social Exchange," in Advances in Experimental Social Psychology, vol. 2, L. Berkowitz Ed.: Academic Press, 1965, pp. 267-299.
Z. Tan, X. Wu and R. Chu, "Impact of Pay Gap on Innovation Performance: The Moderating Role of Top Management Team Diversity," Sustainability, vol. 16, no. 17, p. 7459, 2024. DOI: https://doi.org/10.3390/su16177459.
L. Fu, S. Zhang and F. Wu, "The Impact of Compensation Gap on Corporate Innovation: Evidence from China's Pharmaceutical Industry," International Journal of Environmental Research and Public Health, vol. 19, no. 3, p. 1756, 2022. DOI: https://doi.org/10.3390/ijerph19031756.
S. Wang and Z. Lin, "Pay structure and firm technological innovation: comparative research based on three pay gaps," Humanities and Social Sciences Communications, vol. 11, no. 1, p. 373, 2024. DOI: https://doi.org/10.1057/s41599-024-02820-0.
T. Chen and C. Guestrin, "XGBoost: A Scalable Tree Boosting System," in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, California, USA, 2016. DOI: https://doi.org/10.1145/2939672.2939785.
J. Zhang and K. Yin, "Application of gradient boosting model to forecast corporate green innovation performance," Frontiers in Environmental Science, vol. 11, 2023. DOI: https://doi.org/10.3389/fenvs.2023.1252271.
J. Zhang and Z. Zhao, "Corporate ESG rating prediction based on XGBoost-SHAP interpretable machine learning model," Expert Systems with Applications, vol. 295, p. 128809, 2026. DOI: https://doi.org/10.1016/j.eswa.2025.128809.
S. M. Lundberg and S.-I. Lee, "A unified approach to interpreting model predictions," Advances in Neural Information Processing Systems, vol. 30, 2017. DOI: https://doi.org/10.48550/arXiv.1705.07874.
W. Zheng, Y. Li and X. Guan, "How the executive pay gap affects corporate innovation," Technology Analysis & Strategic Management, vol. 36, no. 11, pp. 3973-3986, 2024. DOI: https://doi.org/10.1080/09537325.2023.2280536.
J. Zheng, H. Chowdhury, M. S. Hossain and K. Gupta, "Tournament-based incentives and media sentiment," Journal of Contemporary Accounting & Economics, vol. 19, no. 2, p. 100353, 2023. DOI: https://doi.org/10.1016/j.jcae.2023.100353.
H. Choi, K. Karim and Y. Liu, "Tournament incentives, corporate overinvestment, and economic consequences," International Review of Financial Analysis, vol. 102, p. 104090, 2025. DOI: https://doi.org/10.1016/j.irfa.2025.104090.
B. Budiandriani and M. Fahlevi, "How Vertical and Horizontal Pay Gaps in Research and Development Affect Corporate Innovation in Indonesian Public Firms," Economics - Innovative and Economics Research Journal, vol. 13, no. 2, pp. 367-387, 2025. DOI: https://doi.org/10.2478/eoik-2025-0048.
U. S. Maqsood, Q. Li, S. Wang and R. M. A. Zahid, "Government CEO pay regulation and corporate innovation performance: The role of CEO's career horizon and shareholding," BRQ Business Research Quarterly, vol. 28, no. 2, pp. 543-568, 2025. DOI: https://doi.org/10.1177/23409444251314891.
X. Li, X. Wang, Z. Zhao and Q. Zhao, "ESG ratings, executive pay-for-performance sensitivity and within-firm pay gap," Humanities and Social Sciences Communications, vol. 12, no. 1, p. 599, 2025. DOI: https://doi.org/10.1057/s41599-025-04908-7.
Y. Jingyi, F. Sijia and J. Hui, "The executive external pay gap and firm innovation performance: An empirical study from the perspective of the market competition environment," Academic Journal of Business & Management, vol. 7, no. 1, pp. 37-44, 2025. DOI: https://doi.org/10.25236/AJBM.2025.070105.
W. Przychodzen and F. Gómez-Bezares, "CEO–Employee Pay Gap, Productivity and Value Creation," Journal of Risk and Financial Management, vol. 14, no. 5, p. 196, 2021. DOI: https://doi.org/10.3390/jrfm14050196.
I. S. Fulmer, B. Gerhart and J. H. Kim, "Compensation and performance: A review and recommendations for the future," Personnel Psychology, vol. 76, no. 2, pp. 687-718, 2023. DOI: https://doi.org/10.1111/peps.12583.
G. Ke, Q. Meng, T. Finley, T. Wang, W. Chen, W. Ma, Q. Ye and T.-Y. Liu, "LightGBM: A highly efficient gradient boosting decision tree," Advances in Neural Information Processing Systems, vol. 30, 2017. DOI: https://doi.org/10.5555/3294996.3295074.
W. Zhu, M. Li, C. Wu and S. Liu, "Comprehensive financial health assessment using advanced machine learning techniques: Evidence based on private companies listed on ChiNext," PLOS ONE, vol. 19, no. 12, p. e0314966, 2024. DOI: https://doi.org/10.1371/journal.pone.0314966.
X. Wang and T. Kong, "Exploring the Drivers of Innovation Capability in Listed Companies: A Machine Learning Approach to Identifying Synergistic Factors," Computational Economics, 2026. DOI: https://doi.org/10.1007/s10614-025-11193-8.
M. A. Omar, I. I. Gomaa, S. H. Sabry and H. Moubarak, "Artificial Intelligence's Role in Predicting Corporate Financial Performance: Evidence from the MENA Region," Journal of Risk and Financial Management, vol. 19, no. 1, p. 51, 2026. DOI: https://doi.org/10.3390/jrfm19010051.
R. Jaiswal, S. Gupta and A. K. Tiwari, "Dissecting the compensation conundrum: a machine learning-based prognostication of key determinants in a complex labor market," Management Decision, vol. 61, no. 8, pp. 2322-2353, 2023. DOI: https://doi.org/10.1108/MD-07-2022-0976.
F. S. Khan, S. S. Mazhar, K. Mazhar, D. A. AlSaleh and A. Mazhar, "Model-agnostic explainable artificial intelligence methods in finance: a systematic review, recent developments, limitations, challenges and future directions," Artificial Intelligence Review, vol. 58, no. 8, p. 232, 2025. DOI: https://doi.org/10.1007/s10462-025-11215-9.
P.-D. Arsenault, S. Wang and J.-M. Patenaude, "A Survey of Explainable Artificial Intelligence (XAI) in Financial Time Series Forecasting," ACM Computing Surveys, vol. 57, no. 10, p. 265, 2025. DOI: https://doi.org/10.1145/3729531.
S. Ergün, "Explaining XGBoost predictions with SHAP value: A comprehensive guide to interpreting decision tree-based models," New Trends in Computer Sciences, vol. 1, no. 1, pp. 19-31, 2023. DOI: https://doi.org/10.3846/ntcs.2023.17901.
Y. Nohara, K. Matsumoto, H. Soejima and N. Nakashima, "Explanation of machine learning models using shapley additive explanation and application for real data in hospital," Computer Methods and Programs in Biomedicine, vol. 214, p. 106584, 2022. DOI: https://doi.org/10.1016/j.cmpb.2021.106584.
Y. Wang, W. Wei, Z. Liu, J. Liu, Y. Lv and X. Li, "Interpretable Machine Learning Framework for Corporate Financialization Prediction: A SHAP-Based Analysis of High-Dimensional Data," Mathematics, vol. 13, no. 15, p. 2526, 2025. DOI: https://doi.org/10.3390/math13152526.
F. Zeng, J. Wang and C. Zeng, "An optimized machine learning framework for predicting and interpreting corporate ESG greenwashing behavior," PLOS ONE, vol. 20, no. 3, p. e0316287, 2025. DOI: https://doi.org/10.1371/journal.pone.0316287.
J. A. Darwish, "Optimization and prediction of corporate credit rating through advanced feature selection based on AI and deep learning," Alexandria Engineering Journal, vol. 127, pp. 586-594, 2025. DOI: https://doi.org/10.1016/j.aej.2025.05.043.
S. Athey and G. Imbens, "Recursive partitioning for heterogeneous causal effects," Proceedings of the National Academy of Sciences, vol. 113, no. 27, pp. 7353-7360, 2016. DOI: https://doi.org/10.1073/pnas.1510489113.
Z. Hua and Y. Yu, "Digital transformation and the impact of local tournament incentives: Evidence from publicly listed companies in China," Finance Research Letters, vol. 57, p. 104204, 2023. DOI: https://doi.org/10.1016/j.frl.2023.104204.
S. Milani and R. Neumann, "R&D, patents, and financing constraints of the top global innovative firms," Journal of Economic Behavior & Organization, vol. 196, pp. 546-567, 2022. DOI: https://doi.org/10.1016/j.jebo.2022.02.016.