Financial Digitalization and Urban Green Innovation: Evidence from Panel Quantile ARDL Model

Authors

  • Antanas Laurinavicius Department of Finance, Faculty of Economics and Business Administration, Vilnius University, Vilnius, Lithuania Author
  • Algimantas Laurinavicius Department of Finance, Faculty of Economics and Business Administration, Vilnius University, Vilnius, Lithuania Corresponding Author
  • Asma Salman American University in the Emirates Author
  • Muthanna G. Abdul Razzaq American University in the Emirates Author
  • Mohamed Elsayed Abdelsalam Ghanem Mansoura University, Egypt Author

DOI:

https://doi.org/10.47654/v30y2026i4p188-219

Keywords:

digital finance, green innovation, quantile ARDL, panel cointegration, metropolitan areas

JEL Classifications:

G20, O31, Q55, R11, C31

Abstract

Purpose – Digital finance is spreading unevenly across cities, and whether it narrows or widens the green-innovation gap is unknown because existing evidence is mean-based. This study asks where in the distribution of green patenting digital finance matters, for 16 large U.S. metropolitan areas observed annually over 2000–2025.

Design/methodology/approach – A panel quantile ARDL model, derived from a directed-innovation model with financing frictions, is estimated in error-correction form. Linearity, cointegration and spurious-regression checks precede estimation, and inference uses metro-level cluster and wild cluster bootstraps.

Findings – The long-run semi-elasticity is positive at every quantile and rises monotonically, roughly doubling across the interquartile range from 0.1370 to 0.2860. Error correction is negative throughout and faster in the upper quantiles, so leading metros gain more and converge sooner.

Originality/value – This is the first metropolitan-level distributional treatment of the digital-finance and green-innovation link, and it shows that the substitution and complementarity accounts are opposite signs of one cross-partial derivative that only a quantile design can identify.

Implications – The estimand is a decision input rather than a descriptive average: it tells an agency allocating scarce innovation funds what an extra unit of digital finance buys in a metro of given rank, which is the sense in which this is a decision-sciences contribution. Because gains accrue where capacity is already deep, promoting digital finance is necessary but not sufficient.

References

Acemoglu, D., Aghion, P., Bursztyn, L., & Hemous, D. (2012). The environment and directed technical change. American Economic Review, 102(1), 131–166. https://doi.org/10.1257/aer.102.1.131

Arshad, R., Zada, H., Sohag, K., Wong, W. K., Ullah, E., & Raza, H. (2024). Does US monetary policy uncertainty affect returns of Asian developed, emerging, and frontier equity markets? Empirical evidence by using the quantile-on-quantile approach. Heliyon, 10(12).

Bai, Z. D., Hui, Y. C., Jiang, D. D., Lv, Z. H., Wong, W. K., & Zheng, S. H. (2018). A new test of multivariate nonlinear causality. PLOS ONE, 13(1), Article e0185155. https://doi.org/10.1371/journal.pone.0185155

Bandyopadhyay, A., & Rajib, P. (2026). Does index investment and speculative sentiment impact price discovery? Annals of Financial Economics, 21(1), Article 2650007.

Bouri, E., Gupta, R., Marfatia, H. A., & Nel, J. (2025). Do climate risks predict US housing returns and volatility? Evidence from a quantiles-based approach. Annals of Financial Economics, 20(1), Article 2550004.

Brock, W. A., Dechert, W. D., Scheinkman, J. A., & LeBaron, B. (1996). A test for independence based on the correlation dimension. Econometric Reviews, 15(3), 197–235. https://doi.org/10.1080/07474939608800353

Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2008). Bootstrap-based improvements for inference with clustered errors. The Review of Economics and Statistics, 90(3), 414–427. https://doi.org/10.1162/rest.90.3.414

Chen, C., Fan, M., & Fan, Y. (2024). The role of digital inclusive finance in green innovation. PLOS ONE, 19(12), Article e0315598. https://doi.org/10.1371/journal.pone.0315598

Cheng, Y., Hui, Y., Liu, S., & Wong, W. K. (2022). Could significant regression be treated as insignificant: An anomaly in statistics? Communications in Statistics: Case Studies, Data Analysis and Applications, 8(1), 133–151.

Cheng, Y., Hui, Y., McAleer, M., & Wong, W. K. (2021). Spurious relationships for nearly non-stationary series. Journal of Risk and Financial Management, 14(8), Article 366. https://doi.org/10.3390/jrfm14080366

Chernozhukov, V., & Hansen, C. (2005). An IV model of quantile treatment effects. Econometrica, 73(1), 245–261. https://doi.org/10.1111/j.1468-0262.2005.00570.x

Cho, J. S., Kim, T.-H., & Shin, Y. (2015). Quantile cointegration in the autoregressive distributed-lag modeling framework. Journal of Econometrics, 188(1), 281–300. https://doi.org/10.1016/j.jeconom.2015.05.003

Feng, S., Zhang, R., & Li, G. (2022). Environmental decentralization, digital finance and green technology innovation. Structural Change and Economic Dynamics, 61, 70–83. https://doi.org/10.1016/j.strueco.2022.02.008

Gohar, R., Salman, A., Uche, E., Derindag, O. F., & Chang, B. H. (2023). Does US infectious disease equity market volatility index predict G7 stock returns? Evidence beyond symmetry. Annals of Financial Economics, 18(2), Article 2250028.

Gomber, P., Koch, J. A., & Siering, M. (2017). Digital finance and FinTech: Current research and future research directions. Journal of Business Economics, 87(5), 537–580. https://doi.org/10.1007/s11573-017-0852-x

Hashmi, S. M., & Chang, B. H. (2023). Asymmetric effect of macroeconomic variables on the emerging stock indices: A quantile ARDL approach. International Journal of Finance & Economics, 28(1), 1006–1024. https://doi.org/10.1002/ijfe.2461

Hossain, M. R., Rao, A., Sharma, G. D., Dev, D., & Kharbanda, A. (2024). Empowering energy transition: Green innovation, digital finance, and the path to sustainable prosperity through green finance initiatives. Energy Economics, 136, Article 107736. https://doi.org/10.1016/j.eneco.2024.107736

Hui, Y., Wong, W. K., Bai, Z., & Zhu, Z. Z. (2017). A new nonlinearity test to circumvent the limitation of Volterra expansion with application. Journal of the Korean Statistical Society, 46(3), 365–374. https://doi.org/10.1016/j.jkss.2016.11.006

Im, K. S., Pesaran, M. H., & Shin, Y. (2003). Testing for unit roots in heterogeneous panels. Journal of Econometrics, 115(1), 53–74. https://doi.org/10.1016/S0304-4076(03)00092-7

Imane, E., & Ghizlane, K. (2025). Exploring tail risk transmission between volatility indices and cryptocurrencies: Evidence from quantile connectedness. Advances in Decision Sciences, 29(3), 1–38.

Koenker, R. (2004). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91(1), 74–89. https://doi.org/10.1016/j.jmva.2004.05.006

Koenker, R., & Machado, J. A. F. (1999). Goodness of fit and related inference processes for quantile regression. Journal of the American Statistical Association, 94(448), 1296–1310. https://doi.org/10.1080/01621459.1999.10473882

Laurinavicius, A., Ahmed, H. M. S., Laurinavicius, A., Mahmoud, S. S., & Sayfidinovich, K. O. (2026). Does settling trade in national currency stabilize the domestic currencies? Nonlinear, asymmetric, and horizon-dependent evidence from developing economies. Advances in Decision Sciences, 30(3), 249–282.

Lee, T. H., White, H., & Granger, C. W. J. (1993). Testing for neglected nonlinearity in time series models: A comparison of neural network methods and alternative tests. Journal of Econometrics, 56(3), 269–290. https://doi.org/10.1016/0304-4076(93)90122-L

Levin, A., Lin, C. F., & Chu, C. S. J. (2002). Unit root tests in panel data: Asymptotic and finite-sample properties. Journal of Econometrics, 108(1), 1–24. https://doi.org/10.1016/S0304-4076(01)00098-7

Lu, Y., & Xia, Z. (2024). Digital inclusive finance, green technological innovation, and carbon emissions from a spatial perspective. Scientific Reports, 14(1), Article 8454. https://doi.org/10.1038/s41598-024-59081-9

Noman, M., Maydybura, A., Channa, K. A., Wong, W. K., & Chang, B. H. (2023). Impact of cashless bank payments on economic growth: Evidence from G7 countries. Advances in Decision Sciences, 27(1), 1–22. https://doi.org/10.47654/v27y2023i1p1-22

Pesaran, M. H. (2007). A simple panel unit root test in the presence of cross-section dependence. Journal of Applied Econometrics, 22(2), 265–312. https://doi.org/10.1002/jae.951

Pesaran, M. H. (2015). Testing weak cross-sectional dependence in large panels. Econometric Reviews, 34(6–10), 1089–1117. https://doi.org/10.1080/07474938.2014.956623

Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics, 16(3), 289–326. https://doi.org/10.1002/jae.616

Pesaran, M. H., & Yamagata, T. (2008). Testing slope homogeneity in large panels. Journal of Econometrics, 142(1), 50–93. https://doi.org/10.1016/j.jeconom.2007.05.010

Ramsey, J. B. (1969). Tests for specification errors in classical linear least-squares regression analysis. Journal of the Royal Statistical Society: Series B, 31(2), 350–371.

Salman, A., Chang, B. H., Abdul Razzaq, M. G., Wong, W. K., & Uddin, M. A. (2023). The emerging stock markets and their asymmetric response to infectious disease equity market volatility (ID-EMV) index. Annals of Financial Economics, 18(4), Article 2350008.

Syed, A., Lamine, A., & Loukil, S. (2025). Decoding market linkages and risk transmission: A dynamic analysis of G7 stock indices and currency pairs against a changing economic landscape. Annals of Financial Economics, 20(4), Article 2650002.

Teräsvirta, T., Lin, C. F., & Granger, C. W. J. (1993). Power of the neural network linearity test. Journal of Time Series Analysis, 14(2), 209–220. https://doi.org/10.1111/j.1467-9892.1993.tb00139.x

Wen, J., Hai, H., Li, L., Dou, J., & Tao, R. (2025). Digital finance as a catalyst for green innovation: Threshold effect of diminishing marginal returns. International Review of Financial Analysis, 110, Article 104840. https://doi.org/10.1016/j.irfa.2025.104840

Westerlund, J. (2007). Testing for error correction in panel data. Oxford Bulletin of Economics and Statistics, 69(6), 709–748. https://doi.org/10.1111/j.1468-0084.2007.00477.x

Wong, W. K., Cheng, Y., & Yue, M. (2024). Could regression of stationary series be spurious? Asia-Pacific Journal of Operational Research, Article 2440017.

Wong, W. K., & Pham, M. T. (2022a). Could the test from the standard regression model make significant regression with autoregressive noise become insignificant? The International Journal of Finance, 34, 1–18.

Wong, W. K., & Pham, M. T. (2022b). Could the test from the standard regression model make significant regression with autoregressive noise become insignificant — A note. The International Journal of Finance, 34, 19–39.

Wong, W. K., & Pham, M. T. (2023a). Could the test from the standard regression model make significant regression with autoregressive Yt and Xt become insignificant? The International Journal of Finance, 35, 1–19.

Wong, W. K., & Pham, M. T. (2023b). Could the test from the standard regression model make significant regression with autoregressive Yt and Xt become insignificant — A note. The International Journal of Finance, 35, 20–41.

Wong, W. K., & Pham, M. T. (2025a). Could the correlation of a stationary series with a non-stationary series obtain meaningful outcomes? Annals of Financial Economics. Advance online publication.

Wong, W. K., & Pham, M. T. (2025b). How to model a simple stationary series with a non-stationary series? The International Journal of Finance, 37, 1–19.

Wong, W. K., & Pham, M. T. (2026a). Could the panel regression be used to examine the relationship between I(0) and I(1) series? Advances in Decision Sciences, 30(2). Advance online publication.

Wong, W. K., & Pham, M. T. (2026b). Could we use correlation to examine panel data with I(0) and I(1) variables? The International Journal of Finance, 38. Advance online publication.

Wong, W. K., Pham, M. T., & Yue, M. (2024). Could regressing a stationary series on a non-stationary series obtain meaningful outcomes — A remedy. The International Journal of Finance, 36, 1–20.

Wong, W. K., & Yue, M. (2024). Could regressing a stationary series on a non-stationary series obtain meaningful outcomes? Annals of Financial Economics, 19(3), Article 2450011.

Woode, J. K., Ayamba, S. B., Adjei, A. F., Musah, F., & Bambir, J. (2025). Conditional dependence between non-ferrous metals and global uncertainties: Insight from the nickel crash. Annals of Financial Economics, 20(3), Article 2550019.

Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data (2nd ed.). MIT Press.

Xiao, Z. (2009). Quantile cointegrating regression. Journal of Econometrics, 150(2), 248–260. https://doi.org/10.1016/j.jeconom.2008.12.005

Xing, L., Chang, B. H., & Aldawsari, S. H. (2024). Green finance mechanisms for sustainable development: Evidence from panel data. Sustainability, 16(22), Article 9762. https://doi.org/10.3390/su16229762

Yang, J., & Hui, N. (2024). How digital finance affects the sustainability of corporate green innovation. Finance Research Letters, 63, Article 105314. https://doi.org/10.1016/j.frl.2024.105314

Zada, H., Mansoor, A., Khan, N., Wong, W. K., & Jibir, A. (2026). Monetary policy uncertainty and stock market returns in developed and emerging countries: Evidence from a quantile-on-quantile approach. Advances in Decision Sciences, 30(3), 1–24.

Published

2026-09-29

How to Cite

Laurinavicius, A., Laurinavicius, A., Salman, A., Razzaq, M. G. A., & Ghanem, M. E. A. (2026). Financial Digitalization and Urban Green Innovation: Evidence from Panel Quantile ARDL Model. Advances in Decision Sciences, 30(4), 188-219. https://doi.org/10.47654/v30y2026i4p188-219