References Acebo, E., Miguel-Dávila, J. A., & Nieto, M. (2022). Do financial constraints moderate the relationship between innovation subsidies and firms’ R&D investment? European Journal of Innovation Management, 25(2), 347-364. https://doi.org/10.1108/EJIM-07-2020-0286. Afcha, S., & García-Quevedo, J. (2016). The impact of R&D subsidies on R&D employment composition. Industrial and Corporate Change, 25(6), 955-975. https://doi.org/10.1093/icc/dtw008. Akcigit, U. (2009). Firm size, innovation dynamics and growth. Paper presented at the meeting of the Society for Economic Dynamics. Retrieved from https://EconPapers.repec.org/RePEc:red:sed009:1267. Appelt, S., Galindo-Rueda, F., González Cabral, A., & Pereira, C. (2020). R&D tax incentives: Evidence on design, incidence and impacts (JRC Science for Policy Report). European Commission, Joint Research Centre. https://joint-research-centre.ec.europa.eu/publications/rd-tax-incentives-evidence-design-incidence-and-impacts_en Arrow, K. J. (1962). Economic welfare and the allocation of resources for invention. In: Rowley, C. K. (eds.): Readings in Industrial Economics. Palgrave, London. Chapter 13, 219-236. https://doi.org/10.1007/978-1-349-15486-9_13. Athreye, S. S., Fassio, C., & Roper, S. (2021). Small firms and patenting revisited. Small Business Economics, 57(1), 513-530. https://doi.org/10.1007/s11187-020-00323-1. Austin, P. C. (2019). Assessing covariate balance when using the score with quantitative or continuous exposures. Statistical Methods in Medical Research, 28(5), 1365-1377. https://doi.org/10.1177/0962280218756159. Becker, B. (2015). Public R&D policies and private R&D investment: a survey of the empirical evidence. Journal of Economic Surveys, 29, 917-942. https://doi.org/10.1111/joes.12074. Becker, B. (2019). The impact of innovation policy on firm innovation and performance: A review of recent research developments. ifo DICE Report, ISSN 2511-7823, ifo Institut – Leibniz-Institut für Wirtschaftsforschung an der Universität München, München, 17(4), 10-15. https://hdl.handle.net/10419/216282. Bellucci, A., Pennacchio, L., & Zazzaro, A. (2019). Public R&D subsidies: Collaborative versus individual place-based programs for SMEs. Small Business Economics, 52, 213-240. https://doi.org/10.1007/s11187-018-0017-5. Bellucci, A., Fatica, S., Georgakaki, A., Gucciardi, G., Letout, S., & Pasimeni, F. (2023). Venture capital financing and green patenting. Industry and Innovation, 30(7), 947-983. https://doi.org/10.1080/13662716.2023.2228717. Bloom, N., Van Reenen, J., & Williams, H. (2019). A toolkit of policies to promote innovation. Journal of Economic Perspectives, 33(3), 163–84. https://doi.org/10.1257/jep.33.3.163. BMWi – Federal Ministry for Economic Affairs and Climate Action. (n.d.). Central Innovation Programme for SMEs (ZIM). https://www.zim.de. Bpifrance. (n.d.). Innovation and R&D support programmes. https://www.bpifrance.fr. Breschi, S., Malerba, F., & Orsenigo, L. (2000). Technological regimes and Schumpeterian patterns of innovation. The economic journal, 110(463), 388-410. https://www.jstor.org/stable/2566240. Brewer, M., Crossley, T. F., & Joyce, R. (2018). Inference with difference-in-differences revisited. Journal of Econometric Methods, 7(1), 20170005. https://doi.org/10.1515/jem-2017-0005. Business Finland. (n.d.). Research, development and innovation funding. https://www.businessfinland.fi. Callaway, B., Goodman-Bacon, A., & Sant'Anna, P. H. (2024). Difference-in-differences with a continuous treatment. Paper No. w32117. National Bureau of Economic Research. https://doi.org/10.3386/w32117. Cassiman, B., & Veugelers, R. (2002). R&D cooperation and spillovers: Some empirical evidence from Belgium. American Economic Review, 92(4), 1169-1184. https://doi.org/10.1257/00028280260344704. Centre for the Development of Industrial Technology (CDTI). (2008). Annual report 2008. Ministry of Science and Innovation, Government of Spain. Cerulli, G. & Potì, B. (2016). Explaining firm sensitivity to R&D subsidies within a dose-response model: The role of financial constraints, real cost of investment, and strategic value of R&D. DEM Working Papers 2016/09. Cerulli, G., Corsino, M., Gabriele, R. & Giunta, A. (2022). A dose-response evaluation of a regional R&D subsidies policy. Economics of Innovation and New Technology, 31(3), 173-190. https://doi.org/10.1080/10438599.2020.1792604. Cohen, W. M., & Klepper, S. (1992). The tradeoff between firm size and diversity in the pursuit of technological progress. Small Business Economics, 4, 1-14. https://doi.org/10.1007/BF00402211. Colombo, M. G., Grilli, L. & Murtinu, S. (2011). R&D subsidies and the performance of high-tech start-ups. Economics Letters, 112 (1): 97–99. https://doi.org/10.1016/j.econlet.2011.03.007. Criscuolo, C., Martin, R., Overman, H. G., & Van Reenen, J. (2019). Some causal effects of an industrial policy. American Economic Review, 109(1), 48-85. https://doi.org/10.1257/aer.20160034. Crump, R. K., Hotz, V. J., Imbens, G. W., & Mitnik, O. A. (2009). Dealing with limited overlap in estimation of average treatment effects. Biometrika, 96(1), 187-199. https://doi.org/10.1093/biomet/asn055. Dai, X., & Cheng, L. (2015). The effect of public subsidies on corporate R&D investment: An application of the generalized propensity score. Technological Forecasting and Social Change, 90, 410–419. https://doi.org/10.1016/j.techfore.2014.04.014. Damanpour, F., & Aravind, D. (2012). Managerial innovation: Conceptions, processes and antecedents. Management and organization review, 8(2), 423-454. https://doi.org/10.1111/j.1740-8784.2011.00233.x. Dimos, C., & Pugh, G. (2016). The effectiveness of R&D subsidies: A meta-regression analysis of the evaluation literature. Research Policy, 45(4), 797-815. https://doi.org/10.1016/j.respol.2016.01.002. Enterprise Ireland. (n.d.). Research and development funding programmes. https://www.enterprise-ireland.com. Enterprise Ireland. (2025). Overview of R&D Fund eligibility and claims. https://www.enterprise-ireland.com/… European Commission. (2012). Guide to research and innovation strategies for smart specialisation (RIS3). Publications Office of the European Union. https://data.europa.eu/doi/10.2776/65746. European Commission. (2014). Commission Regulation (EU) No 651/2014 of 17 June 2014 declaring certain categories of aid compatible with the internal market (General Block Exemption Regulation—GBER). Official Journal of the European Union. http://data.europa.eu/eli/reg/2014/651/2023-07-01. Fieller, E. C. (1954). Some problems in interval estimation. Journal of the Royal Statistical Society, Series B, 16(2), 175–185. https://doi.org/10.1111/j.2517-6161.1954.tb00159.x. Fischer, T., & Ringler, P. (2014). What patents are used as collateral? An empirical analysis of patent reassignment data. Journal of Business Venturing, 29(5), 633-650. https://doi.org/10.1016/j.jbusvent.2014.04.002. Gambardella, A., Giuri, P., & Luzzi, A. (2007). The market for patents in Europe. Research policy, 36(8), 1163-1183. https://doi.org/10.1016/j.respol.2007.07.006. Government of Spain. (2014). Royal Decree 475/2014 of 13 June on reductions in social security contributions for research staff. Official State Gazette (BOE). https://www.boe.es/buscar/doc.php?id=BOE-A-2014-6351 González, X., & Pazó, C. (2008). Do public subsidies stimulate private R&D spending? Research Policy, 37(3), 371-389. https://doi.org/10.1016/j.respol.2007.10.009. Grandi, P., Belin, J., Darriet, E., & Guille, M. (2024). SMEs, R &D financing, and credit shocks. Small Business Economics, 63(1), 325-347. https://doi.org/10.1007/s11187-023-00814-x. Griffith, R., Redding, S., & Reenen, J. V. (2004). Mapping the two faces of R&D: Productivity growth in a panel of OECD industries. Review of economics and statistics, 86(4), 883-895. https://doi.org/10.1162/0034653043125194. Hall, B. H., Lotti, F., & Mairesse, J. (2009). Innovation and productivity in SMEs: Empirical evidence for Italy. Small Business Economics, 33, 13-33. https://doi.org/10.1007/s11187-009-9184-8. Hall, B. H., & Lerner, J. (2010). The financing of R&D and innovation. In Handbook of the Economics of Innovation (Vol. 1, pp. 609-639). North-Holland. https://doi.org/10.1016/S0169-7218(10)01014-2. Haans, R. F., Pieters, C., & He, Z. L. (2016). Thinking about U: Theorizing and testing U‐and inverted U‐shaped relationships in strategy research. Strategic management journal, 37(7), 1177-1195. https://doi.org/10.1002/smj.2399. Heijs, J., Buesa, M., Vergara, D. M., Gutiérrez, C., Díaz, G. A., & Picoita, A. J. G. (2020). Innovación, crecimiento y competitividad: El papel de la política tecnológica en España. Funcas. ISBN: 9788417609467. Heijs, J., Guerrero, A. J. & Huergo, E. (2022). Understanding the heterogeneous additionality of R&D subsidy programs of different government levels. Industry and Innovation, 29(4), 533-563. https://doi.org/10.1080/13662716.2021.1990024. Herrera, L., & Sánchez-González, G. (2013). Firm size and innovation policy. International Small Business Journal, 31(2), 137-155. https://doi.org/10.1177/0266242611405553. Hewitt-Dundas, N. (2006). Resource and capability constraints to innovation in small and large plants. Small Business Economics, 26, 257-277. https://doi.org/10.1007/s11187-005-2140-3. Hirano, K., & Imbens, G. W. (2004). The propensity score with continuous treatments. In Gelman, A. & Meng, X.L. (Eds.): Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives: An Essential Journey with Donald Rubin's Statistical Family, 73-84. Wiley-Blackwell. https://doi.org/10.1002/0470090456.ch7. Huergo, E., & Moreno, L. (2017). Subsidies or loans? Evaluating the impact of R&D support programmes. Research Policy, 46(7), 1198-1214. https://doi.org/10.1016/j.respol.2017.05.006. UK Research and Innovation. (n.d.). Innovate UK: Business innovation funding. https://www.ukri.org/councils/innovate-uk/ Kamien, M. I., & Schwartz, N. L. (1978). Self-Financing of an R and D Project. The American Economic Review, 68(3), 252-261. https://www.jstor.org/stable/1805258. Kennedy, E. H., Ma, Z., McHugh, M. D., & Small, D. S. (2017). Non‐parametric methods for doubly robust estimation of continuous treatment effects. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79(4), 1229-1245. https://doi.org/10.1111/rssb.12212. Keum, D. D., & See, K. E. (2017). The influence of hierarchy on idea generation and selection in the innovation process. Organization Science, 28(4), 653-669. https://doi.org/10.1287/orsc.2017.1142. Kim, K. (2018). Diminishing returns to R&D investment on innovation in manufacturing SMEs: do the technological intensity of industry matter? International Journal of Innovation Management, 22(07), 1850056. https://doi.org/10.1142/S1363919618500561. Kiman, K., & Jongmin, Y. (2022). Linear or nonlinear? Investigation an affect of public subsidies on SMEs R&D investment. Journal of the Knowledge Economy, 13(3), 2519-2546. https://doi.org/10.1007/s13132-021-00823-9. Klette, T. J., & Griliches, Z. (2000). Empirical patterns of firm growth and R&D investment: A quality ladder model interpretation. The Economic Journal, 110(463), 363-387. https://www.jstor.org/stable/2566239. Kullback, S. (1959). Information theory and statistics. New York, NY: John Wiley & Sons. ISBN 9780486696843. Lechner, M. (2001). Identification and estimation of causal effects of multiple treatments under the conditional independence assumption. In Econometric evaluation of labour market policies (pp. 43-58). Heidelberg: Physica-Verlag HD. https://doi.org/10.1007/978-3-642-57615-7_3. Lind, J. T., & Mehlum, H. (2010). With or without U? The appropriate test for a U‐shaped relationship. Oxford Bulletin of Economics and Statistics, 72(1), 109-118. https://doi.org/10.1111/j.1468-0084.2009.00569.x. Marino, M., Lhuillery, S., Parrotta, P., & Sala, D. (2016). Additionality or crowding-out? An overall evaluation of public R&D subsidy on private R&D expenditure. Research Policy, 45(9), 1715-1730. https://doi.org/10.1016/j.respol.2016.04.009. Mazzucato, M., & Semieniuk, G. (2017). Public financing of innovation: new questions. Oxford Review of Economic Policy, (1), 24-48. https://doi.org/10.1093/oxrep/grw036. Ministry of Economy and Competitiveness. (2013). Spanish strategy for science, technology and innovation 2013–2020. Government of Spain. National Research Council. (2008). An Assessment of the SBIR Program. Washington, DC: The National Academies Press. https://doi.org/10.17226/11989. National Research Council of Canada. (n.d.). Support for technology innovation (Industrial Research Assistance Program — IRAP). Government of Canada. https://nrc.canada.ca/en/support-technology-innovation. Meuleman, M., & De Maeseneire, W. (2012). Do R&D subsidies affect SMEs’ access to external financing? Research Policy, 41(3), 580-591. https://doi.org/10.1016/j.respol.2012.01.001. Nelson, R. R. (1959). The simple economics of basic scientific research. The Journal of Political Economy, 67(3), 297–306. http://www.jstor.org/stable/1827448. Nilsen, Ø. A., Raknerud, A. & Iancu, D. C. (2020). Public R&D support and firm performance: A multivariate dose-response analysis. Research Policy, 49(7), 104067. https://doi.org/10.1016/j.respol.2020.104067. OECD. (2023). OECD R&D tax incentives database. Organisation for Economic Co-operation and Development. https://www.oecd.org/sti/rd-tax-stats/ Ortega-Argilés, R., Vivarelli, M., & Voigt, P. (2009). R&D in SMEs: A paradox? Small Business Economics, 33, 3-11. https://doi.org/10.1007/s11187-009-9187-5. Patterson, F., & Kerrin, M. (2014). Characteristics and behaviours associated with innovative people in small-and medium-sized enterprises. In Handbook of research on small business and entrepreneurship (pp. 187-206). Edward Elgar Publishing. https://doi.org/10.4337/9781849809245.00020. Pavitt, K. (1984). Sectoral patterns of technical change: Towards a taxonomy and a theory. Research Policy, 13(6), 343–373. https://doi.org/10.1016/0048-7333(84)90018-0. Pavitt, K., Robson, M., & Townsend, J. (1987). The size distribution of innovating firms in the UK: 1945-1983. The Journal of Industrial Economics, 297-316. https://doi.org/10.2307/2098636. Rothwell, R. (1985). Venture finance, small firms and public policy in the UK. Research Policy, 14(5), 253-265. https://doi.org/10.1016/0048-7333(85)90008-3. Rothwell, R. (1989). Small firms, innovation and industrial change. Small Business Economics, 51-64. https://doi.org/10.1007/BF00389916. Sasabuchi, S. (1980). A test of a multivariate normal mean with composite hypotheses determined by linear inequalities. Biometrika, 67(2), 429–439. https://doi.org/10.1093/biomet/67.2.429. Schumpeter, J. A. (1934). The theory of economic development: An inquiry into profits, capital, credit, interest and the business cycle. Cambridge, MA: Harvard University Press. ISBN: 9780674879904. Schumpeter, J. A. (1942). Capitalism, socialism and democracy. New York, NY: Harper & Brothers. ISBN: 0061330086. Teece, D. J. (1986). Profiting from technological innovation: Implications for integration, collaboration, licensing and public policy. Research Policy, 15(6), 285-305. https://doi.org/10.1016/0048-7333(86)90027-2. Tingvall, P. G. & Videnord, J. (2020). Regional differences in effects of publicly sponsored R&D grants on SME performance. Small Business Economics, 54(4), 951-969. https://doi.org/10.1007/s11187-018-0085-6. Tübbicke, S. (2022). Entropy balancing for continuous treatments. Journal of Econometric Methods, 11(1), 71-89. https://doi.org/10.1515/jem-2021-0002. Tübbicke, S. (2023). ebct: Using entropy balancing for continuous treatments to estimate dose–response functions and their derivatives. The Stata Journal, 23(3), 709-729. https://doi.org/10.1177/1536867X231196291. Vegetabile, B. G., Griffin, B. A., Coffman, D. L., Cefalu, M., Robbins, M. W., & McCaffrey, D. F. (2021). Nonparametric estimation of population average dose-response curves using entropy balancing weights for continuous exposures. Health Services and Outcomes Research Methodology, 21, 69-110. https://doi.org/10.1007/s10742-020-00236-2. Vossen, R. W. (1998). Relative strengths and weaknesses of small firms in innovation. International Small Business Journal, 16(3), 88-94. https://doi.org/10.1177/0266242698163005. Watson, S. K., & Elliot, M. (2016). Entropy balancing: A maximum-entropy reweighting scheme to adjust for coverage error. Quality & Quantity, 50, 1781-1797. https://doi.org/10.1007/s11135-015-0235-8. Zhu, Y., Coffman, D. L. & Ghosh, D. (2015). A boosting algorithm for estimating generalized propensity scores with continuous treatments. Journal of Causal Inference, 3(1), 25–40. https://doi.org/10.1515/jci-2014-0022. Zúñiga‐Vicente, J. Á., Alonso‐Borrego, C., Forcadell, F. J., & Galán, J. I. (2014). Assessing the effect of public subsidies on firm R&D investment: A survey. Journal of Economic Surveys, 28(1), 36-67. https://doi.org/10.1111/j.1467-6419.2012.00738.x. Zhu, Y., Coffman, D. L. & Ghosh, D. (2015). A boosting algorithm for estimating generalized propensity scores with continuous treatments. Journal of Causal Inference, 3(1), 25–40. https://doi.org/10.1515/jci-2014-0022.