## Abstract

This paper investigates the implications that complementary assets needed for the formation of start-ups have on the innovative efforts of incumbent firms. In particular, we highlight a strategic incentive effect by which the innovative efforts of incumbents are decreasing in the availability of the complementary assets needed for the creation of a start-up. Furthermore, we argue that the R&D investments of incumbents are positively related to the presence of policy support to innovation, and to the firm’s endowment of human capital. The empirical relevance of our theoretical hypotheses is investigated—and supported—by using firm level data.

This is a preview of subscription content, log in to check access.

## Notes

- 1.
The importance of tacit knowledge has been highlighted, among others, by Collins (1974) for the development of TEA lasers, by Zucker et al. (1998) for the commercialization of biotechnologies, and by Fallick et al. (2006) for the computer industry. In a theoretical perspective, Spulber (2012) investigates the role of tacit knowledge in the trade-off between entrepreneurship and technological transfer.

- 2.
The argument that firms’ investment is potentially negatively affected by worker mobility lies of the core of the labor poaching literature started by the seminal contribution of Becker (1962). More recently theoretical contributions (e.g., Almazan et al. 2007; Combes and Duranton 2006) have explored the effects of both labor poaching and labor pooling on firms’ location and investment choices.

- 3.
A different stream of literature has investigated the potential creation of start-ups by focusing on ex-ante and ex-post contracting between an incumbent firm and a key employee in the presence of weak (or absent) property rights (see, among others, Anton and Yao 1994, 1995; Anand and Galetovic 2000).

- 4.
The effect that a reduction in the barriers to start-up formation might have on the R&D investments of incumbent firms is, however, hardly understood and typically neglected by the extant literature.

- 5.
- 6.
In general, the start-up faces uncertainty in assessing market demand, but the relevant factor for her decision to form a new firm is her ex-ante expectation. In what follows we assume that the R&D employee and the incumbent firm share the same expectation about the profitability of the start-up.

- 7.
Properly defining the units in which effort is measured gives rise to the coefficient 1/2 of

*e*^{2}. - 8.
We do not claim that the causal mechanism highlighted in Proposition 1 is necessarily the only possible explanation for a negative relationship between the availability of complementary assets and the incumbent’s innovation incentives. However, the empirical analysis in the following Section not only highlights a clear pattern in the empirical data, but it also shows that the implications of our theory are consistent with cross-industry evidence.

- 9.
The mixed empirical evidence with respect to the size of crowding out effects is in accordance with the observation in the framework of our model that the size and even the sign of the derivative \(\frac {\partial (1-\alpha ) I(K^{*};\chi )}{\partial \alpha }\) depends crucially on the specification of the R&D investment function

*I*(.) and of the inverse demand function*p*^{F}(.). - 10.
While both our model (see the proof of Proposition 2 (ii) in the Appendix) and the extant literature just discussed are straightforward in predicting a positive link between the incumbent firm’s human capital and the level of its R&D investment (Hypothesis 3), one may argue that highly skilled employees are more likely to spin-off and found innovative start-ups (see e.g. Olivari 2016; Zwan Van Der et al. 2016). If such is the case, this link might reverse into a negative one for reasons similar to those supporting our first hypothesis, stating a negative relationship between the availability of complementary assets for potential start-ups and the incumbent’s incentive to invest in R&D. Whether this argument will be dominant in affecting the relationship between human capital and R&D expenditures will be tested by our empirical exercise (see Section 4).

- 11.
Since suitable proxies for the loss of tacit knowledge stemming from key employees leaving incumbents and for the impact of start-up formation on incumbents’ market shares are not available in our dataset, we abstain from formulating these observations as hypotheses to be empirically tested.

- 12.
Italian CIS surveys are systematically collected every 3 years. Presidents of the companies’ boards and CEOs are recipients of the questionnaires and in charge of filling them in. Surveys run in different periods slightly differ in the design of the questionnaire and/or in the disclosure policy of some of the variables. For our purposes, the CIS 3 survey is the most complete cross section among the ones currently available. It is important to note that the different Italian CIS surveys are conducted independently, with the only aim to be representative, with no attention to the longitudinal dimension of the data. Therefore, each survey is largely composed by different firms and no panel data are currently available.

- 13.
Firm selection is carried out through a ‘one step stratified sample design.’ The stratification of the sample is based on the following three variables: firm-size, sector, regional location. Technically, in the generic stratum

*h*, the random selection of*n*_{ h }sample observations among the*N*_{ h }belonging to the entire population is realized through the following procedure: (i) a random number in the 0-1 interval is attributed to each*N*_{ h }population unit; (ii) the*N*_{ h }population units are sorted by increasing values of the random number; (iii) units in the first*n*_{ h }positions in the order previously mentioned are selected. Estimates obtained from the selected sample are very close to the actual values in the national population. The weighting procedure follows the Eurostat and Oslo Manual (OECD 1997) recommendations: weights indicate the inverse of the probability that the observation is sampled. Therefore, sampling weights ensure that each group of firms is properly represented and correct for sample selection. Moreover, they help reducing the heteroskedasticity commonly arising when the analysis focuses on survey data. - 14.
As far as the age of the firms in the ‘start-up’ sub-sample is concerned, the 5-year threshold is chosen to solve the trade-off between a lower age and the representativeness of the sub-sample of young companies. With our selection procedure, we end up with about 22% of the entire sample as start-ups.

- 15.
- 16.
While start-ups and spin-offs are not exactly overlapping, previous empirical literature shows that in between 70/80% of start-ups are actually spin-offs by former employees in the same sector, the residual being young people starting their first job experience, unemployed, serial entrepreneurs and founders coming from other sectors. For instance, analyzing a sample of 720 Italian newborn firms in a period not so far from the one investigated in the present study—1988—Vivarelli (1991) found that 68.8% of the interviewed entrepreneurs had come from the same sector (see also Storey 1994; Arrighetti and Vivarelli 1999; Shane 2000; Klepper 2001; Stam 2007; Vivarelli 2013).

- 17.
No information about the knowledge stock—the key variable of our model—is available in the CIS database. However, this is not a problem within our model setting, where the R&D investment (

*I*) is assumed to be positively correlated with the knowledge stock (*K*). In fact, since*I*^{′}(*K*;*χ*) > 0, to empirically show that incumbents’ R&D investments and complementary assets (*γ*) are inversely correlated is equivalent to prove the obtained result that the incumbents’ knowledge stock is decreasing with respect to*γ*. - 18.
As discussed in the Introduction, a variety of complementary assets may be needed to create a start-up, widely differing across industrial sectors. However, the availability of financial resources is the key comprehensive factor in gaining access to those assets in all industries. In other words, while in specific sectors and specific technology fields some particular complementarity assets may be crucial (ranging from IPR consultancy to customer services activities), all of them require a considerable financial effort by the start-up company. Therefore, the proxy adopted here for all sectors is both inclusive and preliminary to any kind of sector-specific complementary asset.

- 19.
Unfortunately, the number of graduates is the only proxy available in the CIS dataset: neither other degrees are available, nor the disaggregation by types of university degrees.

- 20.
As well known, Italy is a rather heterogeneous country both from an economic and social point of view; the purpose of including these regional dummies is to take into account how these differences may have an impact on R&D intensity (regional peculiarities also include aspects that can directly affect innovation, such as the different presence of industrial districts and the different diffusion of science parks and incubators). In general terms, Northern regions are characterized by a better environment for innovation than the Southern ones.

- 21.
This is further confirmed by the post-estimation variance inflation test (VIF), equal to 2.79.

- 22.
As detailed in the previous section, higher values of the score correspond to lower financial constraints, hence the expected negative sign of the coefficient.

- 23.
This can be due to the dominant role of the SMEs in this area of the country, since SMEs are less intensive in R&D in comparison with their larger counterparts.

- 24.
As can be seen, the reported tests seem to support the correlation between the decision to engage in R&D or not (selection equation) and the conditional decision on how much to invest in R&D (main equation). Therefore, the sample-selection model appears appropriate. In order to differentiate the selection equation from the main one, we add two additional regressors in the selection equation. On the one hand, we include firm’s size, since larger firms are more likely to have their own R&D department performing formalized R&D (see Cohen and Levin 1989; Cohen 1995; Cohen and Klepper 1996); note that this aspect is also considered in the main equation where R&D is normalized by firm’s sales. On the other hand, we include the percentage of exports over firm’s sales, also positively affecting the decision to engage in R&D activities, given the higher competitiveness of foreign markets compared to the Italian one (see Melitz 2003; Yeaple 2005; Cassiman et al. 2010). Both these controls turn out to display the expected sign and a high degree of statistical significance. By the same token, both human capital and sectoral belonging seem to play a similar role both in affecting the binary decision to invest in R&D or not, and the further decision about how much to invest in R&D. Finally, in this model the geographical dummies turn out to be significant in the selection equation pointing to an (expected) overall disadvantage of firms in the less-developed Southern regions in being engaged in R&D activities. Note that—in CIS data—information about public support is available only for the R&D performers; for this reason this regressor is not included in the selection equation.

## References

Almazan, A., De Motta, A., & Titman, S. (2007). Firm location and the creation and utilization of human capital.

*Review of Economic Studies*,*74*(4), 1305–1327. doi:10.1111/j.1467-937X.2007.00453.x.Anand, B., & Galetovic, A. (2000). Weak property rights and holdup in R&D.

*Journal of Economics and Management Strategy*,*9*(4), 615–642. doi:10.1111/j.1430-9134.2000.00615.x.Anderson, N.R., & West, M.A. (1998). Measuring climate for work group innovation: development and validation of the team climate inventory.

*Journal of Organizational Behavior*,*18*(3), 235–258. doi:10.1002/(SICI)1099-1379(199805)19:3<235::AID-JOB837>3.0.CO;2-C.Anton, J., & Yao, D. (1994). Expropriations and inventions: appropriable rents in the absence of property rights.

*American Economic Review*,*84*(1), 190–209. http://www.jstor.org/stable/2117978.Anton, J., & Yao, D. (1995). Start-ups, spin-offs, and internal projects. Journal of Law.

*Economics and Organization*,*11*(2), 362–378. doi:10.1093/oxfordjournals.jleo.a036876.Arrighetti, A., & Vivarelli, M. (1999). The role of innovation in the post-entry performance of new small firms: evidence from Italy.

*Southern Economic Journal*,*65*(4), 927–939. doi:10.2307/1061285.Arrow, K. (1962). Economic welfare and the allocation of resources for innovation. In Nelson, R. (Ed.),

*The rate and direction of economic activity*. New York: Princeton University Press.Audretsch, D.B., Bönte, W., & Keilbach, M. (2008). Entrepreneurship capital and its impact on knowledge diffusion and economic performance.

*Journal of Business Venturing*,*23*(6), 687–698. doi:10.1016/j.jbusvent.2008.01.006.Audretsch, D., & Feldman, M. (1996). R&d spillovers and the geography of innovation and production.

*American Economic Review*,*86*(3), 630–640. http://www.jstor.org/stable/2118216.Becker, G. (1962). Investment in human capital: a theoretical analysis.

*Journal of Political Economy*,*70*(5), 9–49. http://www.jstor.org/stable/1829103.Bérubé, C., & Mohnen, P. (2009). Are firms that receive R&D subsidies more innovative?.

*Canadian Journal of Economics*,*42*(1), 206–225. doi:10.1111/j.1540-5982.2008.01505.x.Breschi, S., Malerba, F., & Orsenigo, L. (2000). Technological regimes and Schumpeterian patterns of innovation.

*Economic Journal*,*110*(463), 388–410. doi:10.1111/1468-0297.00530.Bresnahan, T.F., Brynjolfsson, E., & Hitt, L.M. (2002). Information technology, work-place organization and the demand for skilled labor: firm-level evidence.

*Quarterly Journal of Economics*,*117*(1), 339–376. doi:10.1162/003355302753399526.Brynjolfsson, E., & Hitt, L.M. (2000). Beyond computation: information technology, organizational transformation and business performance.

*Journal of Economic Perspectives*,*14*(4), 23–48. doi:10.1257/jep.14.4.23.Busom, I. (2000). An empirical evaluation of the effects of R&D subsidies.

*Economics of Innovation and New Technology*,*9*(2), 111–148. doi:10.1080/10438590000000006.Capron, H., & Van Pottelsbergue, B. (1997). Public support to business R&D: A survey and some new quantitative evidence, OECD,

*Policy evaluation in innovation and technology. Towards best practices*. Paris: OECD.Cassiman, B., Golovko, E., & Martnez-Ros, E. (2010). Innovation, exports and productivity.

*International Journal of Industrial Organization*,*28*(4), 372–376. doi:10.1016/j.ijindorg.2010.03.005.Catozzella, A., & Vivarelli, M. (2016). The possible adverse impact of innovation subsidies: Some evidence from Italy.

*International Entrepreneurship and Management Journal*,*12*(2), 351–368. doi:10.1007/s11365-014-0342-3.Chesbrough, H., & Rosenbloom, R.S. (2002). The role of the business model in capturing value from innovation: Evidence from Xerox corporation’s technology spin-off companies.

*Industrial and Corporate Change*,*11*(3), 529–555. doi:10.1093/icc/11.3.529.Cohen, W.M. Stoneman, P. (Ed.) (1995).

*Empirical studies of innovative activity*. Oxford: Blackwell.Cohen, W.M., & Klepper, S. (1996). A reprise of size and R&D.

*Economic Journal*,*106*(437), 925–951. doi:10.2307/2235365.Cohen, W.M., & Levin, R.C. (1989). Empirical studies of innovation and market Structure. In Schmalensee, R., & Willing, R.D. (Eds.),

*handbook of industrial organization*, Vol. 2. Amsterdam: North-Holland.Collins, H.M. (1974). The TEA set: tacit knowledge in scientific networks.

*Science Studies*,*4*(2), 165–186. http://www.jstor.org/stable/284473.Colombo, L., & Dawid, H. (2016). Complementary assets, start-ups and incentives to innovate.

*International Journal of Industrial Organization*,*44*(1), 177–190. doi:10.1016/j.ijindorg.2015.11.003.Colombo, L., Dawid, H., & Kabus, K. (2012). When do thick venture capital markets foster innovation? an evolutionary analysis.

*Journal of Evolutionary Economics*,*22*(1), 79–108. doi:10.1007/s00191-010-0206-0.Combes, P.-P., & Duranton, G. (2006). Labour pooling, labour poaching, and spatial clustering.

*Regional Science and Urban Economics*,*36*(1), 1–28. doi:10.1016/j.regsciurbeco.2005.06.003.Cowan, R., David, P.A., & Foray, D. (2000). The explicit economics of knowledge codification and tacitness.

*Industrial and Corporate Change*,*9*(2), 211–253. doi:10.1093/icc/9.2.211.Cumming, D.J. (2007). Government policy towards entrepreneurial finance: Innovation investment funds.

*Journal of Business Venturing*,*22*(2), 93–235. doi:10.1016/j.jbusvent.2005.12.002.Cumming, D.J., & MacIntosh, J.G. (2006). Crowding out private equity: Canadian evidence.

*Journal of Business Venturing*,*21*(5), 569–609. doi:10.1016/j.jbusvent.2005.06.002.Fallick, B., Fleischman, C., & Rebitzer, J. (2006). Job-hopping in Silicon Valley: some evidence concerning the microfoundations of a high-technology cluster.

*Review of Economics and Statistics*,*88*(3), 472–481. doi:10.1162/rest.88.3.472.Franco, A., & Filson, D. (2006). Spin-outs: knowledge diffusion through employee mobility.

*RAND Journal of Economics*,*37*(4), 841–860. doi:10.1111/j.1756-2171.2006.tb00060.x.Garcia-Quevedo, J. (2004). Do public subsidies complement business R&D? A meta-analysis of the econometric evidence.

*Kyklos*,*57*(1), 87–102. doi:10.1111/j.0023-5962.2004.00244.x.Gersbach, H., & Schmutzler, A. (2003a). Endogenous spillovers and incentives to innovate.

*Economic Theory*,*21*(1), 59–79. doi:10.1007/s00199-001-0245-8.Gersbach, H., & Schmutzler, A. (2003b). Endogenous technological spillovers: Causes and consequences.

*Journal of Economics and Management Strategy*,*12*(2), 179–205. doi:10.1111/j.1430-9134.2003.00179.x.Gonzales, X., Jaumandreu, J., & Pazo, C. (2005). Barriers to innovation and subsidy effectiveness.

*RAND Journal of Economics*,*36*(4), 930–949. http://www.jstor.org/stable/4135264.Griliches, Z. (1992). The search for R&D spillovers.

*Scandinavian Journal of Economics*,*94*, S29–S47. http://www.jstor.org/stable/3440244.Hall, B. (1996). The private and social returns to research and development. In Smith, B., & Barfield, C. (Eds.),

*Technology, R&D, and the Economy. Washington DC, Brookings Institution and AEI*.Hanson, G.H. (2001). Scale economies and the geographic concentration of industry.

*Journal of Economic Geography*,*1*(3), 255–276. doi:10.1093/jeg/1.3.255.Heckman, J.J. (1979). Sample selection bias as a specification error.

*Econometrica*,*47*(1), 153–161. http://www.jstor.org/stable/1912352.Howells, J. (1996). Tacit knowledge, innovation and technology transfer.

*Technology Analysis and Strategic Management*,*8*(2), 91–106. doi:10.1080/09537329608524237.ISTAT. (2004).

*Statistiche sull’Innovazione delle Imprese. Settore Industria Anni 1998-2000*. ISTAT: Rome.Jaffe, A., Trajtenberg, M., & Henderson, R. (1993). Geographic localization of knowledge spillovers as evidenced by patent citations.

*Quarterly Journal of Economics*,*108*(3), 577–598. doi:10.2307/2118401.Klepper, S. (2001). Employee startups in high-tech industries.

*Industrial and Corporate Change*,*10*(3), 639–674. doi:10.1093/icc/10.3.639.Klepper, S. (2010). The origin and growth of industry clusters: the making of Silicon Valley and Detroit.

*Journal of Urban Economics*,*67*(1), 15–32. doi:10.1016/j.jue.2009.09.004.Klepper, S., & Sleeper, S. (2005). Entry by spinoffs.

*Management Science*,*51*(8), 1291–1306. doi:10.1287/mnsc.1050.0411.Leiponen, A. (2000). Competencies, innovation and profitability of firms.

*Economics of Innovation and New Technology*,*9*(1), 1–24. doi:10.1080/10438590000000001.Leiponen, A. (2005). Skills and innovation.

*International Journal of Industrial Organization*,*23*(5-6), 303–323. doi:10.1016/j.ijindorg.2005.03.005.Malerba, F., & Orsenigo, L. (1995). Schumpeterian patterns of innovation.

*Cambridge Journal of Economics*,*19*(1), 47–65. doi:10.1093/oxfordjournals.cje.a035308.Melitz, M.J. (2003). The impact of trade on Intra-Industry reallocations and aggregate industry productivity.

*Econometrica*,*71*(6), 1695–1725. doi:10.1111/1468-0262.00467.Mohnen, P., & Röller, L.-H. (2005). Complementarities in innovation policy.

*European Economic Review*,*49*(6), 1431–1450. doi:10.1016/j.euroecorev.2003.12.003.Morrison, E.W., & Phelps, C.C. (1999). Taking charge at work: extrarole efforts to initiate workplace change.

*Academy of Management Journal*,*42*(4), 403–419. doi:10.2307/257011.Nickell, S., & Nicolitsas, D. (1997). Human capital investment and innovation: What are the connections? Centre for Economic Performance, CEPDP0370. London.

OECD. (1997).

*Oslo manual: The measurement of scientific and technological activities proposed guideline for collecting and interpreting technological innovation data*. Paris: OECD.Olivari, J. (2016). Entrepreneurial traits and firm innovation.

*Eurasian Business Review*,*6*(3), 339–360. doi:10.1007/s40821-016-0060-6.Park, H., & Steensma, H. (2012). When does corporate venture capital add value for new ventures?.

*Strategic Management Journal*,*33*(1), 1–22. doi:10.1002/smj.937.Parker, S.C. (2011). Intrapreneurship or Entrepreneurship?.

*Journal of Business Venturing*,*26*(1), 19–34. doi:10.1016/j.jbusvent.2009.07.003.Parker, S.K., Wall, T.D., & Jackson, P.R. (1997). That’s Not My Job: Developing flexible employee work orientations.

*Academy of Management Journal*,*40*(4), 899–929. doi:10.2307/256952.Pavitt, K. (1984). Sectoral patterns of technical change: Towards a taxonomy and a theory.

*Research Policy*,*13*(6), 343–373. doi:10.1016/0048-7333(84)90018-0.Piva, M., & Vivarelli, M. (2009). The role of skills as a major driver of corporate R&D.

*International Journal of Manpower*,*30*(8), 835–852. doi:10.1108/01437720911004452.Rothaermel, F., & Hill, C. (2005). Technological discontinuities and complementary assets: a longitudinal study of industry and firm performance.

*Organization Science*,*16*(1), 50–70. doi:10.1287/orsc.1040.0100.Shane, S. (2000). Prior knowledge and the discovery of entrepreneurial opportunities.

*Organization Science*,*11*(4), 448–469. doi:10.1287/orsc.11.4.448.14602.Spulber, D. (2012). Tacit knowledge with innovative entrepreneurship.

*International Journal of Industrial Organization*,*30*(6), 641–653. doi:10.1016/j.ijindorg.2012.07.004.Stam, E. (2007). Why butterflies don’t leave. Locational behavior of entrepreneurial firms.

*Economic Geography*,*83*(1), 27–50. doi:10.1111/j.1944-8287.2007.tb00332.x.Storey, D.J. (1994).

*Understanding the small business sector*. London: Routledge.Teece, D. (1986). Profiting from technological innovation: implications for integration, collaboration, licensing and public policy.

*Research Policy*,*15*(6), 285–305. doi:10.1016/0048-7333(86)90027-2.Vivarelli, M. (1991). The birth of new enterprises.

*Small Business Economics*,*3*(3), 215–223. doi:10.1007/BF00400026.Vivarelli, M. (2013). Is entrepreneurship necessarily good? Microeconomic evidence from developed and developing countries.

*Industrial and Corporate Change*,*22*(6), 1453–1495. doi:10.1093/icc/dtt005.Wallsten, S.J. (2000). The effects of government-industry R&D programs on private R&D: The case of the Small Business Innovation Research Program.

*RAND Journal of Economics*,*31*(5), 82–100. http://www.jstor.org/stable/2601030.Yeaple, S.R. (2005). A simple model of firm heterogeneity, International trade, and wages.

*Journal of International Economics*,*65*(1), 1–20. doi:10.1016/j.jinteco.2004.01.001Zucker, L., Darby, M., & Brewer, M. (1998). Intellectual human capital and the birth of U.S. biotechnology enterprises.

*American Economic Review*,*88*(1), 290–306. http://www.jstor.org/stable/116831.Zwan Van Der, P., Thurik, R., Verheul, I., & Hessels, J. (2016). Factors influencing the entrepreneurial engagement of opportunity and necessity entrepreneurs.

*Eurasian Business Review*,*6*(3), 273–295. doi:10.1007/s40821-016-0065-1.

## Author information

### Affiliations

### Corresponding author

## Appendix

### Appendix

###
*Proof of Proposition 1*

In order to prove the Proposition, we first show the following Lemma concerning the relationship between the elasticity of *π*
^{F} with respect to K, which we denote by \(\epsilon (K)=\frac {{K\pi ^{F}}^{\prime }(K)}{\pi ^{F}(K)}\), and the knowledge stock of the incumbent. □

###
**Lemma 1**

*Under the assumptions in* Eq. 1
*, the elasticity*
*𝜖*(*K*) *is increasing with respect to K*.

###
*Proof of Lemma 1*

Taking into account that the firm is choosing the profit maximizing monopoly quantity *q*
^{m}(*K*) for each K, it follows from the envelope theorem that

Hence,

Taking the derivative with respect to *K*, we obtain

The last inequality follows from assumptions (1) and the observation that \(\frac {\partial q^{m}(K)}{\partial K}>0\), which is implied by the assumption of constant elasticity of *p*
^{F} with respect to *K*. □

Using this Lemma, we can now prove the claim of the Proposition. Consider first the case \(\gamma \in [0, \bar \gamma )\). Due to the global concavity of Eq. 3 for all *γ* such that \(K^{*}(\gamma ) > \bar K \geq 0\), the optimal solution of the profit maximization problem is determined by the first order condition

Implicit differentiation of this condition with respect to *γ* yields

Due to Eq. 4, we have \(\frac {\partial ^{2}J^{F}(K^{\ast };\gamma )}{\partial K^{2}}<0\) such that the sign of \(\frac {\partial K^{\ast }}{\partial \gamma }\) is equal to that of \(\frac {\partial ^{2}J^{F}(K^{\ast };\gamma )}{\partial K\partial \gamma }\). Note that

Taking into account (2), we immediately obtain for all *K* that

Moreover, using Lemma 1, we conclude that

where the inequalities in the last two lines follow from the monotonicity of *π*
^{F}(*K*) and *𝜖*(*K*) with respect to *K*, as well as from *β* ≤ 1.

Therefore, we have

This shows that *K*
^{∗}(*γ*) is decreasing in *γ* for all \(\gamma \in [0, \bar \gamma )\).

Focus now on \(\gamma > \bar \gamma \). In this case, the first-order condition (6) yields an investment level \(\tilde K < \bar K\). However, for this investment level it is \(\pi ^{S}(\delta ^{S} \tilde K) < 0\), which implies that the search effort of the employee is zero. Taking into account that *e*
^{∗} = 0, the actual first order condition for the incumbent becomes

which corresponds to Eq. 6 for *γ* = 0. Hence, under the assumption that no start-up forms the incumbent’s optimal investment level would be \(K^{\ast }(0) > \bar K\). It follows that the incumbent’s profit is an increasing function of *K* for \(K < \bar K\). Putting this together with the observation that the incumbent’s profit is decreasing in *K* for \(K> \bar K\), we obtain that \(K^{\ast }(\gamma ) = \bar K\) for \(\gamma \geq \bar \gamma \). This completes the proof.

###
*Proof of Proposition 2*

Considering the case where \(\gamma \in [0, \bar \gamma )\), the first-order condition characterizing the optimal R&D investment is given by Eq. 6. Hence, we have

Using the same argument as in the proof of Proposition 1, this implies that the sign of the derivative is given by the sign of \(\frac {\partial ^{2}J^{F}(K^{\ast };\gamma )}{\partial K \partial \alpha }\). This cross-derivative can be easily calculated as

which implies that *K*
^{∗} is an increasing function of *α*. Similarly, we have

which implies that *K*
^{∗} is increasing with respect to *χ*. This completes the proof. □

## Rights and permissions

## About this article

### Cite this article

Colombo, L., Dawid, H., Piva, M. *et al.* Does easy start-up formation hamper incumbents’ R&D investment?.
*Small Bus Econ* **49, **513–531 (2017). https://doi.org/10.1007/s11187-017-9900-8

Accepted:

Published:

Issue Date:

### Keywords

- R&D
- Innovation
- Start-up
- Complementary assets

### JEL Classification

- O31
- L26