The present study leaves room for improvement and further research. The theoretical background section develops hypotheses around the moderating effect of resource availability on the relationship between staging on the one hand and the number of newly started and abandoned innovation projects on the other hand. Whereas our argumentation for these hypotheses evolves around the differential presence of overoptimism and managerial discretion in resource-constrained and resource-abundant firms, we were unable to incorporate these mechanisms in our main model. Although supplementary analyses of additional survey waves confirm that resource-abundant firms have higher levels of overoptimism and managerial discretion, we hope future research will be able to develop a mediated moderation model that integrates all the relevant concepts and mechanisms. These endeavors would benefit from measuring the managerial biases of the individual managers involved in innovation project decisions, and from accounting for potential differences in management quality across firms, which we were unable to observe.
Also, in our hypothesis development, we argue that there is a causal relationship between a firm’s use of staging and the number of innovation projects its initiates and abandons. We believe that a reversed causal relationship in this respect is unlikely, and the robustness tests accounting for the possibility of endogeneity that we have conducted were reassuring.
Nevertheless, our empirical findings should be replicated in other settings than the one presented here, where panel data is more readily available or, e.g., particular institutional settings give rise to natural experiments.
In response to the recent call by Ragozzino et al. (2016) to focus on firm heterogeneity in order to better connect real options theory with strategic management, we deliberately chose the firm as the unit of analysis. Our dataset is large and covers a broad section of the economy, thereby allowing to investigate firm heterogeneity (and providing a higher degree of external validity than studies which focus on a specific firm or a specific sector alone). We believe that this ability to investigate heterogeneity in resource availability and staging at the level of the firm is an important advantage of our study. However, whereas this study focuses on a firm’s resource availability as an important moderator of the relationship between staging and project decisions, other firm characteristics may also be important. In particular, future studies may consider the potential moderating effect of the firm’s human capital (D’Este et al., 2012;
Leoncini, 2016), organizational practices and culture (Danneels and Vestal, 2020), size and age (D’Este et al., 2012; Ferriani, Garnsey, and Probert, 2008), performance (Desai, 2015) and strategic objectives (Ragozzino et al., 2016), as well as the characteristics of its project portfolio (Belderbos and Zou, 2009). Moreover, while this study deliberately investigated project staging, resource availability, behavioral biases, and project decisions at the level of the firm, it would be interesting to also study this phenomenon at the level of individual projects.
Finally, there is the question whether our findings are generalizable to other domains where real options reasoning has been applied, such as entrepreneurship, joint ventures and mergers
and acquisitions, and foreign direct investment. For example, future research may want to investigate whether resource availability, cognitive biases, and internal controls also moderate the effect of staging on internationalization decisions, or whether such decisions take place more outside the firm and are therefore less prone to, for example, cognitive biases (as suggested by Adner and Levinthal, 2004, and Adner, 2007). We hope our work can be a sound basis for these further research efforts.
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APPENDIX
In this section, we formally prove the existence of a “value in learning” and “value in abandoning” in a mathematical real options model, which provides the full-rationality benchmark on which we base our hypothesis development in Section 2.2. Consider a firm contemplating to invest in an innovation project. The total sunk costs, I>0 , can be split up in
S discrete stages, indexed by s . Each stage costs a fraction of I , i.e., I=
∑
s S
is , and takes one period to complete. Until completion of all stages the innovation project creates no cash-flow. Its expected value is denoted by V and follows the stochastic process
Vs=Vs−1+ɛs , (1)
with E
[
ɛs]
=0. After incurring is the random variable ɛs is realized and becomes known to the firm.12 Consequently, uncertainty resolution is endogenous in this model and contingent on the investment behavior of a firm (McGrath, 1997; Tong and Reuer, 2007).13 The firm has either the possibility to invest sequentially (staging) and make subsequent investments contingent on the realization of ɛ , or it can decide to complete all stages at once (non-staging). In this case,∑
s S
ɛs is realized at once at the end of period S (i.e., we assume away time advantages in project completion due to non-staging).
Consider the case of V following a continuous-state random walk and two stages required for completion, S=2 . Let total costs be I=i1+i2=α ∙ I+(1−α)∙ I with α∈(0,1) . The project’s value is initially normalized to zero, V0=0. We assume risk-neutrality, no discounting of future profits, and standard normal profitability shocks, ɛs N(0,1) . Because the sum of normal random variables is normal again, it follows from equation (1) that
VS=V0+
∑
s=1 S
ɛs N(V0, S) .
If VS turns out to be negative in the final period S , both staging and non-staging firms can drop the project such that no negative cash-flows are realized. Therefore, as projects with negative ex-post value are abandoned, a firm considers the distribution of V2 truncated at zero. For a non-staging firm, the decision to invest in a project at time 0 is then given by the net present value investment rule,
12 After stage 𝓢 all uncertainty about the project’s value is resolved. Stages cannot be completed in arbitrary order but have to follow the natural order of 1,2, …S . This captures the fact that, e.g., a market acceptance test usually comes after the prototyping stage and not vice versa.
13 Endogenous uncertainty resolution is a novel feature of our model compared to other approaches in the literature, since the random variable of project value moves independently of firms’ actions in standard real options models (Dixit and Pindyck, 1994). We think that this assumption better captures the context of innovation project staging, where firms do not gain any further information if they decide to kill or stall a project indefinitely at a certain stage.
V2
πnon−stage=E¿ | V2≥0¿−I>0 , (2)
with V2
E¿ | V2≥0¿ being the mean of a truncated normal distribution.14
By contrast, a staging firm will decide to abandon a project already after the first stage if the realization of V1 is too low, such that the expected profit of follow-on investment is negative:
V2
E¿ | V2≥0,V1¿−(1−α)× I ≤0 . (3) This assumption captures the go-versus-kill decision – or “gate” – a project has to pass at every stage (Cooper, 2008). If we denote the value of V1 for which the above equation holds with equality by v1 , then the expected profit under staging is given by
V2
πstage=
(
1−ϕ(
v1) )
×{E¿ | V2≥0,V1>v1¿ – I } + ϕ(
v1)
×(−αI) (4)with ϕ(∙) being the standard normal cumulative distribution function (of the per-period project value increment εs¿ . The first summand on the right-hand side represents the case when follow-on investment is optimal; whereas the second summand is the loss that a staging firm incurs if it abandons a project after stage one.
We can now prove that – all else equal – staging firms will start more new innovation projects than non-staging firms. This will hold if the expected (a priori) profit of a single innovation project is weakly larger under staging than under non-staging. We hence need to show that
(
1−ϕ(
v1) )
× I−ϕ(
v1)
× IThe second line follows from rearranging and expanding the terms on the right-hand side. The third line follows from eliminating terms that appear on both sides. Finally, the last line follows from gathering all terms containing I on the left and dividing by ϕ
(
v1)
.The last inequality of equation (5) holds by construction, given how v1 has been defined in light of condition (3). Thus, expected profits of a project are larger under staging than if total investment costs are incurred upfront (for a given distribution of project costs I ). This, in turn implies that firms which stage (some of) their innovation projects will start more new innovation projects than firms that commit all investments upfront. This completes the proof.
We can also demonstrate that, in this model, firms which stage (some of) their innovation projects will abandon more projects than staging firms. Recall that both staging and non-staging firms abandon projects that turn out to have a negative value after all uncertainty is resolved, i.e., if V2≤0 . To prove that staging firms have a higher propensity to abandon projects than non-staging firms, it suffices to show that there are projects with positive V2 (i.e., that are not abandoned by non-staging firms), but which nonetheless fulfill the condition for abandonment by staging firms in (3):
V2
E¿ | V2≥0,V1¿−(1−α)× I ≤0 .
A staging firm will abandon these projects after the first stage, whereas a non-staging firm will complete them, as total project costs I are sunk and the projects’ return is positive.
Recall that v1 was defined as the value of V1 for which (3) holds with equality. Thus, for V1=v1−ε , with ε>0 being arbitrarily small, the left-hand side of (3) will be smaller and staging firms will thus abandon the project. However, even for V1=v1−ε , there is a strictly positive probability that V2 turns out to be positive:
Pr
(
V2>0|
V1=v1−ε¿=1−Pr(
V2≤0|
V1=v1−ε¿>0.The last inequality follows from the fact that the normal distribution has positive probability mass over the entire range of R , so that Pr
(
V2≤0|
V1=v1−ε¿ is never exactly equal to one. Consequently, we have shown that there is a positive probability for projects to occur that would be abandoned by a staging firm but completed by a non-staging firm. At the same time, all projects that are abandoned by a non-staging firm are also abandoned by a staging firm. This completes the proof that staging firms will abandon more projects than non-staging firms.Having demonstrated the value in learning and abandoning under full rationality, we can now
Having demonstrated the value in learning and abandoning under full rationality, we can now