An Evolutionary Micro-Simulation Model of Internal Selection 1 Nadia Jacoby
MATISSE-ISYS
1- Introduction
Evolutionary approaches of the firm devote a part of their analysis to the firm behavior and to some processes acting inside the firm. However the firm internal working is, most of the time, not deeply analyzed.
This paper focuses on internal selection processes which are characterized in this work by the selection criteria the firm defines and by the existence of an internal selector agent guiding the selection process working within the firm. As we will see in the first part of this paper, the selection criteria are specific to the objects under selection.
Internal selection acts on routines but empirically it can act for instance on the R&D projects the firm is engaged in.
The main objective is to present the contribution of a micro-simulation model to the understanding of internal selection and to its impact on the firm performances.
The firms are engaged in diversified production and R&D activities. They carry out two kinds of research and development: R&D for product diversification which eventually allows to create a new production activity within the firm and R&D for process innovation which eventually allows to improve the productivity level through the use of a new technology. The firms don’t run any imitation process. The internal selection determines which is the “best” technology for the firm -according to those available for it-, but internal selection also determines which new product will allow the firm entering a new market. The impact on the performances is measured in particular through the firm profit level, market share and productivity level resulting from the technology and product selected.
1 The model building has benefited from the helpful discussions with G. Bottazzi, G. Dosi and T. Reichstein, I would like to acknowledge them. However, the conclusions and opinions expressed remain my own and any errors or omissions are entirely my responsibility.
2- Internal working of the firm: some preliminaries
In the basic evolutionary perspective, a firm is a set of routines evolving through two simultaneous and interactive mechanisms: variation and selection. Mechanisms of selection are external just as well internal. Changes in the repertoire of routines cause mutations within the firm. Among these mutations are the innovations spinning off from R&D activities. They constitute the changes desired by the firm. Parallel to this, the departure of some members of organization is a mutation that undermines the internal coherence of the firm. It constitutes a change not desired by the firm.
However, the transformation of repertoires does take place with the addition of new knowledge coming from outside the firm and in the wake of the arrival of new members into the organization, but also by the daily implementation of these repertoires in the form of dynamic routines. The process of “remember by doing” then comes into play.
Simplified representation of the firm
ORGANIZATIONAL ROUTINES
Skills
sub-skills Organizational Context
Organizal Qualification Durability of work
environment
Learning Learning Know-How Complementarity btw organization members
Practical
Knowledge
External memories
Tacit Knowledge
Interaction
INTERACTION WITH THE EXTERNAL ENVIRONMENT
The transformation of the firm follows a Lamarckian process in which the main source of mutation is the learning process. The environment is, moreover, an important factor in change. As shown on the graph, there are different sources of mutations for the firm.
They result either from learning or from interactions.
Learning firstly affects individual routines or skills then organizational routines, which in turn, mutate. At the same time, constant interaction between organizational routines and the environment urges routines to adaptation. The conditions of competition, the possible upheavals in macro-economic structures, and institutional changes are thus potential sources of mutations within the firm.
All types of mutations, however, do not have the same impact on the evolution and survival of the firm.
- Some mutations imply a calling into question of the "circular flow"2. Such mutations are, most of the time, linked to the disappearance of a part of the organizational memory of the firm due to the departure of one of the organization members. Then the firm needs to manage this change. When an individual member of organization is leaving, his tacit knowledge is the most lacking element for the firm, since by definition it is not transferable and will not be available any longer within the firm. Such tacit knowledge partially constitutes the organizational memory of the firm.
- Other mutations do not call into question the "circular flow". Most often, they correspond to changes in the environment of the firm, as for example a change in supplier. This type of mutation requires adaptations inside the firm but does not imply modifications of its organizational structure.
The internal selection approach must be relative to the intensity and the nature of the competitive environment, given the nature of its operative modalities and the criteria it uses. Internal selection must in fact be ascertained as an intermediary process between natural, automatic and non-deliberate selection (Nelson, Winter, 1982), and choice.
Internal selection is characterized by selection criteria defined by the firm itself and by the existence of an internal selector agent acting within the firm.
2 We refer to Nelson & Winter (1982) "by considering the analogue of Schumpeter's "circular flow" at the level of individual organization. The situation potrayed is unchanging or cyclically repetitive; it is an unrealistically quiet and static condition." (Nelson, Winter, 1982, p. 98).
This agent - individual or collective - guides the internal selection process. Owing to his tacit skills, the selector agent is supposed a priori to be able to lead the selection process in the direction intended by the firm. This agent is in a way the possessor of one of the organization’s skills contained in the individual human factors composing it. The selector agent guides and/or influences the internal selection process by imposing constraints (minimal profitability or social constraints, for example) and/or by orientating the strategic goals of the firm.
The intensity and efforts in R&D, past successes, the structure of incentives with regard to risk-taking, and the diverse modalities of resource allocation within the firm, are some of the internal selection criteria we can find inside the firm (Warglien, 1995).3 At a more general level, the influence of the external environment and the pressures of the internal environment result in the emergence of complementary criteria. The external environment concerns the market and competition between rival firms. It is the reflection of scientific and technological progress and originates in macro-economic upheavals. Symmetrically, the internal environment is composed of formal or informal decision-making processes and interactions among individuals. It also takes into account the constraints of organizational structures, technological and marketing practices, and financial constraints. Lastly, the degree of irreversibility of engagement as well as the demand for minimum profitability also influences the selection process.
As suggested by Levinthal (1991) but also by Warglien (1995), selection and adaptation processes may coexist as explanations of organizational evolution. Internal selection as well as market selection contributes to shape the evolution of projects portfolio, which influences the diffusion of organizational competences over the firm. A successful effort in R&D can lead to the emergence of an unexpected breakthrough and then to the reorganization of the firm competence basis (Warglien, 1995).
The study of internal selection mechanisms is essential to the analysis of firms evolution and working as far as internal selection is an intra-organizational mechanism of which consequences appear in the external behavior of the firm. However, most of the time, the evolutionary approach of the firm neglects those aspects. In particular, there is a sort of dichotomy between intra-organizational and inter-organizational analyses. Indeed, on
3 Those criteria are represented in the model we present in this paper.
one side, inter-organizational works deal for instance with innovation and its diffusion process or with competitive analysis, but in any case they set a fixed state of internal organization. On the other side, intra-organizational works focus on firms internal working without any link with external environment. Knowledge is then the central object of analysis.
In both cases, there's no link between both dimensions. With this dichotomy, the question of internal selection is even more left aside. Moreover the transposition of the Darwinian framework to the evolutionary analysis of the firm reinforces this distinction between intra and inter-organizational works as far as mutation and external selection are disconnected in the Darwinian paradigm.
The study of the intersection of those dimensions highlights the importance of internal selection processes. Internal selection regulates intra-organizational changes according to the selection criteria defined by the firm itself. Internal selection is then clearly different from market selection. In particular, it restores the internal coherence of the firm which mutations can disrupt. On the whole, internal selection acts on routines but more specifically it can act on R&D projects.
In order to illustrate this theoretical purpose, we developed a micro-simulation model, representing the internal working of the firm and highlighting the importance of internal selection. This model doesn't offer an exhaustive representation of internal mechanisms.
It's a qualitative model which helps with the comprehension of intra-organizational processes.
3 – The Simulation Model Structure
The micro-simulation model we present proposes a simplified representation of the market economy. On the supply side, firms are engaged in productive and research activities. On the demand side, markets are characterized by prices.
As Llerena and Oltra (2000) show, the daily economic development is characterized by the growing diversity of products and services. While some new products appear, some others disappear and then the balance between the emergence of new products and the disappearance of existing goods determines the net static variety of the economic
system at a given point in time (Llerena, Oltra, 2000). Our model highlights the consequences of competition on the markets showing that some goods exit the market because of the high competitive pressure. But the core of the model concerns the internal selection processes acting on R&D projects.
Firms are engaged in productive and R&D activities, they don't performance any imitation process.
As we will see, the diversification strategy of the firms leads them to develop new products, which can enter new markets for the firm. So before the market competitive pressure, the firms are engaged in an internal selection process.
The model building comes within the tradition of Nelson & Winter models centered on technical progresses and Schumpeterian competition. But the simulation model we present focused on internal selection processes and their influence on the performances of the firm.
3-1 – Productive Activities
Each firm is engaged in several productive activities acting on different markets, with a specific demand function. At the same time, firms follow a diversification strategy represented by a specific kind of research and development (see section 3-2-2). The current activities of the firm undergo the competitive pressure on the market they are active on. They fight for increasing their market share and profit level.
Firms use only capital as input, so capital is numeraire and its unit cost is supposed equal to one. The technology used by the firm i in the production process j4 at time t is characterized by its productivity level Aij(t). This productivity level results from the equation:
[
( 1 ) ; ()]
)
(t Max A t A t Aij = ij − ijpc
where is the productivity level resulting from the R&D for process innovationAijpc(t) 5
and which can improve the productivity of the production process. The technological change is not inherent in the capital but it has an external source: firm innovation (see section 3-2-1).
4 j identifies the different activities or production processes the firm is engaged in.
5 Process innovation and diversification activities are identified with the indexes “pc” and “pd”, respectively.
For each activity, the quantity of capital dedicated to the production process is determined according to the equation:
[ ] [ pd]
ij ijpd
ij ij i ij ij ij
ij ij
ij t K t r E t KI t t I t D t I D t I
K ()= ( −1)⋅1− ⋅ ()+ ()+α ()⋅ ()− ()⋅ + ()⋅
The capital stock per productive activity includes four components:
The first one gives the capital depreciation-free, with rij as depreciation rate.
The second element refers to the replacement of the capital depreciated share. The equation KI defined below gives more details.
The third component " " gives the available net investment for the current product "j".
(
i ij ijpd ij(t)⋅I(t)−D(t)⋅Iα
)
Indeed, the total net investment " " is distributed between the different productive activities according to α
ijpd ij
i t D t I
I()− ()⋅
ij which reflects the contribution of each activity to the total cash-flow replacing investment-free.
Finally, Ipd is a "launching investment" the firm dedicates to the new activities.
The distinction between new and old activities follows those rules:
=
otherwise 0
firm by the produced y
effectivel is
if ) 1
( j
t Eij
E indicates the activities which are already producing something.
=
otherwise 0
period launching a
in is if ) 1
( j
t Dij
D indicates the new productive activities which can beneficiate from a "launching investment"6.
The sequence of investment is in favor of the research & development as far as after replacing the depreciated share of capital, the firm firstly determines the R&D budget
6 Only one new activity can be launch at each period.
before affecting the resulting part to the capital net investment. All the firms are innovative, they don't run any imitation process, there's no embodied technical progress, R&D activities are the only source of innovation.
The capital depreciates with the rate rij. It is replaced only if the profit of the productive activity is positive, in this case the replacement respects the following rule:
− < ≥ < − − = =
= 0 (() 1) ififotherwise 0 ()() ( (1) 1&) & PrPr 0 0 )
( rKtt t trKrKt t TimeToTimeTooduceoduce t
KI ij ij ij
ij ij
ij
ij π π π
The share of capital net investment is determined according to αij reflecting the policy of the firm in term of capital net investment. αij takes any value between 0 and 1 and reflects the contribution of the productive activity to the total "cash-flow replacing investment-free".
Ii(t), the capital investment for the entire firm, is computed as:
− ⋅Π Π >
= 0(1 ) () ifotherwise () 0 )
(t t t
Ii δ i i
where δ is the repartition rule of the cash flow between capital net investment and R&D budgets. δ ∈ [0;1].
The "cash flow replacing investment-free", Πi, results from the different productive activities the firm is engaged in:
( )
∑
−= Π
j
ij ij
i(t) π (t) KI (t)
δ determines the repartition strategy of the firms between capital investment and research and development. The firms’ diversification results from their innovation strategy and so from the value of δ. Some of them focuses on R&D (δ is high) while some others have a lower propensity to take risks and prefer to invest in capital (δ is low). As notice by Nelson & Winter (1982), with bounded rationality and radical uncertainty, firms develop different knowledge and skills leading them towards
different innovation trajectories. In this model, the firms can be differentiated, in particular, thanks to their innovation behavior.
The output of the activity j of the firm i at time t is given by:
) 1 ( ) 1 ( )
(t =K t− ⋅A t− qij ij ij
At the market level, the total supply corresponds to the sum of individual quantities produced by the firms active on the market:
∑
=
i ij
j t q t
Q() ()
The price is given by the unit-elastic demand function:
)ε
) ( (t Qdt Pj = j
where d is the demand and ε the elasticity of demand.
We assume the production cost per unit of capital constant over time so the profit of each productive activity is given by:
−− +
− +
−
⋅
−
⋅
= () () ( 1) ( 1) ( (1)1) )
(t qij t Pj t cijKij t RDijpc t RDaipdt t
πij
where cij is the unit production cost, RDpc the cost of R&D for process innovation and RDpd the cost of R&D for diversifcation.
a(t-1) gives the number of productive activities of the firm at t-1.
3-2 – Research Activities
As far as the model focuses on internal selection processes, it is interested only in innovative firms. So, every firm is engaged in R&D activities for which it allocates a budget. The R&D budget is a share of the "cash flow replacing investment-free". We assume that R&D is essential for the firms since their survival depends on their ability to increase their productivity level. So after covering the physical depreciation of capital in each activity, the resulting cash flow replacing investment-free is centralized at
the firm level, which then decides to distribute it between R&D and capital net investment. This simple decision rule reflects the bounded rationality.
The total R&D budget of the firm is given by:
⋅Π Π >
= 0 () otherwiseif () 0 )
( i
i t t t
RD δ i δ∈ [0;1]
Afterwards, the firm shares this budget between R&D for process innovation and R&D centered on the diversification strategy. The innovation process consists in a draw of a productivity level in a normal distribution (Llerena, Oltra, 2000).
3-2-1 - Process innovation
The firm is engaged in as many R&D projects for process innovation as production processes. So the firm determines first the total budget of R&D for process innovation and then it distributes it between the different individual projects. The global budget for process innovation is given by:
⋅ − >
= 0() () otherwiseif ( 1) 0 )
(
ipc t A t
RD t t
RDipc i i
γ
where γ returns -at the firm level- the contribution of R&D for process innovation to the productivity improvement7.
Following the rule we define for the global budget, each individual process innovation R&D budget is determined according to the relative expected productivity level of the project.
The innovation process productivity level ( ) results from a random draw in a distribution of probability following a Normal law
ijpc
A
8:
(
pc ijpc)
ij (t) ;σ Ν m
dynamics of capital productivity,
7 Please refer to appendix for more details.
8 In order to keep in mind the lets remember the following equation
presented above: Aij(t)=Max
[
Aij(t−1 ) ;Aijpc(t)]
where:
) 1 (
) 1 ) (
1 ( )
( = − + −−
t K
t t RD
A t
m ij
ijpc pc ij
ij
is the productivity level of the activity j at t-1 )
1 (t− Aij
) is the R&D budget of j for process innovation 1
(t− RDijpc
is the stock of capital at t-1 for the activity j )
1 (t− Kij
σijpc is the standard deviation of the normal distribution. It’s a parameter of which value reflects the risk of the research process. The higher σ the more risky the R&D.
We assume that the innovative draws are centered, in particular, on the current productivity level. The more the firms have invested at t-1, the higher the chances to obtain a high expected productivity level (Apc).
The path-dependence of innovation resulting from the way m is defined implies that the result of innovation is at least partly determined by past technological performances.
This cumulativeness can be explained by the fact that the firm stays in the same technological trajectory.
3-2-2 – Diversification strategy
Before starting a diversification project, the firm determines randomly a target market among the market space composed by all the markets of the model on which the firm is not active. The R&D budget represents the amount of resources available for the diversification. The budget is given by9:
⋅ − >
= 0 otherwise 0 ) 1 ( if )
( ) ) (
( t RD t A t
t RD
ipd pd i
i
β
The budget for diversification is a share of the total R&D budget of the firm; it exists only if the R&D was "successful" at the previous period, i.e. only if the expected productivity level of the diversification project at t-1 was positive. This share of R&D is determined according to the relative productivity level. The idea is the more successful
9 Please refer to appendix for more details.
the R&D for diversification compared to the other R&D activities the higher the budget.
β reflects this idea.
The project efficiency (Apd) results from a random draw in a distribution of probability following a Normal law:
(
pd ipd)
i (t) ;σ Ν m
where:
σipd is the standard deviation of the normal distribution. It’s a parameter which value reflects the uncertainty of the research process. The higher σ the more risky the R&D.
pd(t)
mi is the mean of the normal distribution, with:
− + −
−
⋅
= ( 1)
) 1 ) (
1 ( )
( K t
t t RD
A t m
i ipd pd i
i λ
where:
∑
=− −
=
− a
j ij
i A t
t t a
A
1
) 1 ) (
1 (1 ) 1
( the average productivity of the firm i at t-1
∑
=− −
=
− a
j ij
i K t
t t a
K
1
) 1 ) (
1 (1 ) 1
( the average stock of capital of the firm i at t-1 a(t) is the number of market occupied by the firm at t
λ represents the entry barrier. λ∈ [0; 1], if λ=1 the market is contestable, if λ=0 the entry barrier is maximum, there is non-contestability.
The mean of the distribution is centered on their average productivity level, the innovation process is path dependent.
3-3 – Internal Selection
Internal selection has different functions within the firm. It concerns the selection of R&D projects for process innovation and for diversification but it also deals with exit and in particular the threshold from which a firm exits a market.
3-3-1 – Selection of R&D projects for process innovation
As ever seen before, process innovation are evaluated through their expected revenue per unit of capital. The selection process for new technologies is based on the following max function:[
( 1 ) ; ()]
)
(t Max A t A t Aij = ij − ijpc
If the technology discovered thanks to the process innovation is more efficient than the one the firm is currently using in this productive activity, the firm switches.
Whatever the propensity of firms for risks, they all use the same selection mechanism.
3-3-2 – Selection of R&D projects for diversification
Internal selection of diversification projects is a process a bit more complex than for process innovation, in particular because it varies according to the propensity of firms to take risks and because of the existence of the internal selector agent. This agent can enforce the selection process when the economic criteria are not sat. He can push in favor of a specific project although it doesn’t seem to be profitable. This situation occurs, in the model, with a probability 0.25%, whatever the propensity of firms to take risks.
Diversification allows the firm to enter a new market. If the R&D is successful i.e. if the economic characteristics of the project sit the internal selection process, the firm develops a new product permitting its entrance on a new market.
The economic criteria of the internal selection process rely on the expected revenue per unit of capital and on the R&D budget. The revenue per unit of capital ( ) is computed with its productivity level and the current price on the target market:
ipd kY
) ( ) ( )
( t A t P t Ypd ipd
k i = ⋅ β
where Pβ is the current price on the target market β.
To be selected a project has to respect an economic criterion on its expected revenue per unit of capital and the R&D budget –for diversification- has to be positive. The higher
the propensity of firms to take risks, the lower the threshold of selection on the expected revenue per unit of capital.
Therefore, firms with a high propensity to take risks develop their diversification projects when their expected revenues per unit of capital are higher than the revenue per unit of capital of their less profitable productive activity. At the contrary, firms with a low propensity to take risks fix their threshold to the revenue per unit of capital of the more profitable productive activity.
3-3-3 – Exit
The last way to catch the concept of internal selection is to be interested in the way firms exit market. This constitutes the third representation of internal selection in the model presented here.
Whatever the propensity of firms to take risks, they exit a market when their production –older than 3 periods- has either market share lower than 0.5% or negative profit and cash-flow.
4 – Main Results
In order to study the impact of internal selection on the firms' performances, we test four configurations dealing with different modalities of internal selection and different environments. Within configurations, firms differ from their propensity to take risks and from the degree of influence of the internal selector agent. There are two homogenous and two heterogeneous configurations with 120 firms each, their composition is reported in Table 1. Configurations A and D are homogenous, they count only firms of the same type; whereas populations B and C are heterogeneous, they mix firms with different propensity to take risks.
Table 1: Configurations composition
A B C D
# of firms 120 120 120 120
Powerful S.A. 60 40 20 0
low propensity
to take risks Neutral S.A. 60 40 20 0
Powerful S.A. 0 20 40 60
high propensity
to take risks Neutral S.A. 0 20 40 60
The firms with a low propensity to take risks spend 20% of their cash flow in R&D and 80% in net capital investment, whereas those with a high propensity to take risks spend 70% of their cash flow in R&D and 30% in net capital investment.
In order to show the stability of the model, we start with a stationary state. An exogenous shock on one demand is introduced after 5 periods, it launches the dynamic of the system.
We run 50 simulations -on 2500 periods- for each configuration in order to ease the effects of the stochastic draws. The idea is to generate enough history to be able to tackle the emergent properties of the system and in particular to infer properties relatively independent of the sequences of random numbers. The sensitivity tests show that the different simulations represent the same economic situation10. Thus, any simulation can be chosen as representative. In this perspective, we present the results of a representative simulation chosen in the modal distribution.
In order to analyze the results, we choose as reference the configuration with the lowest internal selection mechanism (D). Among the studied configurations, the closest to the situation in which there's no internal selection is the homogeneous population where all the firms have a high propensity to take risks. This is also the closest situation to the Nelson & Winter model in which there's no internal selection.
10 For more details on those tests, see Jacoby (2002).
4-1 – Firms survival
In the spirit of Winter (1964), the existence of at least one more rigorous firm in a population strengthens the strictness of internal selection and then promotes the survival of firms with the lowest propensity to take risks.
The results we obtain concerning the survival rates confirm this point - Table 2-. Indeed in hybrid configurations, the survival rates for firms with a low propensity to take risks are higher than those of firms with a high propensity to take risks (27.5%>20%;
15%>10%; 20%>17.5%). Finally even when they are not initially dominant, firms with a low propensity to take risks better survive than those with a high propensity.
Moreover, the existence of a powerful selector agent increases the representation rate of the sub-population, and conversely for neutral selector agent.
Then it seems that the lower the propensity of firms to take risks, the stricter their internal selection mechanism, the higher their survival probability.
Table 2: Survival rates
Low propensity to take risks High propensity to take risks Powerful S.A. Neutral S.A. Powerful S.A. Neutral S.A.
tstart tend tstart tend tstart tend tstart tend
# firms 60 12 60 8 . . . .
%pop° at t 50% 60% 50% 40% . . . .
A
Surv. rate 20% 13% . .
# firms 40 11 40 6 20 4 20 2
%pop° at t 33% 48% 33% 26% 17% 17% 17% 9%
B
Surv. rate 27.5% 15% 20% 10%
# firms 20 4 20 4 40 8 40 7
%pop° at t 17% 17.5% 17% 17.5% 33% 35% 33% 30%
C
Surv. rate 20% 20% 20% 17.5%
# firms . . . . 60 14 60 12
%pop° at t . . . . 50% 54% 50% 46%
D
Surv. rate . . 23% 20%
Finally we can sum up those results with the following proposition:
Proposition 1: Low propensity to take risks and existence of a non-neutral selector agent strengthen the survival probability of firms through the strictness of their internal selection.
4-2 – Diversification
Diversification is measured with the number of different markets a firm is active on.
Intuitively we could think that firms with a high propensity to take risks are more diversified than other firms. However the results show the opposite. At tend, firms with a low propensity to take risks count on average more productive activities than firms with a high propensity to take risks.
Table 3: Average diversification rate
# firms NMO tend Average diversification
rate per type
Average diversification
rate - ∀ type Low propensity -A-
n1 12 34 2.83
Survivors at t2500
n2 8 16 2 2.5
Hybrid 1 -B-
n1 11 31 2.82
n2 6 17 2.83
n3 4 7 1.75
Survivors at t2500
n4 2 5 2.5
2.61 Hybrid 2 -C-
n1 4 12 3
n2 4 8 2
n3 8 20 2.5
Survivors at t2500
n4 7 15 2.14
2.39 High propensity-D-
n3 14 28 2
Survivors at t2500
n4 12 27 2.25 2.11
n1: firms with a low propensity to take risks and powerful selector agent n2: firms with a low propensity to take risks and neutral selector agent n3: firms with a high propensity to take risks and powerful selector agent n4: firms with a high propensity to take risks and neutral selector agent
According to the figures presented in Table 3, we can highlight two mains results:
On average and whatever the propensity of firms to take risks, the diversification is rather weak. The firms are engaged in less than 3 productive activities –on average- while they were producing 12 different goods at the beginning. A deeper analysis shows that this reduction in the number of productive activities appears very quickly after the exit from the initial stationary state. In a second step, some firms increase their productions but the competition leads most of them to a second reduction.
The average diversification rates show that firms with a high propensity to take risks are finally less diversified than firms with a lower propensity to take risks. Indeed, the configurations C and D –with the biggest proportion of risk-taken firms- have the smallest average number of productive activities (2.39 and 2.11). At the opposite, configurations A and B have the highest rates (2.5 and 2.61).
Then it seems that the propensity of firms to take risks influences their diversification strategy. The low propensity seems to strengthen the diversification whereas the high propensity to take risks seems to favor the refocusing11.
As far as firms' strategic decisions are not modelized, the diversification or refocusing behavior relies on selection mechanisms. Indeed, the higher the propensity of firms to take risks, the weaker the internal selection mechanism and then the more influent the market selection.
Finally we can sum up those results with the following propositions:
Proposition 2: The evolution of industrial structure and the competitive pressure lead to the reduction in the number of firms' productive activities.
Proposition 3: Generally speaking, firms are weakly diversified but the lower the propensity to take risks the higher the diversification.
11 With "refocusing", we understand the reduction in the number of firms' productive activities.
4-3 – Performances
Performance is measured through different indicators. The evaluation of firm profitability uses average profit level and cash flow. The technological performance is measured with average productivity whereas capital stock and number of markets occupied inform about the firm size.
We are interested by the performance of surviving firms at the final state. For each configuration and for each variable, the results can be summarized by a box-plot representation. In order to compare the different box-plots, we perform mean comparison tests12.
According to Table 4, the distribution of the configuration D is really different from the others.
Table 4: Distribution of capital stocks
The configurations counting a proportion of firms with a low propensity to take risks have obviously a higher stock of capital. Then it seems that the lowest the propensity of
12 Those tests are Tukey-Kramer tests performed with SAS.
firms to take risks, the higher their capital stock. This is confirmed by the results of Tukey-Kramer tests according to which the configurations B and C are not substantially different with a p-value=0.9995. The results for the comparison between A & B and A
& C are, respectively, p-value=0.4795 and p-value=0.6251.
The explanation relies on the effectiveness of internal selection which, by the strictness of its criteria acting on the diversification projects, strengthens the probability of success of those new products on the market. Indeed if it allows the firm to develop new profitable activities, it influences directly the profit generation which takes part to the capital growth.
Finally we can sum up those results with the following proposition:
Proposition 4: The effectiveness of internal selection promotes firms' capital stock growth.
Table 5: Distribution of capital productivity
The internal selection mechanism acting on process innovation is the same for all the firms in the model whatever their propensity to take risks. However their R&D budgets are not the same, they vary according to this propensity. The higher the propensity the bigger the R&D budget; the lower the propensity the lower the R&D budget.
Let's remember that capital productivity of a firm can increase through process innovation, which allows to introduce new production technologies, or through the diversification strategy which can lead to the development of new activities with their specific production technology.
In this perspective, process innovation and diversification strategy both influence the evolution of productivity.
The box-plots on Table 5 show that all the configurations obtain on average the same results in term of capital productivity. The Tukey-Kramer tests confirm those observations.
Then if we consider the R&D focused on process innovation, as far as whatever their propensity to take risks all the firms use the same internal selection mechanism and as far as there's no reason to think that some firms could use more efficiently their R&D budget13, the explanations of those surprising results rely on the differences between internal selection processes acting on diversification projects.
The quantity of resources the firm dedicates to R&D for process innovation doesn't really influence the firms' performances.
Then if we consider that on average the R&D for process innovation gives the same results in all cases, it appears that firms with smaller R&D budgets (RDpd) and stricter selection criteria obtain the same results than firms with a higher propensity to take risks which spend more in R&D.
The internal selection mechanism is then central in the explanation of technological performance growth.
13 There's no technical reason in the model for such a situation.
Proposition 5: The strictness of internal selection criteria acting on diversification projects positively influences the technological performances of firms.
The amount of R&D firms spend cannot guarantee better performances.
In this perspective, it could be very interesting to introduce in the simulation another configuration with strict selection criteria and bigger R&D budgets.
5 – Conclusion
This paper highlights the importance of internal selection processes and in particular it focuses on their impact on the firms' performances. In this perspective, we propose a micro-simulation model developed in the tradition of the Schumpeterian competition model of Nelson & Winter (1982). We consider two types of firms, each one characterized by its propensity to take risks and the specificity of its internal selection mechanism. Firms are engaged in diversified production and R&D activities. The general idea is to show that internal selection has a significant impact on firms' performances.
The simulation results show that the weakness of internal selection mechanisms slows down firms' progresses, which in this case refer to the market forces much more than to internal forces. Internal selection positively influences the firms' performances growth.
Market selection and internal selection are complementary and essential to the firm growth.
Finally the results suggest that the efficiency of internal selection refers to the strictness of its criteria. The stricter the internal selection criteria, the higher the survival probability, the higher the diversification and the better the technological performances.
In this perspective, there is certainly room for a larger thought within firms in favor of internal selection.
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APPENDIX
• γ allows to determine the share of total R&D budget dedicated to R&D for process innovation.
>
−
>
− −
− +
− − −
=
otherwise
1
0 ) 1 (
&
0 ) 1 ( if ) 1 ) (
1 ) ( 1 (
) 1 ) ( 1 ( )
( A t A t
t t A
t a A
t t a A
t pd ipc ipd
i ipc
ipc
γ
where a(t-1) returns the number of productive activities at t-1 in the firm. γ ∈ [0;1].
• Repartition rule of the total R&D budget for process innovation between the different productive activities:
≤
−
≤
−
>
−
− ⋅
⋅
−
=
∑ ∑
0 ) 1 ( if 0
0 ) 1 (
&
0 ) 1 ( if )
) ( 1 ( ) (
) 1 ( )
( A t
t A t
A t
t RD A t X
t A
t
RD pc
ij
j ijpc ijpc
ipc j
ijpc ij
ijpc
ijpc
where
− >
= 01 otherwiseif ( 1) 0 )
(t A t
Xij ijpc
• β allows to determine the share of total R&D budget dedicated to R&D for diversification activities.
− > − >
−
− +
− −
=
otherwise
1
0 ) 1 (
&
0 ) 1 ( if )
1 ) (
1 ) ( 1 (
) 1 ( )
( A t A t
t t A
t a A
t A t
ipc ipd
ipd ipc
ipd
β
