A computational consumer-driven market model: statistical properties and the underlying industry dynamics Carlos M. Fernández-Márquez, Francisco Fatas-Villafranca & Francisco J. Vázquez Computational and Mathematical Organization Theory ISSN 1381-298X Comput Math Organ Theory DOI 10.1007/s10588-016-9230-4
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Author's personal copy Comput Math Organ Theory DOI 10.1007/s10588-016-9230-4 MANUSCRIPT
A computational consumer-driven market model: statistical properties and the underlying industry dynamics Carlos M. Ferna´ndez-Ma´rquez1 • Francisco Fatas-Villafranca2 Francisco J. Va´zquez3
•
Springer Science+Business Media New York 2016
Abstract We present an agent-based market model in which social emulation by consumers and the adaptation of producers to demand play a significant role. Our theoretical approach considers boundedly-rational agents, heterogeneity of agents and product characteristics, and the co-evolution of consumers’ desires and firms’ adaptation efforts. The model reproduces, and allows us to interpret, statistical regularities which have been observed in the evolution of industrial sectors, and that seem to be also significant in the case of discretionary consumption activities. Thus, we suggest new determinants and explanations (from the consumer-side) for these stylized facts, and we obtain new theoretical patterns which may be of help to better understand the dynamics of discretionary goods markets. This model and results may contribute to guide future research on the field of consumer market. Keywords Agent-based model Industrial stylized facts Emulation Consumer theory Demand-driven model & Carlos M. Ferna´ndez-Ma´rquez
[email protected] Francisco Fatas-Villafranca
[email protected] Francisco J. Va´zquez
[email protected] 1
Department of Economic Analysis: Quantitative Economics, School of Business and Economics, Autonomous University of Madrid (UAM), E-3 205A, Francisco Toma´s y Valiente Street, Number 5, 28049 Madrid, Spain
2
Department of Economic Analysis, Floor 3, School of Business and Economics, University of Zaragoza, Gran Vı´a Street, Number 2, 50005 Saragossa, Spain
3
Department of Economic Analysis: Quantitative Economics, School of Business and Economics, Autonomous University of Madrid (UAM), E-3 312, Francisco Toma´s y Valiente Street, Number 5, 28049 Madrid, Spain
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JEL Classification B52 O33
1 Introduction The evolution of many industries is characterized by certain statistical regularities and stylized facts. Some of these regularities are always present while others suffer variations or disappear under certain circumstances. One of the most studied examples is, perhaps, the S-shaped pattern in the adoption level of many industries; another one is the existence of an industry life cycle with some patterns characterizing the phase of the cycle the industry is in (Klepper 1997; Mowery and Nelson 1999; Hall and Rosenberg 2010). More recent empirical contributions highlight new interesting facts such as: right-skewed distributions regarding firm size and growth rates; inter-sectorial differences in concentration levels; the fact that it is the larger and/or longer-lasting firms which present a lower growth rate, a lower variability in growth rates and a higher probability of survival; or the existence of a turbulence phase before reaching industrial maturity (Cefis 2003; Bottazzi et al. 2003; Bottazzi and Secchi 2003; Lotti et al. 2003; Dosi 2007). Possible theoretical explanations for some of these facts have been posed—usually focusing on the supply-side of the market; regarding others (such as the turbulence phase pattern), we only know that they do not appear in all industries, although we still do not know the reasons for this. In this work, we aim to take a step forward in this sense, analyzing principally how these patterns and statistical regularities can emerge in a computational demand-driven market model. More precisely, considering that recent research in consumer theory is translating findings in neuroscience, experimental economics and behavioural psychology to explain consumer-demand transformation (Bianchi 2002; Camerer et al. 2005; Chai et al. 2007), we aim in this paper at incorporating these advances in an agent-based consumer-driven market model to generate, from the perspective of consumer social learning and consumer exploratory behaviour, some of the afore-mentioned statistical regularities (Pyka and Fagiolo 2007; Rixen and Weigand 2014). Thus, a novel point of our approach is that, by incorporating multidisciplinary research in an ABM-framework, we obtain (theoretically) and suggest the possibility of finding (empirically) the regularities (mainly) observed for cases of industrial capital goods sectors. By looking at the historical paths of certain discretionary consumption activities, we could provide explanations for the dynamics observed in such consumption industries as (e.g.) wine (Ferna´ndez-Ma´rquez et al. 2016); tourism and holiday destinations (Butler 2011; Agarwal 2002); consumer devices (Windrum 2005); and recreational goods-entertainment (De Vany 2004; Vogel 1998). To this end, we develop a model for a demand-driven discretionary-consumption industry which, drawing on specifications suggested by empirical evidence regarding the behavior of agents on the one hand, and reproducing the aggregate patterns mentioned previously on the other hand, allows us to generate interesting dynamics possibly underlying the evolution of these industries. Thus, our model proposes new demand-side explanations for several well-known empirical regularities.
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Regarding the behavioral assumptions of the model, we take into account that increasing evidence suggests that consumers do not behave in the way the Rational Choice theory establishes (Nelson and Consoli 2010). They do not seem to act as utility maximizers in essentially knowable environments, but instead use heuristics to estimate whether a certain product (often new and complex) is better or worse than another one for satisfying their desires (Valente 2003, 2012). Moreover, boundedlyrational consumers seem to attend to socially interpreted characteristics of the goods, and not only to the good physical attributes, to make their choices (Witt 2005; Loasby 2001; Leiss 1983). Hence, for instance emulation, being the most common mechanism of social influence, plays a decisive role both in the creation and eventual evolution of desires, and in the social interpretation of the goods’ characteristics (Aversi et al. 1999; Cowan et al. 1997; Veblen 1899). Emulating the behavior of other agents (considered to be efficient, popular or socially prestigious) is a way to define our own acts in uncertain environments. This behavior is not only related to consumption activities; in general, it is becoming clearer that economic agents, be they consumers or producers, are not optimizers, but that they learn through imitation and adaptation (Witt 2001; Nelson and Winter 1982). Furthermore, many studies suggest that it is necessary to consider the heterogeneity of consumers, their taste for novelty, and their degree of tolerance to changes in the features of goods when analyzing phenomena like business innovation and industrial change (Bianchi 1998; Malerba et al. 2007). These suggestions seem very significant in the case of discretionary-consumption goods1—whose evaluation does not come so much from the material well-being they provide as from the social image formed around the consumption of some of their characteristics (Becker 1996; Baudrillard 1981; Stigler and Becker 1977). Markets of consumer discretionary goods include those of electronic goods, high quality wine and food, the leisure sector, accessories and perfumes. All these goods involve some kind of social component, and so, to a greater or lesser extent, they can all be considered as discretionary and are, consequently, affected by the processes of social emulation. In our model, we consider all the afore-mentioned features, and we incorporate them in an agent-based model (ABM) of consumer-driven industrial dynamics. An important assumption of our model is that, inspired by recent literature on discretionary consumption activities (Lebergott 1993; Deci and Flaste 1996; Bianchi 2002), we consider that non-pecuniary motivations may be more significant drivers of these activities than typical prices/income explanations. This may be so since these activities do not cover basic needs, they do not represent (taken one-byone) a significant share of consumer budgets, and their experiential/recreational nature make them not essential for life (Addis and Holbrook 2001; Gilbert and Abdullah 2004; Moreau et al. 2001). Our model focuses more on consumer social learning, cognitive inertias and motivational issues. Thus, on a micro level, we shall have consumers whose tastes and desires evolve basically through local interaction (via social emulation) and gradual learning, and producers who will adapt by trying to attend the needs of the market through incremental innovations. The macro level (industry/sectorial level) will be the result of the aggregation of some variables of 1
Those goods which are not strictly necessary for everyday life.
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interest, such as the rate of adoption of the good, the number of firms in the market and the Herfindahl index of industrial concentration. In Ferna´ndez-Ma´rquez et al. (2016) we explain in detail the technicalities of the analysis through which we identify the relevant parameters and study the dynamical properties of the model. In the present paper, we show how our computational model can reproduce a high number of the above-mentioned statistical regularities, and they do it by spotlighting the role of demand in the underlying dynamics. That is to say, our model not only reproduces many well-known stylized facts but it also offers demand-side (market selection) explanations for these facts. Furthermore, new phenomena seem to emerge in the model that may be of interest for empirical researchers of industry evolution. In the paper, we suggest specific industries in which our proposed mechanisms may play a key role. The paper is organized as follows: in Sect. 2 we describe all the assumptions of the model, both those corresponding to consumer behavior as well as those related to producers’ decisions. In Sect. 3, we describe the properties or patterns which emerge from the model simulations through three sub-sections. In the first subsection we determine whether it is possible to reproduce from the model those patterns which, according to empirical evidence, are present in real industries; if so, this would indicate that the model is plausible and that the proposed dynamics probably capture interesting aspects of market selection processes. In the second sub-section, we go deeper into some of the determinants for said statistical patterns; moreover, we try to link the emergence of these patterns with specific characteristics of the market selection process. In this sense, it is remarkable that our modeled selection process differs from more simple ones in the literature, such as typical one-dimensional replicator dynamic systems (see Dosi 2007). In fact, our model’s capacity to reproduce such a significant number of regularities may come from the stochastic-dynamic-network structure, which generates endogenous market segmentation that evolves over time. The third sub-section presents a theoretical pattern unknown so far, and indicates which could be some of its determinants. These new explanations and statistical patterns may serve as a guide for future empirical research. Finally, we offer our conclusions in Sect. 4.
2 A computational consumer-driven market model We shall consider different varieties of one discretionary-consumption good (for example, bottled beer or car paint).2 For simplicity, from now on, we shall use the term ‘‘product’’ to refer to one specific variety of the consumption good. Each product is represented by its position in a n-dimensional space, known as the space of characteristics,3 where each dimension represents to what degree the product satisfies a specific technical or service characteristic, considered in a positive and continuous sense in the interval [0,1]. For the case of beer, we can consider four 2
Clearly these goods are heavily influenced by social emulation, and this could explain the emergence of consumer trends and the diversity of tastes.
3
The characteristic space is inspired by Lancaster (1966).
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characteristics (see Rabin and Forget 1998, on beer measurement): bitterness (b, measured in the IBU scale), strength (s, in the Plato scale), alcohol content (a, in terms of the percentage by volume) and color (c, in the Lovibond scale). Likewise, the paint colors can be represented in a three-dimensional characteristic space by the intensity r, g and b of the primary colors, red, green and blue respectively (RGB scale; see Hunt 2004). The market consists of two sets (a set of consumers C and a set of producers P) depicted in the same n-dimensional characteristic space S = [0,1]n. The position of each consumer represents her consumption tastes—in terms of the desired level of product characteristics; in the case of producers, their placement at any time represents the characteristics of their supplied product at that time. Both, consumer and producer positions co-evolve over time. We assume that population of N consumers remains constant over time. Each consumer Ci is represented in the space of characteristics by position ci which corresponds to her desired product or good, no matter whether this variety exists or not at that particular moment. The initial position of the N consumers is distributed uniformly in the space of characteristics, although the consumers’ desires are updated constantly via social emulation and/or innovation in consumption. Furthermore, in each discrete time period, consumers make decisions to buy one unit of a product variety out of all those which minimally satisfy their desires (or not to buy at all if none are satisfactory). A group of consumers sharing similar consumption desires makes up a market niche Gk characterized by position gk of its center. Market niches are identified in our simulations by using a usual hierarchical cluster analysis. Each consumer belongs to one niche, in such a way that niches form a non-overlapped partition of the population of consumers. The number of producers—initially zero—varies according to the needs of the market. The existence of consumer niches stimulates the entrance of producers Pi who offer their product situated at position pi in the space of characteristics. We suppose that all the producers fix the hedonic market price pi of their products (one market price for every bundle of characteristics), so that the price is represented implicitly in the remaining characteristics (in the example of beer pB ¼ Uðb; s; a; cÞ while pP ¼ Uðr; g; bÞ for the case of car paints). We assume that the unit margin is constant among firms (there is a common margin typical of the sector), so that the difference in profits comes from the level of sales. Besides this, we suppose that producers can satisfy all the demand for their products in each time period. 2.1 The consumer side Social emulation and innovation in consumption mean that consumer desires may change over time, which, in turn, leads to changes in market niches (some of them increase or decrease while others appear or disappear). In each discrete time period more than one interaction is possible, so we divide them into steps where at each step only one potential interaction can be carried out.4 In that way, at any step t, 4
In each time period consumers only make one purchase decision but many social interactions can occur, which must take place sequentially in order to be implemented computationally. For this reason, periods
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consumers can update their desires via two routes (a complete study of the social interaction model can be found in Ferna´ndez-Ma´rquez and Va´zquez 2014): •
•
Local emulation We assume that the probability Pij ðtÞ of two consumers Ci and Cj (with positions ci ðtÞ and cj ðtÞ interacting is greater, the more similar they are. In particular, we consider: dij ðtÞ a Pij ðtÞ ¼ Pji ðtÞ ¼ 1 ; ð1Þ dm where dij ðtÞ ¼ ci ðtÞ cj ðtÞ is the preference distance5 between consumers Cj and dm is the maximum distance between two consumers in the space of characteristics. a 1 is a parameter that regulates the degree of localness of affinity and resembles homophily effects (see Jackson 2008): the higher a is, the lower the probability of interaction will be for a given distance, and the affinity will be more local (leading to consumers being distributed in a greater number of niches). For this reason, parameter a determines the fragmentation of demand. Once two consumers Ci and Cj interact at step t, they approach each other, and their consumption desires ci ðt þ 1Þ and cj ðt þ 1Þ become more similar. However, we assume that the movement is not symmetric, so that the consumer who is more visible, famous, better connected or prestigious has higher power of persuasion. To be specific, if Vi denotes the number of interactions with Vj consumer Ci and Vj=i ¼ Vi þV 2 ð0; 1Þ represents the relative visibility (relative j proportion of interactions) of consumer Cj with respect to Ci, we suppose that the movement from Ci to Cj at t is produced over the segment joining ci ðtÞ and cj ðtÞ in the following way: ð2Þ ci ðt þ 1Þ ¼ ci ðtÞ þ mij ðtÞ cj ðtÞ ci ðtÞ ; where mij ðtÞ 2 0; dij ðtÞ s given by: b mij ðtÞ ¼ Vj=i ðtÞ dij ðtÞ: ð3Þ b 1 s a parameter, constant for all consumers and steps, which controls the intensity of emulation. Note that as b grows, a greater relative visibility is needed to obtain the same amount of relative movement. Thus, this parameter is related to the velocity of creation of consumer niches. Innovation in consumption We consider that consumers can also change their desires because of factors unconnected to social interaction. This mechanism captures two ideas: on the one hand, the fact that consumers enjoy trying new things (Bianchi 1998), and on the other hand, that desires can be strongly
Footnote 4 continued are divided into steps and we use an asynchronous–random updating mechanism that sets the order in which consumers interact (see, for example, Miller and Page 2004). 5
We consider the Euclidean distance, although depending on the specific features of each product, other metrics might be more suitable.
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influenced by random events (Nelson and Consoli 2010). Hence, we suppose that each consumer Ci can decide, with a certain probability p 2 ½0; 1, to change their position ci ðtÞ at the end of time period t (once the emulation process has finished) to position ci ðt þ 1Þ calculated from a random n-dimensional variable with a uniform distribution in the space of characteristics S ¼ ½0; 1n . Parameter p measures, therefore, the tendency for innovation in consumption (Steenkamp and Burgess 2002). This effect introduces a component of volatility in endogenous network formation that places our model within the realm of complex evolving networks (see Marsali et al. 2007). In each discrete period t, consumers, as well as updating their desires, must also make decisions based on the following criteria: •
Decision to purchase Consumers, having bounded rationality, decide to consume one particular product variety or another chosen from all the ones which satisfy sufficiently their desires; or they decide not to consume if none are satisfactory. Let r 0 be the radius of ‘‘purchasability’’ which determines the maximum distance at which a consumer considers a good can still satisfy their desires (the level of consumer insistence; Foxall 1990). Thus, we that suppose each consumer Ci preselects the possible products (pj such that d ci ; pj r) and buys one unit of one of them at random, with a probability proportional to the brand image at the start of period t given by: Ij ðtÞ ¼ K þ
t X
dk1 vj ðt kÞ;
ð4Þ
k¼1
Note that K 0 is the autonomous image of the brand (independently of sales), 0 d 1 is the discount rate representing consumers’ memory, and vj ðt kÞ the sales of producer Pj during period t k
2.2 The producer side Producers can make three kinds of decisions: entering, leaving and adapting to the market. They have a certain knowledge about the divisions of demand G, but when making their decision they only consider those Gk niches which are sufficiently representative6 (with #Gk 0:05N). •
Decision to enter It is supposed that at the end of each period t, an arbitrary producer can decide to enter the market with a probability related to their expected market share:
6
We have considered that representative niches are those with a minimum size equivalent to 5 % of the population; clearly, other thresholds could be set up, but these changes produce no significant variations in the model dynamics.
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X
pentry ðtÞ ¼
M ht ðsGk Þ;
ð5Þ
#Gk 0:05N
where 0 M 1 is a fixed parameter and ht ðsGk Þ is the expected market share for niche Gk , given by: ht ðsGk Þ ¼
• •
Kþ
P
K Pj 2PGk
#Gk ; I j ðt Þ N
ð6Þ
where PGk is the group of producers who have sold to cluster Gk during the current period. Once a producer decides to enter the market at t þ 1 to cover the demand of niche Gk , the exact entry place is worked out from a normal distribution with its average at the center gk and a typical deviation r 0 (parameter which measures the level of market opacity).7 Decision to leave All the producers who have not reached the minimum market share (5 % of sales) leave the market with a probability q 2 ½0; 1 Decision to adapt Producers who do not reach the minimum level of sales but remain in the market, adapt their offer to the niche (target) at which their product is aimed. We assume that producers direct the product to only one niche Gk , although this does not imply that they do it in exclusivity. These modifications of the product involve a cost, which will be higher, the greater the distance from the target—so we consider that the producer selects the nearest representative niche. In the process of producer Pj adapting to niche Gk , position pj moves nearer to the center gk by a fixed amount k dm per time period (or by the amount remaining in cases where it is lower). Parameter k 2 ½0; 1 represents the maximum capacity of productive adaptation per period and we assume it is equal for all producers and periods. We can assimilate these firm movements to incremental innovations aiming to adapt the product variety to consumer desires.
To sum up, we detail in Table 1 all the variables, constants and parameters involved in the model. The updating of consumers’ desires is produced by local emulation (depending on parameters a and b) and innovation (with probability p). Purchase decisions are based on the brand image of the product (which in turn depends on parameters K and d) and the consumer insistence (parameter r). Finally, producers make decisions about market entry/exit or adapting the offered product to the consumers’ desires (depending on parameters M, r, q and k). Once the initial positions of the N consumers have been distributed randomly, the iterative process is started and the position of the consumers as well as the number and position of producers evolves over time. The computational algorithm (whose pseudo-code can be found in the ‘Appendix’) was develop on JAVA employing the REPASTJ ABM framework, v3.1 (North et al. 2006). Massive data from simulations were statistically analyzed using PROJECT-R, v3.1.3 (R Core Team 2015). Figure 1 shows the 2d evolution of our model for the (imaginary) case of 7
This parameter can measure two kinds of market opacity. On the demand side, the uncertainty regarding the precise desires of the niche. On the supply side, it shows the possibility of not being able to satisfy exactly the consumer desires, or not knowing how to do it technically.
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2 ½0; 1n
Location of consumer Ci in the characteristic space at step t
pj ðtÞ
2 ½0; 1n
Location of producer Pj in the characteristic space at step t
N
2N pffiffiffi ¼ n
Maximum distance between consumers
dmax
Population of consumers
Updating of consumers’ desires Via local emulation Pij ðtÞ
2 ½0; 1
Probability of interaction between consumers Ci and Cj at step t
dij ðtÞ
2 ½0; dmax
Distance between consumers Ci and Cj at step t
Vj=i ðtÞ
Relative visibility of consumer Cj respect to Ci at step t
mij ðtÞ
2 ½0; 1 2 0; dij ðtÞ
a
1
Degree of affinity localness/Level of demand fragmentation
b
1
Intensity of emulation/Velocity of creation of consumer niches
2 ½0; 1
Probability of innovation in consumption
Amount of movement from Ci towards Cj at step t
Via innovation p
Consumers’ purchase decision Ij ðtÞ
K
Brand image of producer Pj at period t
vj ðtÞ
0
Sales of producer Pj at period t
r
0
Radius of ‘‘purchasability’’/Consumer insistence
K
0
Autonomous brand image (independent from the level of sales)
d
2 ½0; 1
Discount rate (consumers’ memory) for sales on the brand image
Producers’ decisions pentry ðtÞ
2 ½0; 1
ht ðsGk Þ
2 ½0; 1
Expected market share for attending cluster (niche) Gk at period t
M
2 ½0; 1
Weight of the expected share on the probability of market entry
r
0
Typical deviation for entry location/Level of market opacity
q
2 ½0; 1
Probability of market exit
k
2 ½0; 1
Maximum capacity of productive adaptation per period for producers
Probability of market entry at period t
bottled beer with bitterness on the vertical axis and strength on the horizontal axis (lines represent interactions, circles are potential consumers and squares are producers). The figure shows the endogenous creation and co-evolution of market niches from social emulation. For the aggregate study of the system we must focus on the following three variables aggregated at a sectorial level: •
The product adoption rate KðtÞ, given by the proportion of consumers in the sector who purchase it: 1 X KðtÞ ¼ vj ðtÞ; ð7Þ N P 2PðtÞ j
where PðtÞ is the set of producers in the market at t and vj are the sales of producer Pj in this period.
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Fig. 1 Evolution of a 2d characteristic space with N ¼ 250 consumers (black circles). In t ¼ 20 some market niches have appeared and 3 producers (empty squares) have entered into the market
• •
The number of producers in the market, PðtÞ ¼ #PðtÞ. The Herfindahl index H ðtÞ, which measures the degree of industrial concentration, given by: X 2 H ðt Þ ¼ sj ðt Þ ; ð8Þ Pj 2PðtÞ
where sj ðtÞ is the market share of producer Pj in period t. Note that if H 0, then there is an industrial structure of perfect competition, while if H 1 then a monopoly situation is produced.
3 Simulations and stylized facts A stylized fact is an aggregate pattern or a sectorial property observed in the socioeconomic reality and empirical data. A model, as an abstract representation of reality, should stand to empirical evidence to be considered plausible. Drawn on a reduced number of assumptions, our model will allow us to reproduce a high number of well-known statistical regularities, lending plausibility to the model and at the same time finding out common underlying explanations for many of the empirical patterns documented in the literature. Furthermore, it will allow us to find new hitherto unknown regularities. Although the model has 10 parameters, 5 of demand (a, b, p, r and d) and 5 of supply (K, M, r, q and k), in Ferna´ndez-Ma´rquez et al. (2016) we show that only three of them (a, r and d, all representing demand-side factors) play a significant role (particularly the parameter r) in the dynamics of the system. Now we show how several industrial statistical regularities emerge from our computational model,8 8
We are interested in proving that our model can show several well-known industrial patterns, which really requires finding only one specific parameter set that can generate them. In particular, in our simulations we take the default parameter values: N = 75, a = 24, b = 6, p = 0.003, r = 0.3, d = 0.8,
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providing a common explanation to all of them and spotlighting the role of demand in the underlying dynamics. 3.1 Industry level stylized facts as emergent properties of the model Before we look at the different properties one-by-one, we can synthesize the underlying argument by noting that the regularities emerge from a market selection process in which, consumer insistence (r), and endogenous demand fragmentation (a) driven by local emulation, play key roles. Now, we are going to clarify some methodological aspects. Firstly, as some properties involve the size of firms, we need to select a proxy observable variable in the model that can measure it. Hereinafter we shall quantify firm Pi size at t according to its market share si ðtÞ, which is a limited continuous variable [0,1]. i ðt1Þ , and to make Secondly, the growth rate of firm Pi is defined by Dsi ðtÞ ¼ si ðtsÞs i ðt1Þ clearer the results, we will only consider non-negative growth rates (those with Dsi ðtÞ 0) when studying average growth rates. Thirdly, the age of firm Pi at t is calculated by t tentry ðiÞ, where tentry ðiÞ is the time when Pi entered the market. Lastly, since our simulations show that, for the default values of the parameters (see footnote 7), the state of the system9 begins to have a relatively steady evolution (with small oscillations around the asymptotic state) from around t ¼ 100, we consider this time as the start of maturity (last phase of the industrial life cycle in our model). We begin by presenting the properties of our model which require taking into account all the stages of the industrial life cycle (with an excessive predominance of none). For this reason, the following results are derived from the time interval t 200. •
•
Property 1: ‘‘Smaller firms grow more quickly’’ (in Lotti et al. 2003, there is a selection of more than 15 empirical studies which back up this fact). In Fig. 2, we see that our model can reproduce this pattern, since the larger is the firm (s), the lower is its average growth (Ds). One consequence of this is that the ‘‘Gibrat’’ law (the growth rate and the firm size are independent) is not fulfilled (in line with empirical studies such as Evans 1987; Dosi 2007). In our model, small fast-growing firms are often new entrants that focus their activity on unattended market niches. The ongoing transformation of demand opens new opportunities for new competitors that grow faster than large incumbents. Property 2: In real industries it is observed that ‘‘the larger the firm, the less variability in growth rate’’ (there is strong evidence of this, for example, in Evans 1987; Dosi 2007). We measure the variability (dispersion) in the growth rate Ds as the variance in growths VarðDsÞ experienced by producers according
Footnote 8 continued K = 0.1, M = 0.9, r = 0.1, q = 0.05, k = 0.003; although similar time evolutions of the system are obtained over a wide range of parameter values. All figures in this section have been obtained with these default parameter values and averaged from 500 replications (for different random seeds). Q 9 Characterized by the three aggregate variables: level of adoption KðtÞ, number of producers ðtÞ and Herfindahl index H(t).
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•
•
•
to their size s. Figure 3 shows that our model can also generate this regularity, since the larger the producer, the lower the variability in growth, with this eventually becoming irrelevant after a certain size. In a way, large firms stabilize their growth at a rate close to zero. Property 3: ‘‘The longer-lasting firms grow less’’ (see Evans 1987; Dosi 2007). In Fig. 4, we show the growth experienced by every producer according to its time spent in the market. As we can see, the model satisfy the property, as the older the firm is, the lower is its growth rate, although after a certain age, the model reveals that this variable becomes virtually irrelevant. Property 4: ‘‘Longer-lasting firms offer less variability in their market share growth’’ (see Evans 1987; Dosi 2007). As in property 2, the variability in the market share growth Ds is measured by its variance VarðDsÞ. Figure 5 shows the existence of an inverse relationship between a firm’s age and the variability in the growth of market shares. Property 5: ‘‘Growth rates follow a distribution skewed to the right’’ (see Stanley et al. 1995; Bottazzi and Secchi 2003; Dosi 2007). Figure 6 shows clearly that this property can be generated by the model, as that the growth rates follow a distribution skewed to the right; that is, most of the growth values are small, while a few are very high. Note that this is not a spurious result since we have removed those (dummy) producers that remain in the market for less time than the expected lifespan (1/q) of a firm which does not sell anything in any time period, as their permanence in the market is due to randomness instead of the system dynamics.
Now we shall comment on some results related with the probability of firms becoming bankrupt, which require extending the time horizon. If we only consider a time interval of 200 time periods, it may not be sufficiently long for those firms destined to become bankrupt, to actually do so; hence, we have extended the time horizon to 3000 periods. This extended time interval is also more appropriate for studying the time evolution of the industrial concentration (measured by the Fig. 2 Growth rate (Ds) as a function of size (s). Smaller firms grow more quickly
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Fig. 4 Growth rate (Ds) as a function of age. The longerlasting firms grow less
Herfindahl index H ðtÞ). As in property 5, in the study of bankruptcy we shall not take into account those small producers who artificially remain in the market. We do not take into account either those producers who have not become bankrupt at the end of the simulation. •
Property 6: Another interesting stylized fact that our model generates is that ‘‘the larger the firm, the less likely it is to become bankrupt’’ (see Evans 1987). We shall analyze how probable it is that firms of a given size s in period t go bankrupt in t þ 1, thus determining whether the size of firms influences their chances of survival. Figure 7 shows that almost all the cases of bankruptcy occur in small firms, confirming the model can generate this property. This result shows that strong competition mainly operates among small competitors, while loyalty and success-breeds-success mechanisms favor large firms, once they reach a certain size threshold. This should make us wonder whether market selection forces operate evenly across the whole size-range of firms.
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Fig. 6 Density function of growth rate (Ds). Growth rate follows a distribution skewed to the right
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Property 7: ‘‘The longer-lasting firms have a higher probability of survival’’ (see Evans 1987; Dosi 2007). We analyze the probability of firms becoming bankrupt in the following period, thus determining whether the age of the firm influences its probability of survival. Figure 8 shows how our model also reproduces successfully this pattern, since the probability of bankruptcy is drastically reduced as the firm’s age increases, leading to a distribution skewed to the right. This accentuates the fact that the first instants of a firm’s life are decisive for its survival. Property 8: ‘‘Market shares and firm sizes change over time’’ (see Dosi 2007). As the Herfindahl index of industrial concentration H ðtÞ is defined in terms of the market shares s of all producers, we check this property by studying the time evolution of this index. We can see in Fig. 9 that H ðtÞ is not static, but it evolves over time (which implies variations in market shares). Note that, even though the largest variations take place in the first stages of the industrial life cycle, they still keep occurring, even in maturity.
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Author's personal copy A computational consumer-driven market model: Statistical… Fig. 7 Density function of firms with size s that go bankrupt in the following period. The larger the firm, the less likely it is to become bankrupt
Fig. 8 Density function of the age of firms that go bankrupt in the following period. The longer-lasting firms have a higher probability of survival
Finally, we shall comment on the results that emerge in the asymptotic (stationary) stateQ of the system, that is, when the distributions of the three aggregate variables (KðtÞ, ðtÞ and H ðtÞ) all remain fairly constant over time, what happens from t ¼ 5000 (see Ferna´ndez-Ma´rquez et al. 2016). •
Property 9: ‘‘The right-skewed distributions regarding firms’ size’’ (see Bottazzi et al. 2003; Bottazzi and Secchi 2003; Dosi 2007). The pattern refers to the distribution of firms within an industry, at any given time. As in property 5, we shall not take into account those small producers who artificially remain in the market. Figure 10 shows various density functions for the firms’ size obtained from the model simulations at different points of time, once the asymptotic state of the system have been reached. We can see the model can generate distributions of the size of firms that are clearly skewed to the right
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Fig. 9 Time evolution of industrial concentration (H ðtÞ) for different levels of consumer insistence (r). Market shares and firm sizes change over time
(even when dummy producers are not considered). We point out that this pattern is contrary to the existence of an optimum size; that is, contrary to the intuitive idea that empirical distributions must fluctuate around an optimum firm size (along the lines of Dosi 2007). In our model, imperfect information and gradual (local) learning (on the one hand), together with loyalty effects and consumer insistence (on the other hand), explain how a large proportion of small competitors can co-exist with a significant number of consolidated incumbents. Likewise, the combination of consumer innovation, and firm entry/exit and adaptation efforts explain why the market never settles around an optimum firm size.
Fig. 10 Density function of firm size (s) for different time periods (t). Firm size follows a distribution skewed to the right
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Fig. 11 Asymptotic industrial concentration (H) as a function of consumer insistence (r) for different levels of demand fragmentation (a). There are significant differences between sectors, given by specific values or r and a
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Property 10: Another empirical regularity that our model generates is that ‘‘there are significant not temporary differences between sectors regarding industrial concentration’’ (see Bottazzi et al. 2003; Dosi 2007). We use the Herfindahl index H ðtÞ to quantify industrial concentration. Since, in our model, different industries are characterized by different values of parameters, this property would be reproduced if the concentration levels depend on the parameter values even at the asymptotic state. Figure 11 confirms that, in particular, the values of the demand-side parameters r and a have a significant influence on the Herfindahl index H ðtÞ at the asymptotic state.
To close this subsection, we would like to emphasize an important implication of several of our results regarding the role and efficiency of market selection processes: both when we talk about the advantage of being large and consolidated (survival, share, profits), and when we talk about the (localized) strength of competition among small new entrants, our model reveals that the intensity of competition is distributed in a highly uneven way across the market. This result connects with the open debate in evolutionary economics regarding the role and efficiency of selection in evolutionary market processes (Dosi and Nelson 2010). 3.2 The Industry life cycle and the role of demand Let us check now to what extent our model generates the emergence of industry life cycles. We devote a specific subsection to this topic since it is especially relevant. Following Klepper (1997), we assume that the industrial life cycle is made up of different phases, each of which is characterized by a group of properties:
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During the early phase of the industrial life cycle the amount of sales is low, market needs are not well defined, there are few barriers to entry and the number of firms grows quickly. During the development phase: the volume of sales grows rapidly, standardization is produced, the number of firms reaches its maximum level and there is a great variability in their shares. In the turbulence phase, the number of producers falls drastically (in some industries this phase is not present). During the maturity phase: growth is reduced and predictable, consumers know what they want and producers know what the market needs are, market shares have little variability and it is difficult for new producers to displace older ones.
Figure 12 shows that the volume of sales, in terms of adoption rate KðtÞ, starts out from a null value before growing rapidly to maturity, and then stabilizing. Initially, market needs are not well-defined given that consumers are dispersed in the space of characteristics, but later, the demand is organized in the form of consumer niches (see Fig. 1). This structure allows firms to attend consumer demands with a greater degree of standardization. When this occurs, desires become more stable at the same time, as consumers know what they want. For example, if the market needs four producers P1 ; P2 ; P3 ; P4 to attend all consumers at the beginning, after the local convergence of consumers’ desires only two of them could be needed. Figure 13 shows that the probability of a firm’s entry to an industry (pentry ) is initially high (few entry barriers), before swiftly falling to zero (high barriers to entry). Figure 14 shows the evolution of the number of producers PðtÞ in the industry—it is initially zero before experiencing a rapid growth and eventually becoming stable. Figure 15 shows how the variability in growth of market share VarðDsÞ ecreases as the industry becomes more mature. As Figs. 12, 13, 14 and 15 have shown, the model can reproduce the typical profile of an industry life cycle. Our model also reveals that certain demand-side
Fig. 12 Time evolution of adoption rate (KðtÞ) for different levels of consumer insistence (r)
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Fig. 13 Time evolution of market entry probability (pentry ) for different levels of consumer insistence (r)
Fig. 14 Time evolution of the number of producers (PðtÞ) for different values of consumer insistence (r) Fig. 15 Time evolution of share variability (Var Ds)
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Fig. 16 Phase transition of S-shaped curve in adoption rate (KðtÞ) for different levels of consumer insistence (r)
parameters can have some influence on that. Firstly, some industries do not present a turbulence phase. This is a well-known real-world fact (Klepper 1997), and it emerges naturally in our model. Thus, in Fig. 16 the turbulence phase, characterized by a reduction in the number of producers PðtÞ before stabilization, only occurs when the consumers are very insistent (low r). Secondly, many industries develop an S-shaped pattern of adoption rate KðtÞ (Rixen and Weigand 2014). In Fig. 12, this phenomenon is reproduced for very low r, suggesting that consumer insistence could be one of the determinants of this real-world phenomenon. Once we have shown that the model generates the lifecycle as an emergent property, we can qualify some of the results by paying attention to demand-side key determinants. These new results may stimulate future empirical research on the role of demand in industrial dynamics. •
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New explanation 1 In our model seems clear that certain demand-side factors shape the specific profile and duration of the phases of the industry life cycle. As we saw previously, when consumers are not very insistent (high r) and/or we find a low fragmentation of demand (low a) the maturity phase of the cycle can be delayed. New explanation 2 Some of our demand side parameters could explain why only certain industries show the S-shaped pattern in the adoption rate. In the literature it is seen that some industries do not present an S-shaped pattern in the adoption rate KðtÞ, but there is no consensus regarding the causes for this (Rixen and Weigand 2014). As seen previously in Fig. 12, our model offers a possible explanation: the Sshaped pattern emerges for a specific case, that is, when the consumers are extremely insistent (low r). In this regard, we may be interested in determining for what levels of consumer requirements (r), the transition from an S-shaped curve to a purely concave one happens. Figure 16 shows that for r 0:15 the
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Fig. 17 Emergence of turbulence phase (with a reduction in the number of producers PðtÞ) for some levels of consumer insistence (r)
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S-shaped pattern is lost,10 confirming that only when the consumers are very insistent is the known pattern obtained. New explanation 3 Let us know look at the role of demand in order to explain the existence of a turbulence phase in the industry life cycle. Klepper (1997) argued that, empirically, this phase is not always produced, although it is not clear what the causes could be. Our model sheds light on this, indicating that this phase is only produced in those industries with a high level of consumer requirements (low r). Figure 17 shows that the model reproduces the turbulence phase characterized by a fall in the number of producers PðtÞ, with this property being lost for r 0:15. Figure 14 shows, on a larger time scale, the sharp fall in the number of producers PðtÞ for the high levels of consumer requirements, although on the other hand, the granularity of r prevents us knowing when the change in phase exactly happens.
In our opinion, all these determinants on the demand side make it clear that demand is important. Furthermore, our model shows that demand-related future studies could play a key role in understanding industry-level statistical regularities and stylized facts. It seems to us that dynamical industries such as consumer software and applications, videogames, and online social networks (friendship, relational needs, etc.) could be promising targets for the empirical exploration and analysis of our results.
10 We are only interested in proving the existence of a phase transition. The specific value of r that produces it, which depends on the values of the other parameters, is irrelevant for our purposes.
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Fig. 18 Phase transition of increasing–decreasing curve to just decreasing in market entry probability (pentry ) for different levels of consumer insistence (r)
3.3 A new stylized fact The model brings out a theoretical pattern previously undocumented (to our knowledge) in the literature. The model suggests that: some industries present a rate of entry with a first phase of growth, followed by a second phase of downturn, while others just experience a downturn. In our opinion, this is a new and surprising result since it would be expected that industries become more and more attractive (increasing probability of entry pentry ) until maturity begins, a moment usually accompanied by a sub-phase of turbulence, in which a sharp fall in the number of producers PðtÞ occurs; that is, the probability of entry pentry is then much lower than that of exit. However, in our model this is not always so. Figure 18 shows that only when consumers are very insistent (low r), do we find an initially increasing, and later decreasing, probability of entry pentry , and that for r 0:15 a phase transition occurs which makes it strictly decreasing. Future empirical works could determine whether these two kinds of industry exist. The industries mentioned in Cowan et al. (1997) seem to us to be promising candidates for these future studies.
4 Conclusions In this work we have introduced a demand-driven computational model which allows us to analyze industrial dynamics in a consumer-driven market. To be specific, we introduce an agent-based model in which social emulation by consumers and the adaption of producers to the progressive transformation in demand play a significant role. Our theoretical proposal contemplates the bounded rationality of agents (both consumers and producers), the importance of the
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heterogeneity of the product and consumer, the co-evolution of the desires of the consumers (mainly via social emulation), and the endogenous emergence and transformation of market segmentation. The proposed demand-driven model may capture interesting aspects of the dynamics underlying certain industries within an inclusive theoretical framework (instead of employing ad-hoc models designed for each case), being able to reproduce patterns widely studied in the literature (and thus identify their possible theoretical determinants), such as: the S-shaped curve at the adoption level developed by many industries; the existence of an industrial life cycle which marks some general properties characterizing industries according to the phase of the cycle they are found in; the lower growth rate and variability in growth rate, along with the higher probability of survival, exhibited by firms with bigger size and/or firms which are longer-lasting; or the distribution of firm sizes and growth rates skewed to the right. More interestingly, our model also generates simulated evolutions in which significant differences between sectors with respect to industrial concentration may emerge; different (S-shaped or concave) adoption rate curves can be obtained; differences between the firms’ profits persist; and the presence/absence of a turbulence phase before reaching industrial maturity may take place. And all of these different behaviors can be explained in terms of only two parameters: r (representing the level of consumer requirements) and a (which determines the number of market niches). In this way we show how certain empirical patterns traditionally (mainly) linked to supply-side factors, can also be explained from the demand side. Furthermore, new statistical regularities emerge from our model, leaving the door open for future empirical validation: sectors that reach the maturity phase later have less insistent consumers and a lower number of market niches; industries showing the S-shaped pattern and/or a turbulence phase in their industrial life cycle have more insistent consumers; and two possible time evolutions of market entry rates emerge (one with a first phase of growth followed by a second phase of downturn, and another with only the phase of downturn); the concrete pattern depends on consumer requirements. In this sense, the theoretical results we obtain can guide the empirical search for patterns in industry (for example, comparing real data for specific domestic sectors in different countries; i.e. the wine industry in different areas, tourism destinations, bottled beer in different regions and so on). Clearly, this work may serve to corroborate the validity of the presented theory, which, in turn, could inspire subsequent theoretical works on the role of demand in markets. In our opinion, this can lead to a fruitful co-evolution between theoretical and empirical research.
Appendix: Pseudo-code for replication In this section we include a detailed algorithm that describes the specifications of the model in order to make it less ambiguous and reproducible for any researcher.
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Carlos M. Ferna´ndez-Ma´rquez is Assistant Professor at UAM (Autonomous University of Madrid), Spain. He is computer engineer, has a degree in research and marketing techniques. His Ph.D. thesis was on Evolutionary Economics. He works on the study the effect of gregarious behavior of human son certain socio-economical processes by means of computational simulations. In particular he has focused on studying phenomena such as: diffusion of innovations, political voting, co-evolution between supply and demand, ideological extremism, financial speculation or riots. Some of his papers have been published in journals such as Journal of Artificial Societies and Simulation. Francisco Fatas-Villafranca is a Professor of Foundations of Economic Analysis at University of Zaragoza (Spain). He hold a Ph.D. in Economics. His research deals, among others, with modeling of micro-economic systems. Francisco J. Va´zquez is a Professor of Foundations of Economic Analysis at UAM (Autonomous University of Madrid), Spain. He graduated from Complutense University of Madrid and obtained a Ph.D. in Mathematics in 1993. His research deals with the mathematical modeling of economic and social processes.
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