Endogenous Innovation Waves and Economic Growth

Andergassen, Rainer; Nardini, Franco Working Paper Endogenous Innovation Waves and Economic Growth Quaderni - Working Paper DSE, No. 446 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Andergassen, Rainer; Nardini, Franco (2002) : Endogenous Innovation Waves and Economic Growth, Quaderni - Working Paper DSE, No. 446, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4850 This Version is available at: https://hdl.handle.net/10419/159287 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ Endogenous innovation waves and economic growth Rainer Andergassen*, Franco Nardini** * Department of Economics, University of Bologna, E-mail: [email protected] ** Department of Mathematics for Social Sciences, University of Bologna E-mail: [email protected] We propose a simple model where large innovation waves arise from the endogenous propagation of information around sectors. Innovators of each sector invest in internal R&D and in local search for information. We show that depending on the structural parameters of the single sectors, some of the R&D sectors will engage in local search while others will not. Through localised search for information, technology adopted in certain sectors can be adopted also in other sectors, leading to a large technological correlation, and eventually to long ranged innovation waves. We characterise the endogenous balanced growth path of the economy, and the short run fluctuations around it. The model predicts a linear, positive relationship between the short run fluctuations and the long run growth rate. We test this latter relationship and find that we cannot reject the predictions of the model. Keywords: innovation waves, balanced growth rate, aggregate fluctuations, technology diffusion, endogenous growth J.E.L. Classification numbers: D92, E32, E23, O33, O41 This paper has been written parallel to a paper written by the present authors and Massimo Ricottilli on Innovation dynamics. The authors are so much indebted to Massimo Ricottilli for fruitful discussion. We thank also Christopher Laincz and seminar participants at the 2nd edition of the Summer School in Economic Theory, Venice 2002. The usual disclaimer applies. It is widely recognised that technology spill-overs play a primary role in the dynamics of innovations. Rosenberg (1976) highlights their importance in the process of industrialisation. In particular, he emphasises the importance of the technological convergence which emerged in the process of industrialisation. Using Rosenberg’s words: ”... (the) industrialisation was characterized by the introduction of a relatively small number of broadly similar productive processes to a large number of industries (p. 15)”. According to the author, its was this latter event that lead to the possibility of large spill-over effects. Each single firm tried to solve idiosyncratic problems, i.e. specific to her production. Once she succeeded in solving the problem, the innovation introduced was likely to be introduced also in other sectors due to the technological convergence which characterised different sectors. This latter phenomenon lead possibly to large innovation waves. Fai and Von Tunzelmann (2001) show that there exists also today this kind of technological convergence which characterised the process of industrialisation. In order to study the dynamic effects of innovation waves, the idea of general purpose technologies (GPT) has been introduced1. GPT are major innovations such as steam engine, electric dynamo, laser or computer. The introduction of new innovations is costly since it requires a restructuring of the production process (David, 1990). Thus, Helpman and Trajtenberg (1994) argue that resources, such as labor for example, are withdrawn from the production process, and devoted to the R&D sector, and this latter generates a slowdown of aggregate production. Once the innovation has been successfully adopted by the firms, aggregate production increases. In this way there exists a positive relationship between long run growth and short run fluctuations. This framework has been enlarged by Aghion and Howitt (1998) p. 253 in order to study the diffusion of the adoption of GPT. The authors propose a simple model of social learning in order to capture the stylised fact that there exists an ”...uneven transition path for aggregate output, ... where prolonged periods of relative stagnation are followed by an acceleration in the pace of technology diffusion” (Aghion and Howitt, 1998). The diffusion of the GPT occurs through the observation of other firms. Assuming GPT implies superimposing exogenous technology paradigms. In this paper we are interested in how technology paradigms and innovation waves emerge endogenously from the interaction of single sectors. We consider innovations to be idiosyncratic, but through localised interaction of firms, the informational content of the innovation can be diffused. Aghion and Howitt state this problem in the following way: ”... new technologies do not get implemented instantaneously throughout the economy. Instead, they diffuse gradually, through a process in which one sector gets ideas from the research and experience of others.” (Aghion and Howitt, 1998 , p. 85). Our aim is to build a simple model where highly volatile large innovation waves emerge from localised spill-overs of information, leading to a large technological correlation, like the one Rosenberg (1976) highlighted as a crucial element for the process of industrialisation, and 1See for example David (1990) and Helpman (1994). 1 recently evidenced as a stylised fact today by Fai and Von Tunzelmann (2001). The adoption of a new innovation usually requires, at least partially, an internal reorganisation (David, 1990). Thus, innovating firms face sunk costs of reorganisation, and the adoption of innovations is optimal only if the gain from the adoption is larger than its cost. This latter implies that innovations developed by R&D firms must reach a certain degree of perfection such that the gains from their introduction are at least as big as the sunk costs of reorganisation. This latter phenomenon has been highlighted also by Arrow (1974, p. 41) who pointed out that the problem of information channels resembles the problem of inventories under uncertainty. We are going to propose a multi-industry model, each industry possessing the Aghion and Howitt (1992) structure, where the single R&D firm of each industry has to complete an informational process, i.e. accumulate sufficient information, such that the adoption of the innovation by the final good firms of the same industry becomes fruitful. In this process of collection of information the single representative R&D firm invests in internal research, as well as in the observation of technologically related industries, i.e. industries facing similar technological problems. This constraint to the diffusion of information results in the clustering of all R&D sectors into neighbourhoods. Contrary to current economic literature, we are not going to model the localised informational spill-overs as a free lunch for each R&D sector. We are going to assume that specialised workers have to be allocated to the localised information search process, and that these latter can experience a reduced productivity in finding new information. In other words, we assume that once a technologically related industry introduces a new innovation, this latter has to be studied by specialised worker such that the informational content of this innovation can be extracted and eventually used for an innovation in this other industry. We assume that for some R&D sectors this activity is costly in the sense that it reduces the productivity of these workers in creating new information. This reduced productivity arises, for example, because of difficulties in communication between R&D sectors belonging to different, even though technologically correlated, industries, since different R&D sectors followed different directions of research. We will see how this influences the choice between investing in localised search for information or not. In this paper we build an endogenous growth model, where growth is driven by industry specific innovations, i.e. born in a given industry, and endogenous technology spill-overs between industries. We are going to characterise an economy whose aggregate production fluctuates due to the endogenous stochastic innovation waves. Further, we will see that the larger are the innovation waves, the larger will be the short run fluctuations of aggregate production, and the larger will be the long run growth rate of the economy. The empirical literature on the relationship between fluctuations and long run economic growth gives no clear answer, mainly because of a missing theoretical framework2. We are going to test the theoretical relationship which results from the theoretical model and 2See for example Ramey and Ramey (1995), Kormendi and Meguire(1985) and Elmer and Pedersen (1998). 2 find that we cannot reject the results of our model. Further, the results seem to be robust with respect to the specification of the model. The model we are going to develope is consistent with the scale effects recently highlighted in the literature on endogenous growth. Akin to the paper by Peretto and Smulders (2002), our model captures the empirical evidence produced by Backus, et.al. (1992) that GDP growth is not related to the scale of the whole economy, while it is positively related to the scale of the single industry. Like Peretto and Smulders (2002), we obtain that the aggregate scale effect, which in our case is only positive, vanishes asymptotically as the number of industries increases, while the scale effect within the single industry is non-vanishing. The remaining part of the paper is organised as follows. In Section 1 we solve the problem of allocating the specialised workforce between the internal and external search process. Further, we characterise the optimal informational content of innovations. In Section 2 we derive the aggregate innovation dynamics and the long and short run dynamics of aggregate production of the economy. In Section 3 we propose an empirical test for the model. Section 4 concludes. 1 The microfoundations We assume that there are nindustries in the economy, nvery large, each composed of a final good sector, an intermediate good sector and an R&D sector. The intermediate good and the R&D sector are both specifictothefinal good produced in the same industry. The R&D sector discovers new ideas and innovations, which are used in the intermediate good sector of the same industry. Finally, the intermediate good which incorporates the technology is used by the final good sector in order to produce the output. We assume that the final good sector is perfectly competitive, and that the intermediate good sector is made of a single monopolistic firm. Further, we assume that the R&D sector of each industry is composed of two firms, a leader and a follower. These two firms alternate in producing the innovation. Once afirm succeeds in introducing a new innovation, she has no incentive to invest further in a new innovation since the gain of a further innovation would be lower than its cost (Arrow’s replacement effect). Thus, once a new innovation has been introduced this latter firm stops investing in R&D, while the follower starts investing in R&D and to search for the information necessary for the introduction of a new innovation. We assume that firms producing the final good have to pay sunk costs of reorganisation if they want to introduce a new technology, and further, outsider firms have to pay sunk costs if they want to enter the market. If these sunk costs of reorganisation are sufficiently large, then it is no longer optimal to introduce an innovation if a small, idiosyncratic bit of information arrives at the R&D sector of the same industry, since the gains from the introduction this innovation would be lower than the costs of reorganisation. As a consequence, the R&D firm of industry ihas to accumulate a sufficient number of informational bits 3 such that the introduction of the new innovation at the final good sector level of industry ibecomes profitable. As long as the accumulation of information continues, this latter remains tacit, and only once the new innovation has been introduced, other R&D sectors, i.e. R&D sectors belonging to technologically correlated industries, can infer its informational content, and can get in this way new information and ideas for their own. The representative R&D firm faces the problem of allocating specialised workers to internal R&D and to localised search for information. These latter workers observe continuously a limited number of technologically related industries, i.e. industries facing similar technological problems, and contemporaneously they try to create new information for their own. We assume that one specialised worker observes at most one R&D sector belonging to another industry. The number of workers allocated to the localised search for information together with the technological correlation between industries defines the neighbourhood structure along which informational spill-overs occur. The constraints to the diffusion of information translates into a constraint on the productivity of workers allocated to the localised search; an upper bound on the number of these workers is the natural consequence of this formalisation. Once a new innovation has been introduced in a particular industry, the information incorporated in this innovation can be observed and used by R&D firms of technologically correlated industries. We will assume that for some R&D sectors the spill-over effects come in as a free lunch, while for other R&D sectors we will assume that it is not. We will show that, under certain conditions, these latter will not engage in localised search since the marginal productivity of the workers allocated to the local search for information is lower than the marginal productivity of the workers allocated to the internal search for information. In this way, the spill-over dynamics and as a consequence the aggregate innovation waves will be reduced. 1.1 The representative final good sector Consider a generic industry i.Thefinal good iis produced using intermediate good ionly. Neglecting for the moment being the problem of sunk costs, the problem of the representative firm is given by max {pτyτ−P(xτ)xτ−C} s.t. yτ=A(τ)x1−α τ (1) where Care fixed costs of production, τindicates the number of innovations introduced, A(τ)=[1+γ(s)]τ,γ(s)is the increment in productivity and s∈ℵ indicates the informational content of the innovations. We assume that γ0(s)> 0and γ00 (s)≤0.Fromthefirst order condition of problem (1) we obtain the demand function of the intermediate good: P(xτ)=pτA(τ)(1−α)x−α τ(2) and the profitfunction πy,τ=pτA(τ)αx1−α τ−C 4 We are going to assume that there are entry costs for outsider firms and sunk costs of reorganisation for insiders if they want to upgrade the technology, each given by k. We assume that if firms introduce a new technology in τ, prices remain fixed at the previous level for a small time period3∆t, while after this prices decrease to the level pτ=p0 A(τ),where p0=C αx1−α. Within this small time period firms makes profits in order to recover the sunk costs they face in the adoption of a new technology. After this, prices decrease because of the competition among final good producers. In the stationary state where xτ+1 =xτ=x, once an innovation has been introduced, firms make profits equal to γ(s)pτA(τ)αx1−α τ∆t. The condition such that introduction of the innovation is optimal, i.e. the profits from the introduction are larger than the costs of introduction, and the no entry condition require that γ(s∗)= k ∆tC (3) where s∗indicates the optimal number of bits of information the representative R&D firm has to accumulate such that the introduction of the innovation by the final good sector becomes optimal. The optimal informational content of innovations will be s∗=Γ¡k ∆tC ¢. We are going to assume that the R&D firms accumulate discrete units of informational bits, while s∗will be in general arealnumber. Thus,wewilldefine probabilities pand 1−psuch that s∗= sp+s(1 −p),wheres=integer[s∗]and s= integer [s∗]+1. We will assume that the representative firm R&D firm with probability paccumulates sinformational bits, while with probability 1−pshe accumulates sinformational bits. 1.2 The representative intermediate good sector Each industry iis endowed with Hi=Hspecialised workers, where i=1, ..., n. Within each industry, the specialised workers have to be allocated between the intermediate good sector (Hx) and the R&D sector (HA), where H=HA+Hx. Given the demand function (2), we can now turn to the problem of the intermediate good producer. This latter produces the intermediate good using specialised workers Hx. Its problem can be stated as follows max {P(xτ)xτ−wx,τHx,τ} s.t. xτ=1 ηHx,τ Assuming that the intermediate good firm has a monopoly power and that there 3The small time period ∆tand s∗are not perfect substitutes. To see this, consider the case where s∗is small, i.e. for example s∗=1. In this case, if the sunk costs kare sufficiently large and γ0(s)is sufficiently low, ∆thas to be very large such that the final good producers are able to recover the sunk costs of reorganisation. But the lower is s∗, the earlier a new innovation arrives (see Section 1.3.3). Thus, it can happen that the final good producers are not able to recover fully the sunk costs of reorganisation before a new innovation arrives, and as a consequence these latter firms make a loss. In order to avoid this problem, we assume that ∆tis exogenously determined, and arbitrarily small, while s∗is endogenously determined. 5 are labour turnover costs4,wehavethatthewagewx,τand profits are given by wx,τ=p0(1 −α)21 η1−αH−α x,τ πx,τ=p0α(1 −α)1 η1−αH1−α x,τ (4) 1.3 The representative R&D sector Innovations are produced using specialised workers HA. The single representative R&D sector faces the problem of allocating optimally HAbetween internal HIand external HEresearch (local search for information) activity. If a firm succeeds in introducing a new innovation, then she fixes the price for this innovation equal to the profits of the intermediate good sector. Thus, the representative R&D firm has to determine optimally HAin order to maximise the expected present value of profits. Let us first calculate the innovation rate, and after this we will determine the optimal HA. 1.3.1 The innovation rates TherepresentativeR&Dfirm has to collect sufficient information such that the new innovation can be fruitfully adopted by the final good sector. The R&D firm can either be at the beginning, at the end, or in an intermediate phase of this information collection process. We will make the following assumptions about the information collection activity. If a firm has no new information, then it is quite easy for this firm to get or create new information. On the other side, she is just at the beginning of the information collection process, and as a consequence the expected present value of investment in R&D is low. The more information a firm has already collected, the harder it is for this firm to get new information since the new information has to be compatible with the information already collected, i.e. the lower are the degrees of freedom. On the other side, the more information the firm has already accumulated, the sooner the new innovation can be introduced and, as a consequence, the larger will be the expected present value of investment in R&D. These postulates can be summarised in the following assumption: Assumption 1. The marginal incentive to invest in innovation is independent of the number of informational bits accumulated. We are now going to specify the production functions of information. Nearest neighbouring R&D sectors are observed continuously. In particular, we will assume that the firms observe as many neighbouring firmsasthereare workers allocated to this activity. Since the number of observable R&D sectors is constrained by the technological heterogeneity, we assume that at most there 4Given that there are sufficiently large labour turnover costs, the intermediate good sectors will maintain the employment level constant during the time interval ∆twhere the price of the final good sector changes. 6 can be s∗workers allocated to this activity, where s∗indicates the number of bits of information which have to be accumulated. Further, we assume that the mean number of informational bits created by R&D firm iin a time unit is given by ¡ϑiHI+ϑ0iHE¢µ n,whereϑiis the productivity of the specialised workers allocated to internal research, ϑ0iis the productivity of the specialised workers allocated to external research, µis the aggregate stochastic arrival rate, nis the number of industries, whereas µ nis the idiosyncratic stochastic arrival rate of each sector. Further, we assume that ϑi≥ϑ0iindicating that the marginal productivity of workers allocated to the localised research is not larger than the marginal productivity of workers engaged in internal research. If ϑi=ϑ0i, then we have that information spill-overs are free lunch, since the marginal productivity of those workers employed in localised search is the same as the marginal productivity of those workers employed in internal research. On the other side, if ϑi>ϑ0i, then the spill-overs are costly in the sense that the marginal productivity of those workers engaged in localised search is reduced. For example, ϑ0i→0implies that extrapolating the informational content of innovations introduced by neighbouring R&D sectors is so difficult, i.e. time consuming, such that the workers engaged in this activity are not able to create new information for their own. We will assume that there are mR&D sectors, where 1≤m≤n,whichhaveϑi>ϑ0i, while the other n−mR&D sectors are characterised by ϑi=ϑ0i. We are going to call ρcthe stationary average density of R&D firms being in the state where they need just one more bit of information such that the introduction of the new innovation becomes optimal. Thus, we can write the average probability of innovating for a representative R&D firm iengaged and non engaged in localised search for information, δi Land δi NL respectively, as follows5 δi L=max Hi I,Hi E ρc£¡ϑiHi I+ϑ0iHi E¢µ n+δHi E¤ s.t. Hi E≤s∗ Hi I+Hi E=HL.i A (5) δi NL =ρcϑiHNL,i A µ n(6) where s∗is the optimal informational content of innovations and δis the average aggregate innovation rate, which is given by δ=1 nX i∈XL δi L+1 nX i∈XNL δi NL (7) From (5) we observe that, given that the R&D firm idecides to engage in localised search for information, if the marginal productivity of Hi Eis at least as large as the marginal productivity of Hi IthentherepresentativeR&Dsectorhas the incentive to allocate as much as possible specialised workers to the localised search. 5We use a mean-field in modelling the dynamic interaction among agents. See Section 3.1 for details. 7 In order to simplify the exposition, we are going to assume that σ→1.From this latter expression we obtain that r=ρ. Thus, using (19), (17), (18), and (14) we have that the long run growth rate of aggregate output and its short run fluctuations are given by E(γY)=Sd(γY)=¯γ³˜ k´αϑHµ n 1+m (1 −α)m−˜γ³˜ k´ρ(20) where ˜ k=k ∆tC ,˜γ³˜ k´=γ³Γ³˜ k´´,¯γ³˜ k´=γ(Γ(˜ k)) Γ(˜ k),and˜γ0(·)>0, while ¯γ0(·)≤0. Thus, the lower is the number of R&D sectors not engaged (m)in localised search for information, the higher is the long run growth rate and its short run fluctuations. Note also that for each m<nthe growth rate (20) is always larger than the one we observe in the case where no firm engages in local search for information. The growth path of the economy (20) depends on structural parameters characterising the economy. For example, the larger are the sunk costs of reorganisation, the lower will be the long run growth rate and its short run fluctuations. We can also make some few considerations about the scale effects. Hin (20) is the number of specialised workers of each single industry. We observe a scale effect within each industry, like the one highlighted by recent empirical studies (see Backus et al., 1992). On the other side, defining HTthe total amount of specialised worker in the economy, and given the assumption of symmetry used inthepaper,wehavethatH=1 nHT. Thus, there will be positive aggregate scale effects, but these latter are asymptotically vanishing as n,thenumberof industries, diverges towards infinity. 3 Testing the model In this Section we are going to test the prediction of the theoretical model that the long run growth rate of the economy is equal to the size of its short run fluctuations. We are going to test this relationship using data on growth rates of the real GDP per capita of 21 OECD countries9, over the time period 1960 - 1990 (see Figure 1). The countries are Canada, Usa, Japan, Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, UK and Australia. We calculate the average growth rate for each country over the time period and its standard deviation. After this, we run the regression E£γi Y¤=β0+β1Sd£γi Y¤+²i(21) where εiindicates the error term of the regression, i.e. the random deviation from the relationship, where we assume that ²iis i.i.d. normally distributed across the countries. We are going to estimate parameters β0and β1using 9Data are taken from the Penn World Tables. 14 0 1 2 3 4 5 6 012345 Sd(g) E(g) Figure 1: Long run growth rate vs. short run fluctuations for 21 Oecd countries OLS, and after this we are going to test the hypothesis that β1=1and β0=0, which are the theoretical predictions of our model. Our estimates are (standard deviationinparenthesis) β0=0.8072508 (0.7121929) and β1=0.832128 (0.2478091) Thus, we find that we cannot reject the hypothesis that β1is different from zero, and further we cannot reject the hypothesis that β1is equal to one. Further, we find that β0is not statistically different from zero. We performed also a Ramsey-type test of omitted variables and a heteroschedasticity test, and we reject both hypotheses of omitted variables and of heteroschedasticity. The R2 of the regression is equal to 0.3724. We performed also some specification tests. In particular, following the idea of Levine and Renelt (1992) we introduce additional explanatory variables. We introduce so the average population growth rate, the initial human capital level and the average investment fraction of real GDP E£γi Y¤=β0+β1Sd£γi Y¤+β2h60i+β3ni+β4Ii+²i(22) where h60iindicates the average years of schooling for individuals taken from the total population over age 25 years in the year 196010 for country i,ni indicates the average population growth rate over the time period for country i and Iiis the average investment fraction of real GDP for country i.Weobtain the following estimates β0=0.308047 (0.9972457) β1=0.7514994 (0.1956116) β2=−0.0001547 (0.0000601) 10Data are taken from Barro and Lee (1993). 15 β3=−0.7328333 (0.2375725) β4=0.0855499 (0.0297373) Notice first that all the estimates but the constant β0are significantly different from zero. Further, the signs of the estimated values are consistent with theoretical predictions. The results confirm our previous analysis: β0is not significantly different from zero, while we cannot reject the hypothesis β1=1. As a consequence, our previous estimates are robust against the introduction of additional explanatory variables. The adjusted R2of the regression is 0.6970. If we introduce the initial real GDP per capita in regression (22) we observe that the estimates of β1become somehow worse. While the estimated value β1=0.3970314 (0.1786774) is still significantly different from zero, it is also significantly different from 1.Thislattereffect is mainly due to the large negative correlation between the long run growth rate and the initial level of real GDP per capita. This latter leads us to the conclusion that the exogenous arrival rate of information depends negatively on the technology level. This latter could be, for example due to international technology spill-overs and imitation. Thus, countries which have a lower technology will benefit from countries with a higher level through imitation. In this way, the arrival rate in countries with lower technology will have a larger innovation rate due to international informational spill-overs. The aspect of international technology spill-overs has not been addressed in this paper and will be object of future research. 4Conclusions We proposed a simple model where large, highly volatile, aggregate innovation waves emerge endogenously from the propagation of information around the single industries. The single R&D sector face the problem of engaging in localised search for information or not. Those R&D sectors, for whom the spill-over effects are not completely free lunch face the problem of a reduced productivity in the of local search for information. We show that under certain conditions, these latter will not invest in local search for information. The more are those firms not engaging in localised search, the less will be the endogenous propagation of information, and so the less will be the aggregate innovation rate. Growth in our model occurs through large highly volatile innovation waves: the larger are these waves, the higher will be the long run growth rate of the economy. Thus, growth occurs in the model through large short run fluctuations. We showed how the aggregate GDP growth path depends on structural parameters, such as, for example, the sunk costs the final good sectors face in introducing new innovations. We showed that the larger are these costs, the lower will be the aggregate growth rate. 16 References [1] Aghion P. and Howitt P. (1998) Endogenous Growth Theory, Massachusetts Institute of Technology. [2] Aghion P. and Howitt P. (1992) A model of Growth through Creative Destruction, Econometrica 60: 323 - 51. [3] Andergassen R. (2001): Investment, growth and economic fluctuations, University of Siena, working paper n. 318. [4] Arrow K. (1974) The limits of organization, W W Norton & Company, New York, London. [5] Backus D., Kehoe P., and Kehoe T. 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