Neoclassical growth theory prophesizes a log-linear evolution of per capita income. It considers short path deflections as the stochastic result of common business cycles, while longer lasting fluctuations are perceived as the adjustment period towards a new balanced growth path, following any significant structural transformations. On the other hand, “long waves” tradition emphasizes the long-term cyclical variations over the history of capitalism’s development and the reoccurrence of periods of amplified downturns.¹ This approach is neglected by the standard theory, not so much due to any statistical rejection² but mainly because it lagged of theoretical underpinning.

Traditionally, the occurrence of persistent long-lasting recessions triggers both the empirical but also the theoretical search for pro-“long-waves” arguments. Similarly to the 1930’s and 1970’s, the present persistent downturn gave also rise to a vigorous discussion: which could be the driving forces and are these fluctuations sequentially reappearing? With respect to the first question, historically, contributions can be categorised in three different schools: Marxists interpret long waves by the downward trend of the rate of profit, the indisputable driving force of the system. Nevertheless, the underlying process has not (yet) been convincingly introduced in the standard literature. Mandel [23] [24] [25] incorporated dialectically various exogenous factors―wars, geographical/sectoral market expansion and also technological revolutions―that counteract the systemic downward and move the economy back to a new phase of expansion. Closely to this, the Social Structure of Accumulation (SSA) School provides a theory of cyclical movements, where social institutional arrangements reassure the transition to the next upswing (Gordon [26] [27] ; Gordon [28] ; Gordon et al. [29] ). Finally, the Schumpeterian/ Innovation School stresses out the cyclical movement of technological progress. Based on appropriate micro-oriented arguments, theorists consider the fluctuations of economic activity as the result of innovation-clusters (Kleinknecht [15] [30] ; Mensch [31] ; Schumpeter [32] ).³

The second question about the sequential reappearance remains open too. Starting from the neo-classical tradition of Romer [48] and Aghion and Howitt [49] , theorists focus on the slow adjustment to the new applications in order to model the re-emergence of “long waves” (Helpman & Trajtenberg [50] and Aghion & Howitt [51] . Yet, thereby they introduce an initially inverse effect of technology. Trying to avoid this shortcoming, more recent contributions, stepping on Kuhn’s [52] shoulders, discriminate innovations between “basic” (or “fundamental” or “drastic” or “radical) and “incremental” (or “secondary”).⁴ Most of these models associate the emergence of a new paradigm with the reallocation of researchers between the two different kinds of research, basic and applied, driven solely by the expected economic benefits. Long waves result from the exhaustion of economic opportunities (Van Zon et al. [57] ; Yetkiner et al. [58] ) and not from the cyclical evolution of knowledge itself, as this is the case in the modern Anglo-Saxon epistemology. On the other hand, Li [59] and Olsson [56] , although they simulate a discontinuous evolution of technological paradigms, they end up having a growth rate of knowledge that evolves through jumps instead of smoothed cycles.

In the present paper, we discuss a framework that carries forward the described theoretical discussion. Setting a continuous synergy of the two contradictory effects of the existing stock of knowledge, initially introduced by Romer [48] ―“Standing on Shoulders” (SoS) and “Fishing out” effect (FO)―enables us to model a cyclical evolution of knowledge itself, despite the socioeconomic circumstances, as described by Kuhn [52] and Mensch [31] . Moreover, following Sanders’ [60] suggestion, this cyclical evolution depends also on each researcher’s scientific motivation, driven by liking to reputation, which led us to introduce an alternative utility function. Thereby, we present an endogenous explanation of long waves using both, epistemological and micro-economic foundation. The synergy of SoS and FO generates three co-existing mechanisms, leading to a cyclical evolution path of bounded applied knowledge: a direct impact on the productivity of applied research, and two indirect; on the one hand through the decision whether to work in R & D sector or in production (allocation of labour force), while on the other through the allocation of researchers’ efforts between basic and applied research.

The remainder of the paper is structured as follows: Section 2 sets up a detailed analysis of the model as a whole. In Section 3 we simulate the development of economic activity and we proceed with some indicative comparative statics. Finally, in Section 4, we summarize out and make some concluding remarks about the possible directions of future research efforts.

Almost all of the relevant literature, both in orthodox log-linear approaches and in heterodox analysis of cyclical trends, technological progress is recognised as the dominant driving force. In the present paper, as SoS and FO affect simultaneously the effectiveness of research, the evolution of applied knowledge itself follows a longer lasting cyclical path.

The following model relates strongly to the one initially presented by Romer [48] and later by Jones ( [61] [62] ) . We hypothesize an economy with three sectors: the final good sector (Y) with perfectly competitive producers, the intermediate capital-goods sector (x) that consists of a number of monopolistic firms and finally the research sector (R) engaged in both, applied and basic research.

In Section 2 we presented a theoretical framework that notably relates to the one initially presented by Romer [48] and later by Jones ( [61] [62] ). Yet, starting

from the evolving synergy of SoS and FO, we set off three mechanisms inducing cyclicality in the evolution of applied ideas (A): the productivity in applied research itself; an effect through the allocation of researcher’s effort; and finally, another one through the allocation of labour force in L_R and L_Y.¹² Putting these together initiates long waves of per capita output (y).

Standard literature recognises in technical change the engine of growth. Thereafter, having long-lasting cycles of dA/dt allows us to reasonably deduce on the existence of endogenous long waves of per capita output (y = Y/L). As the instability of labour force allocation prevents any analytical solution, we proceed with a sensitivity analysis, simulating the long waves, testing the robustness of the presented model and understanding how the exogenous socioeconomic characteristics affect the economy. (In the following figures, we depict the evolution of the growth rate of per capita income g_y and that of the probability of having a paradigm shift, ε.)

Before we discuss the following simulations in detail, it will be useful to recall the main aspects of the presented framework . The described economy has three sectors: the final good sector (Y) with perfectly competitive producers, the intermediate capital-goods sector (x) consisting of monopolistic firms and finally the research sector (R) engaged in both, applied and basic research. Labour (L) evolves log-linearly with an exogenous, constant growth rate n. Each one decides whether to work in Y- or in R-sector, after comparing the utility she/he can achieve, U_Y and U_R. Note that utility is made out of nominal remuneration and expected reputation: U = U(w, Φ_E). So, any researcher needs to take another decision too, namely how much to be engaged in applied and basic research. The first results into new patents that can be sold to x-sector, ensuring her/his nominal remuneration. The second gives rise to new, revolutionary knowledge, rewarding the researcher simply by the reputation that she/he could get, as being one of the pioneers of human scientific heritage. Given the current price of new patents and the expected reputation, representative researcher allocates appropriately her/his effort to maximize attainable utility. This is apparently a crucial co-determinant of labour’s division in Y- or in R-sector.

Production in the final goods sector employs L_Y labour input and xA_t homogenous capital goods, where A_t is the number of currently existing applicable ideas. Final output is allocated to a share for the labourers, (1 − α)Υ, and another that compensates capital goods (αΥ). On the other hand, production function in x-sector is even simpler: based on the acquired patents, monopolistic firms transform one unit of capital into one unit of any different type of capital good. Solving their profit maximization, the monopolistic firms obtain the optimal mark-up price p_x and the constant marginal costs of producing x_i, namely the interest for using capital (r). Thereby we decompose further αY into α²Y, which is the amount of income that goes back to the capital owners, and α(1 − α)Y that refers to the sum of maximized profits attained by all monopolistic firms. At each moment (or in each period) capital-goods producing firms invest all of their attained profits, α(1 − α)Y, in order to buy the currently developed and supplied patents (dA/dt), in other words the outcome of applied research, where the dynamic synergy of SoS and FO modifies continuously the researchers’ productivity. Clearing the patent market provides the equilibrium price for any new patent p_A, which then defines the nominal remuneration of researchers, w_R. Notice that the sum of savings originated from the income of production workers, s(1 − α)Y, from researchers, s w R L R = s α ( 1 − α ) Y , and from capital owners, sα²Υ, gives total savings for the economy as a whole, sY, which in turn counteracts depreciations and increases the capital stock.

Figure 4 depicts the first simulation, where we check for the effects of saving rate. As s amplifies, capital accumulation is getting stronger, Y is positively affected and thereby also w_Y, which implies further higher L_Y/L. This provokes a slightly longer upward phase pushing the peak to a later time, yet, the intensity is not changing (the peak of the wave remains the same). Analogously, the probability for having a new Paradigm Shift (ε) is being reduced in any moment.¹³

Quite similar is the picture we get when we let ρ to take higher values (Figure 5), yet this time for different reasons. As ρ increases, the structure of utility function changes and favours the attainable utility of researchers, in contrast to the utility of workers that depends solely on the received wage and remains unaffected by any change.

The next figure (Figure 6) illustrates the sensitivity analysis for raising capital’s output elasticity (α). There are two effects: first, the intensity of the wave is being amplified. In other words, there is a clear positive effect on the growth rate g_y during the expansion phase; second, as α increases the peak arises earlier meaning that the duration of expansion phase becomes shorter. In other words, the waves skews positively. The same is obvious in the second diagram, as probability for a paradigm shift is higher throughout the cycle.

We move on to the impact of changes in m, the severity of FO-effect. The picture we get (Figure 7) confirms the previous discussion for the synergy of SoS and FO. Recall that for lower m, the curve depicting the evolution of overall productivity in applied research moves downwards and skews positively (Figure 1). This is exactly the case in g_y: as m decreases, the wave becomes smoother, while the peak moves leftwards and the duration of downturn phase increases. Obviously, for u, the intensity of SoS-effect, we get the opposite picture.

Finally, the effect of population’s growth rate is similar to that of α (Figure 8). Namely, a slightly increasing n generates shorter expansion phase and much more intense waves (higher peaks).

In the previous paragraphs we discussed a theoretical framework that generates endogenous cyclical evolution of the applied knowledge and therefore of economic activity, similar to the tradition of long wave innovation theories. In a way, we combine standard arguments with Kuhn’s tradition. Starting from a dynamically evolving synergy of Romer’s FO and SoS effects, we end up having three mechanisms that provoke cyclicality in the evolution of applied ideas: a direct impact through the productivity in applied research itself; an effect through the allocation of researcher’s effort; and finally, another one through the division of labour force in L_R and L_Y. Putting these together initiates long waves of per capita output (y).

The presented analysis builds upon both epistemological and micro-economic foundation and, contrarily to other contributions, generates smoothly evolving cyclical movements. We incorporate our innovative arguments in a framework similar to the standard models of log-linear growth. Thereby, we enable direct comparisons and we provide a theoretical framework for analysing the effects of various socioeconomic parameters and policy interventions.

The previous pages provide a straightforward justification for the appearance of long waves. Besides, the model we propose explains the sequential character of waves in a more consistent way compared to the existing literature. Recall that as we approach the limits provided by the current scientific paradigm, ε (the probability of having a new, path-breaking basic innovation) tends to one. Indeed, this paradigm shift will be stronger, the more delayed it will be. Notice again that this brings us back to the process described by Kuhn: as the basic knowledge of our society evolves, new areas of possible applications arise, waiting to be discovered. Nevertheless, as we exhaust the limited set of applications, given by the existing fundamental concepts (current Scientific Paradigm), anxiety accumulates gradually in the society. Sooner or later, this tension will be released, leading to new, revolutionary developments of our social knowledge, setting up a new period, where new, previously unthinkable applications can be developed. Moreover, the theoretical framework we present can be easily extended in order to determine endogenously the intensity of the new scientific revolution, as well as the probability of its occurrence in time, given the specific socioeconomic characteristics.

Zarotiadis, G. and Ozouni, E. (2017) Standing-on-Shoulder and Fishing-Out Synergies: A Model for Endogenous Long-Waves. Theoretical Economics Letters, 7, 2194-2212. https://doi.org/10.4236/tel.2017.77150