Innovation, finance, and economic growth: an agent-based approach

Abstract

This paper extends the endogenous growth agent-based model in Fagiolo and Dosi (Struct Change Econ Dyn 14(3):237–273, 2003) to study the finance–growth nexus. We explore industries where firms produce a homogeneous good using existing technologies, perform R&D activities to introduce new techniques, and imitate the most productive practices. Unlike the original model, we assume that both exploration and imitation require resources provided by banks, which pool agent savings and finance new projects via loans. We find that banking activity has a positive impact on growth. However, excessive financialization can hamper growth. Indeed, we find a significant and robust inverted U-shaped relation between financial depth and growth. Overall, our results stress the fundamental (and still poorly understood) role played by innovation in the finance–growth nexus.

Additional analyses

In Appendix, we collect some additional analyses we made to check the robustness of our results.

First we investigate what happens when more “risk averse” explorers are considered. To do that, we assume that the amount of resources necessary to start an exploration is

$$\begin{aligned} (1+\theta )\,\frac{C_{i,t}}{\pi }\ge E^{\mathrm{ex}}_i, \end{aligned}$$

with $\theta \ge 0$ representing a safety buffer. That is, for precautionary motives an explorer requests more resources than those she expects to consume during the travel.

Figure 17 shows the results with different values of $\theta$. As one can notice, no significant difference emerges from the introduction of such safety mechanisms. This is due to the fact that the positive effect of lowering the risk of bankruptcy is counterbalanced by the negative effect of committing more resources to fewer explorations. This is confirmed by the expansion of financial depth. Indeed, banks end up financing less (but larger) projects; thus, when an innovative project fails, it has more severe consequences on the economy.

Fig. 17

Safety buffer for exploration. Left: $\theta =0$ (baseline). Mid: $\theta =0.1$. Right: $\theta =0.2$. Top: MC average of log GDP with a banking sector ($N_b=5$) and without ($N_b=0$). Bottom: MC average of $G_t^{10}$ for the different subsamples generated by the deciles of $\overline{\mathrm{FD}}^{10}_{t-10}$. Confidence bands are set as three standard errors away from Monte Carlo sample averages

Next, we consider the case in which production is possible also during imitation and exploration. To do that, we assume that in each period of sailing an agent is able to generate the amount of GDP she was producing during her last period as miner on the island she left. Figure 18 shows the comparison between our baseline setting and this new scenario. As expected production during navigation has a positive effect on growth, which becomes even more evident when a banking sector is present. Indeed, in this setting the imitation and exploration boosting provided by credit does not correspond anymore to a lack of accumulation. The relation between financial depth and growth is still inverted U shaped, and it is interesting to notice how the financial sectors shrink. Moreover, an expansion of finance produces a negative effect on growth relatively earlier. These are the consequences of larger accumulation of resources, which dynamically increases the risk of over-exploration.

Fig. 18

Production during imitation or exploration. Left: no production (baseline). Right: production during sailing equal to last production. Top: MC average of log GDP with a banking sector ($N_\mathrm{b}=5$) and without ($N_\mathrm{b}=0$). Bottom: MC average of $G_t^{10}$ for the different subsamples generated by the deciles of $\overline{\mathrm{FD}}^{10}_{t-10}$. Confidence bands are set as three standard errors away from Monte Carlo sample averages

In the previous setting, however, production during navigation implies that exploration and imitation activities are basically costless. In the baseline setting, instead, moving in the technological space entails two costs. Indeed, foregone production (an opportunity cost) should be added to the explicit cost of foregone consumption described in Sects. 3.3 and 3.4. Hence, we explore now some intermediate cases. Figure 19 compares the results obtained under the baseline setting with those one gets when firms are allowed to generate a share of their last production as miners to finance explicit exploration and imitation costs. More specifically, we assume that production during sailing finances half of the explicit navigation cost and we investigate what happens when such cost increases by 50% (mid panels) or remains as in the baseline (right panels). Thus, in the first case the total cost of sailing decreases by 25% of the baseline explicit cost in terms of foregone consumption, while in the second case the total cost decreases by 50% of the baseline explicit cost. As one can notice, our results are overall robust to these different specifications. Since in both cases the total cost is significantly reduced, exploration and imitation become cheaper than in the baseline and this has a positive effect on long-run growth. Moreover, in those cases firms need to borrow less resources and the financial sector shrinks. Thus, the negative effect of a large financial sector is reduced and the risk of observing credit fueled over-exploration decreases.

Fig. 19

Production during sailing and cost of exploration and imitation. Left: baseline. Mid: production covers half of the explicit navigation cost which increases by 50%. Right: production covers half of the baseline explicit navigation cost. Top: MC average of log GDP with a banking sector ($N_\mathrm{b}=5$) and without ($N_\mathrm{b}=0$). Bottom: MC average of $G_t^{10}$ for the different subsamples generated by the deciles of $\overline{\mathrm{FD}}^{10}_{t-10}$. Confidence bands are set as three standard errors away from Monte Carlo sample averages

Now we explore how our results change when the strength of cumulativeness in technical change weakens. As in the original FDM, cumulativeness plays an important role since it is at the core of the dynamic increasing returns process that drives self-sustained exponential growth. Indeed, as one can notice in Fig.  20, with lower values of $\phi$ growth declines and such reduction is more evident when a financial sector is active. This follows from the fact that, in this scenario, discovering a new technology is less rewarding and agents take more time to pay back their loans. The inverted U-shaped relation between finance and growth is robust to lower values of $\phi$, even if the negative effect of large financial depth seems to weaken. This is because larger exploration is needed when new technologies are only marginally more productive than old ones; thus, over-exploration becomes less likely.

Fig. 20

Strength of cumulative learning effect. Left: $\phi =0.2$. Mid: $\phi =0.3$. Right: $\phi =0.4$. Top: MC average of log GDP with a banking sector ($N_\mathrm{b}=5$) and without ($N_\mathrm{b}=0$). Bottom: MC average of $G_t^{10}$ for the different subsamples generated by the deciles of $\overline{\mathrm{FD}}^{10}_{t-10}$. Confidence bands are set as three standard errors away from Monte Carlo sample averages

Then, we analyze how our results change when imitators move faster in the technological space. Thus, adopting an already existing technology, as well as having the relevant advantages of being deterministic and moving through the shortest path, has also the advantage of a reduced time for implementation and hence a lower cost. As one can notice in Fig. 21, favoring imitation implies higher growth and such effect becomes even stronger when a financial sector is active. This follows from a mitigation of the incidence of over-exploration: faster and cheaper adoption implies that, on average, firms devote more resources to imitation than to exploration, equilibrating the trade-off. This is confirmed by the form of the inverted U-shaped relation between financial depth and growth, whose maximum shifts to the right.

Fig. 21

Speed of imitators. Left: 1 step per period (baseline). Mid: 1.5 steps per period. Right: 2 steps per period. Top: MC average of log GDP with a banking sector ($N_\mathrm{b}=5$) and without ($N_\mathrm{b}=0$). Bottom: MC average of $G_t^{10}$ for the different subsamples generated by the deciles of $\overline{\mathrm{FD}}^{10}_{t-10}$. Confidence bands are set as three standard errors away from Monte Carlo sample averages

Fig. 22

Minimum capital requirement. Left: $\chi =0.5$. Mid: $\chi =2$. Right: $\chi =5$. Top: MC average of log GDP with a banking sector ($N_\mathrm{b}=5$) and without ($N_\mathrm{b}=0$). Bottom: MC average of $G_t^{10}$ for the different subsamples generated by the deciles of $\overline{\mathrm{FD}}^{10}_{t-10}$. Confidence bands are set as three standard errors away from Monte Carlo sample averages

In the end, we complement the analyses in Figs. 11 and 12 observing how our results vary when large values of minimum capital requirement are considered. As one can notice in Fig. 22, when $\chi$ increases too much growth is negatively affected. This is because, when banks have to restrain credit because of a large capital requirement, the economy suffers of a lack of imitation and exploration, especially in the first phases of development. This is also confirmed by the fact that the relation between financial depth and growth becomes increasingly positive and steep, while over-exploration is a very rare event.