A Schumpeterian growth model on the effect of development banking on growth

Abstract

Research and Development activities are very credit constrained in several poor nations with weak institutions. To curb the financial barrier, governments apply development banking policies. A common one is the subsidization of private banks in order for them to increase the loans for Research and Development. This article analyzes the implication of this policy for economic growth, when it is financed with taxes on old successful entrepreneurs and, at the beginning, the financial market for research loans was completely depressed due to a moral hazard problem and the low quality of the institutions. I found that regardless of the magnitude of the tax rate, a minimum level of quality of the institutions is required for the achievement of any success. Interestingly, if there is a range of tax boosting productivity, it may be very tight and this points at the relevance of the proper design of the development banking policies. Finally, even if this policy can boost the technological level of a poor economy, it is not possible to achieve convergence with leading economies and any positive implication for the welfare of the entrepreneurs is not granted.

Appendices

Appendix A Situation where development banking is better than a direct subsidy to innovators

The government will prefer the policy that given a certain tax revenue, will determine larger resources devoted to research. If the banks receive the tax revenue, the investment in research is the one corresponding to the loan size in Eq. (24). If the resources are granted directly to the innovators, they just receive the tax revenue as in Sect. 4.2.1, which is $\mu _{t-1}{\overline{A}}_{t-1}\tau \varPhi$. Therefore, the government will prefer to grant the subsidy to the banks as long as,

$$\begin{aligned} \frac{{\overline{A}}_{t-1}\mu _{t-1}\beta \varPhi \tau }{\beta (1+d)-c\varPsi (1+\beta )}> {\overline{A}}_{t-1}\mu _{t-1}\tau \varPhi \end{aligned}$$

(A.1)

Which implies,

$$\begin{aligned} \frac{d\beta }{c(1+\beta )}< \varPsi \end{aligned}$$

(A.2)

Combining this with the incentive compatibility condition in Eq. (17), we get the definitive range for $\varPsi$ when there is lack of quality in the institutions and development banking is a better policy than the direct subsidization of the producer,

$$\begin{aligned} \frac{d\beta }{c(1+\beta )}< \varPsi <\frac{\beta (1+d)}{c(1+\beta )} \end{aligned}$$

(A.3)

This means that countries with the weakest institutions are better off granting the subsidies directly to the entrepreneurs.

Appendix B Calibration of the model for the case of Brazil

At first, it is important to explain the choice of Brazil. The Great Depression impacted severely the Brazilian economy through the collapse of coffee prices. At that time, the economy was very oriented to the production of that commodity (Furtado 2005). In consequence, there was an industrialization process supported by the governments in order to reduce that dependence. BNDES, which was created in 1952 to diversify the industry (Fausto 2004), has been the main lender to that sector for decades.

This bank also transfers funds to private banks in order for them to lend at low interest rates. Here, it is important to mention that the long-term loans and transfers of BNDES have lower interest rates than the short-term loans of the private banks. This reflects how heavily subsidized is the lending of BNDES to the productive sector.

Starting from the decade of 1950, the Brazilian economy achieved a remarkable transformation, and it diversified to the agroindustry and the manufacture. Here, it is important to mention that BNDES has financed several Brazilian industries which are intensive in high technology (like aeronautic, automotive and steel) since their creation. All these sectors have developed despite the unfavorable quality of the institutions in Brazil. For example, the country was number 106 out of 180 nations in the Corruption Perception ranking for 2019 (Transparency International 2020).

Therefore, Brazil presented low productivity at the beginning of the development process and it has achieved a significant technological level in a process including development banking support. All this in an environment of weak institutions. Here, we are not assuring a causal link between BNDES loans and the development of the financed industries. We just indicate that Brazil seems to fit the type of nation with weak institutions that we have represented in this paper.

All these elements have been considered in the determination of the values for most of parameters in Table 1. The value of $\beta$ is as in Acemoglu et al. (2008). Despite rampant inflation, during part of the period the interest rates were capped; and, as indexation strategies ameliorated the inflation risk, we set the risk-free interest rate to 12%. In concordance with the underdevelopment of the country at the beginning, we set very low $\mu _{t-1}$ and $a_{t-1}$. In addition, the cheating cost is 0.6. We assume that it corresponds to a middle level of quality of the institutions. The share of capital is set to 0.3 which is similar to other previous works and N is larger than in other studies as we take into account the large population of Brazil. A tax rate of 45% is higher than the actual tax on profits in Brazil, but in our model we only have tax on profits and, in Brazil, the total tax burden on companies surpass that number.

Table 1 List of parameter and variables and their values

The main outputs are shown in Table 2. As most relevant findings, the economy converges to a probability of success of 0.32 and a normalized productivity of 0.91. Although not reported, the set of parameters in Table 1, satisfies all the equations for the economies with weak institutions which succeed in the policy. The readers can easily verify this.

Table 2 Main outcomes for a economy with weak cheating cost which succeeded in the policy