Learning from Biodiversity: Is Diversity in Financial Ecosystems Important for Economic Growth and Stability?

Abstract

We propose a new measure of financial system diversity inspired from biodiversity research and explore its potential benefits for growth and stability. Our measure captures the relative contributions of various financial system constituents as well as their interrelationships. For a sample of 61 countries, we find that diversity in financial “ecosystems” differs widely across countries and over time. Our evidence shows that diversity has a significant growth enhancing effect that is robust to other financial development controls. Diversity also reduces growth volatility and mitigates the negative effect of systemic banking crises on growth. The effect is both statically and economically significant across various construction methodologies for the financial diversity index. Our results suggest that financial policies that promote diversity within the financial system could be a powerful tool to promote sustainable growth while potentially improving resilience and stability.

Appendices

Appendix 1: The Financial System Diversity Index

1.1 Appendix 1.1: Baseline

We provide an abridged version of the discussion of the index construction in the main text here and discuss some of the important properties of the index and the simplifying assumptions used in its practical implementation in the next two subsections. As mentioned before, our diversity index draws heavily from the work of Leinster and Cobbold (2012) in their measurement of species diversity. Our measure of financial system diversity of a particular country’s financial system is given by:

$$\begin{aligned} \begin{aligned} D_{z}(q, a_{i}^{'}, \psi _{ij})&=\left[ \sum _{i=1}^{S} a_{i}^{'} \left( \sum _{j=1}^{S} \psi _{ij} a_{j}^{'}\right) _{i}^{q-1} \right] ^{\frac{1}{1-q}}\\&= \left[ \sum _{i=1}^{S} a_{i}^{'} \left( \Psi a^{'} \right) _{i}^{q-1} \right] ^{\frac{1}{1-q}} \end{aligned} \end{aligned}$$

(3)

where $a_{it}$ is the measure of development of a given financial sector component i at time t. All of our financial sector components development measures are expressed as a percentage of GDP which implies that $a_{i}\ge 0$. We transform $a_{i}$ to $a_{i}^{'}$ such that $\sum a_{i}^{'}=1$. $\Psi = S \times S$ is our correlation matrix with individual elements $\psi _{ij}$ where $0 \le \psi _{ij} \le 1$ and for $i = j$, $\psi _{ij} = 1$. Following Leinster and Cobbold (2012), we choose a sensitivity parameter $0 \le q \le \infty$, which indicates the importance the researcher places on more obscure species, i.e., components of the financial system in our context.

Using the above formula, the higher the value of the diversity index $D_{z}$, the more diverse the financial system of the country. This index is a benchmark for calculating various types of financial system diversity measures by either changing the proxy for the relative level of development of the constituents of the system, expanding or reducing the number of constituents depending on the country context or improving on the measure of similarity (correlation) between constituents.

1.2 Appendix 1.2: Some Properties of the Diversity Index

Range: Since $0 \le \psi _{ij} \le 1$, the diversity measure $D_{z}$ ranges from 1 to S (the number of constituents of the financial sector). Therefore, depending on the number of constituents included in the set S for a given country’s financial system, our resulting diversity measure has an upper limit of S which is achieved if all constituents are equally developed but with zero linkages. On the other hand, if a particular financial system presents many constituents but with perfect linkages (in this case perfect positive correlations) then our measure of diversity will be closer to the lower limit of 1 even if all constituents are equally well developed. As the linkages are important for calculating the diversity index, a well-developed financial sector with many types of financial institutions and markets will have the highest diversity measure for the lowest levels of linkages (or similarities) between its components. Thus, we talk of effective measure of diversity since all countries lie in between this range of 1 to S.

Relationship with concentration: Notice that from Eq. (3), $\psi _{ij} a_{j}^{'}$ basically measures the relative development of each of the financial system components taking into account their relative linkages. Also notice that

$$\begin{aligned} \sum _{i} a_{i}^{'} \left( \sum _{j} \psi _{ij} a_{j}^{'}\right) _{i} \end{aligned}$$

(4)

in Eq. (3) can be thought of as a measure of concentration of the various components of the measures of development of the financial system. For example, assume only one component (such as the banking sector) is particularly well developed while other financial system components are very small or underdeveloped, then Eq. (4) will be high which means our financial system is highly concentrated on one particular component. For simplicity if we assume $q=2$, then our diversity measure in that case is just the inverse of concentration measure. To illustrate this, assume the correlation matrix is equal to an identity matrix with elements $\psi _{ij} = 1$ for $i=j$ and zero otherwise. Applying this matrix and $q=2$ to the expression in Eq. (3), we get the following expression for the diversity index:

$$\begin{aligned} \left( \sum _{i} a_{i}^{'} \left( a_{i}^{' 2-1}\right) \right) ^\frac{1}{1-2} \end{aligned}$$

(5)

which is equivalent to the inverse of a Herfindahl–Hirschman Index (HHI) calculated as the sum of squares of the relative shares of each constituent.

1.3 Appendix 1.3: Practical Implementation

As mentioned before, we construct three different variations of the financial diversity index depending on what is included in the set of constituents S. To insure consistency in the data coverage across countries and over time, we use data from the World Bank’s Global Financial Development Database which provides the most detailed cross-country data for different components of the financial system. In the next discussion, and due to data limitation, we limit our coverage to a maximum of five constituents as per Table 7. Extending the index to cover other constituents (in the set S), is straightforward when data is available and can be constructed using the same index methodology.

Table 7 Constituents of the diversity index

To calculate the diversity index defined in Eq. (3), we need to specify three elements: (i) the components of the financial sector to be used (i.e., the set S), (ii) a measure of similarities/differences between these components (i.e., the correlation matrix $\Psi$) and (iii) the value of q to be used in computing the index.

On the first element, Table 7 shows the composition of the variables used in the calculation of the three variations of the financial diversity index proposed in this paper. These different components certainly do not capture the entirety of the financial sector but due to data limitation we settle on these components as a first step to explore the merits of financial system diversity. As data on different components of the financial sector become available for more countries and over longer time periods, the diversity index can be extended to include them.²³ Dz3 captures three broad components of the financial sector, i.e., the commercial banking sector, the nonbank financial institutions sector and the stock market. By excluding the bond market, this measure allows us to cover more countries (the largest sample of 61 countries) and capture the importance of diversity between two broad categories of financial institutions in addition to the stock market, thus covering both debt and equity financing in the economy. Dz4 extends the previous index to cover the domestic private bond market as an additional component of the financial sector while Dz5 includes both domestic private and public bonds as additional financial sector components.

The second critical element in calculating the index is establishing how to obtain the correlation matrix from the data on the selected components. There are several ways to calculate the correlation matrix. In order to maximize the use of available information on how the different constituents of the financial sector evolve relative to each other, we calculate, for each country, the correlation matrix by using all the data from 1990 to 2020 to calculate a “static” correlation matrix. This represents the long-run structural relationship that exists among the different components of the financial system for each country. In a different version of the index, we also calculate 10-year rolling correlation matrix for each country. This enables us to capture the evolution of the financial system of each country over time. However, the small nature of the sample size using a 10-year window means that the correlations are not precisely estimated, leading to values of the diversity index that are generally more volatile. We show the decomposition of this variation of the index for select countries in Fig. 10 in Appendix 3.

To deal with negative correlations, a rescaling of the coefficients to the range of [0,1] is necessary and allows us to calculate an “effective diversity” measure as defined in Leinster and Cobbold (2012) which should be less than or equal to S (S = # species), the latter being a naïve diversity metric as mentioned above. We follow the suggestion of Leinster and Cobbold (2012) using the following transformation which ensures that all similarity coefficients fall on a spectrum between the extremes of 0 (totally dissimilar) and 1 (identical).

$$\begin{aligned} \psi _{ij} = exp(-ud_{ij}) \end{aligned}$$

(6)

This is essentially the exponential decay function, where higher distances $d_{ij}$ (in our case lower correlations) lead to smaller values of $\psi _{ij}$ (closer to 0). We consider as distance the difference between the actual correlation of two assets and a perfect correlation of 1, i.e., $d_{ij}$ = $(1-correlation_{ij})$. The rate of decay is controlled by the parameter u. The higher the u, the closer the negative values are to zero when applying the transformation. However, this also reduces the positive correlations compared to their original values, resulting in a higher diversity index. Also, higher values of u lead to higher diversity measures for all countries but the pattern remains the same and the ranking of countries is mostly unchanged. In our main index specification in the paper, we use a value of $u=2$ which provides a good balance while reflecting the relative distances of each correlation coefficient from the perfect value of 1 (total similarity).²⁴ In another version of the index we truncate negative correlation to zero. This preserves the actual values of positive correlations while assuming all negative correlations as reflecting total dissimilarity (assigned a value of 0). This treatment of negative correlations represents the lower bound for the financial constituents that are negatively correlated and enables the index to be bounded for ease of interpretation.

As pointed out earlier, q is the smoothing parameter and the choice of its value in the calculation of the diversity index depends on the importance the researcher places on more obscure (i.e., smaller) components of the financial system. We posit that different components of the financial system perform different but complimentary and potentially equally important functions in the overall development of the financial system. In our baseline index, we use a value of $q=2$ indicating that we value the development of the different components of the financial sector as equally important for the overall functioning of the financial system. For robustness, we also use different values of q.²⁵

Appendix 2: Variable Definitions and Sources

See Table 8.

Table 8 Variable definitions

Appendix 3: Financial Diversity vs Other Measures of Financial Development

See Tables 9, 10 and Figs. 6, 7, 8, 9 and 10.

Fig. 6

Diversity Index (Dz3) vs Private Credit

Fig. 7

Diversity Index (Dz3) vs Financial Development Index

Fig. 8

Diversity Index (Dz5) vs Private Credit

Fig. 9

Diversity Index (Dz5) vs Financial Development Index

Table 9 Correlation table

Table 10 Correlation table: with a_prime

Fig. 10

Decomposing Financial Diversity (Dz4): Actual vs Potential (using rolling correlation matrix). This figure shows the decomposition of our diversity index into the contribution of the correlation matrix and the relative abundance. The blue dot indicates the actual diversity index of the country, the red dot represents diversity of the country assuming zero correlation among different financial sector constituents (applying an identity matrix) and the green dot represents the diversity index based on actual rolling correlation but assuming equal relative abundance of each financial constituent. Diversity is calculated using $q=2$ and the decay function to transform the correlation matrix. The correlation matrix is calculated on a 10-year rolling basis (for the blue and green dots)

Appendix 4: Additional Results—Diversity and Growth

1. Financial Diversity and Growth—Index using q=4

See Tables 11 and 12.

Table 11 Systems GMM regression results: Dz3

Table 12 Systems GMM regression results: Dz4

2. Financial Diversity and Growth–Index with correlation of relative importance of constituents (ai-prime)

See Tables 13 and 14.

Table 13 Systems GMM regression results: Dz3

Table 14 Systems GMM regression results: Dz4

3. Financial Diversity and Growth–Index using censored correlation matrix

See Tables 15 and 16.

Table 15 Systems GMM regression results: Dz3_n0

Table 16 Systems GMM regression results: Dz4_n0

Appendix 5: Additional Results: Diversity and Growth Volatility

See Tables 17 and 18.

Table 17 Systems GMM regression results: Dz3_n0

Table 18 Systems GMM Regression Results: Dz4_n0

Appendix 6: Additional Results: Advanced vs Emerging

1. Financial Diversity and Growth

See Tables 19 and 20.

Table 19 Systems GMM regression results: Dz3

Table 20 Systems GMM Regression Results: Dz4

2. Financial Diversity and Growth Volatility

See Tables 21 and 22.

Table 21 Systems GMM regression results: Dz3

Table 22 Systems GMM regression results: Dz4