Financial liberalization and sectoral reallocation of capital in South Africa

Abstract

We examine the impact of financial reforms on efficient reallocation of capital within and between sectors in South Africa using firm-level panel data for the period 1991–2008. The measure of efficient allocation of capital is based on the Tobin’s Q. We find that financial reforms are associated with improvements in within-sector, but not between-sector allocation of capital. These results imply that for South Africa to unleash the potential for take-off that is often associated with reallocation of resources from the primitive to modern sectors, reforms that focus beyond the financial sector are necessary. While more research is necessary to determine what would fully constitute such additional reforms, our analysis shows that reforms that improve the quality of economic institutions may be a step in the right the direction.

Appendix: Measures of dispersion of Tobin’s Q and their decomposition

As discussed in Sect. 3 of the paper, our approach to studying Q-dispersion at the inter-sector vs intra-sector level is to look at a combination of two sectors, and analyze the dispersion of Q that arises due to dispersion “within” each sector of that particular two-sector combination, and that which occurs due to the dispersion “between” the two sectors. Our measures of dispersion are essentially measures of inequality, and as such their decomposition follows analogous measures of decomposition in the literature on inequality indices. For a detailed discussion of this literature, in addition to a more elaborate derivation of these measures of decomposition, see Shorrocks and Wan (2005). In the following discussion, we have closely followed the approach in that paper, applied in the context of the Tobin’s Q rather than income levels. We consider the decomposition of three of the four measures considered in Abiad et al. (2008), namely the mean log deviation, the Theil Index, and the coefficient of variation.²⁴

Since we consider four sectors—namely manufacturing (1), mining (2), retail (3) and services (4), we have six combinations to consider, which are {1,2}, {1,3}, {1,4}, {2,3}, {2,4} and {3,4}. Let these combinations be indexed by c, where c = {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}. Let firms in each sector combination be indexed by i, and let $n_c$ be the number of firms in sector combination c. As mentioned above, our first three measures of Q-dispersion for each of these sector combinations are special cases of the Generalized Entropy Index below:

$$\begin{aligned} E_c (\alpha )=\frac{1}{\alpha (\alpha -1)n_c }\left[ {\sum _{i=1}^{n_c } {\left\{ {\left( {\frac{\hat{{q}}_i^c }{\mu _c }} \right) ^{\alpha }-1} \right\} } } \right] ;\quad \alpha \ge 0; \end{aligned}$$

(10)

Here the adjusted Q for each firm in each subsector of the combination c is computed as in Eq. (7) in Sect. 3, and the above summation is over the pooled adjusted Qs of both sectors. The mean of this pooled set of adjusted Qs is given by $\mu _c$. We consider the cases $\alpha =0,\;1,\;2$, which respectively represent the mean log deviation, the Theil Index and half of the square of the coefficient of variation, specifically expressed as:

$$\begin{aligned} E_c (0)= & {} \frac{1}{n_c }\sum _{i=1}^{n_c } {\ln \left( {\frac{\mu _c }{\hat{{q}}_i^c }} \right) ;} \end{aligned}$$

(11)

$$\begin{aligned} E_c (1)= & {} \frac{1}{n_c }\sum _{i=1}^{n_c } {\frac{\hat{{q}}_i^c }{\mu _c }\ln \left( {\frac{\hat{{q}}_i^c }{\mu _c }} \right) ;} \end{aligned}$$

(12)

$$\begin{aligned} E_c (2)= & {} \frac{1}{2n_c \mu _c^2 }\sum _{i=1}^{n_c } {\left( {\hat{{q}}_i^c -\mu _c } \right) ^{2}}. \end{aligned}$$

(13)

We can analogously compute the above indices for each subsector within each combination c; for the notation it is simply a matter of switching c with s, where s represents the sectors 1, 2, 3, 4, and $\hbox {n}_{s}$ and $\mu _{s}$ the corresponding number of firms in sector and the sectoral mean respectively. Also, the corresponding measures of dispersion for the sectors are given by $E_s (\alpha )$where $s=1,2,3,4$ and $\alpha =0,1,2$.

Now consider the combination c={1,2}. The decomposition of the above measures of dispersion into “within” and “between” components for this combination is given by:

$$\begin{aligned} E_{\{1,2\}} (0)= & {} \frac{1}{n_{\{1,2\}} }\sum _{i=1}^{n_{\{1,2\}} } \ln \left( {\frac{\mu _{\{1,2\}} }{\hat{{q}}_i^{\{1,2\}} }} \right) \nonumber \\= & {} \sum _{s\in \{1,2\}} {\frac{n_s }{n_{\{1,2\}} }} E_s (0)+\sum _{s\in \{1,2\}} {\frac{n_s }{n_{\{1,2\}} }\ln \left( {\frac{\mu _{\{1,2\}} }{\mu _s }} \right) } ;\end{aligned}$$

(14)

$$\begin{aligned} E_{\{1,2\}} (1)= & {} \frac{1}{n_{\{1,2\}} }\sum _{i=1}^{n_{\{1,2\}} } \frac{\hat{{q}}_i^{\{1,2\}} }{\mu _{\{1,2\}} }\ln \left( {\frac{\hat{{q}}_i^{\{1,2\}} }{\mu _{\{1,2\}} }} \right) \nonumber \\= & {} \sum _{s\in \{1,2\}} {\left( {\frac{n_s }{n_{\{1,2\}} }} \right) \left( {\frac{\mu _s }{\mu _{\{1,2\}} }} \right) } E_s (1)+\sum _{s\in \{1,2\}} {\left( {\frac{n_s }{n_{\{1,2\}} }} \right) } \left( {\frac{\mu _s }{\mu _{\{1,2\}} }} \right) ; \end{aligned}$$

(15)

$$\begin{aligned} E_{\{1,2\}} (2)= & {} \frac{1}{2n_{\{1,2\}} \mu _{\{1,2\}}^2 }\sum _{i=1}^{n_{\{1,2\}} } \left( {\hat{{q}}_i^{\{1,2\}} -\mu _{\{1,2\}} } \right) ^{2}\nonumber \\= & {} \sum _{s\in \{1,2\}} {\left( {\frac{n_s \mu _s^2 }{n_{\{1,2\}} \mu _{\{1,2\}}^2 }} \right) } E_s (2)+\sum {\frac{n_s }{2n_{\{1,2\}} }\left[ {\left( {\frac{\mu _s }{\mu _{\{1,2\}} }} \right) ^{2}-1} \right] } . \end{aligned}$$

(16)

In the equations above, the two terms on the right-hand side following the second equality are the within and between components of the three measures discussed above. We can calculate the corresponding decompositions for the other sector combinations in an analogous manner. Note also that we can easily extract the sectoral contribution from the within-sector term, given the within-sector term is simply the weighted sum of the sectoral indices of dispersion. For example, consider the percentage contribution of sector 1 (denoted $\hbox {PC1}_{\{1, 2\}})$ to the within component of (15). This contribution would be expressed as:

$$\begin{aligned} PC1_{\{1,2\}} =\frac{\left( {\frac{n_1 }{n_{\{1,2\}} }} \right) \left( {\frac{\mu _1 }{\mu _{\{1,2\}} }} \right) E_1 (1)}{\sum _{s\in \{1,2\}} {\left( {\frac{n_s }{n_{\{1,2\}} }} \right) \left( {\frac{\mu _s }{\mu _{\{1,2\}} }} \right) } E_s (1)}. \end{aligned}$$