In the first part of our analysis, we estimate a stochastic cost frontier to evaluate the effectiveness of the reforms on banks cost efficiency, as well as its dynamics and determinants. This also provides us with an estimate of the marginal cost of loans, which is necessary for the second part of the analysis that focuses instead on the dynamics of competition. We adopt two separate, complementary approaches: the persistence of profits model (POP) and the Boone indicator. As mentioned in the introduction we do this for reasons of robustness (competition models can often lead to conflicting results) as well as completeness (the models allow for a different analysis of the dynamics of competition). The focus is on the loans market because it is the most important segment of the banking system in developing countries such as Ghana, and because the reforms were specifically targeted to address the challenges in this market. Our three models are explained below.
The stochastic cost frontier model
Given our research question we need a model that not only estimates efficiency and its changes over time, but also allows for its exogenous determinants. Our final specification, after a careful selection process, is Greene’s true fixed effects model with a heteroskedastic, exponentially distributed inefficiency. The true fixed effects specification allows to disentangle the time varying inefficiency component from the individual, time invariant fixed effects. The explicit modelling of heteroskedasticity allows the introduction of exogenous influences on the inefficiency distribution. Two things are worth underlying here: first, unlike in OLS, the presence of heteroskedasticity produces biased and not just inefficient estimators. Secondly, inefficiency estimates would also be biased in the presence of heteroskedasticity.Footnote 4 The model in its general specification reads as follows:
$$\ln {\text{TC}}_{it} = \ln {\text{TC}}(\ln x_{it} ;\,\beta ) + \varepsilon_{it}$$
(1)
$$u_{it} {\sim}E(\sigma_{uit})\,{\text{and}}\,\sigma_{uit} = \exp \left({z_{it};\,w_{u}} \right)$$
(2)
Equation (1) models the stochastic cost frontier with fixed effects, with a dependent variable total cost (TC), a series of independent variables x (output levels, input prices and other control variables) and a vector β of parameters to be estimated. Equation (1) has a composite error term εit = vit + uit given by the sum of statistical noise vit ~ N(0, σ2v) and inefficiency uit. Inefficiency is in turn modelled by Eq. (2) as an exponentially distributed variable with a heteroskedastic variance that depends on a set of covariates zit. Equations (1) and (2) are estimated simultaneously by MLDV.
In line with most of the applied literature, we adopt a translog flexible functional form and follow the intermediation approach in the definition of the inputs and outputs of banks production process [34]. Linearity in inputs prices and symmetry conditions are applied prior to estimation leading to the following final model specification:
$$\begin{aligned} \ln ({\text{TC}}_{it}^{*} ) & = \alpha_{i} + \beta_{0} EA_{it} + \beta_{1} \ln w_{1it}^{*} + \beta_{11} (\ln w_{1it}^{*} )^{2} \\ & \quad + \sum\limits_{r} {\gamma_{r} \ln y_{rit} + \sum\limits_{r} {\sum\limits_{s} {\gamma_{rs} \ln y_{r} \ln y_{s} } } } \\ & \quad + \sum\limits_{r} {\psi_{r} \ln y_{rit} \ln w_{it}^{*} } + \theta_{1} T + \theta_{11} T^{2} \\ & \quad + \eta_{1} \ln w_{1it}^{*} T + \sum\limits_{r} {\zeta_{r} T\ln y_{rit} + \tau_{1} {\text{DER}}_{t} } \\ & \quad + \tau_{2} {\text{DER}}_{t} T + \tau_{3} {\text{CRISIS}} + \varepsilon_{it} \\ \end{aligned}$$
(3)
$$\begin{aligned} \sigma_{uit} & = \exp (\delta_{0} + \delta_{1} {\text{ACTVR}}_{t} + \delta_{2} {\text{ENTRYR}}_{t} \\ & \quad + \delta_{3} {\text{CCR}}_{t} + \delta_{4} {\text{DOM}}_{i} + \delta_{5} {\text{REG}}_{i} \\ & \quad + \delta_{6} {\text{FOR}}_{i} + \delta_{7} \ln {\text{TA}}_{it} + \delta_{8} {\text{CRISIS}}_{t} + e_{it} ) \\ \end{aligned}$$
(4)
In Eq. (3) TC* is the total cost of bank i at time t, given by the sum of interest and operating costs. Our three output variables are performing loans (y1, measured as the difference between total and non-performing loans), other earning assets (y2, given by investments in government securities and placements with other banks) and fee and commission income (y3), which is used as a proxy for off-balance sheet operations. Our input prices are the ratio of interest expense to loanable funds (the price of loanable funds, w1), and the ratio of operating costs to total assets (the unit price of an aggregate input of labour, physical capital and other expenditure, w2). The ratios TC* = TC/w2 and w1* = (w1/w2) are used to impose linear homogeneity in inputs prices. Technological change is modelled via a time trend T that enters the equation quadratically. The trend variable is also interacted with inputs and outputs to model non-neutral and scale changing technology changes, respectively. The equity-to-assets ratio (EA) is a measure of risk and at the same time an indication of the level of compliance with capital regulatory requirements. Finally, the impact of deregulation on the cost frontier itself (as opposed to inefficiency) is modelled via a deregulatory reform variable (DER) derived as the average of three individual deregulation policy variables modelled separately in the inefficiency function. DER is also interacted with the time trend variable to allow for the possible differential impact over time of deregulation over banks technology. For the determinants of inefficiency modelled by Eq. (4), we make the following choices. While deregulation as an aggregate is generally expected to improve efficiency, the individual effects of specific policies could be different and even conflicting, leading to opposite results. Ideally as in Eq. (4), we would like to model separately the deregulation policies via three indexes (ACTVR, ENTRYR and CCR).Footnote 5 ACTVR measures the level of openness of banking activities. The removal of activities restrictions should in theory have a positive effect on the efficiency levels of banks [35], but results can vary depending on the development of the banking sector and on the ability of managers at dealing with activities other than traditional intermediation [32]. ENTRYR measures restrictions to entry, and we expect it to have a positive effect on efficiency via the improvements in competition and/or the technological spillover effects if new banks bring in better technologies. On the other hand, new entrants, especially if technologically superior, could cherry pick the best customers with serious detrimental effects for local banks [36]. CCR measures the extent of credit controls through reserve requirements, whose removal is expected to benefit efficiency. The problem we encountered with specification (4) is that the indexes are very highly correlated, with levels well above 90%, making estimation very difficult and inference meaningless. We therefore use two alternative approaches. First we use the same aggregate variable DER used in (3), to capture the overall effect of deregulation on efficiency. Then, we use principal component analysis to try and disentangle the separate effects. More details are provided when discussing the results.
Three dummy variables distinguish private domestic (DOM), African regional (REG) and foreign non-African (FOR) ownership structures, with state ownership used as the base category. Regional African banks have expanded quite substantially in recent years, and an open question in recent literature is to evaluate how they compare to global, non-African foreign banks given their closer cultural and geographical proximity to the host country. Bank size is controlled for by the (log of) total assets, and finally, CRISIS is a dummy variable set equal to 1 for the years following the global financial crisis. Some basic descriptive statistics are presented in Table 2.
Table 2 Descriptive statistics for the key variables of the translog cost frontier In Table 2, the increasing level of costs and outputs confirms the increase in the size of the banking sector also seen in Table 1, while the lower input prices and the reduction in the ratio of total costs to total assets suggest an improvement in efficiency. The progressive implementation of the deregulatory reforms is also apparent in the increasing values of the regulatory indexes, while banks remain well capitalised. Equations (3) and (4) are estimated simultaneously via MLDV.Footnote 6
The POP model
The idea behind the POP model is that of markets contestability: extra profits do not persist over time if a market is competitive. Vice versa, the less competitive is a market, the longer it will take for any extra profits to be eroded and reach a long run, perfectly competitive equilibrium. This idea can be captured by a partial adjustment model, whose essence can be written as follows [38]:
$$(\ln \pi_{it} - \ln \pi_{it - 1} ) = a\,(\ln \pi * - \ln \pi_{it - 1} ) + bR(\ln \pi * - \ln \pi_{it - 1} ) + \varepsilon_{it}$$
(5)
In Eq. (5) π is the ratio of price to marginal cost, a measure of profitability. The equation models the adjustment of profitability towards its perfectly competitive long-run equilibrium π* where price equals marginal cost and thus the ratio is equal to 1 (and its natural log is 0). The parameter a is the speed of adjustment of this process, with 0 < a < 1 and larger values indicating a faster adjustment towards equilibrium. R is a dummy variable modelling the introduction of policy changes that could lead to a faster (b > 0) or slower (b < 0) adjustment.Rearranging Eq. (5), we get:
$$\ln \pi_{it} = \alpha \;\ln \pi_{it - 1} \; + \gamma R\ln \pi_{it - 1} \; + \varepsilon_{it}$$
(6)
In Eq. (6) we can see that α = 1 − a is the persistence parameter, and that γ = − b. We adopt this set-up in our final specification.
Unlike previous work, instead of simply aggregating all other exogenous macroeconomic factors (for instance, into time effects or GDP growth) we specifically introduce them into the equation. This allows us to clearly identify which, if any, might play a role in determining the level of profitability of the industry at each point in time, besides the interplay of competitive forces. We are particularly interested in this point because there are suggestions in the literature that macroeconomic and/or institutional characteristics might be a hurdle to the full working of reform packages in the developing world. Our final specification reads as follows:
$$\begin{aligned} \ln {\text{LOC}}_{it} & = \alpha \ln {\text{LOC}}_{i,t - 1} + \gamma R*\ln {\text{LOC}}_{i,t - 1} \\ & \quad + \kappa_{1} {\text{CRISIS}}_{t} + \kappa_{2} {\text{GDP}}_{t} + \kappa_{3} {\text{MPR}}_{t} \\ & \quad + \kappa_{4} {\text{TBR}}_{t} + \kappa_{5} {\text{FIS}}_{t} + \varepsilon_{it} \\ \end{aligned}$$
(7)
In Eq. (7) the dependent variable is the (log of the) loan overcharge of bank i at time t (LOCit). This is a measure of profitability on the market of loans (the focus of our competition analysis), and it is defined as the ratio of the price of loans to their marginal cost.Footnote 7 The policy dummy variable R takes a value of 1 for the years following the full implementation of the deregulation reforms (2007 onwards).Footnote 8 A non-significant γ will indicate no change in the competitive conditions following the reforms. A positive and significant γ will reflect a reduction in competition and vice versa. The possible impact of macroeconomic policies is captured by the real monetary policy rate (MPR), the real treasury bill rate (TBR) and the fiscal balance-to-GDP ratio (FIS). The real growth rate of GDP aggregates all other remaining factors, and the dummy variable CRISIS captures the years following the financial crisis. Given its dynamic panel structure the model is estimated using the Arellano–Bond GMM two-step estimator, backed up for robustness checks by the Arellano–Bover. Our primary focus is the result on the persistence parameters α and γ. The macroeconomic and industry-specific variables provide further insight into the determination of the loan overcharge and hence other determinants of competition.
The Boone indicator of competition
To increase the robustness of the results and to track more in detail the dynamics of competition over time, we also estimate the Boone indicator. The framework of analysis of the Boone model is a Cournot–Nash static oligopoly model of firms with different marginal costs. The key idea is to measure the competitive environment by examining the extent to which relatively more efficient firms are able to gain market share or increase profits at the expense of less efficient firms (the so-called reallocation process) [39, 40]. The higher the intensity of competition, the greater the reallocation of market shares from inefficient to more efficient firms, and vice versa. The model accordingly examines the relationship between performance and efficiency to infer competitiveness. In the applications of this model, the former is generally measured as profitability or market share, and the latter as marginal costs.Footnote 9 We follow Van Leuvensteijn et al. [41] and specify our estimable Boone model as follows:
$$\ln {\text{MS}}_{it} = \alpha + \sum\limits_{t = 1}^{T} {\beta_{t} D_{t} \ln {\text{MC}}_{it} } + \varepsilon_{it}$$
(8)
In Eq. (8), MSit is the market share of loans of bank i in year t and MCit is the marginal cost of loans [as estimated from Eq. (3)]. Dt is a vector of T year-specific dummy variables to allow the Boone indicator to vary over time; competition and its yearly evolution are measured by the resulting vector of parameters βt. A priori, β is expected to be negative due to the inverse relationship between marginal cost and loan market share. There is no threshold of reference for the Boone indicator, but the higher the absolute value of β, the greater the intensity of competition.
Due to the possible endogeneity of MC, Eq. (8) is estimated using a GMM-IV estimator, using lagged values of MC as instruments. A simpler 2SLS estimator is also used for robustness comparisons, as is a simple fixed effects estimator. As we will see, despite the endogeneity issue, the resulting pattern of the coefficients is the same in all 3 specifications, hence further supporting our final conclusions.
Our data are an unbalanced panel dataset of 25 banks observed over 15 years (2000–2014) for a total of 321 observations. Bank-level data were compiled from audited financial statements of banks. Macroeconomic data are obtained from the Bank of Ghana annual reports and the IMF’s World Economic Outlook database. All the bank-level data were adjusted to real values using the GDP deflator with 2006 as the base year.