Bancassurance and Scale Economies: Evidence from Italy

Abstract

Integration between banks and insurers is a widely investigated trend in financial markets. Despite heterogeneity of bancassurance across countries, the financial crisis is reshaping both intermediaries and customers’ demand. Although previous research provides evidence of economies of scale in bancassurance, we add to this literature by investigating differences due to alternative ownership models over an extended period (1998–2012) and testing for the effects of the financial crisis through a translog cost function. We focus on the Italian market, where bancassurance plays a major role and all ownership models are present. We find that the cost function changed significantly after 2007 as new unexploited scale economies emerged, especially for independent insurers that showed earlier optimal returns to scale. More integrated groups, despite a remarkable difference in their trend for total costs, diverge in a similar fashion from independent insurers in terms of scale economies.

Appendix

Linear mixed effect models

In analysing panel data we rely on fixed effects if we assume that differences across individuals are characterised by differences of the constant term. However, multiple measurements for each individual, such as repeated observations over time, generally result in correlation of within-subject errors. Moreover, considerable variation among individuals in the number and timing of observations might often affect data. The resulting unbalanced data sets are typically not effectively analysed using a general multivariate model with unrestricted covariance structure.⁴² Instead, data of this form can be analysed using a variant of a two-stage model generally referred to as mixed-effects models. In this formulation the probability distribution for the multiple measurements has the same form for each individual, but parameters of that distribution are allowed to vary across individuals. The distribution of these parameters or random effects in the population constitutes the second stage of the model.⁴²

In our analysis we use a particular type of mixed-effect models considering only random intercepts for subjects and a constant slope with respect to the covariates. In this approach fixed effects describe patterns of change in the mean response over time in the population, while the random variables represent the individual’s deviation from the population mean intercept after the covariates have been accounted for. In order to consider variations among repeated observations of the same individual, data is clustered in groups composed by observations for individual (s) over time. The hierarchical notation is as follows:

with ɛ∼i.i.d. N(0, σ _ɛ ²I) and b∼i.i.d. N(0, Φ).

TC is the response vector that comprises the logarithm of the total costs, α is the vector for the general intercept, γ _t is the dummy for the time effect, Dψ includes the dummy matrix D and the coefficients vector ψ to be estimated in order to grasp the effect of ownership models, Xβ comprises the matrix X with the logarithms of the cost function variables and the vector of coefficient β to be estimated, Zb+ɛ is the stochastic part of the model which encompasses the stochastic error term ɛ _s , a random variable b _s and Z _s =1 _s to include only random intercept and constant slope. Finally, Φ is a positive definite symmetrical matrix independent of s.

The parameters have been estimated through the restricted maximum likelihood approach (REML) using the “nlme” package of R. For a literature review on estimates through maximum likelihood, see Harville.⁴⁵