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Bank efficiency measures, M&A decision and heterogeneity

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Abstract

The empirical literature has obtained mixed results regarding the probability for more efficient banks to be bidders in merger and acquisitions (M&A) operations. From an econometric point of view, this might be attributed to an inaccurate control of unobserved bank heterogeneity that can bias parameter estimation severely. In this paper, we adequately control for unobserved heterogeneity through a finite mixture, random parameters logistic model, and we estimate the probability for a bank to be a bidder in an M&A depending on its ex-ante efficiency, therefore avoiding any parametric assumption on the distribution of the random effect. This leads to a likelihood function defined as the integral of the kernel density with respect to the mixing density, which has no analytical solution. For this reason, we approximate the integral with a finite sum of kernel densities, each one characterized by a different set of model parameters. We then obtain a set of non-overlapping clusters with matching values of ex-ante efficiency, and assign each bank to a cluster based on the estimated posterior probability of it being in that cluster. Moreover, in our analysis we use two different sets of measures of bank efficiency, obtained using parametric as well as semi-parametric techniques. Our results are based on a sample of 612 banks, from 34 countries, between 1991 and 2006. They show that, considering unobserved heterogeneity, cost efficiency has a major impact on the probability for a bank to bid in a cross-border M&A, but no effect in the case of domestic M&A.

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Notes

  1. Amel et al. (2004) and more recently De Young et al. (2009) provide in depth surveys of this literature.

  2. Although it must be recognized that Berger and Mester (1997), in their study of 6000 US banks over the period 1990–1995, consider different forms and estimates of the and profit efficiency, ranging from the Fourier-flexible specification to the distribution free approach, and show that different methodologies provide, on average, similar results.

  3. Other largely used distributions are the half-normal, the gamma and the exponential distribution.

  4. In addition, the cost stochastic frontier approach could violate the monotonicity and concavity constraints implied by economic theory, leading to wrong conclusions concerning efficiency levels (Feng and Serletis 2009).

  5. For example, if heterogeneity is attributed to country specific characteristics, stratification can be made according to the level of financial development, features of the regulatory framework or political and institutional differences. On the other hand, if it is based on bank characteristics, it is to be made according to size or specialization.

  6. For example, this would be the case if the type of financial services produced by each bank were used to estimate a bank’s cost function and also as a source of information to discriminate between bank types.

  7. In the fixed effect model, the time invariant inefficiency must include any other source of time invariant unobserved heterogeneity. In this case, the estimated model would be \(y_{it}=\alpha _0+ {\beta }^{\mathsf {T}}\mathbf {x}_{it}+\varepsilon _{it} -[{max}_{j}(a_j)-a_i]\), and the time invariant inefficiency would be captured by the estimated “residual” term \(u_{i}=[{max}_{j}(a_j)-a_i]\). If the time invariant term fully captures time invariant efficiency, it is not possible to identify unobserved heterogeneity (Greene 2004a, b). The intercept \(a_j\) “ab originae” captures all time invariant differences like country specific characteristics, and not only those directly related to bank efficiency. The identification problem still arises if we consider the “true” fixed (or random) effect model (Greene 2004a, 2008). In this case inefficiency can vary freely over time, while all time-invariant effects are measured by unobserved heterogeneity. However, some additional (out of sample) assumptions on the parametric distribution of \(a_j\) and on \(u_{it}\) are needed in this case; see Kotzian (2009) for a fully parametric specification of the models above.

  8. For a review of DEA estimation methods see, for example, Thanassoulis et al. (2008); for more recent developments of non-parametric methods applied to frontier models, see also Simar and Wilson (2008).

  9. While we only focus on cross-border M&A, part of the literature on this subject has stressed that banks should also enter foreign markets through greenfield investment (Claeys and Hainz 2014). However, cross-border M&A are by far the most common way in the financial industry to enter foreign markets: according to UNCTAD (2014), between 2003 and 2013, only 15.6 % of world foreign direct investment in the financial sector were greenfield investment.

  10. Unreported results, available upon request, broadly confirm our results also including these countries.

  11. The value of \(\Lambda\) using a parametric approach is 61.75 (with a \(std.err=14.88\) and a p vaue = 0.000); and \(\sigma (u)\) is 8.21, with a p value = 0.000.

  12. In particular, according to the the latent efficiency measure, commercial, savings and investment banks are more efficient: using the parametric estimation technique, cost efficiency is higher for Medium and Long Term Credit Banks, for Retail and for Savings; using cost to income the most efficient banks appear to be cooperative and investment banks.

  13. As an example, in unreported analysis available upon request, we have found that the conditional probability that a domestic bidder at time t bids also at time \(t+1\) is 0.64.

  14. Since the Heritage foundation does not provide details on the construction of the Index of Financial Freedom, we could not introduce its raw constituent, as in the case of the Index of Economic Freedom.

  15. In the multinomial logit models, coefficients for both the estimated efficiency measures have been bootstrapped with 1000 replications; results in Table 8 confirm that this specification respects the assumption of the independence of irrelevant alternatives.

  16. The measure for the cost efficiency derived from the latent stochastic frontier model is:

    $$\begin{aligned} costeff_i=\sum ^K_k\{[min(u_i)/u_i]*\hat{\pi }_k\} \end{aligned}$$

    where \(\hat{pi}_k\) is the estimated probability for bank i to belong to cluster \(k=1,\dots ,K\) and \(u_i\) is the cost inefficiency estimated for bank i in that cluster.

  17. Note that the interpretation of the coefficients of the equation for the latent effects in Table 10 is by construction the opposite of that of Table 7.

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Authors and Affiliations

  1. Dipartimento di Economia e Finanza, Università di Roma “Tor Vergata”, Via Columbia 2, 00133, Rome, RM, Italy

    Stefano Caiazza & Giovanni Trovato

  2. Università degli Studi del Molise, Campobasso, Italy

    Alberto Franco Pozzolo

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  1. Stefano Caiazza
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  2. Alberto Franco Pozzolo
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  3. Giovanni Trovato
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Correspondence to Giovanni Trovato.

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Caiazza, S., Pozzolo, A.F. & Trovato, G. Bank efficiency measures, M&A decision and heterogeneity. J Prod Anal 46, 25–41 (2016). https://doi.org/10.1007/s11123-016-0470-6

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