# **V. Variations in the Use of Governance Structures**

In this section, we study associations between the governance structure of firms and their other behaviors or characteristics. This is an exploratory venture in using our methodology to understand the links between governance structures and the broader environment of the firm. We simply explore patterns in the data and do not attempt to isolate ceteris paribus, causal effects of single variables. The latter would need a separate paper in itself.

To illustrate the type of thought experiments explored here, consider firm size. We compare the pattern of governance structures used by small firms with that used by large firms. We show the resultant change in the choice of governance structures as a firm becomes large for any reason and then simultaneously goes through all other changes associated with the differences between small and large firms. In terms of the notation of Section III, we estimate π��Z�� one Z� at a time without considering why the Z� vary with _i_ .<sup>26</sup> By implementing steps 1 and 2 of the 3-step method outlined in Section III, one obtains estimated posterior probabilities of membership for each firm in each of the four governance structures. Then the most natural way of exploring the π��Z�� would be to regress these probabilities on each Z� of interest. However, Bolck, Croon, and Hagenaars (2004) showed that this naïve approach leads to systematic underestimation of the strength of associations. These authors developed a correction procedure to eliminate this bias. Vermunt (2010), Bakk, Tekle and Vermunt (2013), and Bakk, Oberski, and Vermunt (2014) extended the correction procedure, developing a maximum-likelihood method that produced consistent estimates of the parameters defining the π��. �. We apply their method in implementing our step-3 analysis.<sup>27</sup> With the richness of the WBES data and the complex origins of the governance structures used by firms, it is challenging to select a manageable set of covariates that are particularly germane. While some covariates are obviously crucial to examine, e.g. country or sector, others are less so, e.g. a firm's experience of corruption. Recognizing the exploratory nature of the exercise, we selected a set of variables that piqued our curiosity, without requiring a precise theory. Our interest is mainly in checking the validity of the estimated transactional governance structures by examining whether there are significant associations between governance choices and likely covariates. Table D.1 in Appendix D lists the likely covariates, together with summary statistics. For ease of exposition, the variables are organized in seven broad categories, also listed in this table.

We study the associations between the use of the four governance structures and each of the covariates, one covariate at a time. We report Wald _p_ -statistics in the second columns of Tables 4a and 4b. Each of these statistics are constructed to test the compound hypotheses that the

> <sup>26</sup> In addition to providing insights into the associations between governance structure and variables of interest, this section aims to illustrate how others can conduct their own analyses, exploring their favored Z�'s taken from the WBES or elsewhere.

> <sup>27</sup> Mike and Kiss (2017) also conduct an exploratory analysis of the determinants of class membership, but employ the one-step process discussed in Section III.4

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