of all firms ranked by productivity and sales, respectively. Table 12 shows the share of these informal firms, compared to formal firms, for those variables that are significantly associated with productivity and/or sales.<sup>23</sup> Importantly, the share of informal firms in the top productivity and sales deciles having good characteristics is substantial: 37 percent of top decile productivity firms (19 out of 51) and 25 percent of top decile sales firms (11 out of 44) are informal firms. The results are quite similar for the top decile of productivity and sales, reflecting the strong positive association in the Senegal micro-enterprise data between productivity and sales. Both in terms of the smallest absolute and relative (as a multiple of the lower group) differences in shares between informal and formal firms, the top 5 characteristics that are most similar include having electricity and using mobile phones to communicate with suppliers (almost all firms have these characteristics, making them a pre-requisite for being in the top decile of both productivity and sales), as well as using mobile money to pay suppliers (roughly a third of both informal and formal firms use this DT). The largest differences between informal and formal firms in the top decile are whether the firm had a loan, has supplier credit, and has a computer: the differences are in the order of 40-50 percentage points. This suggests, intriguingly, that it is possible to be in the top deciles of productivity and sales even without having access to these forms of financing: roughly 60% of formal firms have not had a loan, and 95% of informal firms have not had a loan, though they are still able to be top performers.<sup>24</sup> Using inventory control/POS software is an important attribute of formal firms in the top productivity and sales decile, with just over one-half of firms using this management tool. In contrast, only one informal firm uses this type of DT: this is both indicative of the small number of informal firms that use computers and smartphones, and suggestive of the potential for further productivity and sales improvements if appropriate applications of this type were used more widely by informal enterprises.

# **_5.3 Cluster-level associations based on combined performance outcomes_**

This sub-section broadens the exploration of the extent to which informal firms are “similar” to good formal firms by creating three clusters of high-, medium-, and low-performance firms, based on a datadriven combination of the four performance variables (productivity, sales, customers abroad, and employment). It then examines the share of informal firms in the top-performance cluster relative to formal firms and relative to the other clusters.

The clustering procedure creates groups that minimize within-group variation according to a specific measure of distance.<sup>25</sup> The results suggest that 3 clusters adequately describe the data.<sup>26</sup>

> 23 The only characteristic variables not included, relative to Table 6, are using internet to look for suppliers, to understand customers, and for e-commerce, as these were only statistically significantly associated with exporting.

> 24 The mean labor productivity of firms without a loan is 190,000 cedis for informal firms and 524,000 cedis for formal firms. The corresponding values for firms that did have a loan are 606,000 and 1,524,000 cedis, respectively.

> 25 The k-medians command of Stata was used to create 2 to 7 clusters using the Gower distance measure. Because the result of this clustering procedure is not unique, for each number of clusters the process was run 200 times and for each run the CalinskiHarabasz pseudo-F index was calculated. This index provides a measure of the ratio of the between to the within sum of squares so that higher values of the index reflect that the sum of squares between clusters is maximized while the sum of squares within clusters is minimized. Higher values thereby reflect more distinct cluster structures. The highest 4 values of the index were attained when the number of clusters was specified as 3. Moreover, in the 100 runs with the highest value of the index, 59 runs had 3 clusters.

> 26 We also tried using the k-means command following a similar procedure. In that case the top and most frequent index values were reached with four groups. The difference is due to the existence of a few observations with large numbers of full-time employees, and the fact that k-means is sensitive to these extreme values relative to k-medians. Both classifications make sense, depending on the objectives of the analysis. In this classification, there are two “high productivity” groups, one group of 6 (high employment) firms, all of them formal, and a group of 46 firms with 18 formal. The medium labor productivity group consists of

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