model that relates each size share on key moments of the firm size distribution. The idea is to get an empirical source to predict the share of micro, small, medium and large firms based on just a few moments of the firm size distribution, reducing notably the data requirements.

The strategy also helps with the harmonization of the resulting dataset. It is not uncommon that countries have their own size shares, corresponding to idiosyncratic interests. While that could be relevant for the country itself, it prevents comparability. Our approach defines one set of thresholds that is applicable to all countries. To further leverage information from the WBES, we define the same size thresholds at 5, 20 and 100 employees.

This also follows the suggestion in Li and Rama (2015) that correcting the biases arising from the exclusion or under-representation of micro- and small firms in enterprise surveys is necessary, using household and labor force surveys to re-calibrate the firm size distribution.

The first goal is to map the relationship between the shape of the distribution and each size proportion through these four moments. Ideally, we would observe several firm size distributions of different shapes that will inform a statistical model that connects size shares and the shape of the firm size distribution. However, we have only 5 countries with microdata that allow this: Burkina . Faso (2016), Cameroon (2009), Ghana (2014) and Rwanda (2014, 2017 and 2020) and Kenya (2017)<sup>8</sup> To increase the number of distributions, we can observe, for which we can derive key moments and firm size shares, we break each country’s microdata into age groups from 0 to 61 to create more distributions with different shapes. This leaves us with 62 firm size distributions by country, totaling 434 distributions from which we can extract size shares and information on the shape of the distribution.

We compute the four size proportions from each firm size distribution and the mean, p25, p50, p75, and p90. We have 434 observations to elucidate their relationship to the firms’ size shape accounted for by these four moments. In practice, this implies estimating<sup>9</sup> the following regression for each of the four size proportions: where _zki_ is the proportion _k_ = _{micro_ , _small_ , _medium_ , _large}_ coming from the firm size distribution of all firms aged _i_ = _{_ 0, ..., 61 _}_ . The algorithm uses the estimated _β_ s to predict all remaining countries based on the four moments we reconstruct in the following step.

It is important to estimate equation 1 using the information of several distributions of different shapes so the _β_ s carry the precise connection between the moments and the size shares. Figure 3 shows the correlation between the actual size shares and the predicted ones in every age group. The model produces accurate estimates of the size shares based on these five moments, mean, p25, p50, p75, and p90.

The next step consists of obtaining the five moments for every country so we can use the _β_ s from equation 1 to predict the size shares. For this step, we rely on ILO and WBES data. With ILO data, it is possible to recover at least the nationwide average firm size for every country

> 8Results of this section, and the overall estimations are robust to excluding Kenya survey data and using only census data. Results available upon request.

> 9STATA implements the maximum likelihood estimator developed by Papke and Wooldridge (1996).

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