allocative wedges in the economy identified jointly from the firm-level data and the model’s equilibrium (Fattal-Jaef, 2022). While less informative than studying how a specific distortion within a class of distortion shapes informality and aggregate productivity, as is the case in most of the literature, our approach subjects the entire class of distortion to a higher hurdle, namely its ability to generate a missing middle in the size distribution.<sup>6</sup><sup>_,_7</sup>

# **3 Data**

## **Firm-Level Data in Sub-Saharan Africa**

The lack of suitable data constitutes one of the main challenges associated with testing the missing middle conjecture. Even though the information required for this type of exercise is extremely basic—the power of looking at the size distribution to assess broader macroeconomic patterns precisely lies in its simplicity and low data requirement—the availability of such information proves to be an extremely binding constraint in developing countries. Such data availability is particularly challenging for most Sub-Saharan African countries, where informality is larger. Additionally, in view of the pervasiveness of informal economic activities in these countries, it is necessary that revisiting the question of a missing middle should use census data of both formal and informal firms across the entire spectrum of sizes.

Fortunately, over recent years, a number of Sub-Saharan African countries have engaged in establishment censuses as part of wider programs aimed at informing economic policies. Crucially for our purpose, the census is by definition taken of all establishments, including unregistered ones, so the ensuing data is representative of the true size distribution. These censuses are typically nothing more than business registers and essentially include contact and location information, legal form, records of business registration, tax and other administrative data, type of economic activity, and the number of workers, which is the crucial element for our purpose.

For this analysis, we obtained establishment censuses from the statistical agencies of some selected Sub-Saharan African countries, namely Burkina Faso, Cameroon, Ghana, and Rwanda. The selection of these countries is primarily because their census datasets feature a number of characteristics that make them closer to the true size distribution. On the whole, these data are consistent with Lewis (1954) widely held view of developing economies as characterized by the coexistence of a few capital-intensive industries and a mass of inefficient businesses (”tiny islands of capitalist employment surrounded by a vast sea of subsistence workers”). Specifically, small establishments (fewer than ten workers) represent the overwhelming majority of the manufacturing sector in our datasets; for comparison, small businesses account for less than half the manufacturing establishments in

> 6 To fix ideas, idiosyncratic distortions are a class of distortions causing allocative inefficiency. Financial frictions are a specific distortion within this class. Similarly, business registration costs are a specific example within the class of entry barriers.

> 7 Alvarez and Ruane (2019) also consider idiosyncratic distortions alongside other specific frictions in the context of Mexico. In our model, however, these distortions are strongly increasing with the physical productivity of the firms, an elasticity which we estimate from the firm-level Ghanaian data. Moreover, the productivity elasticity of distortions interacts with the endogenous innovation decisions of firms, absent in their work. We show that endowing firms with an endogenous life-cycle constitutes an important mechanism through which distortions generate a missing middle in the distribution.

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