or equal to _ω_<sup>_′_</sup> . A fraction (1 _− δ_ ) [1 _− qt_ ( _ω_<sup>_′_</sup> + ∆)] of the mass of firms with productivity between _ω_<sup>_′_</sup> and ( _ω_<sup>_′_</sup> + ∆) survives the exit shock and jumps downward to have productivity less than or equal to _ω_<sup>_′_</sup> . There is also an inflow of new firms into this group, which is given by the mass of entrants, a fraction Γ ( _ω_<sup>_′_</sup> ) of which will feature productivity less than or equal to _ω_<sup>_′_</sup> . The endogenous exit will be driven by the mass of firms that transition downwards from the productivity cutoff, (1 _− δ_ ) _qt_ <u>(</u> _<u>ω</u>_ + ∆) _Mt_ <u>(</u> _<u>ω</u>_ + ∆).

# **6 Quantitative Analysis**

We turn now to the quantitative analysis of the role of entry barriers and idiosyncratic distortions in the formal sector in accounting for the extent of informal production and the shape of the size distribution. We first discuss the calibration strategy and then move on to quantifying the counterfactuals.

## **6.1 Calibration**

Our calibration strategy proceeds in two steps. First, we calibrate structural parameters in the model, such as those governing the elasticity of substitution, the entry costs, and the innovation cost function, to match salient macro and firm-level properties of the United States. Then, we estimate idiosyncratic distortions from Ghanaian firm-level data and feed alternative estimates of entry barriers from the World Bank’s Doing Business Indicators and from (Fattal-Jaef, 2022).

In the first step, we require the relative entry costs, _fe_ 1 and _fe_ 2, and the relative sector-wide productivity levels _A_ 1 and _A_ 2, to be consistent with an informal employment share of 8% in the U.S. and an average firm size in the U.S.’s formal and Ghana’s informal manufacturing sectors of 116 and 3.5 workers respectively.<sup>20</sup> The innovation cost function in the formal sector is parameterized to replicate the life-cycle growth and the employment share in the top 10 largest firms in the U.S. manufacturing sector. The growth and exit rate in the informal sector, in turn, are set to replicate the small share of employment accounted for by large firms in Ghana’s informal firms’ size distribution.

The elasticity of substitution between formal and informal goods is drawn from Bachas et al. (2020), while we adopt a standard value for the elasticity of substitution across varieties from the misallocation literature.

In the second step, we appeal to Ghana’s National Industrial Census of 2003 to calibrate the idiosyncratic distortions and the entry barriers. The National Industrial Census is an alternative database covering industrial production only for registered establishments with ten workers or more, providing rich balance sheet information with which to measure idiosyncratic distortions following the approach in (Hsieh & Klenow, 2009).<sup>21</sup> We follow (Fattal-Jaef, 2022) in measuring idiosyncratic distortions directly from the firm-level data and inferring the entry barrier so that the model’s average firm size for the Ghanaian equilibrium matches the average firm size in the formal-sector data. Given the idiosyncratic distortion

> 20 The average size in U.S. manufacturing is conditional on firms with 10 or more workers, to make it comparable with Ghana’s formal sector database

> 21 This is the database used by Cirera et al. (2019) to characterize misallocation in Sub-Saharan Africa.

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