the control group.<sup>5</sup> Broadly, the idea of Entropy Balancing here is to compare the productivity gap of firms exposed to power constraints with that of unexposed firms that are as similar as possible to the exposed firms. The average difference in productivity between the exposed firms and the ”closest” unexposed firms must then be due to the treatment, i.e. the exposure to the power constraints. In this sense, the empirical approach mimics a randomized experiment by balancing the treatment and control groups on the basis of observable characteristics.

By combining matching and regression analysis, Entropy Balancing has some advantages over other treatment effect estimators. A particularly important advantage over regression-based approaches (including DiD estimation) as well as propensity score-based matching methods is that Entropy Balancing is nonparametric in the sense that no empirical model for the outcome variable or selection into treatment needs to be specified. Moreover, unlike regression-based analyses, there is no multicollinearity, as the reweighting scheme orthogonalizes the covariates to the treatment variable. Furthermore, unlike other matching methods, Entropy Balancing ensures a high balance of covariates between treatment and control groups, even in small samples.

Then, by combining a reweighting scheme with regression analysis, Entropy Balancing allows us to control for both country fixed effects and year fixed effects in the second step of the matching approach, i.e. the regression analysis.<sup>6</sup> The inclusion of country fixed effects is particularly useful to account for the potential unobserved heterogeneity between firms from different countries and to control for time-invariant country-specific conditions that could lead to differences in the productivity gap between firms. Also, knowing that productivity varies with firm and economic characteristics (Syverson, 2011), we include a large set of control variables at the firm and country level.

Finally, as recalled by Chauvet and Ehrhart (2018), the statistical bias resulting from the attempt to measure the effect of macro variables on micro-units was underlined by Moulton (1990).<sup>7</sup> Therefore, as in Chauvet and Ehrhart (2018) and Bambe et al. (2022), the standard errors are clustered at the country level (as we have country level control variables such as economic growth, bank concentration, inflation, etc.).<sup>8</sup>

# **4.2 Data and variables**

In this analysis, we consider 31,406 manufacturing firms in 84 developing countries from 2006 to 2019, 30 of which are in Sub-Saharan Africa (AFR), 8 in East Asia and Pacific (EAP), 14 in Europe and Central Asia (ECA), 20 in Latin America and the Caribbean (LAC), 6 in the Middle East and North Africa (MNA), and 6 in South Asia (SAR).

## **4.2.1 Firm-level data**

We mainly use the World Bank Enterprise Survey (WBES) data in this analysis. The strata of the enterprise surveys are firm size, industry and geographical region within a country. The firm size levels are 5-19 (small), 20-99 (medium), and 100+ employees (large). It is important to note, however, that these surveys

> 5In the regression step, we additionally control for the covariates used in the first step. This is equivalent to including control variables in a randomized experiment to increase the efficiency of the estimation.

> 6We also include region and income group fixed effects in our econometric specification.

> 7Random disturbances in the correlated regression within the groupings that are used to merge the aggregate data with the micro data can lead to a downward bias in the ordinary least squares standard errors (Moulton, 1990).

> 8Clustering the standard errors at the industry level also yields similar results as the country level clustering (see robustness check in the subsection 5.3).

9