4.1. The data envelopment analysis approach to proxy firm productivity

By means of the DEA, we compute efficiency scores as a proxy for firm productivity. The DEA approach is a linear programming technique that envelops observed input-output vectors as tightly as possible (Ji and Lee, Reference Ji and Lee2010). The envelope or efficiency frontier, which is constituted by the most efficient firms, is the benchmark to which less efficient firms under the envelope are compared to; efficiency being broadly understood as the ratio of outputs to inputs. When the efficiency scores are depicted, the distance between a typical decision-making unit (DMU) and the envelope captures inefficiency, that is, by how much the output of the DMU needs to expand for a given level of input to allow the convergence of the DMU’s efficiency towards its peers on the envelope.

We make use of Banker et al.’s (Reference Banker, Charnes and Cooper1984) approach to compute the DEA scores. Unlike Charnes et al.’s (Reference Charnes, Cooper and Rhodes1978) model, which draws on constant returns to scale, Banker et al.’s (Reference Banker, Charnes and Cooper1984) approach assumes variable returns to scale (VRS), either increasing returns to scale or non-increasing returns to scale. While constant-returns-to-scale efficiency suggests independence of productivity ratios with respect to scale, variable-returns-to-scale efficiency is sensitive to scale. The assumption of constant returns holds only when the DMUs are operating at their optimal scale. Such an assumption appears questionable to impose in the context of Senegal, as firms are faced with either economies of scale or diseconomies of scale, which supports the VRS assumption adopted in the current study. Due to the underlying assumption of VRS, Banker et al.’s (Reference Banker, Charnes and Cooper1984) model has the merit that scale efficiency is not confounded with total technical efficiency (Coelli et al., Reference Coelli, Rao, O'Donnell and Battese2005). It decomposes total technical efficiency $(TE)$ obtained under constant returns to scale into pure technical efficiency $(PTE)$ and scale efficiency $(SE)$ (Xin-gang and Zhen, Reference Xin-Gang and Zhen2019), such that scale efficiency is equivalent to the ratio of total technical efficiency to pure technical efficiency, as indicated by:

(1)\begin{equation}TE = \,PTE \times SE.\end{equation}

This decomposition highlights two sources of inefficiency: pure inefficiency (i.e., poor management) and scale inefficiency (i.e., scale inappropriateness) (Seck et al., Reference Seck, Araar, Camara, Diallo, Diop and Fall2022). We compute the three efficiency scores and use pure technical efficiency, obtained under the VRS assumption, as the proxy for firm productivity. We deliberately opted for the input-oriented DEA model. Input-based models minimize inputs for a given level of output, while output-based models maximize output without requiring more of any of the observed inputs. Most of the Senegalese firms, more than half the firms in our dataset, operate in the service sector, where managers have more control over inputs than outputs. As in the public sector, where managers mostly try to minimize inputs, input-oriented models are most suited to extract efficiency scores for the service sector (Lee et al., Reference Lee, Lee and Kim2009). Additional details about the derivation of DEA are presented in Supplementary Appendix C.

4.2. Linking electricity unreliability to firm productivity

4.2.1. Association between electricity unreliability and firm productivity

In the multivariate analysis, we rely on the pure technical efficiency scores analysis from DEA as an outcome measure. The technical efficiency scores denoted by $PT{E_{irs}}$ for the $i$^th enterprise located in region $r$ and operating in sector $s$ are implemented in logarithmic terms. We regress them on different measures of power outages ${P_{irs}}$ (incidence, frequency and duration) and observable firm characteristics ${X_{irs}}$, including dummy variables for regional and sectoral differences. We set up the following empirical model:

(2)\begin{equation}PT{E_{irs}} = {{{\alpha }}_0} + {{{\alpha }}_1}{P_{irs}} + {{{\alpha }}_2}{'}{X_{irs}} + {\varepsilon _{irs}}.\end{equation}

We proxy electricity unreliability ${P_{irs}}$ with self-reported power outages, measured at the extensive and intensive margins. At the extensive margin, the measure is a binary variable taking a value of 1 if the enterprise experienced power outages in the fiscal year preceding the survey and 0 otherwise. At the intensive margin, electricity unreliability is measured by the frequency of power outages and the duration of each power cut in a typical month; the intensive measures are thus average measures at the firm level. The matrix ${X_{irs}}$ includes the age of the firm, the percentage of shares owned by foreigners, the percentage of shares owned by the state, the manager’s years of experience, exports as a share of sales, the current size of the enterprise, the enterprise size at inception, the provision of on-the-job training and the share of working capital from a bank. ${\varepsilon _{irs}}$ is the idiosyncratic error term; ${{{\alpha }}_1}$ is the parameter estimate of interest.

As a first approximation, we conduct a partial correlation analysis. We do not rely on the ordinary least square (OLS) estimator, which assumes a normal distribution and homoscedasticity of both the dependent variable and the error term, since these assumptions are not met by the data at hand; the estimated efficiency scores are censored, i.e., they are greater than zero and less than 100 per cent (Lee et al., Reference Lee, Lee and Kim2009). Therefore, we resort to the Tobit estimator to explore the determinants of the efficiency scores. This approach is in line with similar previous studies, including Ji and Lee (Reference Ji and Lee2010) and Lee et al. (Reference Lee, Lee and Kim2009). Yet, this partial correlation analysis does not account for the potential endogeneity of electricity services. Therefore, we further expand our analysis.

4.2.2. Effect of power unreliability on firm productivity

We resort to an IV approach to address the endogeneity of power outages. Extensive discussion about endogeneity of power outages is available in Supplementary Appendix D. The Lewbel two-stage least squares estimator (Lewbel IV-2SLS) is the most appropriate strategy in the absence of external instruments, when exclusion restrictions of possible external instruments are questionable or when external instruments are weak, as is the case here (Lewbel, Reference Lewbel2012). We construct the internal instruments in the following way. First, we regress our measure of power outage on the set of control variables employing a linear OLS model and recover the estimated residuals ${\hat{\epsilon} _{irs}} = {P_{irs}} - {X_{irs}}\hat \pi _1{'}$. We refer to this regression as the auxiliary regression. Second, we construct the heteroskedasticity-based instruments ( $I_{irs}^L$) as the product of the auxiliary equation residuals and a subset ${Z_{irs}}$ of the set of control variables ${X_{irs}}$ that is assumed to be exogenous and employed in mean-centred form; that is $I_{irs}^L = $( ${Z_{irs}} - \bar Z){\hat{\epsilon} _{irs}}$. The matrix ${Z_{irs}}$ includes the age of the firm, the percentage of shares owned by foreigners, the enterprise size at inception and regional dummies. The idea behind the approach is that if the error terms are heteroskedastic, then the squared residuals can be correlated with some variables in the model, making them valid instruments. In a third step, we implement the standard two-stage least-squares regression (2SLS), using $I_{irs}^L$ as instruments for the endogenous variable power outages while controlling for the other observable confounding factors collected in the matrix ${X_{irs}}$. Thus, in the first-stage, power outages ${P_{irs}}$ are regressed on $I_{irs}^L$ and ${X_{irs}}$, as follows:

\begin{equation*}{P_{irs}} = {\delta _0} + {X_{irs}}\delta _1{'} + I_{irs}^L\delta _2{'} + \,{\nu _{irs}},\end{equation*}

where ${\delta _0}$, $\delta _1^{\text{'}}$ and $\delta _2^{\text{'}}$ are the parameters to be estimated and ${\nu _{irs}}$ represents the remaining error term. In the second stage, firm productivity $PT{E_{irs}}$ is regressed on the fitted values from the first-stage regression ${\hat P_{irs}}$ and the matrix of control variables ${X_{irs}}$ as follows:

\begin{equation*}PT{E_{irs}} = {\beta _0} + {\beta _1}{\hat P_{irs}} + \beta _2{'}{X_{irs}} + {\omega _{irs}}.\end{equation*}

The parameter of interest is ${\beta _1}$. The model is estimated using the Stata command Ivreg2h by Baum and Schaffer (Reference Baum and Schaffer2012).

Lewbel (Reference Lewbel2012) highlights two identifying assumptions under which the constructed external instruments are valid: $({A_1})$ $COV\,\left( {{Z_{irs}},\,{\epsilon} _{irs}^2} \right) \ne 0,$ and $({A_2})$ $COV\,\left( {{Z_{irs}},\,\,{\varepsilon _{irs}}{{\epsilon} _{irs}}} \right) = 0$. Put differently, the constructed external instruments are correlated with the heteroskedastic errors obtained from the auxiliary regression $({A_1})$, but uncorrelated with the covariance of the error term from the auxiliary regression and the error term from the linear model as presented in Equation (2) $({A_2})$. Baum and Lewbel (Reference Baum and Lewbel2019) extensively discussed the three conditions that are sufficient to make these two key assumptions hold. First, ${\varepsilon _{irs}}$ and ${{\epsilon} _{irs}}$ must have a factor structure, with a common unobserved error term and idiosyncratic error terms that are mutually independent, conditional on the set of instruments. Second, the squared term of the common error component should not be correlated with the Lewbel-generated internal instruments (homoskedasticity). As a third condition, the set of internal instruments must be correlated with ${\epsilon} _{irs}^2$, setting the condition of heteroskedasticity of the specific component of the error term ${{\epsilon} _{irs}}$ relative to the instruments. While these three conditions are sufficient for identification, the two key identifying conditions can hold without satisfying all of them at the same time (Baum and Lewbel, Reference Baum and Lewbel2019). Drawing on assumption ${A_1}$ which requires ${\epsilon} _{irs}^2$ to be heteroskedastic with respect to the exogenous variables, it follows that the higher the heteroskedasticity the more relevant are the external instruments (Baum and Lewbel, Reference Baum and Lewbel2019). Therefore, assumption ${A_1}$ can be tested using standard heteroskedasticity tests and is reflected in the F-statistic for the constructed internal instruments in the first-stage regression (Courtemanche et al., Reference Courtemanche, Pinkston and Stewart2020). Assumption ${A_2}$, as presented above, is similar to the classic instrument validity assumption. It posits that the constructed instruments $\left( {{Z_{irs}} - \bar Z} \right){\hat {\epsilon} _{irs}}$ are uncorrelated with ${\varepsilon _{irs}}$ in Equation (2). Thus, ${A_2}$ can be tested using standard tests for over-identifying restrictions, an example being Hansen’s statistic (Baum and Lewbel, Reference Baum and Lewbel2019).

4.3. Testing for female underperformance

Next, we turn to testing the female-underperformance hypothesis. We start with simple descriptive statistics, conducting mean comparison tests by gender. Next, we implement a Tobit model in which pure technical scores are regressed on a gender indicator and some control variables. Significant coefficients associated with the gender indicator would highlight the existence of a gender-based productivity gap. We further use Combes et al.’s (Reference Combes, Duranton, Gobillon, Puga and Roux2012) approach to compare the productivity distribution of female and male firms by assessing dilation, truncation and shift parameters. A productivity distribution that is left-shifted, less dilated and left-truncated compared to another distribution would imply that the former distribution stems from less productive and homogeneous firms that are uncompetitive. In Supplementary Appendix E, we provide more details on the formal derivation of the comparison in distributions and define all involved parameters. We complement our descriptive analysis with the Blinder–Oaxaca decomposition (Blinder, Reference Blinder1973; Oaxaca, Reference Oaxaca1973). More details on the Blinder–Oaxaca framework are presented in Supplementary Appendix F. This framework permits the computation of the gendered productivity gap and allows us to link it to firms’ characteristics, including power outages. The Blinder–Oaxaca framework decomposes productivity into endowment and structural effects and explores their determinants. The decomposition has been extensively used in the literature to assess the agricultural productivity gap, wage differentials, labour productivity gaps and sectoral gaps (Islam et al., Reference Islam, Gaddis, Palacios López and Amin2020; Essers et al., Reference Essers, Megersa and Sanfilippo2021).

5.1. Linking power outages to firm productivity

We first present results from Tobit estimations in Table 1. The reported coefficients stem from different specifications of Equation (2). We allow for three different measures of power disruptions (incidence, duration, frequency) while controlling (or not) for confounding factors as mentioned at the bottom of each column. Every cell and associated standard error represents the result of one regression model. The coefficient associated with power outages measured at the extensive margin is negative and significant across all five models irrespective of the inclusion of control variables. Importantly, the addition of the control variables in the empirical specification does not influence the magnitude of the coefficient estimate associated with power outages. According to our most demanding model (column (5)), on average, the experience of a power outage is associated with a reduction of the efficiency score by 28.7 per cent ( ${e^{ - 0.338}} - 1)$.

Table 1.

Baseline partial correlation estimates derived from the Tobit model

Table 1 Long description

Baseline Tobit regressions estimate how several power-outage measures relate to firms’ logged efficiency scores across five model specifications. Outage incidence is consistently negative and similar in size across columns, ranging from minus 0.321 to minus 0.338, indicating lower efficiency when an outage occurs. Longer outages are also associated with lower efficiency: the minutes-per-outage coefficient ranges from minus 0.006 to minus 0.004. Higher monthly outage frequency is negative but smaller in magnitude, from minus 0.006 to minus 0.002. Transformed versions of duration and frequency are likewise negative, with transformed duration around minus 0.044 to minus 0.031 and transformed frequency around minus 0.075 to minus 0.058. Sample size is 420 in columns 1 and 2 and 362 in columns 3 to 5; controls are added in columns 3 to 5, region indicators appear in columns 2 and 5, and sector indicators appear in columns 2, 4, and 5. Standard errors are reported in parentheses and each outage measure is estimated in a separate model, so coefficients should be compared cautiously across rows.

Notes: Robust standard errors are in parentheses. Estimates are obtained with the Tobit estimator. The coefficient for each power outage variable in each cell is recovered from a different estimation. Arcsinh denotes the IHS transformation used to preserve zero observations. It is computed as Arcsinh (x) = $ln\left( {x + \sqrt {\left( {1 + {x^2}} \right)} } \right)$. For the sake of brevity, the coefficients associated with the control variables are not reported. The control variables included are the age of the firm, the percentage of shares owned by foreigners, the percentage of shares owned by the state, manager’s years of experience, exports as a share of sales, current size of the enterprise, enterprise size at inception, provision of on-the-job training and share of working capital from a bank.

Similarly, the coefficient associated with the duration of power outages, one of our measures at the intensive margin, shows a negative correlation with firm efficiency across models. Again, the coefficients associated with power outages remain stable independent of the composition of the included covariates. According to our most demanding model (column (5)), the unreliability of power evaluated at twice its standard deviation $2 \times 10.208{ }$ minutes (see Appendix Table A1), is associated with a drop of the efficiency score by 7.8 per cent $({e^{ - 0.004 \times 2 \times 10.208}} - 1)$.

The considerable difference between the estimated effects associated with power outages measured at the extensive and intensive margins, requires further consideration. We observe that the incidence of outages, that is exposure to power cuts, is coherently reported in the survey. This is expected since the recall period of a month is short enough and the question only asks for a simple Yes–No answer of an event that is perceived as annoying, and therefore likely to be remembered. Yet not all firms that report the experience of power outages similarly give an estimate of the typical duration. Since the firms were asked for the typical duration, their feedback is already an average and likely prone to error. Further note that the average duration across all firms of around 8 minutes seems rather at the lower end. Thus, we have to take the information about the typical duration as a guesstimate.

Empirically, we address the issue of missing duration information by replacing the missing data with the average duration across all other firms that have reported the incidence of power outages. Thus, we have to interpret the effect associated with the duration with a grain of salt. Based on these considerations, our findings indicate that the event of a power outage per se is harmful. We consider the coefficient associated with the event (extensive margin) to be the upper bound and the coefficient associated with the duration as the lower bound. We observe the same pattern for the frequency of power outages (Table 1, row 5), as it represents a count variable, and the respondents do not always give an indication of the typical frequency of outages per month.

Since we face a considerable number of zeros and thus a skewed distribution, we implement further robustness tests. To accommodate the zeros, we apply the inverse hyperbolic sine (IHS) transformation, which is widely used in the literature (McKenzie, Reference McKenzie2017; Bellemare and Wichman, Reference Bellemare and Wichman2020). Importantly, with the IHS transformation (see the relevant note below Table 1 for its mathematical expression), we do not have to resort to the random addition of a constant as with the logarithmic transformation (Ekwaru and Veugelers, Reference Ekwaru and Veugelers2018; Mullahy and Norton, Reference Mullahy and Norton2024). The estimated coefficients associated with the duration and frequency of power outages (Table 1) are statistically significant, and their magnitudes are larger compared to the initial estimates without transformation. However, as Bellemare and Wichman (Reference Bellemare and Wichman2020) highlight, caution must be taken when interpreting the results as elasticities. Therefore, we only conclude that the negative association between repeated and lasting power outages and firm productivity is supported.

5.2. Linking power outages to the gender-based productivity gap

We next turn to the results obtained with Lewbel’s (Reference Lewbel2012) approach. We consider these findings, which we present in Appendix Table A5 (first-stage) and Table 2 (second-stage), as our main results. Across tables, power outages are measured by incidence, duration and frequency in the first three columns, and by means of the IHS transformation of duration and frequency in columns (4) and (5), respectively. Table 2 indicates a strong correlation of some of the Lewbel-generated instruments with the power outage variables. Importantly, all internally created instruments taken together are jointly significant, as indicated by the F-statistic, suggesting the model fits the data. Specifically, across specifications, the F-statistic of the excluded instruments is greater than 10, suggesting the rejection of the null hypothesis that the instruments have no joint explanatory power. Therefore, the instruments are jointly relevant.

Table 2.

Second-stage regression results – Lewbel IV-2SLS

Table 2 Long description

Second-stage Lewbel IV-2SLS results relate logged efficiency scores to several measures of power outages across five model specifications. Outage occurrence is negatively associated with efficiency, with an estimated effect of minus 0.343 and a robust standard error of 0.045 in model 1. Outage duration per event shows a small negative estimate of minus 0.005 with a robust standard error of 0.003 in model 2, and monthly outage frequency is similarly small at minus 0.003 with a robust standard error of 0.003 in model 3. Using inverse hyperbolic sine transformed measures, duration has an estimate of minus 0.036 with a robust standard error of 0.029 in model 4, while frequency is more negative at minus 0.098 with a robust standard error of 0.027 in model 5. All models use 362 observations and include controls plus region and sector indicators; centered R-squared values range from about 0.195 to 0.285, highest in the outage-occurrence model. Hansen J test probabilities reported in parentheses range from about 0.129 to 0.559, suggesting no strong evidence against instrument validity at common thresholds, but results should still be interpreted as conditional on the IV assumptions and the included controls.

Notes: Robust standard errors are in parentheses, except for Hansen J statistics, which report the probability in parentheses. Estimates are obtained from the second stage of Lewbel’s (Reference Lewbel2012) IV approach. Arcsinh denotes the IHS transformation used to preserve zero observations. For the sake of brevity, the coefficients associated with the control variables are not reported. The relevant note below Table 1 provides detailed information about the control variables. These variables are equally shown in Table 2.

This is further confirmed by the under-identification test of Kleibergen and Paap (Reference Kleibergen and Paap2006), which assesses whether the model is identified, i.e., whether the excluded internal instruments are correlated with the endogenous regressor, and by the instrument weakness test developed by Cragg and Donald (Reference Cragg and Donald1993) and popularized by Stock and Yogo (Reference Stock, Yogo, Andrews and Stock2005). We reject under-identification and weak instruments. We also conduct the over-identification test of all instruments, which checks for the validity of the over-identifying restrictions (Hansen, Reference Hansen1982). The p-values associated with Hansen’s over-identification test are bigger than 15 per cent for the duration and frequency specification and greater than 10 per cent for the incidence specification, supporting the identification strategy.

Overall, the IV results are virtually identical to the partial correlation results from the Tobit model (compare with Table 1). Power outages measured at the extensive margin and their durations have a negative and significant effect on firm productivity (columns (1) and (2) of Table 2). On average, exposure to power outages reduces the efficiency score by 29 per cent and twice the standard deviation of the duration of a power outage of $2 \times 10.208{ }$ minutes (compare with Appendix Table A1) reduces the efficiency score by 10 per cent. These results further suggest that the partial correlation findings are downward biased. In turn, we do not identify a significant effect for the frequency of power outages.

However, we do find significant and negative effects on firm productivity when employing the IHS transformation to the frequency of power outages. This discrepancy between the raw data and the HIS-transformed variables may arise for several reasons. First, the IHS transformation reduces the influence of extreme values and compresses the scale of the variable, which can improve the model fit and uncover non-linear relationships. It may also help mitigate issues of heteroskedasticity or skewness in the original frequency data. Alternatively, the lack of significance in the untransformed model (column (3) of Table 2) is likely also influenced by noise and measurement error in the raw frequency data, as highlighted earlier, which the IHS transformation helps to smooth. These findings suggest that the relationship between outage frequency and productivity is likely non-linear and better captured with an IHS transformation. However, in line with Bellemare and Wichman (Reference Bellemare and Wichman2020), we abstain from directly interpreting the effects as elasticities (see Section 5.1). Overall, our finding that power disruptions have a deleterious effect on firm productivity is consistent with past findings by Moyo (Reference Moyo2012), Allcott et al. (Reference Allcott, Collard-Wexler and O'Connell2016), Cissokho (Reference Cissokho2019), Falentina and Resosudarmo (Reference Falentina and Resosudarmo2019) and Elliott et al. (Reference Elliott, Nguyen-Tien and Strobl2021).

We further use Lewbel’s IV approach to identify the gender-differentiated effects of power outages on firm performance. We achieve this by including an interaction effect of power disruptions with gender. Results are shown in column (1) of Table 3. The coefficient associated with power outages is negative and significant. Importantly, it remains robust to additional controls as introduced in the subsequent columns of Table 3. This result is consistent with the finding reported so far in Table 2 that exposure to power outages induces a significant drop in firm performance. Importantly, the interaction term between power outage and gender of the firm owner is associated with a negative and significant coefficient. No such result is found for the interaction term between the gender of the firm manager and exposure to power outages (column (2) of Table 3). Female-owned firms and male-owned firms are thus differently affected by power disruptions, with the productivity reducing effect being more pronounced for female-owned establishments. Our most demanding estimation result (column (7) of Table 3) suggests that the performance of female-owned firms is 34 per cent ( ${{\text{e}}^{ - 0.412}} - 1)$ lower, while the productivity of male-owned firms is only 26 per cent ${\text{(}}{{\text{e}}^{ - 0.304}} - 1)$ lower, in the context of power instability. We consider this finding as evidence that power outages are negatively associated with the gender-based productivity gap in the study area.

Table 3.

Power outages, gender and productivity – Lewbel IV-2SLS

Table 3 Long description

Regression results using Lewbel-style instrumental variables estimate how power outages relate to firms’ log efficiency scores across seven model specifications. The main power-outage coefficient is consistently negative in every column, ranging from about minus 0.30 to minus 0.34, with standard errors around 0.05, indicating a robust association with lower efficiency. Adding an interaction for female-owned firms yields an additional negative effect of roughly minus 0.09 to minus 0.12 in columns 1 and 5 to 7, suggesting larger losses for female-owned firms in those specifications. The interaction for female-managed firms is small and near zero in column 2, with a comparatively large standard error, offering little evidence of a distinct effect by female management. Triple interactions show mixed patterns: female-owned in manufacturing is negative in columns 3, 5, and 7 (about minus 0.01 to minus 0.10), while female-owned among medium and large firms is positive in columns 4, 6, and 7 (about plus 0.10 to plus 0.22) but imprecisely estimated. Sample sizes are about 359 to 362 observations, and model fit is similar across columns with R-squared near 0.28 to 0.29. All models include controls plus region and sector indicators, and the reported Hansen J probabilities are low (about 0.08 to 0.15), so results should be interpreted with the usual caution about instrument validity and specification sensitivity.

Notes: Robust standard errors are in parentheses, except for Hansen J statistics, which report the probability in parentheses. Estimates are obtained from the second stage of Lewbel’s (Reference Lewbel2012) IV approach. The outcome variable is the logarithm of efficiency scores. For the sake of brevity, the coefficients associated with the control variables are not reported. The relevant note below Table 1 provides detailed information about the control variables. These variables are equally shown in Table 2.

In columns (3)–(7) of Table 3, we further explore mechanisms underlying the differential effects of power outages across the gender of the establishment owner. We achieve this through triple interactions, interacting gender, exposure to power outage and possible testable mechanisms for which we have data, namely the size of the firm and sector of operation. We answer the following question: to what extent are power outages associated with firm productivity conditional on the gender and the size or sector of the firm? Our hypothesis is that female-owned firms may be more vulnerable to power outages because they are more likely to operate small businesses outside the manufacturing sector, where generator adoption is less common. However, our results show that none of the interaction terms is statistically significant. This suggests that neither the firm size nor the sectoral concentration of female-owned firms is driving the lower productivity resulting from power outages. While numerous mechanisms were highlighted in the literature, including sectoral concentration, firm size and constraints on time use (Islam et al., Reference Islam, Gaddis, Palacios López and Amin2020), our data do not support the first two theoretical mechanisms. Yet, this finding does not rule out these mechanisms, as our sample is small and we might lack the power to identify the effects precisely. Drawing on our knowledge of the Senegalese context, we hypothesize that the gender-differentiated effects of power outages are driven, at least in part, by women’s greater time constraints arising from the need to allocate their time between home production and market-based activities. Yet, we were not able to explore this constraint due to data limitations. In the Senegalese patriarchal society, almost all women of working age are culturally required to participate in the unpaid care economy, that is, housework and childcare (Bernard et al., Reference Bernard, Doss, Hidrobo, Hoel and Kieran2020). Therefore, electricity unreliability has the potential to exacerbate gender-based productivity differences by reducing women’s work hours, while increasing time for housework (Sedai et al., Reference Sedai, Vasudevan, Pena and Miller2021). Further investigation with a larger dataset and more detailed information is still required to confidently maintain the time-use hypothesis. For now, we have to defer it to future research.

5.3. Evidence of underperformance among Senegalese enterprises owned or managed by women

We now explore further the productivity gap using descriptive statistical tools and multivariate regressions. We first include gender in our firm productivity assessment in our basic partial regression framework. Results are reported in Appendix Tables A6 and A7. We find a consistent negative relationship between female-owned enterprises and productivity. The coefficient of −0.109 associated with the gender variable (Table A6, column (1)) implies an unconditional productivity gap of 0.11 in log points between female-owned enterprises and their male-owned counterparts, which is equivalent to 10 per cent ( ${e^{ - 0.11}} - 1)$. The coefficients in columns (2)–(7) of Table A6 further reinforce the productivity gap even after adding control variables and interaction terms. Similarly, the gender effect is also consistently negative in female-managed enterprises, albeit not significant in all specifications (Appendix Table A7). We attribute the lack of statistical significance to the very small sample of only 51 observations of female-managed firms.

We further inspect the interaction between gender and power outages. The coefficient associated with the interaction is negative and significant (Table A6, column (3)). This is similar to the results in Table 2, except that we do not account for the possible endogeneity of power outages in Table A6. Still, the result implies that among female-owned enterprises, those exposed to unexpected power outages are even less productive compared to their male-owned counterparts. We further find a negative and significant coefficient associated with the interaction of generator ownership and being a female owner (Table A6, column (4)). While Cole et al. (Reference Cole, Elliott, Occhiali and Strobl2018), Moyo (Reference Moyo2012) and Cissokho (Reference Cissokho2019) showed that ownership of a generator mitigates the deleterious effects of power disruptions, our findings for female-owned enterprises suggest that the ownership of backup power does not improve female-owned firms’ productivity in a significant way compared to their male-owned counterparts. The crowding-out effect of the additional costs from self-generating electricity on other productive investments may explain this result. Another possible reason might be that self-generated electricity is a poor substitute for on-grid electricity. Table A6 further shows a positive and significant coefficient for the interaction between gender and the initial size of the firm, indicating low productivity for small female-owned enterprises at inception. Next, we turn to the coefficient of the interaction of gender and the share of capital from a bank, which is equally positive and significant, suggesting that female-owned firms that have access to credit are way more productive compared to those with limited access to bank loans. Unlike Gui-diby et al. (Reference Gui-Diby, Pasali and Rodriguez-Wong2017) and Seck et al. (Reference Seck, Araar, Camara, Diallo, Diop and Fall2022), our findings suggest that alleviating the financial constraints of female-owned enterprises might increase their productivity. These findings are similar for female-managed enterprises (Appendix Table A7).

Next, we turn to the inspection of the male and female productivity distributions. First, we visually compare both across genders. Appendix Figures A3 and A4 present the productivity distributions across gender for firm owners and managers. The productivity distribution of male-owned enterprises exhibits a right shift compared to their female counterparts (Appendix Figure A3). This shift in the distribution reflects the relative underperformance of female-owned enterprises. Furthermore, the productivity distribution of female-owned firms is left-truncated and less spread out compared to the productivity distribution of male-owned enterprises. However, there seems to be no significant difference in the distributions of male- and female-managed enterprises, even though the productivity distribution of female-managed firms is left-truncated. Again, we largely attribute this result to the small number of observations for female-managed firms.

Appendix Table A8 reports the estimates of the shift, dilation and truncation parameters. The estimated value for the shift parameter, which is about −0.115, is negative and significant, supporting the notion of female underperformance. For women to have the same distribution as their male counterparts, their productivity distribution would have to shift rightward, implying that it needs to increase by 11 per cent ( ${e^{ - 0.115}} - 1)$. This productivity gap is consistent with the findings reported so far. The estimated dilation parameter is statistically significant and less than one, as expected. This suggests a high degree of homogeneity among female-owned firms, indicating that women are more likely to operate in less capital-intensive industries and at a smaller scale. In contrast to the shift and dilation parameters, the truncation parameter is not statistically significant, implying no evidence that female-owned enterprises disproportionately exit the market from the lower tail of the productivity distribution. Furthermore, we find no evidence of underperformance, homogeneity or exit among female-managed firms, as none of the estimated parameters is statistically significant. This result is equally consistent with the findings reported earlier.

Finally, we turn to the decomposition of the gender-related productivity gap. Appendix Table A9 shows the results of the Oaxaca–Blinder counterfactual decomposition. Power outages are measured at the extensive margin as the incidence data is least prone to error. We explore the productivity gap between female- and male-owned enterprises in columns (1)–(3), and we consider the gender of the manager in columns (4)–(6). Column (1) shows the overall productivity gap and its components, including the endowment and structural effects; columns (2) and (3) report their association with firm characteristics, including exposure to power outages.

We identify a significant productivity gap between female- and male-owned firms of the order of 0.116 log points, which corresponds to a gap of 11 per cent. This productivity gap is consistent with the one found in the regression analysis (Appendix Table A6) and Combes et al.’s quantile estimation approach (Appendix Table A8). Our estimated gender productivity gap is close to the ones reported in previous work by Bardasi et al. (Reference Bardasi, Sabarwal and Terrell2011), Islam et al. (Reference Islam, Gaddis, Palacios López and Amin2020) and Essers et al. (Reference Essers, Megersa and Sanfilippo2021). We further find a significant and positive coefficient associated with power outages (column (3)), suggesting that exposure to power outages is significantly associated with a larger productivity gap, driven by structural factors. This result is consistent with the differential effects of power outages observed across gender. In turn, we observe no evidence of a productivity gap between female- and male-managed enterprises, which is equally consistent with our earlier findings.