The GEGI runs from 0% to 100%, with a bigger number indicating a larger gender employment gap. −0 • If there is no female employment at all ( ), then × 100% = 100% (the largest +0 LLMM possible gender gap). LLFF = 0, LLMM = LL GGEEGGII= LLMM • If there is equal employment across females and males, then (no gender gap at all). The GEGI can be calculated directly from employment data, measured as the number of people (e.g., is MM FF LL = LL GGEEGGII= 0 the number of males employed, and is the number of females employed and is total number of people MM LL employed). But often labor market data are reported as the working-age employment-to-population ratio for each FF LL LL gender, which I denote with a lower case: and . In that case, Equation 1 can be rearranged as Equation 2, which is equivalent, and is used in the empirical application later in this paper.<sup>4</sup> MM MM MM FF FF FF EE = LL /PPE EE = LL /PPE (2) B B G G E E E × 100% llMM−llFF Note that the GEGI formula assumes an equal population of men and women, which holds in most BB G EEG EE GGBBEE IIG GGII (GGEEGGII) ≡ llMM+LLFF countries. Appendix 4 considers an adjusted basic GEGI that should be used for eight countries with a higher male population share (Bahrain, Kuwait, Maldives, Nepal, Oman, Qatar, Saudi Arabia, United Arab Emirates).

# **2.2 Economic interpretation**

The basic GEGI has a simple and appealing economic interpretation: _the increase in long-run GDP per capita from closing the gender gap in employment rates_ . For example, if GEGI=19% (the cross-country average), it would imply that long-run GDP (or GDPPC) would be almost 20% higher if the employment gender gap was closed by increasing female employment. See Appendix 1 for a derivation.

The largest increase in GDP would occur in countries with the largest gender gaps. For example, in economy where no women were employed, GEGI=100%, so GDP would increase by 100% moving to equal employment rates (GDP doubles). In contrast, when the GEGI=0, gender parity has already been achieved so there are no untapped gains due to employment gaps.<sup>5</sup> The GEGI has this interpretation because the size of the increase in long-run GDP is proportional to the change in the number of workers in the long-run in simple neoclassical growth models. This is because the capitalto-output ratio is constant in the long run (one of Kaldor’s stylized facts).<sup>6</sup> This means that moving from no female employment to achieving gender parity in employment would double the number of workers, and so long-run GDP would also double. It is important to note that this calculation assumes an _exogenous_ change in female employment, keeping everything else equal (productivity, human capital, etc.). In contrast, looking at a crosscountry relationship in the data between female employment rates and GDP is uninformative about the causal relationship, because female labor supply varies _endogenously_ . For example, an extended drought which lowers productivity and GDP could cause more women to work out of hardship, but this does not imply that higher female labor reduces GDP—that change in female labor supply is endogenous, not exogenous.<sup>7</sup> The GEGI calculation also assumes that human capital is the same across males and females—an accurate assumption based on the World Bank Human Capital Index (see Appendix Figure 3)—and that males and females are otherwise equally productive.

> 4 To see that Equations 1 and 2 are equivalent, substitute in the denominator of Equation (1) and then substitute and . Females and males have almost identical populations, , and so population MM FF cancels in the numerator and denominator, yielding Equation (2). LL= LL + LL 5 MM MM MM FF FF FF MM FF LL Note that in countries where male employment rates are low, parity of employment by gender is a less ambitious target. = EE × PPE LL = EE × PPE PPE = PPE 6 Appendix Figure 4 (reproduced from Jones 2016) shows that the US capital-to-output ratio has been broadly constant at about 3-3.5 since World War 2.

> 7 Across countries, female employment is high in both low and high income countries (Pennings 2020), but this is a correlation, not causation.

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