where<sup>1</sup> _/_ (1 _−θ_ ) is the elasticity of substitution between capital and skilled labor while<sup>1</sup> _/_ (1 _−ρ_ ) is the elasticity of substitution between capital (or skilled labor) and unskilled labor. Under this specification, the elasticity of substitution between capital and unskilled labor and between skilled labor and unskilled labor is the same. This production function exhibits capital-skill complementarities when _ρ > θ_ (when the elasticity of substitution between capital and unskilled labor<sup>1</sup> _/_ (1 _−ρ_ ) is higher than the elasticity of substitution between capital and skilled labor<sup>1</sup> _/_ (1 _−θ_ )).

There are other potential combinations for the nesting of _K_ , _S_ , and _U_ , but we follow Krusell et al. (2000) who have used this production function (distinguishing in addition between equipment and physical structures) to quantify the role of capital-skill complementarities (as opposed to skill-biased technical change) in explaining the increase in the skill premium in the US that accompanied the increase in the supply of skilled labor. They estimate the parameters in Equation 5 using US data, and find that the values for _ρ_ and _θ_ are consistent with complementarities between skill and capital. Krusell et al. (2000) in turn cite the evidence in Goldin and Katz (1998) and Hamermesh (1996) for a nesting consistent with Equation 5. More recently, Duffy et al. (2004) document additional evidence of complementarities between capital and skilled labor using the specification in Equation 5.

We divide Equation 5 by _L_ to obtain output per worker, and use _s_ and _u_ to denote the shares of skilled and unskilled workers, respectively, with _s_ + _u_ = 1: We also assume a law of motion for physical capital as in the Solow-Swan framework and assume that there is no accumulation of skill (the shares of unskilled and skilled labor are given except for changes that follow changes in female employment). We solve for the steady-state level of output and physical capital under different scenarios for gender employment gaps.

**Model Calibration.** We use US values for the different parameters in the model. For the elasticities of substitution, we use the estimates from Krusell et al. (2000): _ρ_ = 0 _._ 401, which implies an elasticity of substitution between unskilled labor and capital of<sup>1</sup> _/_ (1 _−ρ_ ) = 1 _._ 67 (substitutes), and _θ_ = _−_ 0 _._ 495, which implies an elasticity of substitution between skilled labor and capital of 1 _/_ (1 _−θ_ ) = 0 _._ 67 (complements). We set the depreciation rate _δ_ = 0 _._ 039 (the average rate in the US for the past 20 years) and assume a rate of population growth _n_ = 0 _._ 03 (UN World Population Prospects).<sup>21</sup> For simplicity, we set _A_ = 1 and _μ_ = _λ_ = 0 _._ 5 (this way, only the two parameters _ρ_ and _θ_ will govern the choice of _k_ given _s_ and _u_ ). Finally, we calibrate the savings rate _v_ to match the capital-output ratio in the US (around 3), which yields _v_ = 0 _._ 21.

To obtain the shares of skilled workers in each country in the baseline, we multiply the share of

> 21The rate of depreciation is the average for US for the period 1999-2019 in PWT 10.01.

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