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AbstractFor the US the supply and wages of skilled labor relative to those of unskilled labor have grown over the postwar period. The literature has tended to explain this through "skill-biased technical change". Empirical work has concentrated around two variants:(1) Capital-skill complementarity, and (2) Skill-augmenting technical change. Our purpose is to nest and discriminate between these two explanations. We do so in the framework of 2-and 3-level CES production function where factors are disaggregated into skilled and unskilled labor, and the capital stock into structures and equipment capital. Using a 5-equation system approach and several nesting alternatives, we retrieve estimates of the elasticities of substitution and factor augmenting technical changes. Non-technical summaryFor the US and many other countries, the relative supply of skilled labor has grown markedly over the post-war period. Despite this expansion of supply, there has a large increase in the real wages of skilled labor relative to unskilled labor. This wedge is what we call the skill premium. How might we explain this phenomenon? The literature has tended to explain this through "skill-biased technical change". In particular, empirical work has concentrated around two variants: (1) Capital-skill complementarity, and (2) Skill-augmenting technical change. This does not preclude other explanations (off shorting, de-unionization etc.). But it does tend to view those alternative explanations through the lens of these two channels. Taking these two channels, our purpose is essentially to nest and discriminate between these two explanations. We do so in the framework of 2-and 3-level CES production function where input factors of production are disaggregated into finer components. For labor this disaggregation is into skilled and unskilled labor, and, for the capital stock, into structures and equipment capital. We derive the five non-linear equation system with cross-equation constraints. We estimate them under different assumptions on how the four factors and technical change augmenting them are combined in three-and two-level CES production functions. We retrieve estimates of the elasticities of substitution and factor augmenting technical changes. Our framework allows us to decompose in each case the level and growth rate of the skill premium into three separate channels: (1) capital-skill complementarity, (2) technical change channels as well as (3) ...