This paper examines how import liberalization affects labor markets when labor and intermediate inputs can act as complements or substitutes. We incorporate a CES production function into a dynamic quantitative trade model and show that the labor market effects of imports depend on the elasticity of substitution between labor and intermediate inputs, which varies across sectors. Exploiting exogenous tariff reductions in Colombia and applying a difference-in-differences strategy, we separate the reduced-form effects of trade into an input shock and a competition shock. Import competition reduces the wage bill across sectors, whereas cheaper intermediate inputs increase it. This increase is driven by the service sector, with imprecise effects in manufacturing and an opposite-sign effect in agriculture. Combining the model with the reduced-form parameters, we implement indirect inference to recover sector-specific elasticities of substitution and find that labor and intermediates are substitutes in agriculture and manufacturing but complements in services. Allowing for a more flexible production structure meaningfully changes the labor market response to trade.