Revisiting Dynamic Complementarity in the Production of Cognitive Skill and its Implications for a Cognitive Achievement Gap Decomposition

The literature shows evidence of dynamic complementarity in the production of cognitive skill. This means that skill attained at earlier stages increases the productivity of inputs occurring later in the life of children. For educational inputs, however, the relation between their productivity and prior cognitive achievement might not always be positive. If the input has a low cognitive demand, more advantaged students will not necessarily benefit from it, but it can be productive among less advantaged children. This is the first study to explore this possibility. I find evidence of heterogeneity in the relation between preschool cognitive achievement and the effect of primary school inputs in Peru. I find dynamic complementarity but only in the upper quintile of the school quality distribution. In the lower 20% of this distribution, a raise in preschool skill reduces the productivity of school inputs. I also propose a decomposition strategy that accounts for complementarity between preschool skill and school inputs. I use it to measure the contribution of school influences to the cognitive skill gap observed between urban and rural children in Peru. I obtain an estimate for this contribution (37%) larger than that found in previous studies that relied on a linear production function. An important implication of this is that one does not need to wait until urban and rural children share similar levels of preschool skill to exploit the equalizing potential of school influences. It is not “too late” for rural children currently at school, despite their preschool skill deficits.