The study controls for selection on unobservables using a control function approach that leverages the fact that many children spend zero hours per week on enrichment activities. At zero enrichment, confounders vary but enrichment does not, giving us direct information about the effect of confounders on skills.
Using time diary data available in the Panel Study of Income Dynamics (PSID), the researchers find that the net effect of the last hour of enrichment is close to zero for cognitive skills and negative for non-cognitive skills. The negative effects for non-cognitive skills are concentrated in high school, consistent with elevated academic pressure related to college admissions.
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