Researchers at Oxford University and The Open University found that child happiness, as reported by their parents, was linked to how frequently the children were engaged in activities such as reading, storytelling, shopping, painting and doing arts and crafts.
In contrast, passive activities like looking at picture books or watching television brought no discernible benefits.
Watching television appeared, in this analysis, to have a negative impact on child happiness that was statistically significant.
The results also suggested that more active activities may boost the development of a child's motor and social skills.
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More passive activities did not appear to contribute to the development of these skills.
The researchers applied economic models to data drawn from the German Household Survey in the years 2007 to 2010.
The data included responses from over 800 German parents about the happiness and wellbeing of their two and three-year-olds, the activities they took part in and their development of talking, movement, and social skills.
"It should allow us to reassess the role of arts in the development of skills and human potential," Anand said.
"Our results suggest that parents may face difficult trade-offs with regard to time spent actively engaging with their children, versus providing for them materially via the labour market," said Dr Laurence Roope of the Health Economics Research Centre at Oxford University.
"It will be interesting to see whether similar results emerge for slightly older children and using other datasets," Roope said.