Here is a parent involvement study to look out for:
“Parental Effort, School Resources and Student Achievement,” (with Andrew Houtenville), Journal of Human Resources, This website provides this synopsis:
Parental Effort, School Resources, and Student Achievement
Andrew J. Houtenville and Karen Smith Conway
This article investigates an important factor in student achievement—parental involvement. Using data from the National Education Longitudinal Study (NELS), we estimate a value-added education production function that includes parental effort as an input. Parental effort equations are also estimated as a function of child, parent, household, and school characteristics. Our results suggest that parental effort has a strong positive effect on achievement that is large relative to the effect of school resources and is not captured by family background variables. Parents appear to reduce their effort in response to increased school resources, suggesting potential "crowding out" of school resources.