A National Bureau of Economic Research (NBER) Working Paper looks at the effect of offering healthier school lunches on end-of-year test scores for students in California. 

Michael L. Anderson and colleagues analyzed data collected over a five-year period (academic years 2008/2009 to 2012/2013) from around 9,700 elementary, middle, and high schools that reported test scores on California's Standardized Testing and Reporting exam, a state-wide test given to all students in grades 2 to 11. In order to determine the link between food quality and student achievement, they also collected data from the California Department of Education on school districts' meal vendors for the same time span. Over that five-year period, about 12% of California schools contracted an outside company to provide lunch for at least one school year. The nutritional value of the school lunch menus was analyzed by nutritionists at the Nutrition Policy Institute using the Healthy Eating Index.

The results of the study found that in years when schools offered a healthy lunch menu, student test scores were on average higher (effect size +0.03 to +0.04). In addition, test scores for students who qualified for reduced-price or free school lunches, (and therefore more likely to eat the healthy lunches), increased by about 40% in comparison to students who didn't receive free school lunches.  The positive effect of healthy lunches on academic achievement persisted for the duration of a long-term contract.