Does learning longer improve student achievement? Evidence from online education of graduating students in a high school during COVID-19 period

This paper examines the effect of online learning time on graduating students' test scores in a senior high school. Decisions regarding online education, including those related to participation and learning hours, are endogenous due to both reverse causality and omitted variables. This paper is the result of the natural experiment of the outbreak of COVID-19, which made every student to participate in online education when the spring semester began. In addition, this paper uses a value-added model controlling for the scores that preceded online education, which is a sufficient statistic of students' unobserved ability and motivation. If this cannot completely eliminate the endogeneity problem, it should be able to largely alleviate the problem. The results indicate that: online education has positive but limited impacts on test scores on average, particularly those in the subject of math within the natural sciences track; top-tier students are most positively affected by online education; and the benefits of online education vary among students with different backgrounds. The quantile regression suggests that a 10% increase in online education time raises math test scores by more than 0.25 for the students between the 0.60th and 0.80th quantiles. Surprisingly, it is evident that online learning time has a significant negative effect for some students in certain subjects. Finally, online education neither widens nor narrows the inequality of students' test scores.