Learning Through Repetition? A Dynamic Evaluation of Grade Retention in Portugal
High rates of grade retention are a matter of much controversy and debate worldwide. Although some students may learn more with extended classroom time, other students get discouraged and drop out of school. This paper develops and implements a dynamic value-added modeling approach for estimating grade retention effects in Portuguese high schools where over 40% of students were retained. The statistical model is derived from an education production function that describes how knowledge cumulates with sequential years of school attendance, including repeated grades. Model parameters are obtained using simulated method of moments applied to nationwide administrative test score data. The estimated model is used to simulate achievement in math and Portuguese under the existing grade retention and compulsory schooling policies and under alternative policies. Results show that the average impact of the current policy on 12th grade test scores of retained students is positive, 0.2 standard deviations in math and 0.5 s.d. in Portuguese. However, we end that the test score impacts are heterogeneous and roughly one third of students experience learning loss. Retention also significantly increases school dropout, especially for male youth and older students. We compute policy-relevant treatment effects for retention's effects on lifetime earnings, taking into account retention's simultaneous effects on educational attainment, knowledge, and age of labor market entry, and we solve for the optimal retention policy that maximizes average lifetime earnings in the population.