, and Western Ontario for helpful comments. We are responsible for all errors. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

What are the effects of school closures during the Covid-19 pandemic on children's education? Online education is an imperfect substitute for in-person learning, particularly for children from low-income families. Peer effects also change: schools allow children from different socioeconomic backgrounds to mix together, and this effect is lost when schools are closed. Another factor is the response of parents, some of whom compensate for the changed environment through their own efforts, while others are unable to do so. We examine the interaction of these factors with the aid of a structural model of skill formation. We find that school closures have a large and persistent effect on educational outcomes that is highly unequal. High school students from poor neighborhoods suffer a learning loss of 0.4 standard deviations, whereas children from rich neighborhoods remain unscathed. The channels operating through schools, peers, and parents all contribute to growing educational inequality during the pandemic.

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractWe study the effect of family income and maternal hours worked on child development. Our instrumental variable analysis suggests different results for cognitive and behavioral development. An additional $1,000 in family income improves cognitive development by 4.4 percent of a standard deviation but has no effect on behavioral development. A yearly increase of 100 work hours negatively affects both outcomes by approximately 6 percent of a standard deviation. The quality of parental investment matters and the substitution effect (less parental time) dominates the income effect (higher earnings) when the after-tax hourly wage is below $13.50. Results call for consideration of child care and minimum wage policies that foster both maternal employment and child development.JEL classification: H24, H31, I21, I38, J13, J22

What are the effects of school closures during the Covid-19 pandemic on children's education? Online education is an imperfect substitute for in-person learning, particularly for children from low-income families. Peer effects also change: schools allow children from different socioeconomic backgrounds to mix together, and this effect is lost when schools are closed. Another factor is the response of parents, some of whom compensate for the changed environment through their own efforts, while others are unable to do so. We examine the interaction of these factors with the aid of a structural model of skill formation. We find that school closures have a large and persistent effect on educational outcomes that is highly unequal. High school students from poor neighborhoods suffer a learning loss of 0.4 standard deviations, whereas children from rich neighborhoods remain unscathed. The channels operating through schools, peers, and parents all contribute to growing educational inequality during the pandemic.

A recent and growing area of research applies latent factor models to study the development of children's skills. Some normalization is required in these models because the latent variables have no natural units and no known location or scale. We show that the standard practice of "renormalizing" the latent variables each period is over-identifying and restrictive when used simultaneously with common skill production technologies that already have a known location and scale (KLS). The KLS class of functions include the Constant Elasticity of Substitution (CES) production technologies several papers use in their estimation. We show that these KLS production functions are already restricted in the sense that their location and scale is known (does not need to be identified and estimated) and therefore further restrictions on location and scale by re-normalizing the model each period is unnecessary and over-identifying. The most common type of re-normalization restriction imposes that latent skills are mean log-stationary, which restricts the class of CES technologies to be of the log-linear (Cobb-Douglas) sub-class, and does not allow for more general forms of complementarities. Even when a mean logstationary model is correctly assumed, re-normalization can further bias the estimates of the skill production function. We support our analytic results through a series of Monte Carlo exercises. We show that in typical cases, estimators based on "re-normalizations" are biased, and simple alternative estimators, which do not impose these restrictions, can recover the underlying primitive parameters of the production technology.