THE WINDOW PROBLEM IN STUDIES OF CHILDRENS ATTAINMENTS - A METHODOLOGICAL EXPLORATION

Numerous statistical studies of the determinants of children's attainm ents measure the circumstances or events occurring over the childhood period by observations of these variables for a single year or a short duration during childhood. These variables are accepted as proxies fo r information over the entire childhood period. We explore the reliabi lity of estimated results from studies that use such ''window'' variab les. Because window variables describing intermittent events and disco ntinuous periods of more persistent characteristics may fail to corres pond to variables describing the entire childhood experience, the basi c question concerns the extent to which such limited duration informat ion is consistent with that measured over the entire childhood period. We first present an omitted variables model that describes the nature of the ''window'' problem, and which allows us to measure the consist ency of window variables to their longer-duration counterparts. We the n use the distinctions revealed by this model to empirically study the potential problems associated with the use of window variables. We us e 21 years of data on a sample of 1,705 children from the Michigan Pan el Study of Income Dynamics in reduced form models of the determinants of children's schooling and fertility outcomes. We develop four tests of the reliability of estimates using varying window lengths relative to full information on the childhood experience. These include omitte d variable likelihood ratio tests, tests of goodness of fit, a sign an d significance comparison, and a comparison of the magnitude of the si mulated changes using window variables versus those of longer duration . We conclude that single-year and limited duration window variables s erve as weak proxies for information describing the entire childhood e xperience, and often lead to inferences of effects that may be mislead ing; we draw the implications of this finding for future data collecti on and research.