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Abstract
Numerous statistical studies of the determinants of children's attainments 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 for information over the entire childhood period. We explore the reliability of estimated results from studies that use such “window” variables. Because window variables describing intermittent events and discontinuous periods of more persistent characteristics may fail to correspond to variables describing the entire childhood experience, the basic question concerns the extent to which such limited duration information 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 consistency of window variables to their longer-duration counterparts. We then use the distinctions revealed by this model to empirically study the potential problems associated with the use of window variables. We use 21 years of data on a sample of 1,705 children from the Michigan Panel 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 omitted variable likelihood ratio tests, tests of goodness of fit, a sign and significance comparison, and a comparison of the magnitude of the simulated changes using window variables versus those of longer duration.
We conclude that single-year and limited duration window variables serve as weak proxies for information describing the entire childhood experience, and often lead to inferences of effects that may be misleading; we draw the implications of this finding for future data collection and research.
