Statistical properties of data stretching
研究了一种常用估计方法的性质，即当某些变量的观测值聚合程度高于其他变量时，通过重复观测值来拉伸数据。结果表明，该方法会导致系数和误差方差的估计有偏，但在某些情况下，基于拉伸数据的协方差矩阵比基于聚合数据的更小。
Abstract This research examines the properties of an estimation procedure frequently used because observations on some variables are available only at higher levels of aggregation than others. When this occurs, data are often stretched by repeating observations on variables at higher levels of aggregation. We show that this procedure results in biased estimators of coefficients and error variances. Under some circumstances the estimation based on stretched data has a smaller covariance matrix than that based on aggregated data. Comparisons of mean squared errors depend on unknown coefficients.