Implications of seeing economic variables through an aggregation window

A variety of cross-sectional and temporal aggregation cases are considered. It is shown that if cointegration is found at an aggregate level then, strictly, many surprising constraints are implied at the micro level. However, a suitable approximation is suggested using common factors. It is shown that series may not be cointegrated at the time period of generation, but that after temporal aggregation cointegration could occur. This possibility arises because temporal aggregation can move a nuit root at a seasonal frequency to the zero frequency. Finally, the possibility of aggregating income distributions is considered and it is shown that, strictly, the Pareto distribution does not have the required property.