Aggregation, Heterogeneity and Risk: Adding Apples and Oranges, or Apples and Apples

Approaches to aggregation are reviewed. These consist of random parameters, random right hand side variables (Stoker's approach}. and exact aggregation. Each approach utilizes different assumptions and has weaknesses. In a sense, exact aggregation is the nonparametric approach. The penultimate section of the paper shows that these concepts may be very important for risk analysis. A simulation model gives substantially biased estimates of regression parameters when exact aggregation procedures are not followed