Does "aggregation bias" explain the PPP puzzle?

"Recently, Imbs ... [et al.] (2002) have claimed that much of the purchasing power parity puzzle can be explained by aggregation bias'. This paper re-examines aggregation bias. First, it clarifies the meaning of aggregation bias and its applicability to the PPP puzzle. Second, the size of the bias' is shown to be much smaller than the simulations in Imbs et. al. (2002) suggest, if we rule out explosive roots in the simulations. Third, we show that the presence of non-persistent measurement error especially in the Imbs ... [et al.] (2002) data can make price series appear less persistent than they really are. Finally, it is now standard to recognize that small-sample bias plagues estimates of speeds of convergence of PPP. After correcting small sample bias by methods proposed by Kilian (1998) and by So and Shin (1999), the half-life estimates indicate that heterogeneity and aggregation bias do not help to solve the PPP puzzle"--National Bureau of Economic Research web site.