The interpretation of red- and blueshifts in EUV spectral observations remains a challenge that could provide important clues to the heating processes in the solar atmosphere. Hinode/EUV Imaging Spectrometer (EIS) observations near the footpoints of coronal loops show blueshifts for emission lines with temperatures above 1 MK and redshifts for lines below 1 MK. The implications are addressed through numerical modeling of loop dynamics. The simulation results are converted into synthetic EIS observations. A single one-dimensional loop cannot reproduce the observed behavior. However, persistent red- and blueshifts can be understood as a collective spectral signature of a bundle of 10 or more loops that have an average temperature of around 1 MK and evolve in a similar way: small-scale heating events occur randomly along each loop on a timescale of several minutes. Strong blueshifts are accompanied by low intensities. The power-law index of the energy distribution has a minor role in determining the average Doppler shifts.