There are 509 expanding neutral hydrogen shells catalogued in the Small Magellanic Cloud (SMC), all apparently very young, with dynamical ages of a few Myr. To examine their relationship with young stellar objects, we cross-correlated the shell catalogue with various catalogues of OB associations, supergiants, Cepheids, Wolf-Rayet stars, supernova remnants and star clusters. The incidence of chance line-ups was estimated via Monte Carlo simulations, and found to be high. However, it is important that there are 1.5 times more shells that are not spatially correlated to an OB association, than shells that are. Moreover, 59 of the 509 shells lie mainly in low stellar density fields and have no young stellar objects associated with them, and therefore no obvious energy source. It is shown that, on the whole, the properties of these 'empty' shells are very similar to the properties of the rest of the shells, once selection biases are taken into account. In both cases, the shell radius and expansion velocity distribution functions are consistent with the standard model, according to which shells are created by stellar winds and supernova explosions, as long as all shells were created in a single burst and with a power-law distribution of the input mechanical luminosity. This would indicate a burst of star formation. This interpretation, however, cannot explain why the 59 shells, with no young stellar counterparts, show almost exactly the same behaviour as shells with OB associations within their radius. Gamma-ray bursts could account for some but certainly not for the majority of the 'empty' shells. Many 'empty' shells, including most of the high-luminosity ones, are located in the north-western outer regions of the SMC, and may be associated with a chimney-like feature that is known to exist in that area. Finally, it is noted that turbulence is a promising mechanism for the formation of the shell-like structures, but direct comparison with the observations was not possible at this stage, due to lack of detailed models.