Dynamic compression in speakers themselves?

The primary audio characteristics I want to achieve in my system is an open, uncompressed, unstrained, and highly dynamic presentation.  What I don't know much about is how much speakers can or do contribute to loss of dynamics and impact.  I have a very powerful amp, but it seems that when I increase the volume, yes, the speakers get louder, but perhaps not commensurate with the increase in the volume control.  I do think I understand that this type of presentation is more easily achieved with larger scale speakers, but even with my large speakers, I feel something is wanting. 

I guess my question is, what factors contribute to any compression occurring in the speakers themselves?  Also, can the age of a speaker cause a loss of dynamics?  Mine are ~20 years old.  I'm thinking to get new speakers in the foreseeable future, so I'd like to understand more about this.  This question is in regard to traditional dynamic speakers.