Their economy has expanded enormously, while ours, by contrast, has declined.

by 是介词，在这里表示"通过某种方式"或"以某种标准"。 contrast 是名词，意思是"对比、对照"。 by contrast 是一个固定短语，意思是"相比之下"，用于引出与前文形成对比的情况。