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The baidu baike (http://baike.baidu.com/) often has the abbreviation listed under the main entry. 中华人民共和国国家发展和改革委员会, for example, has 国家发改委. 中华人民共和国国务院办公厅 lists both 国务院办公厅 and 国办. And yes, 家用电器 points to 家电 as the simpler form, although it is somewhat hidden in the entry.
Look for news articles, especially those from Xinhua, which are considered "official". Typically if an article contains a long-winding name like "人力资源和社会保障部", it is bound to introduce an abbreviation to reduce the verbosity. If you cannot find such articles, which should be unlikely for well-known entities, I suggest that you not abbreviate, especially not ...
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