They do but they also have to have the right policies in place to take advantage of the world economy, no one single factor is the make or brake factor.
Yes they claim it's not there fault in an economic down turn but they get the blame for it and they have to deal with it and there is usually criticism of what they do. Rudd's stimulus packages after the GFC can rightly be criticised for mismanagement and waste but we did avoid a resession
