The euro has declined roughly 13% against the dollar over the past six months.  This is supposed to be stimulative for the eurozone economy, but it remains moribund.  What gives?  

Part of the problem is that the bilateral exchange rate is not the proper metric in this context.  To understand how a currency's fluctuation impacts an economy it is better to look at the currency on a trade-weighted basis.  

The Bank of England has trade-weighted indices for all the major currencies.  This Great Graphic shows its euro trade-weighted index (white line) and the euro-dollar nominal exchange rate (yellow line).  One of the reasons that the euro's depreciation may not have helped the euro area economy is that it has been quite modest on a trade-weighted basis.  On a trade-weighted basis, the euro has declined by a little more than 3% over the past six month.    

One of the reasons then that the decline in the euro has not provided much support for the economy is that the depreciation has been so minor.  Prior to monetary union, Europe was mostly relatively small and relative open (measured by exports plus imports as a percentage of GDP).   Since monetary union, it is larger but relatively closed.  This means that the euro area as a whole is less sensitive to the currency depreciation than the individual countries were before EMU. 

In some ways, a similar argument applies to the decline in oil prices.  Much has been made of the dramatic decline in the price of oil, but it too does not appear to have lending much support to the eurozone.    

There are two basic reasons.  First, most of the talk about the decline in oil prices is in terms of dollars.  The euro's decline against the dollar means that the price of oil has not declined as much in terms of the euro.    Since last June's peak, the price of Brent has fallen by 56% in dollar terms, and a more modest, though still significant, 43% in euro terms.