"Real net exports have increased since the last quarter of 2012. While the increase is modest, it is an increase; in contrast, in nominal terms, net exports continue to decline in both absolute terms, and as a share of nominal GDP."
Although Japanese nominal exports have surged by 15.2% between 2012Q4 and 2013Q3, nominal imports are up by even more, or by 16.5%:
Devaluation improves a country’s trade balance only if the Marshall-Lerner condition on trade elasticities holds, and research shows that they’re not met in the majority of cases, either past or present:
That's not to say that currency devaluation isn't beneficial, of course it is, but the benefit flows primarily from increased domestic demand. Here is a study of the competitive devaluations of the Great Depression by Barry Eichengreen and Douglas Irwin:
The Great Depression is a particularly important historical example because then, as now, most of the advanced world was up against the zero lower bound in policy interest rates.
An examination of Figure 4 on page 48 reveals that the only countries that experienced import growth from 1928 to 1935 (the UK, Japan, Sweden and Norway) were members of the sterling block that devalued early (1931). In most of these countries net exports actually declined over the period because imports rose more than exports.
The order of recovery from the Great Depression follows the order in which they abandoned the gold standard perfectly:
The US devalued in 1933 which immediately led to a swift recovery from the Great Depression. Nominal exports doubled from 1933 to 1937. But nominal imports increased by 110.5%:
As a result net exports went from a small surplus (about 0.2% of nominal GDP) to being roughly in balance.
France was part of the Gold bloc of countries that devalued late (1936). From 1936 to 1938 nominal exports increased by 95.4% and nominal imports increased by 80.9%:
However, since imports were already substantially greater than exports, the nominal deficit actually increased by 55.4%.
Japan’s original ryōteki kin’yū kanwa (QE) was officially announced in March 2001 and concluded in March 2006. The following is a graph of the BOJ’s estimate of Japan’s real effective exchange rate which is trade weighted with respect to 16 different currencies and takes into account their relative inflation rates:
The real effective exchange rate fell from 116.25 in February 2001 to 91.09 by March 2006, when the BOJ announced the completion of QE, a decline of 21.6%.
Exports rose from 10.2% of nominal GDP in 2001Q4 to 19.3% of GDP in 2008Q3. Imports rose from 9.4% of GDP in 2001Q4 to 19.5% of GDP in 2008Q3. From 2002Q1 to 2008Q1 real (adjusted by the GDP implicit price deflator) grew at an average annual rate of 11.0%. Real imports grew at an average annual rate of 12.1%.
So there was boom in both exports and imports. But imports grew faster than exports, and net exports actually moved from surplus (0.8% of GDP) to deficit (-0.2% of GDP) between 2001Q4 and 2008Q3:
It's very telling that today the only major currency area up against the zero lower bound in interest rates that hasn't done QE (the Euro Area) is also the only major currency zone where the trade balance has improved substantially since 2009, going from 0.6% of GDP in 2009Q1 to 3.5% of GDP in 2013Q2:
But this has occurred in large part because nominal imports have been falling since 2012Q3 due to falling domestic demand. Nominal exports have barely changed since 2012Q3.