Krugman has written a lot about Japan, and Abenomics. According to Krugman's own analysis, Abenomics would not be very effectual and warned that particular Abenomics policies (like the tax increases) would indeed worsen the economy. It's a little disingenuous to say the economy is worse: growth did improve (until the VAT increase Krugman warned would be disastrous) and unemployment did fall, and Krugman wasn't worried about the debt in the first place since the Japanese can still borrow at very low rates.
Abenomics does not correspond almost at all to Krugman's prescriptions, it was simply expected to be slightly less bad than what was happening before.
To get that growth, Japan massively debased the Yen, chopping down the Japanese standard of living and reduced the real value of all of that debt Japanese citizens are expecting to be paid back by the government.
If you have to significantly harm your currency to get growth, what you're getting is not actual growth, merely an illusion.
In what sense do you mean Japan has "debased" the yen? Inflation has been virtually nonexistent. A weaker yen promotes exports; obviously not something that is automatically bad for the economy. It's absolutely not true that having a weaker currency means growth is illusory.
If you reduce the value of your currency by 25%, and get 3% GDP growth in the process, you have to adjust the baseline lower and what you've actually got is a drastic reduction in real economic value.
The Japanese government has been aggressively devaluing the Yen, because they're bankrupt and can no longer afford to pay even the interest on their debt without either using printing or new debt issuance. They're stuck in a downward spiral. Japanese savings have collapsed to zero, so the Japanese people can no longer afford to fund continued government debt expansion as they were before. That has left the Japanese government with no other options but currency debasement, ie devaluing the real worth of outstanding Yen based debt (which is mostly held by Japanese citizens, which is then ultimately a slashing of their wealth).
Japan has suffered zero deflation over the last 25 years. That's why Japan is one of the most expensive places on earth to live in most every respect. If they had suffered 25 years of deflation, their prices would have gone down accordingly.
The notion they've been stuck in deflation is keynesian economists confusing what deflation is. Under keynesian economics, if a bubble is inflated, and then bursts, taking down real estate prices, they call those falling prices deflation - when in fact it is not. This is one of the many obvious flaws at the heart of keynesian economics, which has helped lead the globe into its current perpetual stimulus addiction path.
It is the dollar that has appreciated, not the yen that has depreciated. The dollar has appreciated against most currencies in the last year – probably because people expect interest rate hikes this year. It has nothing to do with Japan per se.
Abenomics does not correspond almost at all to Krugman's prescriptions, it was simply expected to be slightly less bad than what was happening before.