Always nice to see a great mind such as @paulkrugman thinking about Brazil's macro problems, but he gets a lot of things wrong in his most recent article (nytimes.com/2018/11/09/opi…)
First, Brazil's dependence on commodities is largely a myth. Brazil's commodity exports as a share of GDP is lower than Mexico's and not much higher than Turkey's -- and nobody claims these countries are commodity-dependant. 
(@mark_dow explores that well in this post: behavioralmacro.com/brazil-is-not-…)
Second, most of the inflation spike in 2015 cannot be explained by a weaker currency. Dilma Rousseff's administration kept electricity tariffs and fuel prices at unsustainable levels until she got reelected.
The 2015 price liberalization (see "administered prices" rising 18% y/y below) was the main inflation driver that year.
With headline inflation running at 11% y/y, rising the policy rate to 14.25% doesn't seem to be a panic move for an inflation targeter -- in real terms, rates stayed much lower than the historical average.
As for austerity: the primary deficit kept widening until 2016. Government spending as a share of GDP didn't collapse after the "sharp spending cuts".
Of course the slump prescribed expansionary fiscal policy, but how to balance that with a strong perception of insolvency risk? Perhaps the counterfactual would be even worse, with skyrocketting debt costs and the risk of a "sudden stop" crisis.
Krugman correctly calls attention to the role of the massive boom in credit, explored in the @AtifRMian et al. article (nber.org/papers/w25170). This is often neglected and well worth exploring further.
In its final phase, the boom involved a massive injection of credit through the state-owned banks, apparently under very poor selection criteria. The fiscal cost of that will keep showing in the public deficit for years.
What, then, the hell happened to Brazil? Yes, it was a perfect storm -- but mostly of terrible policy choices leading to massive capital misallocation and corruption.
The crackdown on corruption probably also contributed to the slump, although it may have positive net effects in the long term -- this is also something that deserves to be investigated by people much more competent than me.
(End of my Friday night attempt to rebut a Nobel prize. Now to beer & pizza.)
Adding some more nuance -- Brazil as commodity-dependant: BRL indeed behaves as a commodity currency (bcb.gov.br/pec/wps/ingl/w…), what should be expected given the country's export mix.
But the country is quite closed to foreign trade (data.worldbank.org/indicator/NE.T…), so whatever happens to the trade balance shouldn't have a large impact in the economy as a whole.
In the case in point, definitely the effects of falling commodity prices were dominated by what was happening elsewhere in the economy.
An important discussion about commodity prices is how the boom helped to ease Brazil's external financing restriction, which contributed to above trend GDP growth between 2003-12. But, again, the domestic credit boom probably dominated that effect too.
Austerity: austerity is nowhere to be seen in the macro indicators, but, given the very regressive nature of Brazil's government transfers, stabilizing govenrment spending may have a quite negative effect on the income of the have-nots.
In other words, in "austerity" times transfers to the wealthy (who are more likely to hoard cash) continue to grow, whereas transfers to the poor (more likely to spend) fall. This may have contributed to the slump.
(This is very speculative and I haven't seen any research on that topic -- I may be dead wrong.)
