Albert Einstein is said to have defined insanity as doing the same thing over and over again and expecting different results. By failing to change their way of thinking since the global financial crisis, the world’s main central banks are proving Einstein right.

Many in the markets worry that central banks are running out of ammunition to boost global growth and generate inflation. They are not. The Bank of Japan’s adoption of negative interest rates, the European Central Bank’s extension of its quantitative easing (QE) programme and the Federal Reserve’s decision to slow the normalisation of US interest rates show that policymakers can still draw on plenty of firepower.

So it is not that central banks are not doing enough. It is that their policies are misguided and are hampering global rebalancing. In particular, investors should be worried that policymakers have failed to learn three main lessons from the subpar performance of the global economy since the 2008-09 crisis.

First, if an economy is drowning in debt, the solution is not to pile on even more debt. That is why the ECB’s offer, under the terms of its new targeted longer term refinancing operations, to pay eurozone banks to increase their lending is badly judged. The ECB is right to do QE, but at the same time it should use its new powers as the supervisor of eurozone banks to force a swifter write-off of bad debts. Almost 20 per cent of Italian bank loans are non-performing. Until now, the ECB has counted on QE to work by weakening the euro. Its strategy instead should be to use QE to buy time to cleanse bank balance sheets.

Second, no one wins from competitive devaluation when global consumer demand is weak because of excessive savings, as is the case today. The Bank of Japan has deployed the big battalions in the currency wars. Abenomics, the economic strategy of prime minister Shinzo Abe, was meant to combine monetary easing, fiscal stimulus and structural reform. Instead, in the past two years it has boiled down to a devaluation of the yen. On that narrow criterion, Abenomics might be judged a success — the yen has become so undervalued as a result of the BoJ’s loose monetary policy that traders are snapping it up.

But in fact the BoJ’s policy is as ill-thought-out as the ECB’s. Japan’s biggest economic imbalance is that too much income flows to companies, which sit on mountains of cash instead of investing it or returning it to shareholders. A cheaper yen compounds this problem. By boosting export earnings and making imports dearer, a weaker exchange rate transfers ever more income from households to the corporate sector. So the BoJ should welcome the recent recovery in the yen.

Unfortunately, the central bank has waited far too long to do the right thing. A financial crisis in Japan is now a matter of when, not if. As unlikely as it sounds in an economy fighting falling prices, the crisis will take the form of inflation. That will happen when Japanese banks run out of government bonds to sell to the BoJ, which will be forced to increase its purchases from insurers and other non-bank financial institutions. The result will be a rapid expansion in broad money, unmatched by growth in the real economy. That will unnerve domestic investors and spark a flight into US Treasuries and other overseas assets, sapping the yen. If the crunch comes in the next year or two the rest of the world will be too weak to withstand it.

Third, tepid growth since the crisis shows that a short, sharp adjustment and purging of past excesses is better in the long term than prolonged attempts to preserve the economic status quo. The Fed should have stuck to its plan to raise interest rates four times in 2016 instead of worrying that higher rates might hurt the rest of the world or asset markets might throw a tantrum. An upbeat message that higher borrowing costs were justified by positive domestic economic trends, notably a strong labour market, would have given US consumers the confidence to spend their windfall gains from cheaper oil.

In short, the ECB, the BoJ and the Fed have missed a golden opportunity this month to make much-needed course corrections. As a result, the euro area and Japan remain fragile while the US is not making the most of much-improved fundamentals, so the global economy is still perilously unbalanced. The world might muddle through for another year, but its leading central banks have failed to banish the risk of a calamitous 2017.