Last week in Fortaleza, Brazil, the five Brics nations – Brazil, Russia, India, China and South Africa – finally signed a deal to create a $50bn new development bank and a $100bn contingent reserve arrangement. The new financial institutions are seen by many as nothing less than a challenge to the existing financial world order led by the IMF and the World Bank.

These new institutions have many hurdles to overcome before they can be established, but perhaps their greatest challenge is the one they pose to entrenched thinking. Why have any intervention of this scale if growth, as many argue, is mainly driven by private finance and privatebusiness?

Economist Joseph Schumpeter, known for his cutting-edge work on the effect of technological change in transforming capitalist economies, and who brought the term "creative destruction" to prominence, got one thing wrong: he called financial markets the ephors (Spartan leaders) of capitalism. He believed finance to be so powerful because innovation must be financed: without new financial instruments willing to fund activities outside the current status quo, entrepreneurs will not be able to bring their ideas to market.

The reason he got it wrong is that he did not realise what would happen later: finance not funding investment or innovation in the "real economy" but finance funding… well, finance.

Indeed, the origins of the financial crisis and the massive and disproportionate growth of the financial sector originated in the 1970s, as finance became increasingly de-linked from the real economy. Things became worse in the early 2000s when banks began increasingly to lend to other financial institutions, via wholesale markets, to make loans not matched by deposits. They lent mainly to hedge funds, private equity, and subprime mortgages, as well as to derivatives built on these, because the returns were higher than lending to industry or government. We all know what happened next. The result was that banks' assets ballooned, but were increasingly based on thin air. When asset prices fell, and bank equity wiped out, they were so highly leveraged it required only a 3% fall for the major bust to occur.

In the attempt to "rebalance" economies away from speculative finance towards the real economy, there have been proposals to reform finance so that it helps to fuel more innovation. Various measures have been tried to help those few small and medium enterprises willing to go after difficult high-risk investments, the backbone of innovation. Yet these reforms have been inadequate, slow and incomplete, with the proportion of profits from quick trades in the financial sector, rather than long-run investments, rising not falling. And one of the key tools for long-termism, the financial transaction tax, has still not been applied.

But among there have been glimmers of hope. In some parts of the world public financial institutions have been taking on a greater role, financing ailing infrastructure and lending to the most innovative (and high-risk) firms. These include the new Brics bank and also public investment banks such as Germany's KfW, Brazil's BNDES and China's CDB, the great support of Huawei, number one today in telecommunications. Indeed, Jean-Claude Juncker's new commission called last week for the European Investment Bank to play a greater role in nurturing investment-led growth in Europe(rather than debt-driven growth) precisely because EU private finance continues to make speculative profits elsewhere.

As Schumpeter's private ephors have not nurtured but tyrannised the real economy, these public banks are having to increase their role beyond counter-cyclical lending and infrastructure. They are financing innovation, which requires not any type of finance, but patient long-term committed finance. Venture capital, which was meant to be more risk-loving than private banks, has become short-termist itself, focused on early exits, when innovation can take up to 15-20 years. Indeed, public banks have become the lead investors in what many hope will be the next technological revolution: green innovation. In 2012 the share of "development finance institutions" in the "climate finance landscape" was 34% (the highest share of any single type of actor).

Keynes called policymakers "slaves of defunct economists". The idea that at best the public sector can fix "market failures" and "de-risk" business, means that when the banks become too active in an area, they are accused of "crowding out" the private sector. That is, of taking up too big of a share of total investments (all of which in the end must be financed from savings). While some Keynesians defend such investments by arguing they actually "crowd in" – ie, government investments increase the total pie through the spending multiplier – this defence only captures half the story. Even in the boom there are plenty of areas that private finance does not dare tread. The internet was funded by public money in boom times, as were biotech and nanotech. And even if we were in a boom today, there would still be little private finance in those capital-intensive high-risk areas of clean tech.

There is a more interesting argument to justify such banks. What public spending/investment is needed for is not to fix markets but to actively shape and create them. As Keynes argued in 1926: "The important thing for government is not to do things which individuals are doing already, and to do them a little better or a little worse; but to do those things which at present are not done at all."

Rather than judge public investments as if they are acting upon existing markets, we must admit that this is their role: to create and shape markets. This should lead to indicators of performance for such public investments that capture their "mission-oriented" role.

Today's challenge is thus not only to activate the public sector, but rethink its role. I have organised practitioners from public R&D agencies and public financial institutions from all over the world to meet this week to discuss this challenge in the Commons, hosted by Vince Cable. Hopefully, it will help change the conversation. The problem is not about "fixing finance" while leaving the real economy sick, but how to change the framework to one in which socio-economic challenges can be addressed, by public and private actors alike. And key to all is admitting that the public side can be transformational. But only once it is released from the shackles of defunct thinking.

Professor Mariana Mazzucato is author of The Entrepreneurial State: Debunking Private vs Public Sector Myths