From Emanuele Campiglio, New Economics Foundation:
The absence of money, debt and banks from the overwhelming majority of “mainstream” economic models has been one of the more pressing criticisms aimed at economists after the financial crisis exploded: how were they supposed to foresee the crisis – or even reach a proper understanding of its mechanisms afterwards – if conventional economic theory didn’t acknowledge the role of banks, nor consider money and debt as influential variables?
Given the fundamental importance that banks have in the process of credit creation and allocation, excluding them from the picture would instinctively sound like an unwise choice. And it is. Nonetheless, banks have been mostly absent from economic theory for many decades. Even some of the major central banks use macroeconometric models where private banks play no role whatsoever (see for example the models of the Bank of England, the European Central Bank and the Federal Reserve).
The situation now looks more hopeful. Discussion is underway within the discipline as to how banking and credit can be included in macroeconomic theory, and many researchers have started building models where their role in shaping the wider economy is explicitly recognised.
nef (The New Economics Foundation) has been developing a model with the objective of offering an original and sound perspective on the functioning of the economic system, and study the macro mechanisms linking the ‘real’ economy to environmental variables (energy and climate change), on one side, and to the financial and banking system on the other.
Here they present the way in which they are currently modeling the banking system: