The Cubic IS Curve: debt and its implications

How the bursting of the debt bubble leads to a combined balance sheet and liquidity trap recession

“More importantly, perhaps, we need a theory that encompasses crises and rapid jumps between one kind of equilibrium and another. Ideally this will combine “Old Keynesian” analysis of economic imbalances with a Minsky-style focus on financial instability.”

 John Quiggan, Zombie Economics, page 124.

Recall from the last post  the new cubic function:

where total debt (D) and the number of households (not) in the debt market (α) are added to the function from the Fed research paper to form a cubic specification. We can now use this specification of the IS curve to show a diagrammatic story of how the build up of (private) debt will lead to a multiple equilibrium situation – or the Minsky style moment that John Quiggan was referring to in the above quote.

In the first picture presented below, we have a linear IS curve, which is the basic representation of the IS curve from the Fed research paper. In the context of the cubic consumption function, this can be thought of as a situation where there is no debt in the economy. Algebraically, with no debt in the economy, the cubic and quadratic terms drop out of the equation above and it reduces to the Fed’s consumption function.

As debt is added to the economy, possibly via an increase in house price expectations or a relaxation in lending standards, the curve begins to appear (In reality, the economy does not begin with zero debt, but this abstraction does not take away from the implications of the model. Perhaps the ‘zero debt’ situation should be thought of the ‘safe’ or long run equilibrium of household debt, with significant movements away from this level leading to the curvature of the IS curve. This will be addressed in a later post)

While a moderate build up of private debt may not have a significant impact on the economic equilibrium, a large build up will. This is displayed in the diagram below in a scenario where the curvature has become so exaggerated that we now have multiple equilibria. The old equilibrium, therefore, is now unstable and the new equilibrium will move to one of the outer junctions. This is the bursting of the private debt bubble and it is more likely that the lower of these outer equilibria will be the initial result of the bursting bubble.

If the shock is big enough – one could imagine the financial crisis of 2008 – then the economy could find itself in a more severe scenario. This is depicted below, which is a representation of the typical liquidity trap. With the IS curve intersecting the LM curve in this position, the Central bank has lost its influence of traditional policy levers to restore the economy to full health.

With the cubic representation of the IS curve, we can also depict something like a balance sheet recession effect. After a large economic shock caused by the build up of private credit, it is logical that private agents engage in deleveraging as they pay down debt.

Thus we can describe the two opposing forces affecting the equilibrium in this situation. The central bank, just like in the Fed Research paper, can target an increase in inflation expectations that would lift the IS upwards and towards a more normal intersection with the LM curve – that is, with interest rates back above the zero lower bound. Countering this effect, and consequently working to dull the effects of monetary policy, is the deleveraging process of the private sector. This will be greater as more houses are engaging in the process and it works to flatten the IS curve by pulling it downwards and to the left.

This is the reason that both monetary policy, discussed here  and housing policy discussed here  are both incredibly important and incredibly interesting. With the Federal Reserve pushing the boundary on unconventional monetary policy, it becomes clear why there has been criticism of the current Administration’s policy on the housing market. As the research by Mian and Sufi revealed , deleveraging can have a major impact on the real economy. Hopefully the next US Administration, whoever wins the White House, can move to address this policy vacuum.


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