The Liquidity Trap In the IS/MY Model (“Sitges Equation”)

by Dirk Ehnts, Econoblog101

I have recently built a small model which builds on the “Sitges” balance of payments identity. “Sitges” – originally a little town close to Barcelona – helps me to remember that the change in debt of the private sector (private sector savings – investments) plus that of the public sector (taxes – government spending) equals the current account balance (exports – imports): S-I+T-G=E-s! Here is the small graphical apparatus:

Click to enlarge

Given some expectations about the real economy (I), the banking sector expands credit by accommodating loan demand (II). This determines demand (including debt-financed investment), which determine income (III). At the equilibrium that I have constructed the private sector debt is stable, private savings equal investment (IV).

Now let us assume that nevertheless a bubble bursts and the private sector wants to increase net savings. This is the new situation:

Click to enlarge

There has been a shift in behavior of the economy, since now the deleveraging activities in the private sector drive the economy and not profit-led activities (IV). Hence, loans are repaid, the monetary aggregate falls (II). Less investment is financed, which means that demand has fallen (III). Expectations about the real economy have changed to the worse and loan demand is now in a situation which we call the liquidity trap. That is why the loan demand curve has shifted in the south-west diagram. Loan demand is not interest rate elastic at the new equilibrium, hence a lower interest rate will not induce more debt-financed investment. This means that aggregate demand is weak and will not increase.

Government spending can save the day by shifting the C+I+G+NX curve in the north-east upwards. This will have no feedback on the south-west corner, since the short-term interest rate is set by the central bank and will not increase even if the government borrows and spends huge amounts of money. Inflation will only arise when aggregate demand goes above potential output (however that is defined) and/or the exchange rate weakens. However, the central bank could instantly react by pulling the interest rate up which should a) decrease aggregate demand (via investment) and b) attract foreign capital inflows, which will move lead to appreciation.

One interesting fact in my model is that the liquidity trap is not “fixed” as in the IS/LM model. The loan demand curve depends in conditions of balance sheets and expectations and shifts around over time. This could be called a “dynamic liquidity trap” versus a traditional “static liquidity trap”. Hence, the zero lower bound is not the big issue but instead the balance sheet conditions and the way the public perceives them (expectations in the widest sense). The public can pile up debt in an irrational manner, it might even be human to do this, until the Wile E Coyote moment arrives and the public moves into a position where it frantically increases net savings. Hence, the same conditions prevail as before but the shift of the dynamic liquidity trap is what puts the economy into a position where monetary policy is without effect and government spending is needed to bring aggregate demand back up.

This is a technical analysis and as that says nothing about what should be done. If you are fine with a GDP loss as a result of a bubble that bursts, that’s fine. If you like to stabilize GDP by increasing government spending, that’s fine, too. It should be left to the public to decide what they want: austerity and mass unemployment or increased government spending and stable GDP growth. This is what my theory says is available for nations with sovereign currencies (sorry, euro zone, you must change the rules first!). To those that pretend to offer austerity and stable GDP growth under existing circumstance (weak foreign demand, high private sector debt) and those who pretend to offer increase government spending with mass unemployment I would say that my model speaks against it.
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