Chapter 14 – 2008 Crisis and the Short-Run Model.

Problem 1 – A Financial Crisis

Suppose the economy starts with GDP at potential, the real interest rate and the marginal product of capital both equal to 3 percent, and a stable inflation rate of 2 percent. A mild financial crisis hits that raises the risk premium from zero to 2 percent.

(a) Analyze the effect of this shock in the IS/MP diagram. 

In Equilibrium, the IS/MP Diagram looks like,

Risk Premium & Where It May Come From - Recall Problem 4 from the 2008 Crisis Overview Chapter, we discussed systemic risk and how loans between banks could expose creditor banks to risk for which they were otherwise unaware. With the previous chapter’s problem, a debtor bank’s exposure to a dramatic fall in housing prices spread to a creditor bank through interbank loans.

This would presumably imply that when banks loan to each other they would charge a risk premium. This risk premium increases with the chances of a crisis that could harm a debtor bank’s balance sheet. This premium would decrease in times of relative calm.

The real interest rate would therefore take the form;

Where  is the “risk free rate” (think: the rate set by the central bank)

and  is the risk premium

IS-Curve – Normally a “mild financial crisis” will shift the IS curve inward. But because this equation didn’t mention anything about a shift, I’ll assume the IS is unchanged focus on how the new risk premium changes the MP curve.

This shift will push short-run output into recessionary territory.

(b) What policy response would you recommend to the Federal Reserve? What would be the effect of this policy response on the economy?

In this model, the Fed influences the risk free rate . After the jump up on the risk premium from zero to 2%, in order to get the real interest rate back up to the equilibrium of the marginal product of capital of 3%, the Fed would need to offset the risk premium change and lower  by 2%

With Fed response:

This Fed response would look like the following in a IS/MP diagram;

The Fed lowered its interest rate,  to 1%, making the real interest rate 3%, and bringing the economy back to equilibrium with .

(c) How would your answer to part (b) change if the financial crisis were very severe, raising the risk premium to 6 percent? 

With a 6% risk premium, our IS/MP diagram would have looked something like this,

To get the economy back to equilibrium with a 6% risk premium the Fed will want to lower rates by 6%. But when setting the risk free rate , the central bank faces a zero-lower-bound. It can’t set rates below zero. Thus the Fed in this scenario  can only lower rates by 3% (the current risk-free-rate). This means the best response of the central bank to this crisis still leaves the economy in a slumping economy.

(d) What other policy responses might be considered in this case? 

Other options include fiscal expansion. Plus….