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Brooks Wilson's Economics Blog: Quantitative Easing

Friday, November 12, 2010

Quantitative Easing

On November 3, the Federal Open Market Committee announced a plan to implement a second round of quantitative easing, an idea floated by Fed Chairman Ben Bernanke in his speech at Jackson Hole on August 27, 2010.  The Fed will increase its holdings of bonds by $600 billion before the second quarter of 2011.   
Economists are not certain of exactly how quantitative easing increases economic activity, but those who support it illustrate how it works by lowering interest rates throughout the economy using the following story. 

The value of any asset is equal to the discounted value or present value of all payments earned from that asset.  In the formula, PV represents the present value or market value of an asset and it is equal to the sum of the annual payments (P1 through Pn) and the sales price of the asset (Sn) discounted by the market interest rate ((1+i).  For a bond, dividends represent the annual payments and the sales price, the value of the bond in the nth year.

When the Fed buys bonds, it must convince current bondholders who were satisfied holding bonds at the existing market price to sell.  It does this by offering a higher price than the current market price.  To keep the present value in balance, the part of the equation to the right of the equality sign must increase.  Because the payments are fixed, and because the Fed has little ability to control the sales price of the bond for reasons I will not explain here, increases in the right-hand side of the equation must come through a decrease in the market interest rate, i.  Lower interest rates affect not only bonds, but all other assets in the nation’s investment portfolio as well.  Prior to the Fed’s quantitative easing, individual investment portfolios were in equilibrium, meaning that investors were satisfied with the risk/return tradeoffs of the investments they held.  As bond prices rise, current bondholders earn higher than expected profits on their bond investments if they sell.  They are left with cash holdings which earn little, and because of the flood of new cash into investor portfolios from the sale of bonds, the interest earned on these holdings fall.  Investors reexamine investment alternatives, and given current conditions in the bond and cash holdings market, find other investments such as stock or real estate relatively more attractive.  Investors bid up the prices of the other investment to induce the current owners to sell, thus forcing down market interest rates for these assets.  Increases in wealth encourage people to spend and invest more.

Not all investments will be from the purchase of existing assets.  Some will be made in the production and sale of new goods and services or the construction of new assets which become  more profitable because of lower interest rates throughout the economy.

Quantitative easing also affects the interest rates because it increases the probability of inflation as demonstrated with asset prices.  The nominal exchange rate (e) is the amount of a foreign currency we can buy with a dollar.  It is equal to the real exchange rate (RE), the real or inflation adjusted amount of foreign currency we can buy with a dollar, multiplied by the ratio of a foreign price index and dividend by the U.S. price index (PF/PD). 

Because policy does not affect the real price index and does not directly affect foreign prices, increases in domestic prices lower the real exchange rate; the dollar now purchases less foreign currency than before.  Conversely, foreign currency can buy more dollars.  Because foreign currency if more expensive, foreign goods, our imports, are more expensive, and our exports are cheaper in foreign markets.  If other countries through their central banks do not respond by lowering their interest rates, our exports will increase, expanding economic activity at home.

I will reserve criticisms of quantitative easing for future blog posts. 

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