14 C H A P T E R Prepared by: Fernando Quijano and Yvonn Quijano And Modified by Gabriel Martinez Expectations: The Basic Tools

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal Versus Real Interest Rates 14-1  Nominal interest rates are interest rates expressed in terms of dollars.  Real interest rates are interest rates expressed in terms of a basket of goods.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal Versus Real Interest Rates Definition and Derivation of the Real Interest Rate i t = nominal interest rate for year t. r t = real interest rate for year t. (1+ i t ): Lending one dollar this year yields (1+ i t ) dollars next year. Alternatively, borrowing one dollar this year implies paying back (1+ i t ) dollars next year. P t = price this year. P e t+1 = expected price next year. Derivation

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal Versus Real Interest Rates Consequently,, which is the exact relation between nominal interest rates, real interest rates, and inflation. We know Now,

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal Versus Real Interest Rates If the nominal interest rate and the expected rate of inflation are not too large, a simpler expression is:  The real interest rate is (approximately) equal to the nominal interest rate minus the expected rate of inflation.  Notice that higher rates of expected inflation reduce the real interest rate, given the nominal interest rate.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal and Real Interest Rates in the United States Since 1978 Nominal and Real One-Year T-bill Rates in the United States, While the nominal interest rate has declined considerably since the early 1980s, the real interest rate is actually higher in 2001 than it was then.  Despite the large decline in nominal interest rates, borrowing is actually more expensive in 2001 than it was in Nominal

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal Versus Real Interest Rates  Expected and actual inflation may differ.  r = i –  is called the ex-post real interest rate.  r = i –  e is called the ex-ante real interest rate.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Expected Present Discounted Values Computing Present Discounted Values 14-2  The expected present discounted value of a sequence of future payments is today’s value of this expected sequence of payments.  The term 1/(1+i t ) is called the discount factor, and the one-year nominal interest rate, i t, it is often called the discount rate.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Computing Expected Present Discounted Values (a) One dollar this year is worth 1+i t dollars next year. (b) If you lend 1/(1+i t ) dollars this year, you will receive dollar next year.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Computing Expected Present Discounted Values (c) One dollar is worth (c) One dollar is worth dollars two years from now. (d) The present discounted value of a dollar two years from today is equal to

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard A General Formula  The present discounted value of a sequence of payments, or value in today’s dollars equals:  When future payments or interest rates are uncertain, then:

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Using Present Values: Examples  This formula has these implications: –Present value depends positively on today’s actual payment and expected future payments. –Present value depends negatively on current and expected future interest rates.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Constant Interest Rates  To focus on the effects of the sequence of payments on the present value, assume that interest rates are expected to be constant over time, then: –PDV is a weighted sum of the payments. –The weight of future payments declines geometrically over time.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Constant Interest Rates and Payments  When the sequence of payments is equal—call them $z, the present value formula simplifies to:  The terms in the expression in brackets represent a geometric series. Computing the sum of the series, we get:

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Constant Interest Rates and Payments, Going on Forever  Assuming that –Interest rates are constant, –payments are constant and start next year and –payments go on forever (this is a “consol”), then:  Using a property of geometric sums, the present value formula above is:  Which simplifies to:

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Constant Interest Rates and Payments, Going on Forever  It’s quite clear from this formula that –Higher payments increase the value of the security. –Higher interest rates reduce the value of the security.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal Versus Real Interest Rates, and Present Values  Replacing nominal interest with real interest rates to obtain the present value of a sequence of real payments, we get:  Which can be simplified to:

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal Versus Real Interest Rates, and Present Values  Why have two formulae? –Bonds, for example, promise a nominal payment, so we need the nominal PDV equation. –Expectations about Income, and Consumption and Investment decisions, depend on real variables (why bother with the extra uncertainty about inflation). So we use the real PDV equation.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Interest Rates and Investment  Investment is the purchase of a capital good.  If V t is the value of a capital good, the amount of investment will depend  … positively on z t –I.e., the expected income from investment, determined by sales and Y t.  … and negatively on r t + –

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal and Real Interest Rates, and the IS-LM Model  When deciding how much investment to undertake, firms care about real interest rates.  They compare the (real) marginal product of capital with the real interest rate.  Then, the IS relation must read: 14-3

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal and Real Interest Rates, and the IS-LM Model  The interest rate directly affected by monetary policy—the one that enters the LM relation—is the nominal interest rate, then:  Recall Md is affected by the opportunity cost of holding money, which includes inflation.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal and Real Interest Rates, and the IS-LM Model

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Money Growth, Inflation, and Nominal and Real Interest Rates  This section explains the following assertions: 14-4 After a Monetary Expansion Nominal interest rates, i Lower in the short run Higher in the medium run Real Interest Rates, r Lower in the short run Unchanged in the medium run

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Revisiting the IS-LM Model Equilibrium Output and Interest Rates The equilibrium level of output and the equilibrium nominal interest rate are given by the intersection of the IS curve and the LM curve. The real interest rate equals the nominal interest rate minus expected inflation. If i falls, r falls, I rises, and equilibrium output rises in the goods market: the IS curve slopes down.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal and Real Interest Rates in the Short Run The Short-run Effects of an Increase in Money Growth An increase in money growth increases the real money stock in the short run (because P does not adjust in the short run). This increase in real money leads to an increase in output and a decrease in both the nominal and the real interest rate. Notice we are assuming that  e does not change in the short run: this means the IS curve does not shift.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal and Real Interest Rates in the Medium Run  In the medium run,, then IS becomes:  The relation between the nominal interest rate and the real interest rate is:  In the medium run, the real interest rate equals the natural interest rate, r n, then: r n is the interest rate that will make spending equal to the natural level of output.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal and Real Interest Rates in the Medium Run  In the medium run,  e = , expected inflation is equal to actual inflation, so  Recall  =g m -g y  Higher output growth leads to more money demand. If g m >g y, there must be inflation.  This implies that  =  g m.  Hence, in the medium run:

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Nominal and Real Interest Rates in the Medium Run  In the medium run, the nominal interest rate increases one for one with inflation. This result is known as the Fisher effect, or the Fisher Hypothesis. –For example, an increase in nominal money growth of 10% is eventually reflected by a 10% increase in the rate of inflation, a 10% increase in the nominal interest rate, and no change in the real interest rate.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard From the Short Run to the Medium Run  In the short run, higher g m leads to lower nominal interest rates, i. –Because inflation is pre-determined, real interest rates fall in the short run.  Low real interest rates lead to high output, low unemployment, and eventually high inflation.  High inflation leads to a decrease in the real money stock, and to an increase in nominal interest rates.  In the long run, higher g m leads to higher nominal interest rates, i. –But r rises back to r n.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard From the Short Run to the Medium Run  Suppose g m ’>g m. Using the Phillips Curve,  Over time, inflation keeps increasing, and keeps increasing…  When  > g m, real money growth turns negative, which raises nominal interest rates. MPMP

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard From the Short Run to the Medium Run  What happens to r? We know two things: –Initially, r fell.  Immediately after the monetary expansion, nominal rates fell while inflation was predetermined. –In the medium run, r = r n.  So we know that r must rise back to r n.  How? When  > g m, real money growth turns negative, which raises nominal interest rates … and, at a given level of , it raises real interest rates.  As r rises back to r n, I and Y fall back to Y n.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard From the Short Run to the Medium Run –Notice inflation must overshoot for r to rise to r n.  So we know that r goes back up to r n. What happens to i? –It must be equal to r n plus the new, higher level of inflation.  In the medium run,

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard From the Short Run to the Medium Run The Adjustment of the Real and the Nominal Interest Rate to an Increase in Money Growth An increase in money growth leads initially to a decrease in both the real and the nominal interest rate. Over time, the real interest rate returns to its initial value. The nominal interest rate converges to a new higher value, equal to the initial value plus the increase in money growth.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Evidence on the Fisher Hypothesis  To see if increases in inflation lead to one- for-one increases in nominal interest rates, economists look at: –Nominal interest rates and inflation across countries. The evidence of the early 1990s finds substantial support for the Fisher hypothesis. –Swings in inflation, which should eventually be reflected in similar swings in the nominal interest rate. Again, the data appears to fit the hypothesis quite well.

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Evidence on the Fisher Hypothesis Nominal Interest Rates and Inflation Across Latin America in the Early 1990s Roughly half of the points are above the line, the other half below. This is evidence that a 1% increase in inflation should be reflected in a 1% increase in the nominal interest rate. Nominal

© 2003 Prentice Hall Business PublishingMacroeconomics, 3/e Olivier Blanchard Evidence on the Fisher Hypothesis The Three-Month Treasury Bill Rate and Inflation, The increase in inflation from the early 1960s to the early 1980s was associated with an increase in the nominal interest rate. The decrease in inflation since the mid- 1980s has been associated with a decrease in the nominal interest rate.