Lecture 15 Economics UN3213 Intermediate Macroeconomics Professor - - PowerPoint PPT Presentation

Columbia University Department of Economics

Lecture 15

Economics UN3213 Intermediate Macroeconomics Professor Mart ´ ın Uribe Spring 2019

Announcements: Welcome back! HWK 4 will be returned on wednesday. Recitations: Review of midterm.; usual place/time. OH: usual place/time.

Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Topics Today

• The nominal interest rate, the real interest rate, and inflation.
• Long-run regularities about inflation and nominal interest rates
• The Fisher Equation
• The Fisher Effect
• The Neo Fisher Effect

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Real and Nominal Interest Rates The Nominal Interest Rate. The nominal interest rate in period t, denoted it, says that if you invest 1 dollar in period t, then in period t + 1 you receive your 1 dollar back plus it dollars in interest. The Real Interest Rate. Now consider the following question: if you sacrifice one unit of consumption (say one slice of pizza) in period tand invest the value of that unit of consumption in the bank for one period, how many units of consumption do you get in period t + 1? If the price of one unit of consumption in period t is Pt, then you can invest Pt dollars in period t. In t + 1, the bank will give you your capital back plus interest, that is, the bank will give you Pt(1 + it). How many units of consumption can you buy with this money ? If the price of one unit of consumption in period t+1 is Pt+1, then you will be able to buy Pt(1+i)

Pt+1

units of goods in period t + 1. Summing

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up, if you invest one unit of good in period t, then in period t + 1 you get your unit of good back plus Pt(1+i)

Pt+1

−1 units of consumption in interest. We call this the real interest rate and denote it by rt. So we have that 1 + rt = (1 + it) Pt Pt+1 (1) The real interest rate determines how much households will con- sume today and how much they will save for the future. You may recall that in the two-period economy we studied in the previous two lectures, consumption in period 1, C1, and savings in period 1, S1, depend on (1 + i)P1

P2, which is precisely the real interest rate.

Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Inflation and Interest Rates The percent change in the price level between periods t and t + 1 is called the inflation rate, which we denote by πt+1. That is, πt+1 = Pt+1/Pt − 1. So we can write the expression (1) as 1 + rt = (1 + it)/(1 + πt+1) Taking natural logarithms yields ln(1 + rt) = ln(1 + it) − ln(1 + πt+1) and using the approximation that for x small ln(1 + x) ≈ x we have rt = it − πt+1

• r,equivalently

it = rt + πt+1. (2)

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Because, as we argued above, consumption and savings depend on the real interest rate, the central bank would like to control rt. But it can only controls the nominal interest rate, it. If, however, prices were sticky in the short run, so that Pt is relatively fixed, and Pt+1 expectations about the next period price level are well anchored, so that Pt+1 is also more or less fixed, then inflation, πt+1, is also more

• r less fixed in the short run. In this case, since rt = it−πt+1, we have

that the central bank, in the short-run, can control the real interest rate by simply controlling the nominal interest rate. In particular, a monetary tightening whereby the central bank increases the nominal interest rate by 1 percentage point results in an increase in the real interest rate by 1 percentage point. That is, the real rate moves

• ne-for-one with the nominal interest rate. This is precisely what we

did in the previous two classes when analyzing the two-period model with sticky prices. There, we discussed how to set the nominal rate so that aggregate demand equals aggregate supply and the economy displays full employment.

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

The Fisher Equation The American economist Irving Fisher was the first to explicitly note that the nominal interest rate is the sum of two compensations to those who save in assets denominated in dollars: One is a real compensation that rewards the saver for postponing consumption for a period. The other one compensates the saver for the loss of purchasing power that an asset denominated in dollars is expected to suffer during the investment period due to inflation. Formally, the Fisher equation is 1 + it = (1 + rt)(1 + Eπt+1) (3) where E denotes expected value, so that Eπt+1 is expected inflation between periods t and t + 1. Note that this expression is identical to (2), except that πt+1 is replaced by Eπt+1. The reason why the Fisher equation features expected rather than realized inflation is that in period t we don’t know what Pt+1 will be. In other words, in equation (2) rt and πt+1 are the realized real interest rate and inflation, whereas in equation (3), rt and Eπt+1 are the expected real interest rate and the expected rate of inflation.

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Taking logs on both sides of (3), we approximately have that it = rt + Eπt+1 In words, the Fisher equation says that the nominal interest rate is the sum of the real interest rate and expected inflation.

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Inflation and Interest Rates in the Long Run: The Fisher Effect Now we change focus and consider the long-run relationship between nominal interest rates, real interest rates, and inflation. Irving Fisher argued that in the long run the real interest rate rt is determined by real factors, such as the state of technology, demo- graphics, etc. In addition, unlike what happens in the short run, in the long run inflation is not rigid. In other words, in the short run Eπt+1 is relatively fixed so that, by the Fisher equation it = rt + Eπt+1, changes in it are associated with one for one changes in rt. By contrast, according to Fisher, in the long run the real rate, rt, is determined by real factors and is therefore independent of the level

• f the nominal rate, it. It then follows by the Fisher equation (3)

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that changes in the nominal interest rate, it, must be associated with one for one movements in expected inflation in the long-run. Let see if the Fisher effect is borne out in the data. That is, let see if over long horizons the nominal interest rate and expected inflaiton are linked more or less a one to one fashion. In the next graphs we show long-run averages of the nominal interest rate and inflation (which is a proxy for the average of expected inflation) to illustrate the point that (i) the real rate seems to be largely independent of the level of the nominal rate and (ii) that inflation moves one-for-one with nominal rates in the long-run. Our sample consists of 25 OECD countries. Each dot represents one

• country. The solid line is the 45-degree line. The average sample is

1989 to 2012.

Econ UN3213: Interm. Macro Monetary Economics Lecture 15

5 10 15 5 10 15 Average of πt, in percent Average of it in percent

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Observations on the figure: The 25 dots are remarkably close to tracing out a line with slope 1 and a positive intercept. The figure thus provides support to the hypothesis that in the long run nominal rates and inflation move one for one. We next plot the same data (that is, the same 25 points) in another way to see if there is any systematic relationship between it − πt and it in the long run. If higher nominal rates mean higher real rates even in the long run, then this plot should be upward sloping. If,

• n the other hand, in the long run rt is independent of monetary

factors, then the plot should not have a clear slope and should look more like a horizontal line with an intercept equal to r.

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

5 10 15 −1 1 2 3 4 5 6 7 Average of it, in percent Average of it − πt in percent

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Let’s summarize our findings thus far as follows: Two Important Long-Run Empirical Regularities involving in- terest rates and prices (a) In the long run, average inflation increases one-for-one with the nominal interest rate. (b) In the long run, the real interest rate is unrelated to the average nominal interest rate.

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

From the Fisher Equation to the Fisher Effect and to neo Fisheri- anism When people talk about the Fisher Effect they typically have in mind the long-run empirical relationship we just documented: in the long-run high nominal rates come together with high inflation rates. That is, in the long run high nominal rates cannot be used to bring about low inflation. Robert E. Lucas, Jr., Nobel Prize in Economics 1996, expresses this idea as follows in his Nobel Lecture: Central bankers and even some monetary economists talk knowledgeably of using high interest rates to control infla- tion, but I know of no evidence from even one economy linking these variables in a useful way, let alone evidence as sharp as that displayed in figure 1.

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

The definition of the Fisher Effect is that a long-run increase in the nominal rate increases inflation in the long run. An implication of the Fisher Effect is therefore that in the long-run real rates don’t respond much to nominal rates.

• Most economists agree that in the long-run a permanent increase in the nominal

interst rate increases inflation.

• Most economists also agree that in the short-run a temporary increase in the

nominal interest rate depresses aggregate demand, putting downward pressure on inflation.

• However there is disagreement on what happens in the short-run in response

to a permanent increase in the nominal interest rates. Some economists argue that a permanent increase in the nominal interest rates raises inflation already in the short run. This effect has come to be known as the Neo Fisher Effect . Others however maintain that a permanent increase in the nominal rate, in the short run, raises real rates, and in this way puts depresses aggregate activity and

• inflaiton. Hence raising rates, even if intended to be permanent, they argue, leads

to a recession and lower inflaiton in the short run. So, which view has more empirical support, the Neo-Fisherian or the conventional

• ne?

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Why is this debate happening now (and not in the 1970s, say, when inflation was high)? In an environment with falling inflation, inflation expectations may become unanchored and in such a situation an increase in nomi- nal rates may contribute to re-anchoring expectations around the intended target and lifting the economy out of a slump (the neo- Fisher effect). So the Neo-Fisher effect suggests that a way out of the Liquidity Trap is to raise rates, that is, the United States, Japan, and the Euro area should normalize rates. Of those 3, only the U.S. has raised rates thus far. Japan and Euro area are still at the zero lower bound.

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Empirical Evidene on the neo-Fisher Effect What does the data say? Uribe (2017) estimates the neo-Fisher effect in the United States and Japan. His estimated model produces dynamics consistent with the neo-Fisherian prediction that a credible and gradual increase of nominal interest rates to normal levels can generate a quick reflation of the economy with low real interest rates and no output loss.

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Estimated Impulse Responses to Interest-Rate Shocks: United States

5 10 15 20 0.5 1 1.5 2 quarters after the shock deviation from pre−shock level percentage points per year Permanent Interest−Rate Shock Response of the Interest Rate and Inflation Interest Rate Inflation Inflation 95% band 5 10 15 20 −1 −0.5 0.5 1 quarters after the shock deviation from pre−shock level percentage points per year Temporary Interest−Rate Shock Response of the Interest Rate and Inflation Interest Rate Inflation Inflation 95% band 5 10 15 20 −0.5 0.5 1 1.5 quarters after the shock percent deviation from pre−shock level Permanent Interest−Rate Shock Response of Output Output 95% band 5 10 15 20 −2 −1.5 −1 −0.5 0.5 quarters after the shock percent deviation from pre−shock level Temporary Interest−Rate Shock Response of Output Output 95% band

Source: Uribe, 2017.

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Estimated Response of the Real Interest Rate to Permanent and Transitory Interest-Rate Shocks: United States

5 10 15 20 −1 −0.5 0.5 1 1.5 quarters after the shock Deviation from steady state percent per year Real Rate Response Permanent shock Transitory shock Source: Uribe, 2017. The real interest rate is defined as Rt − Eπt+1.

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Econ UN3213: Interm. Macro Monetary Economics Lecture 15

Observations on the Previous Two Figures

• By assumption/construction, in response to a permanent posi-

tive interest-rate shock both the nominal interest rate and inflation increase by 1 percent in the long run.

• The main result conveyed by the figure is that inflation reaches its

long-run value in the short run.

• In fact, inflation adjusts faster than the nominal interest rate, so

the real interest rate falls on impact and converges from below.

• The adjustment does not entail output loss.
• By contrast, the responses of nominal and real variables to a

transitory increase in the nominal interest rate are conventional: The real interest rate increases on impact and converges from above, and

• utput and inflation fall.

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