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 1
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 i t , says that if you invest 1 dollar in period t , then in period t + 1 you receive your 1 dollar back plus i t 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 t and 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 P t , then you can invest P t dollars in period t . In t + 1, the bank will give you your capital back plus interest, that is, the bank will give you P t (1 + i t ). How many units of consumption can you buy with this money ? If the price of one unit of consumption in period t +1 is P t +1 , then you will be able to buy P t (1+ i ) units of goods in period t + 1. Summing P t +1 2
up, if you invest one unit of good in period t , then in period t + 1 you get your unit of good back plus P t (1+ i ) − 1 units of consumption P t +1 in interest. We call this the real interest rate and denote it by r t . So we have that 1 + r t = (1 + i t ) P t (1) P t +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, C 1 , and savings in period 1, S 1 , depend on (1 + i ) P 1 P 2 , 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 π t +1 . That is, π t +1 = P t +1 /P t − 1. So we can write the expression (1) as 1 + r t = (1 + i t ) / (1 + π t +1 ) Taking natural logarithms yields ln(1 + r t ) = ln(1 + i t ) − ln(1 + π t +1 ) and using the approximation that for x small ln(1 + x ) ≈ x we have r t = i t − π t +1 or,equivalently i t = r t + π t +1 . (2) 3
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 r t . But it can only controls the nominal interest rate, i t . If, however, prices were sticky in the short run, so that P t is relatively fixed, and P t +1 expectations about the next period price level are well anchored, so that P t +1 is also more or less fixed, then inflation, π t +1 , is also more or less fixed in the short run. In this case, since r t = i t − π t +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 one-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. 4
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 + i t = (1 + r t )(1 + Eπ t +1 ) (3) where E denotes expected value, so that Eπ t +1 is expected inflation between periods t and t + 1. Note that this expression is identical to (2), except that π t +1 is replaced by Eπ t +1 . The reason why the Fisher equation features expected rather than realized inflation is that in period t we don’t know what P t +1 will be. In other words, in equation (2) r t and π t +1 are the realized real interest rate and inflation, whereas in equation (3), r t and Eπ t +1 are the expected real interest rate and the expected rate of inflation. 5
Econ UN3213: Interm. Macro Monetary Economics Lecture 15 Taking logs on both sides of (3), we approximately have that i t = r t + Eπ t +1 In words, the Fisher equation says that the nominal interest rate is the sum of the real interest rate and expected inflation. 6
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 r t 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 Eπ t +1 is relatively fixed so that, by the Fisher equation i t = r t + Eπ t +1 , changes in i t are associated with one for one changes in r t . By contrast, according to Fisher, in the long run the real rate, r t , is determined by real factors and is therefore independent of the level of the nominal rate, i t . It then follows by the Fisher equation (3) 7
that changes in the nominal interest rate, i t , 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 15 10 Average of i t in percent 5 0 0 5 10 15 Average of π t , in percent 8
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 i t − π t and i t 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, on the other hand, in the long run r t 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 . 9
Econ UN3213: Interm. Macro Monetary Economics Lecture 15 7 6 5 Average of i t − π t in percent 4 3 2 1 0 −1 0 5 10 15 Average of i t , in percent 10
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. 11
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. 12
Recommend
More recommend
