Notes Inflation and Interest Rates in the Medium Run

Transcription

1 Notes Inflation and Interest Rates in the Medim Rn Point of the class Math maniplating an eqation algebraically maniplating graphs Model bilding Using previos models to develop insight Economic concepts and intition Determination of otpt, inflation and nemployment in the short rn and the medim rn Definitions Sacrifice ratio Point years of excess nemployment Staggered wage contracts credibility Homework Problems On the webpage.

2 Facts [M]any of the hawks [people who think the Fed shold do more to fight inflation] do not jst differ in their otlooks [their perceptions of ftre inflation], bt in how monetary policy works. The conventional view, shared by Mr. ernanke, Donald Kohn, his inflential vice-chairman, and their professional staff, is that monetary policy affects inflation via its impact on the real economy. Higher interest rates redce demand relative to the economy s potential to spply goods and services. Redce it enogh, and nsed slack will accmlate, forcing firms and workers to compete for scarce cstomers and jobs by lowering prices and wages. The opposite happens when demand rises relative to spply. This relationship is captred in the Phillips crve, which shows inflation falling when nemployment is above its natral rate. In this view, it does not matter whether it is monetary policy or a credit crnch that raises nemployment: both pt downward pressre on inflation. What is more, Mr ernanke and his colleages reckon today s low fed fnds rate is merely offsetting tighter financial conditions from the credit crnch. The hawks, by contrast, think that nemployment and other measres of economic slack have limited bearing on the transmission of monetary policy. Fed actions affect inflation primarily by altering inflation expectations. They worry that a low fnds rate in itself threatens to lift inflation, and rising nemployment and the credit crnch will do little to contain it. The Economist, When hawks cry, Sep 11th 2008, Model ilding ilding locks The medim rn is defined as the period of time when inflation expectations and actal inflation are eqal. The Phillips Crve is Okn s Law is or ggregate Demand Inflation crve is 1 So, for any given period, the level of otpt is determined by the amont of spending by hoseholds, firms, government, etc.; by the size of the money spply, and by the inflation rate. So the change in otpt from year to year (in the short rn and in the medim rn) shold be determined by the change in the amont of spending (which we ll ignore from now on); by the change in the size of the money spply, and by the inflation rate.

3 Nominal Money Growth ggregate Demand Otpt Growth Okn s Law Inflation Phillips Crve Unemployment Ptting the ilding locks Together Medim Rn 1. In the medim rn, expectations of inflation are met,. y the Phillips Crve, this means that, nemployment eqals the natral rate of nemployment, Medim rn Phillips Crve This combines the Phillips Crve with the definition of the medim rn,. 2. In the medim rn, otpt is at the natral level of otpt,. What determines the rate of growth of the natral level of otpt? The Solow Model (chapter 11) says that long rn otpt growth depends on prodctivity growth

4 greater availability of resorces, particlarly labor and capital Neither the rate of growth of money spply nor inflation play any role in medim rn otpt growth. Trillions of $ nd if is growing, then has to be growing at the same pace. If the natral level of otpt is growing at, then that has to be the growth rate of actal otpt. growth rate, % Real GDP Potential GDP The ggregate Demand Inflation crve implies that at any point in time, otpt, money, and inflation are related: Real GDP Potential GDP However, in the medim rn, the growth rate of (the natral level of) otpt does not depend on money growth or inflation. nd money growth is exogenos. Then it mst be the case that inflation is flly determined by and by. So at any point in time, the level of inflation is nd in the medim rn This combines the D π crve with medim rn economic growth,. Medim rn inflation is determined by the rate of growth of the money spply and the growth rate of the natral level of otpt. Medim rn inflation will be higher if money spply is

5 growing faster; and it will be smaller if the natral level of otpt is growing more qickly. In other words medim rn inflation will be o o higher if the money spply grows more qickly. In the medim rn, the level of inflation is closely connected to the rate of growth of money spply. Inflation is always and everywhere a monetary phenomenon applies in the medim rn. higher if the medim rn spply of goods (the natral level of otpt) grows more slowly. ggregate Demand at Medim rn eqilibrim is determined by the intersection of these two crves. Sppose that the growth rate of the natral level of otpt rises. Then, in the medim rn, inflation shold fall. Medim rn Phillips Crve ggregate Demand at

6 Examining the Reslt and Using the Model Short Rn in D S The above implies that the monetary athority can pretty mch pick its preferred level of inflation by changing the rate of growth of money spply. S π Sppose the economy starts at the medim rn. Call it eqilibrim. Then the Central ank redces : there s a monetary contraction becase the Central ank slows down the pace at which it increases money spply. D π The graph to the right illstrates one sch sitation. In 1978, the Fed redced drastically the rate at which money spply grew. Money spply kept growing (the graph above), bt mch more slowly. If money demand doesn t change, then interest rates will rise. This will redce investment and eqilibrim short rn otpt growth,, shifting the D π crve to the left. If the natral level otpt keeps growing at the same pace, the redction in the growth rate of actal otpt leads to a recessionary gap. This raises nemployment above the natral rate of nemployment by Okn s Law. Higher nemployment lowers inflation below expected inflation, by the Phillips Crve. The economy moves along the S π crve to point. nother way of seeing this is to say that becase people are expecting an nrealistically high level of inflation, they are asking for relatively fast wage raises. Since firms can t qite afford that (as they can t raise prices that fast inflation is relatively low), some firms go bankrpt and/or lay workers off. s nemployment S π D π

7 rises, other firms are able to convince workers not to be so insistent and to accept lower wage raises. Inflation falls, bt not as mch as the decline in nominal money spply, so the real money spply contracts. Otpt doesn t fall by a mch as the decline in nominal money spply, bt it does decline. S π Medim Rn in D S D π C Over time, people realize what s happening. s inflation trns ot to be mch lower than they expected (and nemployment mch higher than normal), they begin to lower their expectations of inflation and their wage raise reqests. First, they set their new so that it is eqal to the actal. Firms recover profitability and are even able to lower their inflation rate (): S shifts. lower inflation rate means a higher level of real money spply, which leads to lower interest rates and higher otpt, moving along the D crve. Eventally, inflation falls enogh to bring otpt back to the natral level of otpt. The economy reaches a new medim rn eqilibrim at point C. If otpt retrns to the natral level, it mst be taht falls by as mch as fell. In the medim rn, otpt retrns to the natral level of otpt and the disinflation is accomplished. That is how the economy moves from medim rn to medim rn. The Short Rn Phillips Crve We can also think throgh this in terms of what happens to the Short Rn Phillips Crve. The monetary athority engineers a monetary contraction, raising nemployment. s nemployment falls below the natral rate of nemployment, inflation falls. In time, as people realize that inflation is lower than they had expected, expected inflation falls. This cases the intercept of the Phillips Crve to become smaller, and the Phillips Crve shifts down. s the economy adjsts, otpt retrns to the natral level of otpt and nemployment falls back to the natral rate of nemployment. Phillips Crve Phillips Crve C

8 The Short Rn Phillips Crve pls D Okn s Law nice way of really seeing what happens is to combine the aggregate demand crve (solving for inflation; in the short rn) with Okn s Law, expressed in growth rate terms. In the medim rn, and, and Okn s Law is 0 on both sides. Okn s Law only makes sense in the Short Rn, so we can se it to stdy the short rn. So, first, solve OL for. 1 D+OL 1 Then plg the reslt into D This gives s a graph like the one to the right. We combine OL with D and get a positive relation between nemployment and inflation: higher nemployment lowers otpt and increases inflation, for a given level of money growth. Remember that inflation is too mch money chasing too few goods. What this OL+D crve tells s is that a) if we don t hire many workers, too few goods are prodced; b) if too few goods are prodced and the amont of money is the same, inflation will rise. So, what happens when there s a disinflation? The Central ank lowers (exogenosly). This means that the D+OL crve shifts down (as the intercept becomes smaller). If the economy s short rn eqilibrim is where the Phillips Crve and D+OL intersect, then inflation falls and nemployment rises. Notice inflation is above in the middle of a disinflation, bt it s always eqal to. The reason for this is that, in the middle of a disinflation,. Eventally, lower inflation cases expected inflation to fall and the Phillips Crve shifts down. The economy retrns to medim rn eqilibrim with nemployment at its natral rate, and inflation eqal to. PC D+OL PC D+OL C

9 The Medim Rn Phillips Crve If we jst look at medim rn pictres (withot bothering to think abot the transition), the pictre looks like this (remember Okn s Law doesn t work in the medim rn, so we are jst intersecting medim rn PC with D at ). Medim rn Phillips Crve ggregate Demand at 1. In the medim rn, since the natral rate of nemployment hasn t changed, the Medim Rn Phillips Crve is vertical at the same place. 2. In the medim rn, the growth rate of the natral level of otpt,, hasn t changed. t since the rate of growth of money spply,, is smaller, the medim rn inflation rate is lower.

10 Extending the Model How mch does nemployment have to rise to bring inflation down? We can measre this by the sacrifice ratio. Consider the Phillips Crve Traditional pproach Sppose we want to change inflation by a particlar amont. We know lowering inflation means increasing nemployment above the natral rate: that is, generating cyclical nemployment. How mch? Label the desired change in inflation. If doesn t change, 0. Then Then Sppose that 0.5, and we want to redce inflation by 3 percentage points, 3. Then. 6 nemployment has to be 6 percentage points above the natral rate dring one year; or nemployment has to be 3 percentage points above the natral rate dring two years; or nemployment has to be 2 percentage points above the natral rate dring three years; or nemployment has to be 1 percentage point above the natral rate dring six years

11 Expectations and Credibility Robert Lcas and Thomas Sargent arged that if the monetary athority changes not only the rate of growth of money, bt expectations of inflation (by telegraphing the ftre path of monetary policy, perhaps), it can redce the sacrifice ratio significantly. If the Central ank has enogh credibility as an inflation fighter, it can bring inflation down with little pain. What if the annoncement of the Central ank s plans is so credible that falls immediately? We can see that the necessary cyclical nemployment will be less if expected inflation falls. So sppose that 0.5, and we want to redce inflation by 3 percentage points, 3, and falls by 2 percentage points, 2. Then nemployment has to be 2 percentage points above the natral rate dring one year; or nemployment has to be 1 percentage point above the natral rate dring two years 2 3 Nominal Rigidities and Contracts Often, even if people change their expectations of inflation, the wage contracts are written so that it s not possible to change very qickly, so inflation cannot fall very qickly. In particlar, wages are renegotiated at different times in the year: they are staggered. It wold take a hge amont of nemployment to bring inflation down qickly. To prevent this, one has to wait ntil wage contracts are changed. Stanley Fischer and John Taylor arged that the path of inflation oght to be more like this:

12 The monetary athority annonces its intentions to follow this path at time 1, and over time workers adjst their wage reqests to match the annonced path. The problem is that people might not believe a monetary athority s intention to redce inflation if inflation takes years and years to come down. Empirical Evidence The disinflation of the 1980s created 12 point years of excess nemployment, along the lines of the Traditional pproach. 1. Disinflations typically are accompanied by higher nemployment (spports traditional). 2. Faster disinflations have smaller increases in nemployment (spports Lcas Sargent). 3. Sacrifice ratios are smaller in contries with shorter wage contracts (Spports Fischer Taylor).

13 Nominal and Real Interest Rates in the Short Rn and in the Long Rn ssme the economy starts at. Then the Central ank raises the rate of growth of money spply. We know that in the short rn, higher money spply growth shifts the D+OL crve p, leading to lower nemployment and higher inflation. (In terms of or Chapter 7 analysis, it shifts D to the right, pshing otpt above the natral level; otpt growth is faster than the normal rate.) PC D+OL S π D D π Inflation rises, bt it doesn t rise by very mch becase expectations of inflation are fixed. Unemployment falls below the natral rate of nemployment (and otpt goes above the natral level of otpt) pshing inflation above expected inflation. In the medim rn, when expectations of inflation rise too, inflation will rise by more. Then nemployment rises back to the natral rate and otpt falls back to the natral level; otpt growth is eqal to the normal rate. PC C D+OL C S π S π D D π Sticky Inflation This means that in the short rn, inflation is somewhat sticky. Expectations of inflation don t change very fast, so inflation doesn t move a whole lot in response to changes in otpt. In the medim rn, inflation is flexible, so inflation adjsts flly. y how mch?

14 In the medim rn, otpt doesn t change. y the D inflation crve, the real money spply mst go back to the original level. This only happens if, in the medim rn, prices rise by as mch as the nominal money spply. o That is, if inflation rises as mch as t inflation is slow to adjst. Then, when inflation begins to move, it has to speed p at first above the new rate of growth of money spply, and then come back to the original speed. o Imagine a car race in which car starts at 100 miles per hor while car is slow to start, starting at only 80 mph. The only way car can catch p with car is by first speeding p to, say, 120 mph, and then, once it s level with car, slowing to 100 mph. % Inflation rate, % C Money Spply growth rate, % time Nominal Interest rates If then is constant (points,, and C) If then falls (between and ) If then rises (between and C) t the beginning, sticky inflation fails to catch p with the new, higher rate of growth of money spply. Nominal interest rates fall. Lower interest rates case otpt to be higher than the natral level of otpt, so inflation rises and rises ntil it catches p ( ), and nominal interest rates stop falling. However, nominal interest rates have stopped falling bt at a low level. Otpt is still higher than the natral level of otpt, so inflation keeps rising. Now and nominal interest rates rise. They keep rising ntil they get otpt to fall back to the natral level of otpt. s otpt falls, inflation slows down. Eventally again, now to stay. Real Interest Rates In the first few months, becase inflation changes jst a little bit, real interest rates fall a little bit more than nominal interest rates. Remember

15 What happens afterwards? In the long rn, otpt goes back to the natral level of otpt. What happens to medim rn real interest rates? In the case of an expansion in spending (e.g., government spending), in the medim rn otpt goes back to the natral level, bt medim rn interest rates change. The reason is that a change in spending at any level of otpt implies a change in saving. Imagine The government decides to spend more bt leave taxes alone. It will borrow more, at any level of private saving Real interest rates (the real cost of borrowing) will rise. So changes in saving and investment change the real interest rate. 1 On the other hand, consider the case of a monetary expansion. Nothing happens in the medim rn to the levels of consmption, investment, government spending, or net exports. Therefore, in the case of a monetary expansion, nothing happens to the real interest rate in the long rn. There are two possibilities. i Y n LM Crve IS Crve Y 1. Money spply rises, bt the growth rate of money spply doesn t rise (it s a one off increase). a. In the medim rn prices rise as mch as the money spply. b. Expected inflation doesn t rise (its s only a one off increase in money spply, so prices grow bt inflation goes back to the original level). c. The LM crve shifts back to where it started and nominal interest rates go back to the original level. 2. The growth rate of money spply rises. a. In the medim rn prices rise as mch as the money spply. b. Expected inflation eventally rises, in the medim rn, to match the growth rate of money spply (to keep nominal interest rates from constantly changing). c. ecase nothing happens to the real interest rate in the long rn, if expected inflation rises, the change in nominal interest rates mst eqal the i change in expected inflation. In the case of a monetary expansion, nothing happens to the real interest rate in the long rn. t the beginning, as sticky inflation fails to catch p with the rate of growth of money spply and nominal interest rates fall, real interest Y LM Crve IS Crve Y 1 The qantity of investment and the qantity of saving mst eqal in eqilibrim. If government spending rises, real interest rates will rise, hoseholds will want to increase the qantity of saving, and firms will find borrowing more expensive, and will redce the qantity of investment.

16 rates fall too, by a little more than the fall in nominal rates. ecase inflation keeps rising, real interest rates keep falling even after nominal interest rates have stopped and even begn to rise. s nominal rates rise, real interest rates also begin to rise (bt more slowly, becase expected inflation rises). In the medim rn, real interest rates mst go back to the original level and expected inflation mst eqal the new rate of growth of money spply. So nominal interest rates eqal their sm.