{ "cells": [ { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%%javascript\n", "\n", "IPython.OutputArea.prototype._should_scroll = function(lines) {\n", " return false;}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Phillips Curve, Expectations, and Monetary Policy\n", "\n", "**QUESTIONS**\n", "\n", "1. What can shift the Phillips curve?\n", "\n", "2. What is the Monetary Policy Reaction Function? \n", "\n", "3. What determines the slope of the Monetary Policy Reaction Function?\n", "\n", "4. What is the natural rate of unemployment? How has its value changed?\n", "\n", "5. What are static expectations of inflation? Adaptive? Rational? Panglossian? Eeyore? Diagnostic?\n", "\n", "6. How has the expected rate of inflation changed?\n", "\n", "7. How do we use the Phillips curve, the Monetary Policy Reaction Function, and the way in which expectations of inflation are determined to analyze the economy?\n", "\n", "8. How do we connect the sticky-price model of Part IV with the flexible-price model of Part III?\n", "\n", " \n", "\n", "**output gap**: The difference between the actual and potential levels of output, Y - Y*.\n", "\n", "**Okun's law**: Periods of low (or high) national product relative to potential output correspond to periods of high (or low) unemployment relative to the natural rate.\n", "\n", "**natural rate of unemployment**: The rate of unemployment where actual and expected inflation are equal, and there is no downward or upward pressure on inflation.\n", "\n", "**sticky prices**: When wages and prices do not move smoothly and immediately to keep supply equal to demand in the labor and goods markets.\n", "\n", "**Phillips curve**: The downward-sloping relationship between unemployment and inflation: The higher expected inflation, the higher the unemployment rate needed to keep inflation at any particular level.\n", "\n", "**expected inflation** The rate at which the inflation rate was expected to increase. Today's expected inflation rate is yesterday's guess about today's inflation rate.\n", "\n", "**\"neutral\" baseline real rate of interest**: The real interest rate that the central bank would set if the inflation rate were equal to the central bank's target inflation rate.\n", "\n", "**interest rate rule**: A description of how the real interest rate that the central bank sets depends on the gap between the current inflation rate and the central bank's target inflation rate.\n", "\n", "**monetary policy reaction function (MPRF)**:\n", "An upward-sloping relationship between the inflation rate and the unemployment rate. When the inflation rate rises, a central bank wishing to fight inflation will raise interest rates to reduce output and thus increase the unemployment rate.\n", "\n", "**static expectations**: Visions of the future that do not change at all in response to changes in the current economic situation.\n", "\n", "**adaptive expectations**: Expectations of the future formed by assuming the future will be like the past.\n", "\n", "**rational expectations**: Expectations about the future formed by using all information about the structure of the economy and the likely course of government policy.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This may well be the most important section of our analysis of business cycles. This draws together the flexible-price business cycle model of Part III and the sticky-price business cycle model of the previous portions of Part IV. It provides a bird’s-eye overview of demand, monetary policy, and inflation. At the start of Part IV we analyzed demand and the multiplier. We then added interest rates and their effect on investment and exports. Here we build on those two and add unemployment, inflation, and monetary policy—how the Federal Reserve makes its decisions.\n", "\n", "When you finish this section, you will have a comprehensive view of how business cycles and demand management work. The Federal Reserve responds to unemployment and inflation by choosing a monetary policy that aims at price stability and full employment with the first goal taking priority. That monetary policy then—through the IS-Curve mechanisms—determines investment and exports and—through the Keynesian-cross and multiplier mechanisms—the level of production. The level of production relative to potential output itself feeds back and generates unexpected rises and declines in inflation relative to what was previously anticipated.\n", "\n", "But that is not all this section does. It also analyzes expectations—how the previous anticipations of prices and inflation are formed. Expectations are key, for they provide the linkage between the sticky-price model of Part IV and the flexible-price model of Part III.\n", "\n", "That is how this section accomplishes its two major goals: to complete the construction in this Part IV of the sticky-price model and to link the sticky-price macroeconomic model analysis to the flexible-price macroeconomic model analysis of Part III. The key to accomplishing both of these is an analytical tool called the Phillips curve. The Phillips curve describes the relationship between inflation and unemployment, according to which a higher rate of unemployment is associated with a lower rate of inflation.\n", "\n", "The plan of this chapter is to first examine aggregate supply and the Phillips curve: Why is there—in the short run of our sticky-price model—a positive relationship between production Y on the one hand and the price level P and the inflation rate π on the other (and thus also a negative relationship between unemployment and inflation)? This leads into an analysis of how the existence of the aggregate supply relationship and the Phillips curve affects modern central banks’ conduct of monetary policy and the important concept of the Monetary Policy Reaction Function. Then it is time to put all the pieces together by bringing into the picture the key elements of the determinants of the natural rate of unemployment and the kinds of expectations that play an overwhelmingly important role in determining how modern economies behave.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12.1 Aggregate Supply and the Phillips Curve\n", "\n", "### 12.1.1 Unemployment\n", "\n", "So far in this book one of our six key economic variables, the unemployment rate, has been largely absent. In Part II, the long-run growth section, unemployment was not a significant factor. In Part III, the flexible-price macroeconomic model section, there were no fluctuations in unemployment. Wages and prices were flexible, and so labor supply balanced labor demand.\n", "\n", "But this is Part IV. And now it is time to bring unemployment and its fluctuations to center stage.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.1.1.1 Unemployment and Okun's Law\n", "\n", "We have seen above that there is generally an inverse relationship between the unemployment rate u and the output gap—the level of real GDP relative to potential output Y\\*: each one percentage point fluctuation in the unemployment rate has been associated with a roughly 2.5 percentage point fluctation in the opposite direction in national income relative to potential output. This relationship is called Okun’s law. \n", "\n", "If we can trust Okun’s law, we do not have to conduct separate analyses of real GDP and unemployment: We know that when one is high the other is low, and vice versa.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.1.1.2 Unemployment and Its \"Natural Rate\"\n", " \n", "Milton Friedman and Ned Phelps back in 1966 strongly argued for using the unemployment rate as the most reliable gauge of the state of the business cycle. He defined a concept that he was among the first to call the \"natural rate\" of unemployment—let’s call it u\\*. At that unemployment rate, he argued, the labor market would be putting neither upward nor downward pressure on the rate of inflation. At that unemployment rate, he argued, there would be only the normal, frictional number of workers without jobs and onky the normal, frictional number of vacancies—jobs empty, and open to workers. \n", "\n", "At a lower unemployment rate, employers would find it surprisingly hard to fill vacancies—and they would raise the wages they paid and the prices they charged by surprising amounts to try to run their businesses. \n", "\n", "At a higher unemployment rate, workers would find it surprisingly hard to get jobs—and those who had jobs would forego wage increases and so provide employers with the room to charge less than they would have otherwise. Only if unemployment was equal to its \"natural rate\", Friedman argued, would the labor market be in a proper equilibrium—and would surprisingly high and surprisingly low inflation both be avoided.\n", "\n", "Friedman defined this no-surprise level of the unemployment rate as the way of determining when output Y would be equal to potential output Y\\*. Were output Y above potential output Y\\*, the unemployment rate u would be below the natural rate of unemployment u\\* and there would be upward pressure on the rate of inflation. Were output Y below potential output Y\\*, the unemployment rate u would be above u\\*, and there would typically be downward pressure on the rate of inflation.\n", "\n", " \n", "\n", "\"Consumer\n", "\n", ">**U.S. Core Inflation Rate and Unemployment Rate since the Late 1950s**\n", "\n", " \n", "\n", "There is definitely a great deal to Friedman and Phelps's argument. In U.S. economic history during World War II, times of high unemployment are no typically times when inflation is or is about to be low, but rather times when inflation is or is bout to be falling. Times of low unemployment like 1999-2000, 1988-1990, and the late 1960s are frequently times in which inflation is or is about to rise.\n", "\n", "But there is a lot more going on. The high unemployment of 2008-2011 did not produce anything but the mosat transient fall in inflation. The low unemployment of 2016-2018 did not produce signs of an inflation pickup. And th big spikes in inflation that came along with the oil-price supply shocks of 1973 and 1979 are grossly disproportionate to any upwards pressure on inflation coming from low unemployment and high production relative to potential.\n", "\n", "It is only to a very weak degree that we can forecast from unemployment (or employment) how inflation in the future will be different from inflation today.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.1.1.3 \"Natural Rate\" or NAIRU?\n", " \n", "Some economists objected to Friedman's calling this no-surprises-in-inflation level of unemployemnt the \"natural rate\". Things that are \"natural\" are often understood as good or desirable. They prefer to call it the NAIRU, for \"non-accelerating inflation rate of unemployment\". They prefer to abandon Milton Friedman's definition of the natural rate as what unemployment _should_ be were the economy not being disturbed by fluctuations in monetary policy and in government purchases, but rather as simply this: the unemployment rate below which inflation begins to accelerate, as people find themselves unable to buy commodities and hire workers at the prices they were expecting to be able to—is not and has never been constant.\n", "\n", "Reading the tea leaves on just what the NAIRU—the natural rate—is at any moment is difficult and hazardous. The situation is complicated by the occurrence of major supply shocks: large jumps in prices, almost always in oil prices, that induce large shifts in inflation. The Organization of Oil-Exporting Countries—OPEC—tripled world oil prices in 1973. The Iranian Revolution and the consequent cutoff of Iranian oil supplies again tripled world oil prices in 1979. Saudi Arabia's decision to punish its OPEC partner countries for pumping more oil than their assigned quotas led to a collapse of world oil prices in 1986. And the years 2006-7 saw another oil shortage as OPEC took advantage of China's immense and rapidly-growing demand for oil to raise prices again. \n", "\n", "All of these episodes leave clear marks on the trajectory of inflation that are different from the effects of the unemployment rate and output relative to the natural rate and potential that are at the heart of the Phillips Curve.\n", "\n", "Nevertheless, the Phillips Curve relationship does work: In the late 1960s inflation began to accelerate when the unemployment rate dropped below 4%. Inflation then accelerated from 2% per year to 6% per year, and then declined when the unemployment rate rose above 5%, strongly suggesting a then-NAIRU or natural rate of 5%. But in the late 1970s inflation began to accelerate when the unemployment rate dropped below 7%. The late 1980s, however, saw the unemployment rate decline almost to 5% before their were signs of accerlatig inf;lation. And in the late 1990s it took a decline in the unemployment rate to less than 4.5 before inflation began to creep up.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.1.2 Okun's Law\n", "\n", "The unemployment rate is of interest because a high unemployment rate means a lot of people are without market incomes, and so in all likelihood materially poor and psychologicall depressed. A high-unemployment economy is very likely to be one with low social welfare. But a high unemployment economy is also one that is performing poorly because high unemployment (or, alternatively, low prime-age employment as a share of the population) is a reading on a thermometer telling us that production is below potential output. High unemployment goes with a large output gap—a large shortfall of national income and product below the economy's sustainable productive potential.\n", "\n", "Okun’s law relates the unemployment rate u (relative to the natural rate of unempployment u\\*) to real GDP Y (relative to potential output Y\\*). When Y is equal to Y\\*, then the unemployment rate u is equal to the natural rate of unemployment u\\*. When real GDP Y is different from Y\\*, the unemployment rate u will be different from the natural rate of unemployment u\\* by an amount described by the equation:\n", "\n", "> $ u - u^* = -0.4\\left(\\frac{Y - Y^*}{Y^*}\\right)$\n", "\n", "> $ -2.5\\left(u - u^*\\right) = \\frac{Y - Y^*}{Y^*}$\n", "\n", "When real GDP is above potential output, unemployment will be below the natural rate of unemployment. When real GDP is below potential output, unemployment will be above the natural rate. And the percentage-point gap between unemployment and its natural rate is roughly two-fifths the magnitude of the percentage gap between real GDP and potential output. For example, if real GDP is 10 percent below potential output, then the unemployment rate will be 4 percentage points above the natural rate of unemployment: If the natural rate of unemployment u\\* is 5 percent, then the unemployment rate u will be 9 percent.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.1.2.1 A Recent Shift in Okun's Law?\n", "\n", "Unfortunately, there are signs that Okun's Law has been becoming less reliable as an empirical regularity in this millennium, and especially so since 2008.\n", "\n", " \n", "\n", "\"Preview\n", "\n", ">**Decreased Reliability of Okun's Law in This Millennium?**\n", "\n", " \n", "\n", "From 1980 to 1990 the unemployment rate was a better guide to whether the level of national income and product in the economy was close to potential output. The feminist revolution in the workforce was still ongoing. Women's participation in the labor force and in employment was growing rapidly. The start of 1980 and the end of 1990 saw similar unemployment rates: about 6.5 percent. But the share of American 25-54 year-olds—too old for many of them to be school, too young for many of them to be plausibly retired—was 4 percentage points higer at the end of 1990 than it had been at the beginning of 1980.\n", "\n", "From the early 1990s to the mid-2000s, both the 25-54 year-old employment rate and the unemployment rate told the same story about the state of national income and production relative to potential output. But by 2007 they were sending different signals. The unemployment rate then was only half a percentage point above the level it had reached in 2000—suggesting an economy close to if not at the same relationship to potential output. But the prime-age 25-54 year-old employment rate was two percentage points lower—suggesting that great deal of headroom remained for further economic expansion before production relative to potential reached the mark it had attained in 2000.\n", "\n", "And since 2007 the two have told very different stories. The unemployment rate today is lower than the mark attained at the business-cycle peak of 2000. The prime-age employment rate is still 2.5 percentage points lower. The first suggests no headroom for further expansion without pushing production above sustainable potential. The second suggests substantial remaining headroom.\n", "\n", "Which is correct? Either there are a lot more people who want and would take jobs if they were offered right now than we would think from the level of the unemployment rate, or something like one out of every 40 Americans 25-54 has mysteriously lost their desire to work at paid employment.\n", "\n", "In our models here we will use the unemployment rate as our thermometer of whether production and national income are below, at, or above potential output. But beware! When we move to applying our models to the real world, perhaps we should be using not:\n", "\n", "> $ \\frac{Y - Y^*}{Y^*} = -2.5\\left(u - u^* \\right) $\n", "\n", "but rather something like:\n", "\n", "> $ \\frac{Y - Y^*}{Y^*} = 1.5\\left(E - E^* \\right) $\n", "\n", "where E is the prime-age 25-54 employment rate, in order to usefully understand the real economy.\n", "\n", "However, whatever happens with the form nd parameters of the quantitative relationship, we are still sure about the qualitative direction: Higher real GDP Y (relative to potential output Y\\*) means lower unemployment u (relative to the natural rate u\\*) and higher employment and vice versa.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.1.3 Costs of High Unemployment: Relevance for Economic Policy\n", "\n", "In a typical U.S. recession, unemployment rises by 2 percentage points. By Okun’s law, that means that the output gap—real GDP relative to potential output—falls by some 5 percent. Five percent is about three years’ worth of growth in output per worker.\n", "\n", "Moreover, recessions are not permanent; with important exceptions, they are over in a year or three and followed by a strong recovery—with notable exceptions, like the long drawn-out and very weak recovery fter the Great Recession of 2007-2009. Morever, such strong recoveries are often followed by periods of growth sufficiently rapid to return real GDP to its prerecession growth trend. Before 2008, even the steepest post-World War II recession raised the unemployment rate by only 4 percentage points, and it took only three years after the recession trough for unemployment to fall back to a normal level. \n", "\n", "The Great Recession that began in 2008, however, was very different. Because it was so deep, and because the subsequent recovery was so weak, it was an economic disaster an order of magnitude greater than other post-World War II recessions.\n", "\n", "Moreover, recessions appear to have a bigger effect on social welfare than the size of the reductions in production they cause would lead us to expect. A typical recession reduces production by less than two years' economic growth, and reduces production relative to the growth trend only temporarily. Yet such episodes of recession and high unemployment appear to have a larger psychological impact relative to growth slowdowns than any comparison of their relative magnitudes in terma of their effect on real incomes would lead us to expect.\n", "\n", "Why is this the case? The most likely answer is that recessions are feared because their impact is not distributed equally. Workers who keep their jobs are only lightly affected, whereas those who lose their jobs suffer a near-total loss of income. People fear a 2 percent chance of losing half of their income much more than they fear a certain loss of just 1 percent of income. So it is much worse for 2 percent of the people to each lose half of their income than for everyone to lose 1 percent. Thus the unequal distribution of the costs of recessions is what makes them so feared—and makes voters so anxious to elect economic policymakers who will successfully avoid them.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.1.4 Aggregate Supply\n", "\n", "In our sticky-price model prices (and wages, and debts) are sticky, not stuck. They do move over time. They just don’t move fast enough to get us to the flexible-price situation of Part III immediately. Up until now we have paid next to no attention to the fact that prices are not stuck fast in the sticky-price model. But now this will change as we start to analyze what the price level P and the inflation rate it are in our sticky-price model.\n", "\n", "In the short run, we find that whenever real GDP Y is higher than potential output Y\\*, the inflation rate $ \\pi_t $ and the price level P are likely to be higher than people had previously anticipated. There are many reasons for this:\n", "\n", "One is that whenever demand for products is stronger than anticipated, firms raise their prices higher than they had previously planned. When planned expenditure is higher than potential output, demand is strong in nearly every industry Nearly all firms raise prices and hire more workers. High demand gives workers extra bargaining power. Unions threaten to strike, knowing that firms will have a hard time finding replacement workers. Individuals quit, knowing they can find better jobs elsewhere. Such a high-pressure economy generates wages that rise faster than anticipated. Rapid wage growth is passed along to consumers in higher prices and accelerating inflation. Thus high real GDP Y relative to potential output Y* generates a higher price level P and a higher inflation rate it than people had previously expected.\n", "\n", "A second reason is that when planned expenditure is higher than potential output, individual economic sectors and industries in the economy quickly reach the limits of capacity: Bottlenecks emerge. Since a building cannot be built without cement, construction companies will pay nearly any price for cement if it is in short supply. Such high prices signal to the market that the bottleneck industry should expand and eventually trigger investment that in the end boosts productive capacity. But in the meantime, developing bottlenecks lead to prices that increase faster than expected, thus to accelerating inflation and a higher price level.\n", "\n", "Note that expectations play a key role. What calls forth higher (or lower) production in the bottleneck industries is that prices and inflation turn out to be higher (or lower) than people had been counting on because demand is so high. It’s not high prices but higher-than-expected prices and inflation that are associated with high output. Economists call this correlation between real GDP Y (relative to potential output Y*) and the price level P and the rate of inflation it (relative to their previously expected values) the short-run Aggregate Supply (AS) curve.\n", "\n", " \n", "\n", "**The Course of Inflation in the American Economy**:\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.1.4.1 Aggregate Supply and the Phillips Curve\n", "\n", "Note also that there is little reason to make a big deal of distinguishing between inflation and the price level. Inflation is the change between last year’s and this year’s price level. A high price level relative to what was previously expected is a high inflation rate (relative to what was previously expected), and vice versa. \n", "\n", "So we can think of Aggregate Supply as an upward-sloping positive relationship between the price level P (relative to the previously expected price level) and the level of real GDP Y (relative to potential output). Or we can think of it as an upward-sloping positive relationship between the inflation rate it (relative to the previously expected inflation rate) and the level of real GDP Y (relative to potential output). Or we can think of it using Okun’s law. Because high real GDP Y means low unemployment u, we can think of aggregate supply as a relationship between the inflation rate it (relative to the value that people had previously expected inflation to be ire) and the unemployment rate u (relative to the natural rate u\\*).\n", "\n", "This last form of the relationship is the modern Phillips curve:\n", "\n", "> $ \\pi = {\\pi}^e - \\beta(u - {u}^*) $\n", "\n", "where we once again use $ \\pi^e $ to stand for previously expected inflation, with the e-superscript reminding us that it is an expectation. This equation tells us that inflation it is higher than it was previously expected to be when unemployment u is lower than its natural rate u\\*. By how much? That depends on the parameter $ \\beta $, the slope of this relationship. Note that this equation has time subscripts: low unemployment now means higher inflation relative to expectations next year. \n", "\n", "This is the relationship that is called the Phillips curve, after the New Zealand economist A. W. Phillips, who first wrote back in the 1950s of the relationship between unemployment and the rate of change of prices.\n", "\n", "Since Phillips’s time, economic events have led economists to change the Phillips curve to take account of shocks that can affect the inflation rate—like the major shocks to oil prices noted above. So we add an extra term to the Phillips curve:\n", "\n", "> $ \\pi = {\\pi}^e - \\beta(u - {u}^*) + SS $\n", "\n", "where SS stands for large sudden “supply shocks” that affect the rate of inflation by changing prices directly, without first changing the unemployment rate and so putting pressure on wage levels.\n", "\n", "We sketch the Phillips curve on a graph with the unemployment rate on the horizontal axis and the inflation rate on the vertical axis.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**The Phillips Curve**: When inflation it is higher than expected inflation and production is higher than potential output, the unemployment rate u will be lower than the natural rate of unemployment. There is an inverse relationship in the short run between inflation and unemployment.\n", "\n", " \n", "\n", "Recall that the Phillips curve is only one of the three possible ways of thinking about aggregate supply. The underlying economic meaning is the same no matter which form—national income and product-price level, national income and produdt-inflation, or unemployment-inflation—we use. From this point on, however, we will typically use the unemployment-inflation Phillips curve form simply for convenience.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**Three Faces of Aggregate Supply**: You can think of aggregate supply as a relationship between production (relative to potential output) and the price level, between production (relative to potential output) and the inflation rate, or between unemployment (relative to the natural rate of unemployment) and the inflation rate. These are three different views of what remains the same single relationship.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.1.4.2 The Phillips Curve Examined\n", " \n", "The slope of the Phillips curve depends on how sticky wages and prices are. The stickier are wages and prices, the smaller is the parameter $ \\beta $ and the flatter is the Phillips curve. The parameter $ \\beta $ varies widely from country to country and era to era. In the United States today it is about 0.2: a current rate of unemployment u one percentage point below the natural rate of unemployment u\\* tends to raise next year's inflation rate relative to expectations by 0.2 percentage points. When the Phillips curve is flat, even large movements in the unemployment rate have little effect on the inflation rate. When wages and prices are less sticky, the Phillips curve is nearly vertical. Then even small movements in the unemployment rate have the potential to cause large changes in the inflation rate.\n", "\n", " \n", "\n", "\"Banners\n", "\n", ">**The Slope of the Phillips Curve**: When wages and prices are very sticky, $ \\beta $ is low and the Phillips curve is flat, so a large\n", "change in the unemployment rate—say, from u\\* to $ u_1 $ in the left panel—results in a relatively small change in the inflation rate. But when wages and prices are less sticky, ySis large and the Phillips curve is steep, so even a small change in the unemployment rate—say, from u\\* to $ u_2 $ in the right panel—results in a relatively large change in the inflation rate.\n", "\n", " \n", "\n", "Whenever unemployment is equal to its natural rate u\\* and there are no supply shocks, the inflation rate $ \\pi $ will be equal to expected inflation $ \\pi^e $. Thus we can determine the position of the Phillips curve if we know the natural rate of unemployment and the expected rate of inflation. A higher natural rate shifts the Phillips curve right. Lower expected inflation shifts the Phillips curve down.\n", "\n", "If the past half-century has made anything clear, it is that the Phillips curve shifts around substantially as both expected inflation and the natural rate change. Neither is a constant. Neither is known precisely. That is one of the things that makes the Federal Reserve’s job of trying to stabilize the macroeconomy so hard, and so interesting. In America today the current natural rate of unemployment u\\* is thought to be near 4 percent. The current rate of expected inflation $ \\pi^e $ is about 2 percent per year. But both have been different in the past and will be different in the future.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**Shifts in the Phillips Curve**: When the natural rate of unemployment or expected inflation changes, the position of the Phillips curve changes too.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.1.5 RECAP: Aggregate Supply and the Phillips Curved\n", "\n", "The Phillips curve is an inverse relationship between inflation arid unemployment. It is the most convenient form of the aggregate supply relationship; so it is the one that we use. The Phillips curve tells us that when unemployment is below its natural rate, inflation is higher than expected inflation; conversely, when unemployment is above its natural rate, inflation is lower than expected inflation. \n", "\n", "The stickier wages and prices are, the flatter the Phillips curve is. \n", "\n", "When the Phillips curve is flat, even large movements in the unemployment rate have little effect on the inflation rate. \n", "\n", "When wages and prices are less sticky, the Phillips curve is nearly vertical. Then even small movements in the unemployment rate have the potential to cause large changes in the inflation rate. When the natural rate of unemployment rises (falls), the Phillips curve shifts to the right (left). When the expected inflation rate falls (rises), the Phillips curve shifts down (up).\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12.2 Monetary Policy, Aggregate Demand, and Inflation\n", "\n", "### 12.2.1 The \"Neutral\" Interest Rate and the Intereset-Rate Rule\n", "\n", "Modern central banks do not sit by and passively watch the business cycle. They play a very active role in managing the macroeconomy. Monetary policy of modern central banks reacts to the macroeconomy’s condition. And when the central bank reacts to the economy’s condition, the action it takes is to change the real interest rate.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.2.1.1 An Interest Rate Rule\n", "\n", "How do central banks decide what value the interest rate should be? Start with a simple model of how central banks act. Modern central banks pay a great deal of attention to the inflation rate. So think of the central bank as having a target value for the inflation rate $ \\pi^t $ (t for “target”): what they would like the inflation rate to be. And think of them having a belief about the “neutral” baseline value $ r_n $ of the interest rate. If inflation is higher than the central bank’s target value, the central bank raises the real interest rate r above what it considers to be the real interest rate’s “neutral” baseline value $ r_n $. If inflation is lower than its target value, the central bank reduces the real interest rate r. In the form of an equation\n", "\n", ">$ r = r_n + r_\\pi(\\pi - \\pi^e) $\n", "\n", "where the parameter $ r_\\pi $ tells us how much the central bank changes the real interest\n", "rate r in reaction to a gap between the actual and target inflation rates. If the central bankers believe the cost of fighting inflation—increased unemployment due to the higher real interest rate—is too great, $ r_\\pi $ will be low and little will be done to fight inflation. If they believe the costs of inflation outweigh the cost of increased unemployment, $ r_\\pi $ will be high. \n", "\n", "Inflation above the central bank’s target level prompts the central bank to raise the real interest rate. A higher real interest rate leads, through the IS curve relationship, to a lower level of national income and product Y relative to potential output Y\\*. Recall the steps: A higher real interest rate dampens planned expenditure—particularly investment and gross export spending—and, through the multiplier, lowers total demand. National income and product relative to potential output Y\\*, falls. And Okun’s law reminds us that reducing output Y relative to potential output Y\\* reduces employment and raises the unemployment rate.\n", "\n", "Thus the interest rule describing how the central bank’s monetary policy reacts to inflation, together with the behavior of planned expenditure, and the Okun’s law relationship between unemployment and output produce a relationship between the inflation rate r and the unemployment rate u. When the inflation rate rises, the central bank raises the real interest rate, which increases unemployment. When the inflation rate falls, the central bank lowers the real interest rate, which decreases unemployment. \n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.2.1.2 The Neutral Interest Rate\n", "\n", "How do central bankers pick their values for $ r_n $, for what they think the economy's \"neutral\" interest rate currently happens to be? A central bank does not wish for an interest rate so high that produces a level of spending, aggregate demand, so low there is excess and unnecessary unemployment—that people have a hard time finding jobs. A central bank also does not wish for an interest rate so low that aggregate demand is so high that spending outruns production—that people find themselves unable to buy the commodities they want at average prices they had expected, and so firms unexpectedly and surprisingly raise their prices so that inflation takes hold. What a central bank wants is for it to choose the $ r_n $ that is the Goldilocks value, neither too high nor too low, generating neither excessive unemployment nor surprisingly high inflation.\n", "\n", "What the central bank wants, in short, is the value for $ r_n $ to be equal to the value of r in the flexprice model: the value that drives the supply and demand for loanable funds to equality. A sticky-price economy is so built that there is nothing in the marketplace to push the real interest rate r to that flexprice full-employment equilibrium value. So the central bank tries to substitute, and repair the market failure by using its own ability to influence interest rates to substitute.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.2.2 The Monetary Policy Reaction Function\n", "\n", "We call this relationship the Monetary Policy Reaction Function (MPRF).\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**The Monetary Policy Reaction Function (MPRF)**: The MPRF summarizes a great deal of information in one curve. Inflation $ \\pi_2 $ above the central bank's target level $ \\pi^t $ leads the central bank to increase the real interest rate above $ r_n $ (interest rate rule), which decreases planned expenditure and real output (IS curve), increasing unemployment (Okun's law).\n", "\n", " \n", "\n", "The MPRF captures all of the linkages—from inflation to the real interest rate to planned expenditure to output to unemployment—at once. It tells us how the central bank’s reactions to inflation π will affect unemployment.\n", "\n", " \n", "\n", "#### 12.2.2.1 Writing the Monetary Policy Reaction Function\n", "\n", "We write this monetary policy reaction function—this MPRF—as the equation:\n", "\n", ">$ u = u_o + \\phi(\\pi - \\pi^t) $\n", "\n", "where:\n", "\n", "* $ u_o $ is the value of the unemployment rate when the central bank has set the real interest rate to what the central bank believes to be the “neutral” baseline value $ r_n $.\n", "* $ \\pi^t $ is the central bank’s target value for inflation.\n", "* $ \\pi $ is the current inflation rate to which the central bank is reacting.\n", "* u is the resulting unemployment rate.\n", "* And $ \\phi $ is the parameter that tells us how much unemployment rises when the central bank raises the real interest rate r because it thinks that inflation is too high and needs to be reduced.\n", "\n", "This parameter $ \\phi $ is itself the combination of three different factors:\n", "\n", "* The extent of the central bank’s distaste for inflation—how much the central bank typically raises interest rates in response to an acceleration in inflation, the parameter $ r_\\pi $\n", "* The slope of the IS curve—how much national income and product changes in response to a change in the real interest rate, which we have seen above as the factor $ \\mu(I_r + x_\\epsilon\\epsilon_r) $\n", "* The Okun’s law coefficient—how large a change in unemployment is produced by a change in real GDP.\n", "\n", "When will the parameter $ \\phi $ be large? When will a small increase in inflation above its target level call forth a reaction from the central bank that will push unemployment up significantly? The parameter will be large—and the MPRF will be relatively flat—if the central bank cares strongly about keeping inflation close to its target, or if investment and export spending are very sensitive to the interest rate, or if the multiplier is relatively large, or if the Okun’s law coefficient is large. The parameter will be small—and the MPRF will be steep—if the central bank is not that concerned about keeping inflation close to its target all the time, and if investment and export spending are not very sensitive to the interest rate, and if the multiplier is small, and if the Okun’s law coefficient is small.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.2.2.2 Calculating the Monetary Policy Reaction Function: An Example\n", "\n", "Recall that the monetary policy reaction function brings together three relationships at once: \n", "\n", "1. The interest rate rule: $ r = r_n + r_\\pi(\\pi - \\pi^t) $\n", "2. The IS curve equation: $ Y = \\mu(A_o) - \\mu(I_r+x\\epsilon\\epsilon_r)r $\n", "3. Okun's Law: $ u = u^* - 0.4\\left((Y-Y^*)/Y^*\\right) $\n", "\n", "Sppose:\n", "\n", ">$ \\pi^t = 0.02 $ \n", "$ \\pi = 0.05 $ \n", "$ r_\\pi = 1/3 $ \n", "$ r_n = 0.025 $\n", "\n", "Then by the interest rate rule:\n", "\n", ">$ r = 0.025 + \\frac{1}{3}(0.05 - 0.02) = 0.035 $\n", "\n", "The central bnak will conduct monetary policy to try to set the real interest rate equal to 3 percent.\n", "\n", "Suppose further that:\n", "\n", ">$ MPE - 0.5 $ \n", "$ A_o = 2.15 $ trillion \n", "$ I_r = 8 $ \n", "$ x_\\epsilon\\epsilon_r = 2 $\n", "\n", "Then the IS curve tells us that with an interest rate of 3.5 percent:\n", "\n", "> $ Y = \\frac{2.15}{1 - 0.5} - frac{8+2}{1 - 0.5}(0.035) = 3.6 $ trillion\n", "\n", "Finally, suppose that:\n", "\n", ">$ u^* = 0.05 $ \n", "$ Y^* = 4 $\n", "\n", "Then Okun's Law tells us that when output is 3.6 trillion:\n", "\n", ">$ u = 0.05 - 0.4((3.6-4)/4) = 0.09 $\n", "\n", "When the inflation rate is 5 percent rather than the central bank’s target of 2 percent, the central bank will raise the real interest rate from its normal baseline rate of 2.5 percent to 3.5 percent, which will cause output to fall to 3,600 billion and generate an unemployment rate of 9 percent.\n", "\n", "What then would the unemployment rate be if the inflation rate π were to the central bank’s target inflation rate $ \\pi^t $? In this case, the central bank will set the real interest rate to its normal baseline level $ r_n $, which in this example is 2.5 percent. Using the IS curve, we find that output Y is 3.8 trillion:\n", "\n", ">$ Y = \\frac{2.15}{1 - 0.5} - \\frac{8+2}{1 - 0.5}(0.025) = 3.8 $ trillion\n", "\n", "From Okun’s law, we then see that when the interest rate is 2.5 percent, the unemployment rate equals 7 percent:\n", "\n", ">$ u_n = u = 0.05 - 0.4((3.6-4)/4) = 0.09 $\n", "\n", "We can use $ u_n $ to stand for the rate of unemployment when $ r = r_n $.\n", "\n", "The MPRF for this economy is:\n", "\n", " \n", "\n", "\"DeLong\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.2.3 Equilibrium: The MPRF and the Phillips Curve\n", "\n", "Together, the MPRF relationship:\n", "\n", ">$ u = u_n + \\phi(\\pi - \\pi^t) $\n", "\n", "and the Phillips curve equation\n", "\n", ">$ \\pi = \\pi^e - \\beta(u - u^*) + SS $\n", "\n", "let us find out what the inflation rate π and the unemployment rate u will be in the economy. The MPRF determines the unemployment rate as a function of the inflation rate, as the central bank reacts to changes in inflation by using its monetary policy control over interest rates to manipulate planned expenditure. The Phillips curve determines inflation as a function of the unemployment rate. Both must be satisfied for this system of equations to be in equilibrium.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.2.3.1 The Slope of the Monetary Policy Reaction Function: An Example\n", "\n", "In our example above we found two combinations of inflation and unemployment that were on the MPRF: (1) when the inflation rate was 5 percent, the central bank set the real interest rate at 3.5 percent and the resulting unemployment rate was 9 percent; and (2) when the inflation rate was at its target level of 2 percent and the real interest rate was set at its “normal” baseline rate of 2.5 percent, the resulting unemployment rate was 7 percent.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**The Slope of the Monetary Policy Reaction Function**: The slope of the MPRF is $ 1/\\phi $. When the central bank's reaction to a high inflation rate results in very little change in the unemployment rate, as in the left panel, the MPRF is steep. When the central bank's reaction to inflation results in a relatively large change in the unemployment rate, as in the right panel, the MPRF is flat.\n", "\n", " \n", "\n", "The equation for the MPRF is:\n", "\n", ">$ u = u_n + \\phi(\\pi - \\pi^t) $\n", "\n", "The value of the parameter $ \\phi $ is simply the change in unemployment for a 1-unit change in the inflation rate. In our example, then:\n", "\n", ">$ \\phi = \\frac{{\\Delta}u}{{\\Delta}\\pi} = \\frac{0.09 - 0.07}{0.05 - 0.02} = \\frac{2}{3} $\n", "\n", "The slope of the MPRF line—where the inflation rate is on the vertical axis (the rise) and the unemployment rate is on the horizontal axis (the run) — is “rise over run,” or the change in inflation over the change in the unemployment rate. So the slope of the MPRF is $ {{\\Delta}\\pi}{{\\Delta}u} $, which is simply $ \\phi $, or, in our example, 1.5.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.2.3.2 From Income-Expenditure to the MPRF: Some Details\n", "\n", "Whole chapters’ worth of detail underpin the parameter $ \\phi $ that governs the slope of the MPRF:\n", "\n", ">$ u = u_n + \\phi(\\pi - \\pi^t) $\n", "\n", "To see these details, write the determinants of $ \\phi $ as four different factors multiplied together:\n", "\n", ">$ \\phi = (r_\\pi)(I_r+x_\\epsilon\\epsilon_r)(\\mu)\\left(\\frac{0.4}{Y^*}\\right) $\n", "\n", "The first term:\n", "\n", ">$ r_\\pi $\n", " \n", "comes from central bankers’ distaste for inflation. It is the amount by which central bankers raise the real interest rate when inflation is 1 unit higher.\n", "\n", "The second term\n", "\n", ">$ (I_r+x_\\epsilon\\epsilon_r) $\n", "\n", "comes from the IS Curve. It is the interest sensitivity of autonomous spending. It incorporates both the effect of interest rates on investment spending and the effect of interest rates on the exchange rate and hence on export spending too.\n", "\n", "The third term:\n", "\n", ">$ \\mu $ \n", "\n", "is the basic multiplier that is at the heart of the sticky-price model and which tells us how much real GDP changes when there is a change in autonomous spending.\n", "\n", "The last term:\n", "\n", ">$ \\left(\\frac{0.4}{Y^*}\\right) $\n", "\n", "comes from Okun’s law. It tells us the change in the unemployment rate produced by a change in real GDP relative to potential output $ Y^* $.\n", "\n", "Thus there is a sense in which much of the work of the sticky-price model is encapsulated in this single parameter $ \\phi $. \n", "\n", "In the example above, we had:\n", "\n", ">$ r_\\pi = \\frac{1}{3} $\n", "\n", ">$ I_r+x\\epsilon\\epsilon_r = 10 $\n", "\n", ">$ \\mu = 2 $\n", "\n", ">$ Y^* = 4 $\n", "\n", "So then our parameter $ \\phi $ should equal:\n", "\n", "\n", ">$ \\frac{1}{3}(10)(2)\\left(\\frac{0.4}{4}\\right) = \\frac{2}{3} $\n", "\n", "which had better be—and is—the same as the value in the example above.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 12.2.3.3 Calculating Equilibrium\n", "\n", "For the economy to be in equilibrium, both the Phillips Curve and the MPRF must be satisfied. We can draw both of these relationships on a unemployment-inflation graph, and so read off the economy's MPRF-Phillips Curve equilibrium off the graph or calcuate it algebraically. for this system of equations to be in equilibrium.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**Equilibrium Levels of Unemployment and Inflation**: The equilibrium levels of unemployment and inflation occur where the MPRF and Phillips curve cross. In the short run, equilibrium inflation can be different from the central bank's target inflation rate $ \\pi^t $ and from the expected rate of inflation $ \\pi^e $. In the short run, equilibrium unemployment can be different from the natural rate of unemployment $ u^* $ and from the unemployment rate $ u_n $ when the central bank sets the interest rate at its neutral baseline value $ r_n $.\n", "\n", " \n", "\n", "When the Phillips Curve and the MPRF are satisfied, then neither unemployment nor inflation are changing. \n", "\n", "Why is the point where the curves cross the only equilibrium? To see the answer, let’s choose any unemployment rate along the horizontal axis of the graph. The Phillips curve tells us what inflation rate the resulting wage and price bargaining in input markets will generate. But unless that unemployment rate and inflation rate combination from the Phillips curve is also on the MPRF, the central bank will react to that inflation rate by changing the real interest rate. And a change in the real interest rate will ultimately change the unemployment rate, moving us to yet another point on the Phillips curve!\n", "\n", "At what combination of unemployment and inflation rates will the supply-side forces that determine inflation be in concert with the central bank’s monetary policy and resulting demand for output? Only a combination of unemployment and inflation rates that is on both the Phillips curve and the MPRF will accomplish this. Any other combination of u and π is not an equilibrium combination because the central bank’s reaction to inflation will change the unemployment rate (move us along the MPRF), which in turn will change the inflation rate (move us along the Phillips curve). The economy will be in equilibrium at that unemployment rate and inflation rate where the Phillips curve and the MPRF cross.\n", "\n", "How can the level of inflation be different in the short run from both expected inflation ire and the central bank’s target inflation rate $ \\pi^t $? And how can this equilibrium level of unemployment u be different in the short run from both the natural rate of unemployment $ u^* $ and from the level of unemployment $ u_n $ when the central bank sets the interest rate at what it believes to be the interest rate’s neutral baseline value $ r_n $?\n", "\n", "Actual inflation π can be different from expected inflation $ \\pi^e $ because economic decisions have to be made in advance, and people update their expectations only with a time lag. Workers, firms, investors, and financiers would have to have superhuman powers of observation and analysis for actual inflation to be—except occasionally and luckily—exactly equal to expected inflation.\n", "\n", "Actual inflation π can be different from the central bank’s target $ \\pi^t $ because the central bank has other things to worry about as well. If all the central bank worried about was keeping inflation at its target, it could do so: The MPRF would then be flat, at the target level.\n", "\n", "But the parameter $ r_\\pi $ is not infinitely large, which it would need to be to create a completely flat MPRF. Central banks do not want to cause the financial upset that would result from the large rapid swings in interest rates needed to create a flat MPRF.\n", "\n", "Unemployment will in general not be equal to the central bank’s view of normal unemployment u0 because inflation will rarely be exactly equal to its target. Unemployment is the central bank’s inflation-fighting tool. So the central bank will want to push unemployment above or below its view of normal in order to reduce or increase inflation.\n", "\n", "In a good world, with a perfect central bank, the central bank’s idea of what the normal unemployment is would be equal to the natural rate of unemployment, and the central bank’s target inflation rate would be equal to expected infla­ tion. Then inflation and unemployment would be stable, and the business cycle would be a nonevent. But changes and shocks to the economy—and misperceptions by the central bank and by the economy’s workers, firms, investors, and financiers—will keep that from being the case except for moments of exceptional good luck.\n", "\n", " \n", "\n", "#### 12.2.3.4 Solving for Equilibrium: An Example\n", "\n", "How do we actually figure out what the economy’s inflation and unemployment rates are? If we have the equations for the Phillips curve and the MPRF, we can solve those equations jointly to determine the equilibrium inflation and unemployment rates.\n", "\n", "We have already derived the MPRF: \n", "\n", ">$ u = u_n + \\phi(\\pi - \\pi^t) = 0.07 + \\frac{2}{3}(\\pi - 0.02) $\n", "\n", "Suppose the parameter $ \\beta $ in the Phillips curve equation is 1/2, that expected inflation $ \\pi^e $ is 4 percent, there are no supply shocks, and the natural rate of unemployment $ u^* $ is 5 percent. Then the Phillips curve is:\n", "\n", ">$ \\pi = \\pi^e - \\beta(u - u^*) = 0.04 - \\frac{1}{2}(u - 0.05) $\n", "\n", "To solve for the equilibrium value of the unemployment rate we can substitute the Phillips curve equation for π into the MPRF equation and solve for the unemployment rate:\n", "\n", ">$ u = 0.07 + \\frac{2}{3}(\\pi - 0.02) $\n", "\n", ">$ u = 0.07 + \\frac{2}{3}\\left(\\left[\\pi^e - \\beta(u - u^*)\\right] - 0.02\\right) $\n", "\n", ">$ u = 0.07 + \\frac{2}{3}\\left(\\left[0.04 - \\frac{1}{2}(u - 0.05)\\right] - 0.02\\right) $\n", "\n", ">$ u = 0.07 + \\frac{2}{3}\\left(\\0.045 - \\frac{1}{2}u\\right) = 0.10 - \\frac{1}{3}u $\n", "\n", ">$ \\frac{4}{3}u = 0.10 $\n", "\n", ">$ u = 0.075 $\n", "\n", "Now to solve for the equilibrium value of the inflation rate, we just substitute u = 0.075 into the Phillips curve equation:\n", "\n", ">$ \\pi = \\pi^e - \\beta(u - u^*) = 0.04 - \\frac{1}{2}(u - 0.05) $\n", "\n", ">$ \\pi = \\pi^e - \\beta(u - u^*) = 0.04 - \\frac{1}{2}(0.075 - 0.05) = 0.275 $\n", "\n", "In equilibrium in this example, the unemployment rate will be 7.5 percent and the inflation rate will be 2.75 percent.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.2.4 Using the MPRF-Phillips Curve Model\n", "\n", "We can use this framework to analyze the effects of a shift in policy or in the economic environment on the economy’s equilibrium. \n", "\n", " \n", "\n", "#### 12.2.4.1 Using MPRF-PC to Analyze a Fall in Exports: An Example\n", "\n", "For example, consider a depression abroad that lowers demand for exports. This change in the economic environment causes a decrease in planned expenditure—a shift left of the IS curve—and leads to a rise in the unemployment rate. The Monetary Policy Reaction Function has shifted to the right, and the economy’s equilibrium has moved down and to the right along the Phillips curve. The unemployment rate rises. The inflation rate falls.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**Effects of a Fall in Exports**: A fall in exports with no countervailing change in the central bank's view of the normal interest rate $ r_n $ shifts the MPRF right, raises the equilibrium unemployment rate, and lowers the inflation rate\n", "\n", " \n", "\n", "#### 12.2.4.2 Other Cases\n", "\n", "Now consider instead an expansion of government purchases at home. We would show this as a shift to the right of the IS curve of Chapter 10, which shifts the MPRF curve in and to the left. If the central bank does not change its notion of the normal baseline interest rate $ r_n $, and expected inflation does not change, the unemployment rate will fall and the inflation rate will rise.\n", "\n", "What if there is no aggressive central bank acting to stabilize the economy by raising interest rates when inflation rises? Does the economy spin out of control? No. Without a central bank to control interest rates, inflation itself sets in motion forces that raise interest rates and so “cool off’ the economy and raise unemployment. Inflation raises the price level. A higher price level makes the nominal money supply in the economy worth less. A smaller real money stock means higher interest rates. This can perform the same economy-stabilizing function automatically that modern central banks accomplish through their active control over interest rates. But it will take a great while for a shortage of cash to do what a central bank could do quickly.\n", "\n", "What about a negative—costly—supply shock such as the oil price hikes in the 1970s? We would show this as a rightward shift in the Phillips curve. The unemployment rate would rise and the inflation rate would rise as well. The MPRF- Phillips curve model is deceptively simple but satisfyingly powerful. It can help us to understand the short-run effects on inflation and unemployment of any number of macroeconomic events.\n", "\n", " \n", "\n", "### 12.2.5 RECAP: Monetary Policy, Aggregate Demand, and Inflation\n", " \n", "Central banks resjpond to higher-than-desired inflation rates by raising interest rates to “cool off” the economy, thus lowering real GDP Y and raising the unemployment rate u. We model this facet of central bank behavior by a monetary policy reaction function—MPRF—that is an upward-sloping relationship between inflation tt and unemployment u. We combine this with our Phillips curve—a downward-sloping relationship between inflation it and unemployment u—to determine the equilibrium levels of the unemployment rate and inflation rate in our sticky-price economy We can use the MPRF and the Phillips curve to analyze the effects of economic policy\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12.3 The Natural Rate of Unemployment\n", "\n", "In English, the word “natural” carries strong positive connotations of normal and desirable, but a high natural rate of unemployment $ u^* $ is a bad thing. Unemployment cannot be reduced below its natural rate without accelerating inflation, so a high natural rate means that expansionary fiscal policy and expansionary monetary policy are largely ineffective as tools to reduce unemployment.\n", "\n", "Today, most estimates of the current U.S. “natural” rate of unemployment are around 4 percent, although uncertainty about the level of the natural rate is substantial. And the natural rate has fluctuated substantially over the past two generations.\n", "\n", " \n", "\n", "\"Civilian\n", "\n", ">**Fluctuations in Unemployment and in Its Natural Rate**: The natural rate of unemployment is not fixed. It varies substantially from decade to decade. Moreover, variations in the natural rate in the United States have been much smaller than variations in the natural rate in other countries.\n", "\n", " \n", "\n", "Broadly, four sets of factors have powerful influence over the natural rate:\n", "\n", " \n", "\n", "### 12.3.1 Demography and the Natural Rate\n", "\n", "First, the natural rate changes as the relative age and educational distribution of the labor force changes. Teenagers have higher unemployment rates than adults; thus an economy with a lot of teenagers will have a higher natural rate. Looking for a job is easier for more experienced and more skilled workers. They need less time to find a new job when they leave an old one, so the natural rate of unem­ ployment will fall when the labor force becomes more experienced and more skilled. Women formerly had higher unemployment rates than men, although this is no longer true in the United States. The more educated tend to have lower rates of unemployment than the less well educated. African-Americans and Hispanic- Americans have higher unemployment rates than whites.\n", "\n", "A large part of the estimated rise in the natural rate from 5 percent or so in the 1960s to 6 or 7 percent by the end of the 1970s was due to changing demography. Some component of the decline in the natural rate since then derives from the increasing experience at searching for jobs of the very large baby-boom cohort. But the exact, quantitative relationship between demography and the natural rate is not well understood.\n", "\n", " \n", "\n", "### 12.3.2 Institutions and the Natural Rate\n", "\n", "Second, institutions have a powerful influence over the natural rate. Some economies have strong labor unions; other economies have weak ones. Some unions sacrifice employment in their industry for higher wages; others settle for lower wages in return for employment guarantees. Some economies lack apprenticeship programs that make the transition from education to employment relatively straightforward; others make the school-to-work transition easy. In each pair, the first increases and the second reduces the natural rate of unemployment. Barriers to worker mobility raise the natural rate, whether the barrier be subsidized housing that workers lose if they move (as in Britain in the 1970s and the 1980s), or high taxes that a firm must pay to hire a worker (as in France from the 1970s to today).\n", "\n", "However, the link between economic institutions and the natural rate is neither simple nor straightforward. The institutional features many observers today point to as a source of high European unemployment now were also present in the Euro­ pean economies in the 1970s — when European unemployment was low. Once again the quantitative relationships are not well understood.\n", "\n", " \n", "\n", "### 12.3.3 Productivity Growth and the Natural Rate\n", "\n", "Third, in recent years the rate of productivity growth has become increasingly implicated as a major determinant of the natural rate. The era of slow productivity growth from the mid-1970s to the mid-1990s saw a relatively high natural rate. By contrast, rapid productivity growth before 1973 and from 1995-2005 seems to have generated a relatively low natural rate. Since 2007, productivity growth has greatly diminished—yet we have not seen any impact on the natural rate from this renewed productivity growth slowdown.\n", "\n", "Why should a productivity growth slowdown generate a high natural rate? A higher rate of productivity growth allows firms to pay higher real wage increases and still remain profitable. If workers’ aspirations for real wage growth depend on the rate of unemployment, then a slowdown in productivity growth will increase the natural rate as indicated in Figure 12.11. If real wages grow faster than pro­ ductivity for an extended period of time, profits will disappear. Long before that point is reached businesses will begin to fire workers, and unemployment will rise. Thus if productivity growth slows, unemployment will rise. Unemployment will keep rising until workers’ real wage aspirations fall to a rate consistent with current productivity growth.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**Real Wage Growth Aspirations and Productivity** Workers aspire to earn higher real wages. How much workers demand in the way of increases in the average real wage is a function of unemployment: The higher unemployment is, the lower workers' aspirations for real wage growth are. But in the long run real wages can grow no faster than productivity. Hence the natural rate of unemployment is whatever rate of unemployment curbs real wage demands so that they are consistent with productivity growth.\n", "\n", " \n", "\n", "Attributing movements in the natural rate to shifts in productivity growth, however, runs aground on the puzzle of what is happening to the U.S. economy in the late 2010s. Productivity gowwth is low. Yet the natural rate of unemployment appears to be low as well.\n", "\n", " \n", "\n", "### 12.3.4 The Past Level of Unemployment and the Natural Rate\n", "\n", "Fourth and last, the natural rate will be high if unemployment has been high. Before 1980 western European economies had unemployment rates lower than the 5 percent to 6 percent that the United States averaged back then. But the mid-1970s brought recessions. European unemployment rose, but it did not fall back much in subsequent recoveries. Workers unemployed for two or three years lost their skills, lost their willingness to show up on time, and became so discouraged that they lost their interest in even looking for new jobs. Thus the natural rate rose sharply in Europe with each business cycle. By the late-1990s European unemployment averaged 8 percent, and inflation was stable.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**The Rise in European Unemployment in the 1980s**: Unemployment in western European countries grew between 1975 and 2004 as their natural rates of unemployment increased. Source: Olivier Blanchard and Justin Wolfers, \"The Role of Shocks and Institutions in the Rise of European Unemployment: The Aggregate Evidence,\" Economic Journal 110 (March 2000); extended by the authors.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.3.5 Declining Reliability of the Natural Rate Hypothesis?\n", "\n", "Unfortunately for us economists' understanding of the economy, there are signs that the natural rate of unemployment hypothesis has been becoming less reliable as an empirical regularity in this millennium, and especially so since 2008.\n", "\n", " \n", "\n", "\"Https\n", "\n", " \n", "\n", "From 1980 to 1990 the unemployment rate was a better guide to whether the level of national income and product in the economy was close to potential output. The feminist revolution in the workforce was still ongoing. Women's participation in the labor force and in employment was growing rapidly. The start of 1980 and the end of 1990 saw similar unemployment rates: about 6.5 percent. But the share of American 25-54 year-olds—too old for many of them to be school, too young for many of them to be plausibly retired—was 4 percentage points higer at the end of 1990 than it had been at the beginning of 1980.\n", "\n", "From the early 1990s to the mid-2000s, both the 25-54 year-old employment rate and the unemployment rate told the same story about the state of national income and production relative to potential output. But by 2007 they were sending different signals. The unemployment rate then was only half a percentage point above the level it had reached in 2000—suggesting an economy close to if not at the same relationship to potential output. But the prime-age 25-54 year-old employment rate was two percentage points lower—suggesting that great deal of headroom remained for further economic expansion before production relative to potential reached the mark it had attained in 2000.\n", "\n", "And since 2007 the two have told very different stories. The unemployment rate today is lower than the mark attained at the business-cycle peak of 2000. The prime-age employment rate is still 2.5 percentage points lower. The first suggests no headroom for further expansion without pushing production above sustainable potential—that current unemployment is at or below the natural rate. The second suggests substantial remaining headroom—that current unemployment is substantially above the natural rate.\n", "\n", "Moreover, there appears to have been a substantial shift—a decline—in the Phillips curve slope coefficient. While a one-percentage-point reduction in unemployment relative to the natural rate might have raised inflation over the next year by 3/5 of a percentage point or more in the 1970s, it now appears to raise inflation by only 1/5 of a percentage point, if that.\n", "\n", " \n", "\n", "\"Https\n", "\n", " \n", "\n", "Which is correct? Either there are a lot more people who want and would take jobs if they were offered right now than we would think from the level of the unemployment rate, or something like one out of every 40 Americans 25-54 has mysteriously lost their desire to work at paid employment. And does it matter what thermometer we use to try to assess full employment, if deviations from full employment do not have noticeable and substantial effects on inflation?\n", "\n", "In our models here we continue to use the unemployment rate as our thermometer of whether production and national income are below, at, or above potential output. But beware! When we move to applying our models to the real world, perhaps we should be using not:\n", "\n", "> $ \\frac{Y - Y^*}{Y^*} = -2.5\\left(u - u^* \\right) $\n", "\n", "but rather something like:\n", "\n", "> $ \\frac{Y - Y^*}{Y^*} = 1.5\\left(E - E^* \\right) $\n", "\n", "where E is the prime-age 25-54 employment rate, in order to usefully understand the real economy.\n", "\n", "However, whatever happens with the form nd parameters of the quantitative relationship, we are still sure about the qualitative direction: Higher real GDP Y (relative to potential output Y\\*) means lower unemployment u (relative to the natural rate u\\*) and higher employment and vice versa.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.3.6 Conclusion: The Fluctuating Natural Rate\n", "\n", "This laundry list of factors affecting the natural rate is incomplete. Do not think that economists understand much about why the natural rate is what it is. Almost every economist was surprised by the large rise in the natural rate in western Europe over the past quarter century. Almost every economist was surprised by the sharp fall in America’s natural rate in the 1990s. And economists cannot confi­ dently account for these shifts even in retrospect.\n", "\n", " \n", "\n", "### 12.3.7 RECAP: The Natural Rate of Unemployment\n", "\n", "The natural rate of unemployment is not a constant. It has fluctuated sub- stantially over the past two generations, and it will continue to fluctuate. Four sets of factors drive fluctuations in the natural rate of unemployment. First, the natural rate changes as the relative age and educationaldistribution of the labor force changes. Second, countries with inflexible labor markets are likely to have high natural rates of unemployment Third, faster productivity growth brings a lower natural rate with it. Fourth, the natural rate will be high if unem­ ployment has been high in the past and large numbers of workers have become discouraged.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12.4 Expectations of Inflation\n", "\n", "The natural rate of unemployment and expected inflation together determine the location of the Phillips curve because it passes through the point where inflation is equal to expected inflation and unemployment is equal to its natural rate. This is how the Phillips curve is defined: When inflation π is equal to its expected value $ \\pi^e $, then that tells us that the labor market is in rough balance—that unemployment u is equal to its natural rate $ u^* $. Thus higher expected inflation shifts the Phillips curve upward. But who does the expecting? And when do people form expectations relevant for this year’s Phillips curve?\n", "\n", "Economists work with three basic scenarios for how managers, workers, and investors go about forecasting the future and forming their expectations:\n", "\n", "* Static expectations of inflation prevail when people ignore the fact that inflation can change.\n", "\n", "* Adaptive expectations prevail when people assume the future will be like the recent past.\n", "\n", "* Rational expectations prevail when people use all the information they have as best they can.\n", "\n", "We will sometimes use a fourth—a hybrid between static and adaptive expectations, with a parameter $ \\lambda $ assigning the degree of relative importance of the two in the mix. A value of $ \\lambda = 1 $ means that expectations are fully static. A value of $ \\lambda = 0 $ means that expectations are fully adaptive. And in between there is a mix:\n", "\n", "The Phillips curve and the Phillips curve-MPRF models behave very differently under each of these scenarios.\n", "\n", " \n", "\n", "### 12.4.1 The Phillips Curve under Static Expectations\n", "\n", "If inflation expectations are static, expected inflation never changes. People just don’t think about inflation. There will be some years in which unemployment is relatively low; in those years inflation will be relatively high. There will be other years in which unemployment is higher, and then inflation will be lower. But as long as expectations of inflation remain static (and there are no supply shocks, and the natural rate of unemployment is unchanged), the trade-off between inflation and unemployment—the position of the Phillips curve—will not change from year to year.\n", "\n", "\"DeLong\n", "\n", ">**Static Expectations**: of Inflation\n", "If inflation expectations are static, the economy moves up and to the left and down and to the right along a Phillips curve that does not change its position so long as there are no supply shocks and the natural rate of unemployment is constant.\n", "\n", " \n", "\n", "If inflation has been low and stable, businesses will probably hold static inflation expectations. Why? Because the art of managing a business is complex enough as it is. Managers have a lot of things to worry about: what their customers are doing, what their competitors are doing, whether their technology is adequate, and how applicable technology is changing. When inflation has been low or stable, everyone has better things to focus their attention on than the rate of inflation. The 1960s were an era of static expectations.\n", "\n", " \n", "\n", "### 12.4.1.1 Static Expectations of Inflation in the 1960s: An Example\n", "\n", "The standard example of static expectations is expectations of inflation in the 1960s. When unemployment was above 5.5 percent, inflation was below 1.5 percent. When unemployment was below 4 percent, inflation was above 2.5 percent. This Phillips curve, shown in Figure 12.14, did not shift up or down in response to changes in expected inflation during the decade. Instead, the economy moved along a stable Phillips curve.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**Static Expectations and the Phillips Curve, 1960-1968**\n", "\n", " \n", "\n", "### 12.4.2 The Phillips Curve under Adaptive Expectations\n", "\n", "Suppose that the inflation rate varies too much for workers and businesses to ignore it completely. What then? As long as inflation last year is a good guide to inflation this year, workers, investors, and managers are likely to hold adaptive expectations and forecast inflation by assuming that this year will be like last year. Adaptive forecasts are good forecasts as long as inflation changes only slowly and adaptive expectations do not absorb a lot of time and energy that can be better used thinking about other issues.\n", "\n", "Under such adaptive inflation expectations, we need to specify exactly what moments we are talking about. We need to write the Phillips curve with time subscripts, like this:\n", "\n", ">$ \\pi_{t+1} = {\\pi_{t+1}}^e - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", "And under adaptive expectations:\n", "\n", ">$ {\\pi_{t+1}}^e = \\pi_t $\n", "\n", "people expect that inflation next year will be just what inflation is this year. We can then remove the expectations variable from this equation, and write:\n", "\n", ">$ \\pi_{t+1} = \\pi_t - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", "Under such a set of adaptive expectations, the Phillips curve will shift up or down depending on whether inflation now is higher or lower than it was last year. Under adaptive expectations, inflation accelerates when unemployment is less than the natural unemployment rate. Under adaptive expectations, inflation decelerates when unemployment is less than the natural unemployment rate.\n", "\n", "If we use the symbol \"$\\Delta$\" to stand for the change in inflation from one year to another, then under adaptive expectations:\n", "\n", ">$ \\Delta\\pi_{t+1} = - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", "And if we want to calculate what inflation is at some fixed time T in terms of the unemployment rate, supply shocks, and what inflation initally was in the year we assign to t=0, we have:\n", "\n", "$ \\pi_T = \\pi_o - \\beta\\sum\\limits_{t=0}^{T-1} (u_t - {u_t}^*) + \\sum\\limits_{t=0}^{T-1} (SS_t) $\n", "\n", "If inflation is going to be the same at time 0 and at time T, we can calculate the average unemployment rate from this equation:\n", "\n", "$ 0 = - \\beta\\sum\\limits_{t=0}^{T-1} (u_t - {u_t}^*) + \\sum\\limits_{t=0}^{T-1} (SS_t) $\n", "\n", "$ \\frac{1}{T}\\sum\\limits_{t=0}^{T-1} u_t = \\frac{1}{T}\\sum\\limits_{t=0}^{T-1} {u_t}^* + \\frac{\\sum\\limits_{t=0}^{T-1} (SS_t)}{T\\beta} $\n", "\n", "On average, the unemployment rate will be equal to the average natural rate of unemployment, plus the average effects of supply shocks on inflation divided by the parameter $ \\beta $. Note what does not appear in this equation: _nothing whatever from aggregate demand_. Except for supply shocks, nothing in the economic environment—not consumer confidence, not business animal spirits, not foreign exchange speculators' views, not foreign national income, not foreign interest rates—affects the average level of employment. And nothing in economic policy—not government purchases, not the tax rate, and not the real interest rate which is affected by economic policy—affects the average level of unemployment.\n", "\n", "Unless a government wants to accept a permanent rise in inflation, therefore, in an economy with fully-adaptive expectations the government's macroeconomic stabilization policy can have no effect on the average level of unemployment. If Okun's Law holds, this tells us that the government's macroeconomic stabilization policy can have no effect on the average output gap—on how close on average national income and product is to the economy's sustainable productive potential.\n", "\n", "Thus policies to stabilize production, employment, and unemployment seem all but wortheless, seem pointless: they cannot make things better or worse on average—if inflation expectations are fully adaptive.\n", "\n", " \n", "\n", "#### 12.4.2.1 A High-Pressure Economy under Adaptive Expectations: An Example\n", "\n", "Suppose the central bank tries to keep unemployment below the natural rate for a long time in an economy with adaptive expectations. Then year after year inflation will be higher than expected inflation, and so year after year expected inflation will rise. Suppose that the government pushes the economy’s unemployment rate down 2 percentage points below the natural rate, that the /3 parameter in the Phillips curve is 1/2, that last year’s inflation rate was 4 percent, and that there are no supply shocks. Then, because each year’s expected inflation rate is last year’s actual inflation rate, and because:\n", "\n", ">$ \\pi_{t+1} = \\pi_t - \\frac{1}{2}(-0.02) + 0 $\n", "\n", "next year’s inflation rate will be:\n", "\n", ">$ 0.04 - \\frac{1}{2}(-0.02) = 0.05 $\n", "\n", "the following year’s inflation rate will be:\n", "\n", ">$ 0.05 - \\frac{1}{2}(-0.02) = 0.06 $\n", "\n", "and inflation the year following _that_ will be:\n", "\n", ">$ 0.06 - \\frac{1}{2}(-0.02) = 0.07 $\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**Accelerating Inflation**\n", "\n", " \n", "\n", "When inflation increases, expected inflation increases. And as expected inflation increases, the Phillips curve shifts up.\n", "\n", " \n", "\n", "And, under adaptive expectations, inflation decelerates when unemployment is more than the natural rate. The early 1980s were such an era.\n", "\n", " \n", "\n", "#### 12.4.2.2 Adaptive Expectations and the Volcker Disinflation: Economic Policy\n", "\n", "At the end of the 1970s the high level of expected inflation gave the United States an unfavorable short-run Phillips curve trade-off. Between 1979 and the mid-1980s, the Federal Reserve under Chair Paul Volcker reduced inflation in the United States from 9 percent per year to about 3 percent.\n", "\n", "To accomplish this goal of reducing expected inflation, the Federal Reserve raised interest rates sharply, discouraging investment, reducing aggregate demand, and pushing the economy to the right along the Phillips curve. Unemployment rose, and inflation fell. Reducing annual inflation by 6 percentage points required “sacrifice”: During the disinflation, unemployment averaged some 1.5 percentage points above the natural rate for the seven years between 1980 and 1986. Ten percentage-point-years of excess unemployment above the natural rate—that was the cost of reducing inflation from near 9 percent to roughly 3 percent.\n", "\n", "Because inflation expectations were adaptive, the fall in actual inflation in the early 1980s triggered a fall in expected inflation as well. The early 1980s therefore saw a downward shift in the short-run Phillips curve, a downward shift that gave the United States a much more favorable short-run inflation-unemployment tradeoff by the mid-1980s than it had had in the late 1970s.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">**The Phillips Curve before and after the Volcker Disinflation**\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.4.3 The Phillips Curve under Rational Expectations\n", "\n", "What happens when government policy and the economic environment are changing rapidly enough that adaptive expectations lead to significant errors, and are no longer good enough for managers or workers? Then the economy will shift to rational expectations. Under rational expectations, people form their forecasts of future inflation not by looking backward at what inflation was, but by looking for­ ward. They look at what current and expected future government policies tell us about what inflation will be.\n", "\n", "Under rational expectations the Phillips curve shifts as rapidly as, or faster than, changes in economic policy that affect the level of aggregate demand. This has an interesting consequence: Anticipated changes in economic policy turn out to have no effect on the level of production or employment.\n", "\n", "Consider an economy where the central bank’s target inflation it1rate is equal to the current value of expected inflation rre and where uq, the unemployment rate when the real interest rate is at its normal value, is equal to the natural rate of unemployment u\\*. In such an economy, the initial equilibrium has unemployment equal to its natural rate and inflation equal to expected inflation.\n", "\n", "Suppose that workers, managers, savers, and investors have rational expectations. Suppose further that the government takes steps to stimulate the economy: It cuts taxes and increases government spending in order to reduce unemployment below the natural rate, and so reduces the value of u0. What is likely to happen to the economy?\n", "\n", "We write $ \"E_t()\" $ to signal that what is in our equation is not the actual economic variable, but rather the expectation of it taken at some time t. Thus under rational expectations with our Phillips curve:\n", "\n", ">$ \\pi_{t+1} = {\\pi_{t+1}}^e - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", "Inflation expectations are:\n", "\n", ">$ {\\pi_{t+1}}^e = E_t\\left(\\pi_{t+1}\\right) $\n", "\n", "This tells us that inflation next year will be equal to what we expect it to be this year plus a surprise—which we will write $ \\nu_{t+1} $—made up of things that nobody this year could or could be expected to forecast:\n", "\n", "> $ \\pi_{t+1} = {\\pi_{t+1}}^e + \\nu_{t+1} $\n", "\n", "Substituting this last into our Phillips Curve:\n", "\n", ">$ {\\pi_{t+1}}^e + \\nu_{t+1} = {\\pi_{t+1}}^e - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", "cancelling terms:\n", "\n", ">$ \\nu_{t+1} = - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", "But since $ \\nu $ comes as a surprise in year t+1, the only value it makes sense to assign it in year t is 0:\n", "\n", ">$ 0 = - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", "Solving for the current unemployment rate:\n", "\n", ">$ u_t = {u_t}^* + \\frac{SS_t}{\\beta} $\n", "\n", "Thus _if_ the economy is subject to rational expectations, _and if_ the Phillips Curve holds, _then_ the unemployment rate must be equal to the natural rate of unemployment plus the supply shocks term. There is thus no room for any demand-side factors—not monetary policy influencing interest rates, not government purchases, not the tax rate, not consumer confidence, not business animal spirits, not foreign exchange speculators' views, not foreign national income, and not foreign interest rates—to affect the level of unemployment. And, from Okun's Law, that leaves no room for any demand-side factors to affect the level of national income and product either.\n", "\n", "If the government’s policy comes as a surprise—if the expectations of inflation that matter for this year’s Phillips curve have already been set, in the sense that the contracts have been written, the orders have been made, and the standard operating procedures have been identified—then government policy can havce an effect. Then a stimulative policy boosts the economy and lowers unemployment. the economy moves up and to the left along the Phillips curve in response to the shift in aggregate demand produced by the change in government policy: Unemployment falls and the inflation rate rises.\n", "\n", "\"DeLong\n", "\n", ">**Results if the Shift in Policy Comes as a Surprise**: A government pursuing an expansionary economic policy shifts the MPRF. An increase in production is associated with a reduction in unemployment, so an expansionary shift is a shift to the left in the MPRF. A surprise expansionary policy moves the economy along the Phillips curve, raising inflation and lowering unemployment (and raising production) in the short run.\n", "\n", " \n", "\n", "But if the government’s policy is anticipated—if the expectations of inflation that matter for this year’s Phillips curve are formed after the decision to stimulate the economy is made and becomes public—then workers, managers, savers, and investors will take the stimulative policy into account when they form their expectations of inflation. The inward shift in the MPRF will be accompanied, under rational expectations, by an upward shift in the Phillips curve as well. How large is the upward shift? The increase in expected inflation has to be large enough to keep expected inflation after the demand shift equal to actual inflation. Otherwise people are not forming their expectations rationally.\n", "\n", "Thus an anticipated increase in aggregate demand has, under rational expectations, no effect on the unemployment rate or on real GDP. Unemployment does not change; it remains at the natural rate of unemployment plus the suppluy shock term because the shift in the Phillips curve has neutralized in advance any impact of changing inflation on unemployment. Economists will sometimes say that under rational expectations “anticipated policy is irrelevant.” But this is not the best way to express it. It is only the effects of policy on real GDP and the unemployment rate—effects that are associated with a divergence between expected inflation and actual inflation—that are “irrelevant.”\n", "\n", "\"DeLong\n", "\n", ">**Results if the Shift in Policy Is Anticipated**: If the expansionary policy is anticipated, workers, consumers, and managers will build the policy effects into their expectations: The Phillips curve will shift up as the MPRF shifts in, and so the expansionary policy will raise inflation without having any impact on unemployment (or production).\n", "\n", " \n", " \n", "When have we seen examples of rational inflation expectations? I know of only one: France around the election of Socialist President Frangois Mitterand in 1981. Throughout his campaign Mitterand had promised a rapid expansion of demand and production to reduce unemployment. Thus when he took office French businesses and unions were ready to mark up their prices and wages in anticipation of the expansionary policies they expected. The result? From mid-1981 to mid-1983 France saw a significant acceleration of inflation, but no reduction in unemployment. The Phillips curve had shifted upward fast enough to keep expansionary policies from having any effect on production and employment.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.4.4 The Phillips Curve Under Hybrid Expectations\n", " \n", "Recall the Phillips Curve:\n", "\n", ">$ \\pi_{t+1} = {\\pi_{t+1}}^e - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", "Under hybrid expectations, the expected inflation variable on the right-hand side is determined by:\n", "\n", ">$ {\\pi_{t+1}}^e = \\lambda\\pi^* + (1 - \\lambda)\\pi_t $\n", "\n", "people expect that inflation next year will be some weighted average of what inflation is this year $ \\pi_t $ and the fixed and anchored \"static\" expectation $ \\pi^* $. We can then remove the expectations variable from this equation, and write:\n", "\n", ">$ \\pi_{t+1} = \\lambda\\pi^* + (1-\\lambda)\\pi_t - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", "If we use the symbol \"$\\Delta$\" to stand for the change in inflation from one year to another, then under adaptive expectations:\n", "\n", ">$ \\Delta\\pi_{t+1} = \\lambda(\\pi^* - \\pi_t) - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", "If inflation is above the static-expectations value $ \\pi^* $ it will tend to revert toward that static-expectations value by $ \\lambda $ times the gap, plus or minus the standard Phillips Curve unemployment and supply-shock terms that we have seen every time we have considered the inflation Phillips Curve.\n", "\n", "With fully adaptive inflation expectations, except for supply shocks, nothing in the economic environment or economic policy could affect the average level of employment. Thus policies to stabilize production, employment, and unemployment seemed all but pointless. That is not true with hybrid expectations: under hybrid expectations, there is a definite point to successful, active, and competent management of fiscal and monetary policy tools to make the economy better.\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.4.5 What Kind of Expectations Do We Actually Have?\n", "\n", "#### 12.4.5.1 Expectations Depend on the Economic Environment\n", "\n", "If inflation is low and stable—as it was before 1967, and as it has been since the late 1990s—expectations are probably static: Even thinking about what one’s expectations should be is not worth anyone’s while. \n", "\n", "If inflation is moderate and fluctuates, but slowly, expectations are probably adaptive: To assume that the future will be like the recent past—which is what adaptive expectations are—is likely to be a good, simple to implement, rule of thumb.\n", "\n", "When shifts in inflation are clearly related to changes in monetary policy, swift to occur, and are large enough to seriously affect profitability, then people might shift in the direction of having rational expectations. When the stakes are high—when people think, “Had I known inflation was going to jump, I would not have taken that contract”—then every economic decision becomes a speculation on the future of monetary policy. Because their bottom lines and their livelihoods are at risk, people will turn all their skill and insight into generating inflation forecasts.\n", "\n", "Thus the kind of expectations likely to be found in the economy at any moment depends on what has been and is going on. A period during which inflation is low and stable will lead people to stop consciously making, and stop paying attention to, inflation forecasts—and tend to cause expectations of inflation to revert to static expectations. A period during which inflation is high, volatile, and linked to visible shifts in economic policy will see expectations of inflation become more rational. An intermediate period of substantial but slow variability is likely to see many managers and workers adopt the rule of thumb of adaptive expectations.\n", "\n", " \n", "\n", "#### 12.4.5.2 Expectations Depend on How Long Typical Contracts Last\n", "\n", "The ways that people make contracts and form and execute plans for their economic activity are likely to make an economy behave as if expectations are less “rational” than true expectations in fact are. People do not wait until December 31 to factor next year’s expected inflation into their decisions and contracts. They make decisions about the future, sign contracts, and undertake projects all the time. Some of those steps govern what the company does for a day. Others govern decisions for years or even for a decade or more.\n", "\n", "Thus the “expected inflation” that determines the location of the short-run Phillips curve has components that were formed just as the old year ended, but also components that were formed two, three, five, ten, or more years ago. People buying houses form forecasts of what inflation will be over the next 30 years—but once the house is bought, that decision is a piece of economic activity (imputed rent on owner-occupied housing) as long as they own the house, no matter what they subsequently learn about future inflation. Such lags in decision making tend to produce “price inertia.” They tend to make the economy behave as if inflation expectations were more adaptive than they in fact are. There will always be a large number of projects and commitments already under way that cannot easily adjust to changing prices. It is important to take this price inertia into account when thinking about the dynamics of inflation, output, and unemployment.\n", "\n", " \n", "\n", "#### 12.4.5.3 Types of Inflation Expectations in the U.S. Economy since 1960\n", "\n", "Hybrid expectations, tending toward static recently, tending toward adaptive in the 1970s and 1980s. Well-anchored,\n", "\n", "\"Https\n", "\n", "\"Https" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.4.5 RECAP: Expected Inflation\n", "\n", "The dynamics of how expectations evolve are key to understanding the economy. Economists work with three basic scenarios for how managers, workers, and investors go about forecasting the future and forming their expectations:\n", "\n", "* Static expectations of inflation prevail when people ignore the fact that inflation can change. \n", "* Adaptive expectations prevail when people assume the future will be like the recent past. \n", "* Expectations shift toward \"rational\" when people need to use all the information they can gather as best they can because the inflation rate has become a key factor influencing their economic well-being.\n", "\n", "The Phillips curve behaves very differently under each of these three sce­ narios. Under static expectations the Phillips curve doesn’t shift, so changes in policy have powerful effects on unemployment and real GDP. Under rational expectations the Phillips curve shifts immediately and drastically in response to policies so that anticipated changes in policy have powerful effects on inflation, but not on unemployment and real GDP. And adaptive expectations are in the middle.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12.5 From the Short-Run to the Business-Cycle Long-Run\n", "\n", "Our picture of the determination of real GDP and unemployment under sticky prices is now complete. We have a comprehensive framework to understand how the aggregate price level and inflation rate move and adjust over time in response to changes in aggregate demand, production relative to potential output, and unem­ ployment relative to its natural rate. There is, however, one loose end. How does one get from the short-run sticky-price patterns of behavior covered in Part 4 to the long-run flexible-price patterns of behavior that were laid out in Part 3? How do you get from the short run to the long run?\n", "\n", " \n", "\n", "### 12.5.1 Rational Expectations\n", "\n", "In the case of an anticipated shift in economic policy under rational expectations, the answer is straightforward: You don’t have to get from the short run to the long run; the long run is now An inward (or outward) shift in the monetary policy reaction function on the Phillips curve diagram caused by an expansionary (or contractionary) change in economic policy or the economic environment sets in motion an offsetting shift in the Phillips curve. If expectations are rational, if changes in economic policy are foreseen, and if there are no supply shocks, then expected inflation will be equal to actual inflation:\n", "\n", ">$ \\pi_{t+1} = {\\pi_{t+1}}^e $\n", "\n", "\"DeLong\n", "\n", ">**Rational Expectations: The Long Run Is Now**: Under rational expectations there simply is no business-cycle short-run, unless changes in policy come as a complete surprise. Otherwise, the unemployment rate is equal to the natural rate, and national income and product are equal to potential output. \n", "\n", " \n", "\n", "In this case, all the analysis of the flexprice model holds immediately—indeed, rational expectations _are_ the flexprice model: wages and prices (and debts) are flexible enough to get the economy back to full employment and potential output immediately in response to any demand shock. Under rational expectations, the long-run is now. The flexprice analysis we did in Part III is always relevant, and the sticky-price analysis of Part IV is never relevant.\n", "\n", "Back in the early 1920s the British economist John Maynard Keynes wrote that it was not enough to do just a long-run analysis, because by the time the long run rolled around we would all be dead. But if everyone in the economy has rational expectations, then Keynes was wrong: The long run comes immediately:\n", "\n", " \n", "\n", "### 12.5.2 Adaptive Expectations\n", "\n", "If expectations are and remain adaptive, then the economy is in the stick-price business-cycle short-run equilibrium of the Keynesian cross, the multiplier, and the IS-Curve. But as time passes it approaches the business-cycle flexprice equilibrium laid out in Part III. The approach is gradual.\n", "\n", "An expansionary initial shock increases planned expenditure and shifts the monetary policy reaction function inward, generating a fall in unemployment, an increase in national income and product, and a rise in inflation. Call this stage 1. Stage 1 takes place before anyone has had any chance to adjust his or her expectations of inflation.\n", "\n", "Then comes stage 2. Workers, managers, investors, and others look at what inflation was in stage 1 and raise their expectations of inflation. The Phillips curve shifts up by the difference between actual and expected inflation in stage 1. The central bank begins to fight inflation by increasing the real interest rate, which increases unemployment. Between stage 1 and stage 2 unemployment rises, real GDP falls, and inflation rises.\n", "\n", "Then comes stage 3. Workers, managers, investors, and others look at what inflation was in stage 2 and raise their expectations of inflation again. The Phillips curve shifts up by the difference between actual and expected inflation in stage 2. As inflation rises further, the central bank ratchets up its fight against inflation, increasing the real interest rate yet again and thus increasing unemployment. Between stage 2 and stage 3 unemployment rises further, real GDP falls again, and inflation again rises. As time passes the gaps between actual and expected inflation, between real GDP and potential output, and between unemployment and its natural rate shrink toward zero. Eventually unemployment returns to the natural rate of unemployment and the only lasting effect of the increase in spending is an increase in the inflation rate.\n", "\n", "\"DeLong\n", "\n", ">**Adaptive Expectations Converge to the Business-Cycle Flexprice Equilibrium in the Long-Run**: Under adaptive expectations, shifts in policy have strong initial effects on unemployment and production, but those effects slowly die off.\n", "\n", " \n", "\n", "Under adaptive expectations, people’s forecasts become closer and closer to being accurate as more and more time passes. Thus the “long-run” in which the economy reaches the business-cycle flexprice equilibrium arrives gradually. Each year the portion of the change in demand that is not implicitly incorporated in people’s adaptive forecasts becomes smaller and smaller. Each passing year a larger and larger proportion of the shift is “long-run”—flexprice—and a smaller and smaller proportion is “short-run”—sticky-price.\n", "\n", "Adaptive expectations provide an intermediate case between rational and static expectations.\n", "\n", " \n", "\n", "### 12.5.3 Static Expectations\n", "\n", "Under static expectations, the long run never arrives, and thus the flexible-price analysis of Part III never becomes relevant. Under static expectations, the gap between expected inflation and actual inflation can grow arbitrarily large as different shocks affect the economy.\n", "\n", "However, note this well: If the gap between expected inflation and actual inflation becomes large, workers, managers, investors, and consumers will not remain so foolish as to retain and maintain static expectations.\n", "\n", " \n", "\n", "### 12.5.4 RECAP: From the Sticky-Price Short-Run to the Flexprice Long-Run\n", "\n", "The amount of time that must pass before the relevant framework shifts from the sticky-price models of Part IV to the flexprice models of Part III depends on the kind of inflation expectations held in the economy. If workers, bosses, savers, and investors hold static expectations and never update them, then the flexprice models never become relevant. If the expectations are adaptive, the shift from Part IV to Part III takes place slowly and gradually. But if expectations are rational, then the shift to Part 3 takes place very quickly indeed—as soon as policy changes are announced or recognized.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12.6 Summary: The Phillips Curve, Expectations, and Monetary Policy\n", "\n", "1. The location of the Phillips curve is determined by the expected rate of inflation and the natural rate of unemployment (and possibly by current, active supply shocks). In the absence of supply shocks, the Phillips curve passes through the point at which inflation is its expected value and unemployment is its natural rate.\n", "2. The slope of the Phillips curve is determined by the degree of price stickiness in the economy. The more sticky are prices, the flatter is the Phillips curve.\n", "3. Modern central banks respond to higher-than-desired inflation by raising interest rates, thus reducing output and raising unemployment. This monetary policy reaction function (MPRF) is a powerful stabilizing factor in modern economies.\n", "4. The MPRF and Phillips curve can be used to analyze the effect of changes in economic policy on the economy’s inflation and unemployment rates.\n", "5. The natural rate of unemployment in the United States has exhibited moderate swings in the past two generations, from perhaps 4.5 percent at the end of the 1950s to perhaps 7 percent at the start of the 1980s, and now down to about 5 percent. Changes in the natural rate of unemployment shift the Phillips curve to the left or right.\n", "6. The principal determinant of the expected rate of inflation is the past behavior of inflation. If inflation has been low and steady, expectations are probably static and the expected inflation rate is very low and unchanging. If inflation has been variable but moderate, expectations are probably adaptive and expected inflation is probably simply equal to last year’s inflation. If inflation has been high or moderate but has varied extremely rapidly, then expectations are probably rational and expected inflation is likely to be households’ and businesses’ best guesses of where economic policy is taking the economy. Changes in inflation expectations shift the Phillips curve up or down.\n", "7. The best way to gauge how expectations of inflation are formed is to consider the past history of inflation. Would adaptive expectations have provided a significant edge.\n", "8. How fast the flexible-price model becomes relevant depends on the type of inflation expectations in the economy. Under static expectations, the flexible-price model never becomes relevant. Under adaptive expectations, the flexprice model becomes relevant gradually, in the long-run. Under rational expectations the long run is now; the flexprice model analysis is relevant always and immediately.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Catch Our Breath\n", "\n", "\n", "\n", "* Ask me two questions…\n", "* Make two comments…\n", "\n", " \n", "\n", "* Further reading…\n", "\n", "
\n", "\n", "----\n", "\n", "Lecture Support: \n", "The Phillips Curve and Expectations, and Monetary Policy: \n", "Expectations and Monetary Policy: \n", "The Monetary Policy Reaction Function: \n", "\n", "\n", " \n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Phillips Curve, Expectations, and Monetary Policy\n", "\n", "### Ideal Types of Inflation Expectations\n", "\n", "* Static: $ {\\pi}^e = {\\pi}^* $\n", "* Adaptive: $ {\\pi_t}^e = {\\pi}_{t-1} $\n", "* Rational: $ {\\pi_t}^e = E_{t-1}\\left({\\pi}_{t}\\right) $\n", "* Panglossian $ {\\pi_t}^e = min({\\pi_t}^a, {\\pi_t}^b, {\\pi_t}^c, {\\pi_t}^d) $\n", "* Eeyorian $ {\\pi_t}^e = max({\\pi_t}^a, {\\pi_t}^b, {\\pi_t}^c, {\\pi_t}^d) $\n", "* Diagnostic $ {\\pi_t}^e = (1+\\theta)\\left(E_{t-1}\\left({\\pi}_{t}\\right) - E_{t-2}\\left({\\pi}_{t}\\right)\\right) + E_{t-2}\\left({\\pi}_{t}\\right) $\n", "\n", " \n", "\n", "### Phillips Curve\n", "\n", "* $ {\\pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) $\n", "\n", "\n", " \n", "\n", "\"Https\n", "\n", "\"Https\n", "\n", "**Olivier Blanchard**: _[The US Phillips Curve: Back to the 60s?](https://piie.com/publications/pb/pb16-1.pdf)_\n", "\n", "\"Preview\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Static Expectations\n", "\n", "* $ {\\pi}^e = {\\pi}^* $\n", "* $ {\\pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) $\n", "* $ {\\pi}_t = {\\pi}^* - {\\beta}(u_t - {u_t}^*) $\n", " * Push the unemployment rate down, the inflation rate goes up\n", " * Push the unemployment rate up, the inflation rate down\n", " * Costs of inflation are (within limits) low; costs of unemployment high...\n", " * Why not attempt to systematically exploit this?\n", " \n", " \n", "\n", "### Static Expectations: An Example\n", "\n", "* $ {\\pi}^e = {\\pi}^* $\n", "* $ {\\pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) $\n", "* $ {\\pi}_t = {\\pi}^* - {\\beta}(u_t - {u_t}^*) $\n", "* $ {\\beta} = 0.2 :: {\\pi}^* = 0.02 :: u^* = 0.04 $\n", "* If $ u_t = 0.04 $ then $ {\\pi}_t = 0.02 $\n", "* If $ u_t = 0.01 $ then what is $ {\\pi}_t $?\n", "\n", "To your iClickers...\n", "\n", ">A. 0.02 \n", "B. 0.022 \n", "C. 0.026 \n", "B. 0.04 \n", "E. None of the above\n", "\n", " \n", "\n", "### Why Not Attempt to Exploit This?\n", "\n", "WELL, WHAT MADE EXPECTATIONS STATIC IN THE FIRST PLACE?\n", "\n", " \n", "\n", "### Adaptive Expectations\n", "\n", "* $ {\\pi_t}^e = \\pi_{t-1} $\n", "* $ {\\pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) $\n", "* $ {\\pi}_t = {\\pi}_{t-1} - {\\beta}(u_t - {u_t}^*) $\n", "* $ \\Delta{pi}_t = - {\\beta}(u_t - {u_t}^*) $\n", " * If you push unemployment down—thus running a high pressure economy—you push inflation up, and up, and up...\n", " * If you want to keep unemployment below its natural rate, you have to accept an accelerating price level...\n", " * If you want to keep inflaiton constant, you have to make it the case that the average unemployment rate equals $ u^* $...\n", " * Hence no benefit to worrying about unemployment: what you lose one year you will gain back in another...\n", " \n", " \n", " \n", "### Adaptive Expectations: An Example\n", "\n", "* $ \\Delta{pi}_t = - {\\beta}(u_t - {u_t}^*) $\n", "* $ {\\beta} = 0.2 :: u^* = 0.04 :: {\\pi_1}^e = {\\pi}_o $\n", "* If $ u_o = 0.04 $ then $ {\\pi}_o = 0.02 $\n", "* If $ u_1 = 0.02 $ then what is $ {\\pi}_5 $?\n", "\n", "To your iClickers...\n", "\n", ">A. 0.02 \n", "B. 0.022 \n", "C. 0.026 \n", "B. 0.04 \n", "E. None of the above\n", "\n", " \n", "\n", "### Perfect Foresight\n", "\n", "* $ {\\pi_t}^e = \\pi_{t} $\n", "* $ {\\pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) + SS_t $ :: complicate the Phillips Curve with supply shocks\n", "* $ {\\pi}_t = {\\pi}_t - {\\beta}(u_t - {u_t}^*) + SS_t $\n", "* $ 0 = - {\\beta}(u_t - {u_t}^*) + SS_t $\n", "* $ u_t = {u_t}^* + \\frac{SS_t}{\\beta} $\n", "\n", " \n", "\n", "### Rational Expectations\n", "\n", "* $ {\\pi_t}^e = E_{t-1}\\left(\\pi_{t}\\right) $\n", "* $ {\\pi_t} = {\\pi_t}^e + \\epsilon_t $ (unforecastable)\n", "* $ {pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) + SS_t $ :: complicate the Phillips Curve with supply shocks\n", "* $ {pi}_t = {\\pi}_t + \\epsilon_t - {\\beta}(u_t - {u_t}^*) + SS_t $\n", "* $ 0 = - {\\beta}(u_t - {u_t}^*) + \\epsilon_t + SS_t $\n", "* $ u_t = {u_t}^* + \\frac{\\epsilon_t + SS_t}{\\beta} $\n", " * $ SS_t $ :: things that temporarily push the natural rate around\n", " * $ \\epsilon_t $ :: surprises\n", " * No room for policy...\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Intermediate Cases\n", "\n", "* $ \\pi_t = (1-\\lambda)\\pi^* + \\lambda\\pi_{t-1} - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", " \n", "\n", "* Here we have something we can estimate!\n", "\n", " \n", "\n", "### Here Is Our $ \\lambda $...\n", "\n", "\"Expectations\n", "\n", " \n", "\n", "### Here Is Our $ \\beta $...\n", "\n", "\"Expectations\n", "\n", " \n", "\n", "### Here Is Our $ \\beta $...\n", "\n", "* Where are the supply shock terms in the regression?\n", "* What happens if you leave out an important variable from the right hand side?\n", "\n", ">A. It’s OK: your estimates of the variables will still be unbiased—the missing variables go into the regression error ε, and your estimates will be less precise… \n", "B. It’s not OK: the missing variables are highly likely to be correlated with the stuff you have on the RHS, and the computer will attribute as much of the effect of the missing variable it can to the variable it sees…\n", "\n", "* Implications for their estimates of λ…\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### To Your iClickers\n", "\n", "The Keynesian multiplier is:\n", "\n", ">A. A process that amplifies a shock to autonomous spending and leads it to have a multiplied effect on the level of real national income and product in the sticky-price model \n", "B. A force that keeps national income and product equal to potential output in the flexprice model \n", "C. The process by which a change in bank reserves produces an amplified change in the money stock \n", "D. None of the above\n", "\n", " \n", "\n", "The IS-Curve relationship is primarily:\n", "\n", ">A. The relationship between national income and product Y and the long-term real risky interest rate r \n", "B. The relationship between national income and product Y and the multiplier μ \n", "C. The relationship between national income and product Y and the marginal propensity to consume $ c_y $ \n", "D. The relationship between national income and product Y and the money stock M \n", "E. None of the above\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Why Do We Care About Inflation?\n", "\n", "* Quite clear why we care about production…\n", "* Quite clear why we care about unemployment/employment…\n", "* But why do we care about inflation?\n", " * It’s zero sum…\n", " * Yet we do…\n", " \n", "\"Expectations\n", "\n", " \n", "\n", "### John Maynard Keynes on Inflation\n", "\n", "* Lenin is said to have declared that the best way to destroy the Capitalist System was to debauch the currency. By a continuing process of inflation, governments can confiscate, secretly and unobserved, an important part of the wealth of their citizens. By this method they not only confiscate, but they confiscate arbitrarily; and, while the process impoverishes many, it actually enriches some…\n", "\n", "\"John\n", "\n", " \n", "\n", "### Costs of Inflation\n", "\n", "* But that is inflation of 25% per year or so…\n", "* Inflation of less than 10% per year?\n", "Paul Volcker and Alan Greenspan think inflation above 5% per year\n", " * Causes confusion…\n", " * Distracts businessmen from what it would be more productive for them to think about…\n", " * Thus slows productivity growth\n", "* Inflation of less than 5% per year?\n", " * Volcker was happy with it…\n", " * Greenspan pushed for 2%…\n", " * Greenspan did not push for 0%…\n", " \n", " \n", "\n", "### Costs of Low Inflation\n", "\n", "* Limited running room on the part of the Federal Reserve\n", "* DeLong and Summers (1988) at Jackson Hole, WY…\n", "\n", " \n", "\n", "### But We Keep Inflation Very Low, Even So?\n", "\n", "* Why? Because voters hate it!\n", " * Money illusion?\n", " * Evidence of governmental incompetence?\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Monetary Policy: The Federal Reserve and Its \"Reaction Function\"\n", " \n", "* The policy rate—the short-term safe nominal interest rate: i\n", "* The long-term safe interest rate: $ i + {\\rho}_T $ (T for \"term risk premium\")\n", "* On top of this, we pile:\n", " * The rest of the risk premium: $ i + {\\rho}_T + {\\rho}_D $ (D for \"default risk premium\")\n", " * Whole risk premium: $ \\rho = \\rho_T + \\rho_D $\n", " Subtract the inflation rate $ \\pi $\n", "* Trying to alter the term risk premium via: “forward guidance” and “quantitative easing”\n", " * Not very powerful tools\n", "\n", " \n", "\n", "* Does the Federal Reserve's pattern of behavior makes sense?\n", "* Applied math optimal control tells us:\n", " * Bang-bang…\n", " * Minor course corrections…\n", "* The Fed does neither...\n", "\n", "\"10\n", "\n", " \n", "\n", "### Monetary Policy: The Federal Reserve and Its \"Reaction Function\"\n", " \n", "* The zero lower bound—purple line: $ -\\pi $\n", " * The Fed cannot push any interest rate below the negative of the inflation rate\n", "* The real policy rate, the short-term safe real interest rate—blue line: $ i - \\pi $\n", "* The long-term real safe Treasury rate—red line: $ i - \\pi + \\rho_T $\n", "* The long-term risky real interest rate—green line: $ i - \\pi + \\rho_T + \\rho_D = i - \\pi + \\rho $\n", "\n", "\"Expectations\n", "\n", " \n", "\n", "### Understanding the Recent History of the Federal Reserve\n", "\n", "* The Volcker disinflation 1979-83\n", "* Post-1983 “policy easing” (Volcker)\n", " * Trying to make Say’s Law true in practice\n", "* The 1987 shock (caused by Haas)\n", " * Greenspan’s reaction 1987-1989\n", "* “Overheating” 1990-2 (Greenspan)\n", "* Accomodating fiscal contraction 1992-4 (Greenspan)\n", "* Monetary tightening 1994-5 (Greenpan)\n", "* Accommodating the dot-com boom 1995-9 (Greenspan)\n", "\n", " \n", "\n", "* Slow to react 2000-2 (Greenspan)\n", "Keeping rates low (2002-5) and encouraging housing and derivatives bubbles (Greenspan)\n", "* Raising (2005-7) (Bernanke)\n", "* Slow to cut (2007-8) (Bernanke)\n", "* The crisis (2008-10) (Bernanke)\n", "* Declaring victory (2010-12) (Bernanke)\n", "* Fiscal headwinds (2012-16) (Yellen)\n", "* Tightening cycle (2016-present) (Yellen, Powell)\n", "\n", " \n", "\n", "### Implications for the Output Gap\n", "\n", "\"Expectations\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interest Rate Rules\n", "\n", "#### $ r = r_o + r_π(π - π^t) - r_u(u - u*) $\n", "\n", "* (also McKibben and Henderson)\n", "\n", " \n", "\n", "### The Atlanta Fed's Interest Rate Rule Calculator\n", "\n", "$ r = r_o + r_π(π - π^t) - r_u(u - u*) $\n", "\n", "* Taylor: r = 0.03 + (0.5)(π - 0.02) - (0.25)(u - 0.06)\n", "\n", "\n", "\n", "\"Expectations\n", "\n", " \n", "\n", "### r*\n", "\n", "\"Expectations\n", "\n", " \n", "\n", "### The Bernanke Letter\n", "\n", "\n", "\n", "* We believe the Federal Reserve’s large-scale asset purchase plan (so-called “quantitative easing”) should be reconsidered and discontinued…. The planned asset purchases risk currency debasement and inflation…\n", "* We do not think they will achieve the Fed’s objective of promoting employment…\n", "* We disagree with the view that inflation needs to be pushed higher…\n", "* Another round of asset purchases, with interest rates still near zero over a year into the recovery, will distort financial markets and greatly complicate future Fed efforts to normalize monetary policy…\n", "* Quantitative easing by the Fed is neither warranted nor helpful…\n", "\n", " \n", "\n", "### Enough Inside Baseball!\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Monetary Policy Reaction Function\n", "\n", "\"Expectations\n", "\n", "* $ r = r_o + r_π(π - π^t) - r_u(u - u*) $\n", "* $ u = u_o + {\\phi}(π - π^t) $\n", "\n", "The MPRF brings together three relationships at once:\n", "\n", "1. Interest rate rule: $ r = r_o + r_π(π - π^t) - r_u(u - u*) $\n", "2. IS Curve: $ Y = AD = \\mu(A_o - (I_rr_\\epsilon)r $\n", "3. Okun's Law; $ u = u^* - 0.4\\left(\\frac{Y - Y^*}{}Y^*\\right) $\n", "\n", " \n", "\n", "### The Monetary Policy Reaction Function: An Example\n", "\n", "Suppose:\n", "\n", ">$ {\\pi}^t = 0.02 $ \n", "$ \\pi = 0.05 $ \n", "$ r_{\\pi} = \\frac{1}{3} $ \n", "$ r_o = .025 $\n", "\n", "Then by the interest rate rule:\n", "\n", ">$ r = 0.025 + \\frac{1}{3}(0.05 - 0.02) = 0.035 $\n", "\n", "The central bank will conduct monetary policy so that the real interest rate is 3.5%.\n", "\n", "Suppose further that:\n", "\n", ">$ MPE = 0.5 $ \n", "$ A_o = 2.15 $ trillion \n", "$ I_r = 8 $ \n", "$ x_{\\epsilon}{\\epsilon}_r = 2 $\n", "\n", "Then the IS Curve tells us that when the interest rate is 3.5 percent:\n", "\n", ">$ \\mu = \\frac{1}{1 - MPE} = 2 $ \n", "$ Y = \\mu(A_o) - \\mu(I_r + x_{\\epsilon}{\\epsilon}_r)r = 4.3 - (2)(10)(.035) = 3.6 $ trillion\n", "\n", "Planned expenditure will equal real output and national income when they are 3.6 trillion.\n", "\n", "Finally, supppose that:\n", "\n", ">$ u^* = 0.05 $ \n", "$ Y^* = 4 $ trillion\n", "\n", "Then Okun's Law tells us that when output is 3.6 trillion:\n", "\n", ">$ u = 0.05 - 0.4\\frac{3.6-4}{4} = 0.05 + 0.04 = 0.09 $\n", "\n", "The unemploymente rate is then 9 percent.\n", "\n", "When the inflation rate is 5 percent rather than the central bank's target of 2 percent, the central bank will raise the real interst rate from its normal baseline rate of 2.5 percent to 3.5 percent, which will cause output to fall to 3.6 trillion and generate an unemployment rate of 9 percent.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Monetary Policy Reaction II Function\n", "\n", "\"Expectations\n", "\n", "* $ π = π^e - {\\beta}(u - u^*) + SS $\n", "* $ r = r_o + r_π(π - π^t) - r_u(u - u*) $\n", "* $ u = u_o + {\\phi}(π - π^t) $\n", "\n", "Nomenclature:\n", "\n", ">r :: real risky interest rate \n", "$r^*$ :: neutral rate \n", "$r_π$ :: reaction of central bank to higher (or lower) inflation \n", "$π^t$ :: central bank’s inflation target \n", "$r_u$ :: reaction of central bank to higher (or lower) unemployment \n", "u :: unemployment rate \n", "$u^*$ :: NAIRU: unemployment rate at which inflation equals expectations \n", "π :: inflation \n", "$π^e$ :: expected inflation \n", "β :: slope of Phillips Curve: relationship of inflation to unemployment \n", "SS :: supply shock to inflation \n", "φ :: a combination of Okun’s Law, the multiplier, and interest sensitivity of investment and exports \n", "δ :: demand shock\n", "\n", " \n", "\n", "### Add Lags\n", "\n", ">$ r_t = r^* + r_π(π_t - π^t) - r_u(u_t - u*) $\n", "\n", ">$ π_t = π^e - β(u_{t-1} - u*) + SS_t $\n", "\n", ">$ u_t = u* + φ(r_t - r*) + δ_t $\n", "\n", " \n", "\n", ">$ u_t - u^* = +{\\phi}r_{\\pi}(\\pi_t - \\pi^t) - {\\phi}r_u(u_t - u*) + \\delta_t $ \n", "\n", ">$ (u_t - u^*) = \\frac{{\\phi}r_{\\pi}(\\pi_t - \\pi^t) + \\delta_t}{1 + {\\phi}r_u} $\n", "\n", "With adaptive expectations:\n", "\n", ">$ π_t = π_{t-1} - β(u_{t-1} - u*) + SS_t $\n", "\n", ">$ (π_t - π^t) = (π_{t-1} - π^t) - \\beta\\left(\\frac{{\\phi}r_{\\pi}(\\pi_{t-1} - \\pi^t) + \\delta_{t-1}}{1 + {\\phi}r_u}\\right) + SS_t $\n", "\n", ">$ (π_t - π^t) = \\left(\\frac{1 + {\\phi}r_u -\\beta{\\phi}r_{\\pi}}{1 + {\\phi}r_u}\\right)(\\pi_{t-1} - \\pi^t) - \\beta\\left(\\frac{\\delta_{t-1}}{1 + {\\phi}r_u}\\right) + SS_t $\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Alternatively: They Could Try to Get Ahead of the Curve\n", "\n", ">$ (u_t - u^*) = {\\phi}(r_t - r^*) + \\delta_t $\n", "\n", ">$ π_t = π_{t-1} - β(u_{t-1} - u*) + SS_t $\n", "\n", " \n", "\n", ">$ (π_t - π^t) = (π_{t-1} - π^t) - β{\\phi}(r_{t-1} - r^*) - β\\delta_t + SS_t $\n", "\n", "Try to stabilize inflation:\n", "\n", ">$ 0 = (π_{t-1} - π^t) - β{\\phi}(r_{t-1} - r^*) - β\\delta_t + SS_t $\n", "\n", ">$ β{\\phi}(r_{t-1} - r^*) = (π_{t-1} - π^t) - β\\delta_t + SS_t $\n", "\n", ">$ r_{t-1} = r^* + \\frac{(π_{t-1} - π^t)}{β{\\phi}} - \\frac{\\delta_t}{\\phi} + \\frac{SS_t}{β{\\phi}} $\n", "\n", "Then:\n", "\n", ">$ \\pi_t = \\pi^t $\n", "\n", " \n", "\n", "### Why Doesn't the Federal Reserve Try Harder to Get Ahead of the Curve?\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### To Your iClickers...\n", "\n", "The interest rate rule is:\n", "\n", ">A. A way of capturing how the Federal Reserve and other central banks typically react to the changing economic environment \n", "B. The rule that higher interest rates reduce investment spending \n", "C. The fact that higher interest rates make the future look “cheaper” relative to the present \n", "D. Required by Congress that the Federal Reserve follow—or explain why it is not following \n", "E. None of the above\n", "\n", " \n", "\n", "The Keynesian multiplier is:\n", "\n", ">A. An amplified relationship between shifts in autonomous spending—exports, government purchases, investment, consumer confidence—and shifts in real national product \n", "B. The fact that the money supply expands by a multiplied factor times the expansion in the monetary base \n", "C. The fact that a sticky-price economy has multiple possible equilibrium positions for national income and product \n", "D. The fact that investment increases when production increases because investment depends largely on business-sector cash flow \n", "E. None of the above\n", "\n", " \n", "\n", "Living standards were more-or-less stagnant from 5000 BC to 1800 largely because of:\n", "\n", ">A. Keynesian factors \n", "B. Schumpeterian factors \n", "C. Ricardian factors \n", "D. Malthusian factors \n", "E. None of the above\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Catch Our Breath\n", "\n", "\n", "\n", "* Ask me two questions…\n", "* Make two comments…\n", "\n", " \n", "\n", "* Further reading…\n", "\n", "
\n", "\n", "----\n", "\n", "Lecture Support: \n", "The Phillips Curve and Expectations, and Monetary Policy: \n", "Expectations and Monetary Policy: \n", "The Monetary Policy Reaction Function: \n", "\n", " \n", "\n", "----" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }