{ "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": [ "# 10 The IS Curve: Investment, Net Exports, and Interest Rates: TEXTBOOK DRAFT\n", "\n", "**QUESTIONS**\n", "\n", "1. How do the determinants of investment and net exports* in the sticky-price model differ from those of the flexible-price model?\n", "2. How do changes in interest rates affect the equilibrium level of real GDP and national income in the sticky-price model?\n", "3. What is the IS curve? How do we use it?\n", "4. How do we calculate the equilibrium level of real GDP in the sticky-price model when the central bank's policy is to peg the real interest rate?\n", "\n", " \n", "\n", "**long-term interest rate**: The interest rate required if you are going to borrow money not for a short term of months but for a long term of decades.\n", "\n", "**short-term interest rate** The interest rate paid to borrow money for the short term—three to six months.\n", "\n", "**risky interest rate**: The interest rate on assets where there is some chance the debtor will default.\n", "\n", "**safe interest rate**: The interest rate on assets where there is no significant probability of default.\n", "\n", "**IS curve**: The downward-sloping relationship between the (real, long-term) interest rate and the equilibrium level of national product and aggregate demand.\n", "\n", "**baseline autonomous spending**: Written $ A_o $.Those components of\n", "autonomous spending that are independent of the level of the interest rate.\n", "\n", "**interest rate targeting**: A process whereby a central bank focuses its policies on controlling—i.e., targeting—the interest rate at some stable level.\n", "\n", "----\n", "\n", " \n", "\n", "If we can understand the causes and consequences of changes in investment spending, we will understand much of what we need to know in order to understand the causes of America’s business cycles. We do so in this chapter by building an analytical tool called the IS curve, where “IS” stands for “investment-saving.” The IS curve tells us the relationship between total expenditure or real GDP on the one hand and the long-term risky real interest rate on the other. Changes in the interest rate increase or depress investment and gross exports and so move the economy down or up along the IS curve. Changes in businesses’ optimism or pessimism cause increases or decreases in investment unrelated to changes in interest rates, and so shift the entire IS curve itself either out or in.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 10.1 Interest Rates and Aggregate Demand\n", "\n", "### 10.1.1 The Importance of Investment\n", "\n", "Changes in investment spending are the principal driving force behind the business cycle. \n", "\n", "Without exception, reductions in investment have played a powerful role in every single recession and depression. Falls in investment spending played an important role in generating the recessions of 1970, of 1974-1975, of 1979-1982, of 1990-1991, of 2001-2002, and of 2008-9. Increases in investment have spurred every single boom—whether the late 1960s, the early 1970s, the late 1970s, the mid-1980s, the late 1990s, or the 2000s.\n", "\n", " \n", "\n", "\"Real\n", "\n", ">>_**Real Investment Spending as a Share of Real Potential GDP**: Over the past half-century, the business-cycle boom peaks of 1973, 1979, 2000, 2007, and today have all been accompanied by strong investment. Only the peak of 1989 does not stand out from the years around it in terms of the flow of investment spending. And the recession troughs of 1975, 1982 1992, 2002, and 2009 are all marked as the troughs in investment following sharp falls in it as well._\n", "\n", " \n", "\n", "\"Gross\n", "\n", " \n", "\n", ">_**Nominal Investment Spending as a Share of Nominal Potential GDP**: The substantial year-to-year swings in investment are the principal drivers of the business cycle. When investment booms, the economy as a whole booms too. The nominal investment graph over the past fifty years looks somewhat different than the real investment graph. The difference is a sharp fall in the relative price of capital goods starting in the 1990s: with the coming of the computer age, the same savings buck produces more of an investment bang._\n", "\n", "Because of the multiplier process, the swings in real GDP have invariably been larger than the swings in investment spending themselves. Swings in investment have carried with them swings in consumption as well, as the greater employment in investment goods industries has funded yet more employment elsewhere in the economy. And fluctuations in government purchases, in gross exports, and in baseline consumption spending driven by consumer confidence have played a lesser role in driving the business cycle.\n", "\n", " " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# graph sources\n", "\n", "# real/real investment spending as a share of potential gdp\n", "# https://fred.stlouisfed.org/graph/?graph_id=516169&rn=790#0\n", "\n", "# nominal/nominal investment spending as a share of potential gdp\n", "# https://fred.stlouisfed.org/graph/?graph_id=516170&rn=485#0\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 10.1.1.1 The Role of Investment\n", "\n", "Our analysis here of the role of investment spending will parallel the earlier analysis carried out in the flexible-price model. The determinants of investment are unchanged: Investment is still determined by (1) a baseline \"animal spirits\" level of investment $ I_o $, (2) a sensitivity of investment to the real interest rate $ I_r $, and (3) the level of the long-term risky real interest rate r. But the kind of equilibrium the economy reaches and the process by which the economy reaches equilibrium are different. Hence the investment function plays a very different role in the two models.\n", "\n", "In the flexible-price model, the real interest rate was the market-clearing price. It was pushed up or down by supply and demand to equate the flow of saving into financial markets (from households and businesses, the government, and foreigners) to the flow of investment funding out of financial markets (to finance replacement of depreciated capital and increases in the capital stock). Supply and demand in the loanable funds market determined the interest rate. In the flexible-price model, the level of saving determined the level of investment, and the strength of investment demand determined the interest rate.\n", "\n", "In the sticky-price model, the interest rate is not set in the loanable funds market. Instead, it is set directly by the central bank or indirectly by the combination of the stock of money and the liquidity preferences of households and businesses. The interest rate then determines the level of investment, which then plays a key role in autonomous spending. Together, autonomous spending and the multiplier determine the level of output.\n", "\n", "“What happened to equilibrium in the loanable funds market?” you may ask. In a sticky-price model the fact that businesses match the quantity they produce to aggregate demand automatically creates balance in the financial market, no matter what the interest rate. Any interest rate can be an equilibrium interest rate because the inventory-adjustment process has already made saving equal to investment.\n", "\n", " \n", "\n", "#### 10.1.1.2 Sources of Fluctuations in Investment\n", "\n", "Fluctuations in investment have two sources. Some are triggered by changes in the real interest rate r. A lower real interest rate means higher investment spending, and a higher real interest rate means lower investment spending. Other fluctuations are triggered by shifts in investors’ expectations about future growth, profits, and risk. These two sources of fluctuations in investment correspond, respectively, to changes in investment spending I produced by (1) the interest sensitivity of investment parameter $ I_r $ times changes in r, and (2) changes in the baseline \"animal spirits\" level of investment $ I_o $ in the investment function:\n", "\n", "> $ I=I_o - I_rr $\n", "\n", "Both sources of fluctuation are important. Neither is clearly dominant.\n", "\n", " \n", "\n", "### 10.1.2 Investment and the Real Interest Rate\n", "\n", "A business that undertakes an investment project always has alternative uses for the money. One alternative would be to take the money that would have been spent building the factory or buying the machines and place it instead in the financial markets—that is, lending it out at the market real rate of interest. Thus the opportunity cost of an investment project is the real interest rate. The higher the interest rate, the fewer the number and the smaller the value of investment projects that will return more than their current cost, and the lower the level of investment spending. But which interest rate is the relevant one? There are many different interest rates.\n", "\n", " \n", "\n", "#### 10.1.2.1 The Real Interest Rate\n", "\n", "The interest rate that is relevant for investment spending decisions is not the nominal but the real interest rate. The nominal price a business charges rises with inflation. If a business is willing to invest when the interest rate is 5 percent and inflation is 2 percent per year (and so the real interest rate is 3 percent per year), then the business should also be willing to invest when the interest rate is 10 percent and inflation is 7 percent per year (and so the real interest rate is still 3 percent per year). Figure 10.3 on page 286 shows both nominal and real interest rates in the United States. There is a big difference between the two.\n", "\n", " \n", "\n", "\"ICE\n", "\n", ">>_**Gaps between Real and Nominal Interest Rates**: Borrowers care not about the nominal interest rate (in blue)—the interest rate in terms of money—but about the real interest rate on loans (in red)—the interest rate in terms of goods. The difference between the nominal and the real interest rates is the inflation rate. Thus the real interest rate that companies that borrow to finance investment care about is now some 2.5 percentage points below the nominal interest rate. The gap has varied little over the past twenty years because inflation had remained stable and quiescent._\n", "\n", " \n", "\n", "#### 10.1.2.1 The Long-Term Interest Rate\n", "\n", "The interest rate that is relevant for determining investment spending is a long-term interest rate. Investments are durable and long-lasting. Whenever a manager considers undertaking an investment project, he or she must compare the potential profits from the project to the opportunity to make money from a long-term alternative commitment of the funds elsewhere. The interest rate that is the oppor­ tunity cost of undertaking an investment project with a life length of a decade or more is the interest rate on a long-term loan for a period of a decade or more: the long-term interest rate.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**Bond Yield Curves**: The interest rate the U.S. government must pay to borrow money depends on how long it wants to borrow the money. The same applies to private borrowers as well: Usually, the longer the term for which one wishes to borrow, the higher the interest rate one must pay._\n", "\n", " \n", "\n", "This distinction matters because long- and short-term interest rates are different and do not always move in step. Below is a standard yield curve chart, the term structure of interest rates, that plots the interest rate on safe U.S. government bonds of three different maturities—3-month Treasury bills, 3-year Treasury notes, and 10-year Treasury bonds—at three different moments—1992, 1996, and 2003. Looking at the shifts over time in such a yield curve chart shows that different interest rates do not always fluctuate together. The variable premium in the interest rate that the market charges on long-term loans vis-a-vis short-term loans is called the term premium. This creates the potential for problems for the Federal Reserve: What if it wants to lower interest rates to stimulate investment, and so buys three-month Treasury bills for cash to reduce the short-term interest rate, but finds the term premium rising and thus the long-term interest rate that matters for investment unchanged?\n", "\n", "Long-term interest rates are usually higher than short-term rates because longterm assets are riskier, and investors demand a higher average return to compensate them for bearing this extra risk. When Wall Street bond traders expect short-term interest rates to rise in the future, the term premium is large. When they expect short-term interest rates to fall steeply, the term premium is negative, but such an inverted term premium is rare—the term structure of interest rates or yield curve is almost always upward sloping.\n", "\n", "In 1992 and 2003 the yield curve was steep: long-term loans carried significantly higher interest rates than short-term loans; the term premium was high. In 1996 the yield curve was nearly flat; the term premium was low. In 1992 and 1996 the general levels of interest rates were about the same. By 2003 the general level of interest rates had fallen all across the maturity structure; all three sets of Treasury assets paid lower returns than they had in 1992 or 1996.\n", "\n", "Why was the term premium so high in 1992 and 2003? Two reasons:\n", "\n", "First, in both cases the Federal Reserve had aggressively pushed interest rates down in the recent past to try to boost investment and employment, so short-term interest rates were depressed below their normal levels, and markets were expecting the Federal Reserve to reverse itself as soon as employment returned to normal levels. The term premium is likely to be high when interest rates are expected to rise. \n", "\n", "Second, savers and investors in both 1992 and 2003 could look forward to a future in which there were large budget deficits that the government seemed to have no plans for reducing. In the flexible-price model, high budget deficits produce higher than normal interest rates. And so investors were expecting interest rates to soon be not just at normal but at higher than normal runaway-deficit levels.\n", "\n", " \n", "\n", "\"ICE\n", "\n", ">>_**Risky Long, Safe Long, and Safe Short-Term Nominal Interest Rates**: Loans that are not made I to the U.S. government are risky. The representative risky interest rate—that paid by companies rated \"BBB\" by Bank of America Merrill Lynch—(in blue) has, over the past two decades, varied between 1.5 and 7 percentage points more than the safe long-term rate paid by the U.S. government (in red). Lenders ought to charge a risk premium that depends both on their tolerance for risk and on the amount of risk involved when they lend to other organizations. There is no reason why this should be constant. But the actual swings we see in the risk premium are much larger than any plausible shifts in the relative or absolute riskiness of a diversified portfolio of loans to and bonds of companies._ \n", "  \n", "_The long-term rate—that received if you lend to the U.S. government for ten years (in red)—has varied up to 3.75 percentage points more than the short-term rate (in olive)—that received if you lend to the U.S. government for three months. The yield curve has even become \"inverted\": the long-term rate has fallen below the short-term rate, inevitably because financial markets anticipate that a recession will come soon, and that the central bank will then be frantically cutting interest rates to try to boost investment spending, so now is a good time to buy a long-term Treasury bond to lock in a relatively high return._\n", "\n", " \n", "\n", "#### 10.1.2.3 The Risky Interest Rate\n", "\n", "Lending money to a business always carries an element of risk. Perhaps the borrower will go bankrupt before the loan is due. Perhaps the creditors will find themselves last, or nearly last, in line as a small amount of leftover postbankruptcy assets are divided up. Financial institutions lending money are keenly interested in the financial health of those to whom they lend. The riskier they believe the loan is—the larger the possibility of a bankruptcy or a debt rescheduling appears to be—the higher is the interest rate that lenders will demand to compensate them for risk.\n", "\n", "The interest rate that a firm faces is the interest rate charged to risky borrowers, not the interest rate charged to safe borrowers (like the U.S. government) to whom people lend when they want to sleep easily at night. The premium that lenders charge for loans to companies rather than to safe government borrowers is called the risk premium. Financial and economic disturbances, like the default of the Russian government in August 1998 or even more so the financial crisis in late 2008, can cause large and swift moves in the risk premium. In 1998 the rise in the risk premium was neutralized by the Federal Reserve under Alan Greenspan, who lowered short-term rates and pledged that he would lower them further and keep them lower longer if that was necessary to keep the spike in the risk premium from raising businesses' borrowing costs. In 2008 the \n", "Federal Reserve under Ben Bernanke simply could not lower short-term rates far enough and credibly pledge to keep them lower long enough to neutralize the much larger rise in the risk premium. Hence the 1998 rise in the risk premium imposed no ripples on the rest of the economy, while the 2008 rise in the risk premium was the most destructive economic tsunami since the Great Depression of the 1930s.\n", "\n", "The risky interest rate thus does not always move in step with the safe interest rate. Its swings are much larger than any plausible shifts in the relative or absolute riskiness of a diversified portfolio of loans to and bonds of companies. These swings are large and sudden changes in the \"risk tolerance\" of the market that do not have explanations in terms of rational investors insuring themselves against fundamental risks in the economy.\n", "\n", "Thus—bringing this all together—to determine the level of investment spending, take the baseline level of investment $ I_o $ (determined by businesses’ optimism, expected economic growth, and a bunch of other factors for which the level of the stock market serves as a convenient thermometer). Subtract from this baseline level the interest sensitivity of investment parameter $ I_r $ times the relevant interest rate r expressed in decimal form, so an interest rate of 3 percent is expressed as 0.03. The relevant interest rate must be long-term because most investments are long-term. The relevant interest rate must be real because investment projects are real assets: Their values rise with inflation. And the relevant interest rate must be risky because businesses borrowing to invest may go bankrupt. In the investment function:\n", "\n", "> $ I = I_o - I_rr $\n", "\n", "the relevant interest rate r is the long-term, real, risky interest rate. Both safe and risky nominal interest rates can be directly observed: It is what the newspapers print every day in their analyses of the bond market. The real interest rate is just the nominal interest rate minus the expected rate of inflation, which will almost always be close to the current rate of inflation.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**Investment as a Decreasing Function of the Long-Term, Real, Risky Interest Rate**: The baseline level of investment $ I_o $ tells us what the level of investment would be if the real interest rate were zero. The interest rate sensitivity parameter $ I_r $ tells us how much investment is dis­ couraged by a 1-unit increase in the long-term, real, risky interest rate._\n", "\n", " \n", "\n", "For as long as there have been industrial market economies, there have been large swings in interest rates. Sometimes these have been stabilizing: central banks \"leaning against the wind\", trying to make it more profitable to borrow-and-invest when unemployment is high and output below potential, and trying to make it less profitable to borrow-and-invest when unemployment is low and output near to potential. \n", "Sometimes these have been destabilizing: financial crises and episodes of irrational exuberance pushing borrowing costs and thus incentives to borrow-and-invest up and down not counter to but in synch with fluctuations in \"animal spirits\" and the rest of the business cycle.\n", "\n", " \n", "\n", "\"ICE\n", "\n", ">>_**Risky Long, Safe Long, and Safe Short-Term Real Interest Rates in the Long Run**: Over the past 55 years the dance of real interest rates has been a major force affecting the macroeconomy. Driven by fluctuations in inflation, in the short-term safe nominal federal funds rate controlled by the Federal Reserve, in the so-called term premium between short- and long-term rates, and by the risk premium between safe and risky interest rates, upward fluctuations have played a major role in causing the two largest post-World War II recessions of 1982 and 2009 as well as smaller downturns, and downward fluctuations have played large roles in generating the inflationary booms of the 1970s._\n", "\n", " \n", "\n", "#### 10.1.2.4 The Stock Market as an Indicator of Future Investment: Some Tools\n", "\n", "Can we find an easy way to observe the rest of the determinants of investment spending—all of those that are packed into the baseline level of investment spending $ I_o $? We can, by looking at the stock market.\n", "\n", "Recall that if investors in the stock market are acting rationally, the level of the stock market Ps will be equal to:\n", "\n", "> $ P^s = E^a\\left(\\frac{E^s}{E^a}\\right)\\left(\\frac{1}{r + {\\rho}_s}\\right) $\n", "\n", "where:\n", "\n", "* $ E^a $ is the accounting earnings corporations report.\n", "* $ E^s/E^a $ is the ratio of the long-run “permanent” earnings investors expect to today’s accounting earnings. It is a measure of optimism—of expected future growth.\n", "* $ r $ is the long-term real interest rate on bonds.\n", "* $ {\\rho}_s $ is the risk premium investors require to invest in stocks rather than in less risky assets.\n", "\n", "Thus the level of the stock market sums up—in one easy-to-find readily-at-hand number, reported instantly all the time—the relative state of the real interest rate r plus the other important influences—profitability, expected growth, and attitudes toward risk—that determine the baseline level of investment $ I_o $.\n", "\n", "Think of it this way: An investor deciding whether or not to commit his or her portfolio to stocks (rather than bonds) is making more or less the same decision as that made by a business’s investment committee deciding whether to build a factory. The purchase of a share of stock gives you title to a share in the ownership of past investments—factories, buildings, inventories, and organizations—that have been undertaken by one company. The same things that determine whether it is a good idea to undertake the construction of a new factory also determine whether it is a good idea to spend money to acquire title to a share of an old factory. And the conclusions reached by investors in the stock market, which we observe every day in stock price fluctuations, are likely to be much the same as the conclusions reached by businesses’ investment committees.\n", "The higher the stock market, the higher is the likely future level of investment spending.\n", "\n", " " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# graph URLS\n", "\n", "# nominal and real BAML BBB bond rate\n", "# https://fred.stlouisfed.org/graph/?graph_id=516191&rn=821\n", "\n", "# risky long, safe long, and safe short-term nominal interest rates\n", "# https://fred.stlouisfed.org/graph/?graph_id=516192&rn=961#0\n", "\n", "# risky long, safe long, and safe short-term real interest rates\n", "# in the long run\n", "# https://fred.stlouisfed.org/graph/?graph_id=516195&rn=268" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.1.3 Exports and Autonomous Spending\n", "\n", "Investment spending is not the only component of autonomous spending that is affected by the real interest rate. In the aggregate-demand function\n", "\n", ">AD = A + (MPE)Y\n", "\n", "autonomous spending A—spending that does not depend upon income Y—includes not just baseline consumption, investment, and government purchases, but gross exports as well:\n", "\n", "> $ A = c_o + I + G + GX\n", "\n", "Gross exports depend on foreign total incomes $ Y^f $ and the real exchange rate $ \\epsilon $. So we can expand the determinants of gross exports in the expression for autonomous spending:\n", "\n", "> $ A= c_o + (I_o - I_rr) + G + (x_fY^f + x_{\\epsilon}\\epsilon) $\n", "\n", "As we also saw, the real exchange rate $ \\epsilon $ depends on the domestic real interest rate r as well as on foreign exchange speculators’ opinions of fundamentals $ \\epsilon_o $ and foreign and domestic interest rates $ r^f $ and $ r $:\n", "\n", "> $ \\epsilon = \\epsilon_o + \\epsilon_r(r^f - r) $\n", "\n", "Substituting this equation for the determinants of the exchange rate into the autonomous spending equation, we can see that there are two components of autonomous spending affected by changes in the real interest rate:\n", "\n", "> $ A= c_o + I_o + G + x_fY^f + x_{\\epsilon}\\epsilon_o + x_{\\epsilon}\\epsilon_rr^f - I_rr - x_{\\epsilon}\\epsilon_rr $\n", "\n", "A higher real interest rate reduces autonomous spending by reducing exports (the $ - x_{\\epsilon}\\epsilon_rr $ term) as well as by reducing investment (the $ - I_rr $ term).\n", "\n", "Why does a higher domestic interest rate reduce exports? A higher real interest rate makes purchasing financial assets in the home country more attractive: Foreign exchange speculators try to take advantage of this opportunity to earn higher returns by shifting their portfolio holdings to include more home-currency-denominated assets. This increase in demand for home-currency-denominated assets and decrease in demand for foreign-currency-denominated assets drives down the exchange rate, which is the value of foreign currency.\n", "\n", " \n", "\n", "\"DeLong>_**From the Real Interest Rate to the Change in Exports**: A change in the real interest rate changes the real exchange rate and thus changes gross exports as well._\n", "\n", " \n", "\n", "A lower value of foreign currency makes our exports more expensive to foreigners: Their currency buys less here because it is less valuable. This diminishes their ability to purchase our exports. Since exports are a part of autonomous spend­ ing, a rise in the real interest rate diminishes autonomous spending through this channel as well. Thus a change in interest rates has a bigger effect on output than one would think from the effect of interest rates on investment alone.\n", "\n", " \n", "\n", "### 10.1.4 Interest Rates and Aggregate Demand\n", "\n", "The investment function in the sticky-price model looks the same as it does in the .flexible-price model, But it plays a different role. \n", "\n", "In the flexible-price model the real interest rate is a market-clearing price. Supply and demand in the loanable funds market determine the interest rate. The level of saving determines the level of investment, and the strength of investment demand determines the interest rate. \n", "\n", "In the sticky-price model, the interest rate is not set in the loanable funds market, but is set directly by expected inflation; the financial market's judgment as to the lending risk premium; and either the central bank directly or, if there is no central bank, indirectly by the combination of the stock of money and the liquidity preferences of households and businesses. The interest rate then determines the level of investment, which plays a key role in autonomous spending. \n", "\n", "Together, autonomous spending and the multiplier determine the level of output. In a sticky-price model the fact that businesses match the quantity they produce to planned expenditure automatically creates balance in the financial market, no matter what the interest rate. Any interest rate can be an equilibrium interest rate because the inventory-adjustment process always forces saving equal to investment.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 10.2 The IS Curve\n", "\n", "### 10.2.1 Dividing Autonomous Spendingt\n", "\n", "We rearrange the equation for autonomous spending to put the two terms that depend on the interest rate together:\n", "\n", "> $ A= [(c_0 + I_o +G) + (x_fY_f + x_{\\epsilon}\\epsilon_o + x_{\\epsilon}\\epsilon_rr^f)] - (I_r + x_{\\epsilon}\\epsilon_r)r $\n", "\n", "we see that a one-unit increase in the long-term risky real interest rate r will reduce autonomous spending A by $ (I_r + x_{\\epsilon}\\epsilon_r) $ units. Let us separate autonomous spending A out into a piece that depends on the real long-term risky interest rate r:\n", "\n", "> $ - (I_r + x_{\\epsilon}\\epsilon_r)r $\n", "\n", "and a piece—baseline autonomous spending—that does not:\n", "\n", "> $ A_o = [(c_0 + I_o +G) + (x_fY_f + x_{\\epsilon}\\epsilon_o + x_{\\epsilon}\\epsilon_rr^f)] $\n", "\n", "Recall that the equilibrium level of real GDP depended on the level of autonomous spending, so we can write the determination of national incoem and product Y as :\n", "\n", "> $ Y = {\\mu}A = {\\mu}A_o - {\\mu}(I_r + x_{\\epsilon}\\epsilon_r)r $\n", "\n", "Because a change in the real interest rate r changes autonomous spending A by changing investment I and exports GX, it will change the equilibrium level of real GDP. Plotting this relationship on a national income-real interest rate graph, we see a downward-sloping relationship between the long-term risky real interest rate and national income and product.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**Autonomous Spending as a Function of the Real Interest Rate**: The level of autonomous spending defined in Chap­ ter 9 depends on the real interest rate: The higher the real interest rate, the lower is autonomous spending. The slope of the line depends not just on the interest sensitivity of investment spending but also on the interest rate sensitivity of exports—the sensitivity of exports to changes in the ex­ change rate times the sensitivity of the exchange rate to changes in the interest rate._\n", "\n", " \n", "\n", "By how much does a change in the interest rate change real national income and product? By an amount equal to the change in r times the product of the interest sensitivity of autonomous spending and the multiplier: $ {\\mu}(I_r + x_{\\epsilon}\\epsilon_r) $.\n", "\n", "What are the other determinants of national income and product? They are the multiplier $ \\mu $ times the determinants of baseline autonomous spending $ A_o $:\n", "\n", "> $ \\mu{A_o} = \\mu(c_0 + I_o + G) + \\mu(x_fY_f + x_{\\epsilon}\\epsilon_o + x_{\\epsilon}\\epsilon_rr^f) $ \n", "\n", "Note that baseline autonomous spending $ A_o $ has components that depend on things going on at home (consumer confidence, business animal spirits, and government purchases: $ c_0 + I_o + G $) and components that depend on things going on abroad (foreign national income, foreign exchange speculators' opinions, and interest rates abroad: $ x_fY_f + x_{\\epsilon}\\epsilon_o + x_{\\epsilon}\\epsilon_rr^f $).\n", "\n", "### 10.2.2 From the Interest Rate to Investment to Aggregate Demand\n", "\n", "The change in the interest rate will change autonomous spending. And the whole point of the multiplier discussion in Chapter 9 was that changes in autonomous spending have multiplied effects on total expenditure. This relationship between the level of the real interest rate r and the equilibrium level of national income and product Y has a name that was coined by economist John Hicks more than 60 years ago: the “IS curve,” where IS stands for “investment-saving.” The IS curve is a workhorse tool that macroeconomists and macroeconomics courses use very, very frequently.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**The IS Curve**: For each possible value of the real interest rate, there is a different level of autonomous spending. For each level of autonomous spending, the income-expenditure process generates a different equilibrium level of real GDP. The IS curve tells us what equilibrium level of real GDP corresponds to each possible value of the real interest rate._\n", "\n", " \n", "\n", "To construct the IS curve, we must first draw a diagram with equilibrium real GDP on the horizontal axis and the real interest rate on the vertical axis. We begin by picking a value for the real interest rate and then determine the level of autonomous spending at that real interest rate. Then we plug the corresponding level of autonomous spending into an income- expenditure diagram and draw the resulting planned-expenditure line. The point where the planned-expenditure line crosses the 45-degree line is the point at which planned expenditure equals national income. That is the value of equilibrium real GDP corresponding to our initial choice of the real interest rate.\n", "\n", "The interest rate we started with and the real GDP level we ended with make up a single point on the IS curve. We repeat the process for as many different possible interest rates as we need. Plotting the points on the IS diagram and connecting them produces the IS curve.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**The IS Curve**: The position of the IS curve summarizes all the determinants of equilibrium real GDP and how the level of equilibrium real GDP changes in response to changes in the interest rate._\n", "\n", " \n", "\n", "The algebra of the IS curve is straightforward. We separate the determinants of autonomous spending into those that don’t depend on the interest rate and those that do, writing the IS Curve itself as:\n", "\n", "> $ Y = {\\mu}A_o - {\\mu}(I_r + x_{\\epsilon}\\epsilon_r)r $\n", "\n", "calling the first set of determinants “baseline autonomous spending” $ A_o $ which is, recall:\n", "\n", "> $ A_o = [(c_0 + I_o +G) + (x_fY_f + x_{\\epsilon}\\epsilon_o + x_{\\epsilon}\\epsilon_rr^f)] $\n", "\n", " \n", "\n", "### 10.2.3 The Slope and Position of the IS Curve\n", "\n", "#### 10.2.3.1 The Slope of the IS Curve\n", "\n", "The slope of the IS curve depends on four factors. Anything that affects the multiplier will change the slope of the IS curve. Anything that affects the responsive­ ness of investment to a change in real interest rates will change the slope of the IS curve. Anything that affects how sensitive exports are to the real exchange rate will change the slope of the IS curve. And anything that changes how large a swing in real exchange rates is induced by a change in interest rates will change the slope of the IS curve.\n", "\n", "These changes are all clearly visible in the term that multiplies the interest rate in the IS curve equation (which is the reciprocal of the slope of the IS curve):\n", "\n", "> $ -\\mu(I_r + x_{\\epsilon}\\epsilon_r) $\n", "\n", "The first of these factors is the multiplier: $ \\mu = 1/(1 - MPE) $. The larger the multiplier, the larger is the impact on planned expenditure set in motion by a given change in investment spending and gross exports, and so the flatter is the IS curve. \n", "\n", "The second factor is the interest sensitivity of investment: the $ I_r $ term. The larger is $ I_r $, the larger is the impact on investment due to a change in the real interest rate, and so the flatter is the IS curve. \n", "\n", "The third factor is how large a change in exports is generated by a change in the real interest rate: the $ x_{\\epsilon}\\epsilon_r $ term, which is the product of the exchange rate sensitivity of exports and the interest rate sensitivity of the exchange rate. The larger is Xesr, the larger is the impact on gross exports due to a change in the real interest rate, and so the flatter is the IS curve.\n", "\n", "All this means that a great many shocks to the economy change the slope of the IS curve. Thus in analyzing events, the correct calculation of the slope of the IS curve is important.\n", "\n", " \n", "\n", "##### 10.2.3.1.1 Calculating the Dependence of Aggregate Demand on the Interest Rate: An Example\n", "\n", "To calculate how much a change in the interest rate will shift the equilibrium level of planned expenditure, you need to know four things:\n", "\n", "* The marginal propensity to expend (MPE), and thus the multiplier: $ \\mu = 1/(1 — MPE) $.\n", "* The interest sensitivity of investment $ I_r $.\n", "* How much a change in the interest rate will affect the real exchange rate $ {\\epsilon}_r $.\n", "* How much a change in the exchange rate will affect exports $ x_r $.\n", "\n", "Suppose that you know that the marginal propensity to expend MPE is 0.5 and the interest sensitivity of investment is 10,000, that is, a 1-percentage-point rise in the annual interest rate (${\\Delta}r = 0.01$) decreases annual investment by 100 billion dollars. Then the direct effects of interest rates on investment coupled with the multiplier would lead you to conclude that a 1-percentage-point increase in the interest rate would decrease equilibrium aggregate demand by 200 billion, acting through the investment channel alone.\n", "\n", "However, there is another channel through which interest rates affect aggregate demand—the export channel. If a 1-percentage-point increase in the interest rate (${\\Delta}r = 0.01$) reduces the value of the exchange rate by 10 units, and if each 1-unit reduction in the exchange rate reduces exports by 500 billion, then there would be an additional decrease of 2 x (500) x (10) x (0.01) = 100 billion in aggregate demand through the exports channel.\n", "\n", "Thus the total decline in aggregate demand would be 300 billion. The slope of the IS curve would be $ {\\Delta}A/{\\Delta}Y $ or -1/30,000.\n", "\n", " \n", "\n", "#### 10.2.3.2 The Position of the IS Curve\n", "\n", "The position of the IS curve depends on the baseline level of autonomous spending $ A_o $ times the multiplier 1/(1 — MPE). To see how many factors can change the position of the IS curve, let’s for the moment expand $A_o $ and MPE and write them in terms of their more fundamental determinants:\n", "\n", "> $ {\\mu}A_o = \\frac{A_o}{1-MPE} = \\frac{[(c_0 + I_o +G) + (x_fY_f + x_{\\epsilon}\\epsilon_o + x_{\\epsilon}\\epsilon_rr^f)]}{1 - [c_y(1-t) - im_y]} $\n", "\n", "Anything that changes any of the non-interest-dependent components of autonomous spending will shift the position of the IS curve. An increase in government purchases will shift the IS curve to the right and raise the equilibrium level of real GDP for any fixed value of the real interest rate. An increase in the baseline \"animal spirits\" level of investment spending or in consumption confidence will do the same. Other events that shift the IS curve to the right include increases in foreign national income, increases in foreign exchange speculators’ judgments about the value of foreign currency, and increases in foreign interest rates. In analyzing almost any change in the economic environment or in the government’s fiscal policy, the position of the IS curve will shift.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**A Change in Fiscal Policy and the Position of the IS Curve**: Practically any shift in policy or in the economic environment will change the position of the IS curve. In this case an increase in government purchases shifts the IS curve to the right._\n", "\n", " \n", "\n", "#### 10.2.3.3 Moving the Economy to the IS Curve\n", "\n", "What happens if the current level of national income and product and the interest rate is not on the IS curve? If the economy is above the IS curve on the diagram, then national income is higher than aggregate demand. Inventories are rising rapidly and unexpectedly. So businesses cut back production. Employment, real GDP, and national income fall. If the economy is below the IS curve, aggregate demand is higher than national income. Inventories fall. Firms try to expand production in order to meet unexpectedly high demand. As they do, real GDP, employment, and national income rise.\n", "\n", "The process that pulls the economy back to the IS curve works relatively slowly, over months and quarters. Firms respond to increases in inventories by contracting (and to decreases in inventories by raising) production. As was noted above, the economy can stay away from its equilibrium on the income-expenditure diagram for a substantial time, all the while with inventories building up or falling. And if the economy is away from its equilibrium level of real GDP on the income-expenditure diagram, it is not on the IS curve either.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**Off of the IS Curve**: The economy's position does not have to correspond to a point on the IS curve. But if the economy is not on the IS curve, then powerful forces will push it toward the IS curve._\n", "\n", " \n", "\n", "### 10.2.4 RECAP: The IS Curve\n", "\n", "The higher the real interest rate, the lower are the investment spending and exports components of autonomous spending and the lower is real GDP in the sticky-price model. The relationship between the real interest rate and real GDP is called the IS relationship. When plotted on a graph with real GDP on the horizontal axis and the real interest rate on the vertical axis, it is called the IS curve. \n", "\n", "The IS curve is downward-sloping. Its horizontal intercept is equal to baseline autonomous spending $ A_o $—what autonomous spending A would be if the real interest rate were zero—times the multiplier $ \\mu $. Its slope is equal to the reciprocal of the multiplier $ \\mu = 1/(1 — MPE) $ times the sum of two terms; (1) the interest sensitivity of investment spending $ I_r $, and (2) the product of the exchange rate sensitivity of gross exports and the interest sensitivity of the exchange rate $ x_{\\epsilon}{\\epsilon}_r $.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 10.3 Using the IS Curve to Understand the Economy\n", "\n", "### 10.3.1 Shifting the IS Curve\n", "\n", "We have seen that anything that affects the non-interest-dependent components of autonomous spending shifts the position of the IS curve. Changes that increase baseline autonomous spending shift the IS curve to the right and raise equilibrium real GDP (if interest rates are constant). Changes that reduce baseline autonomous spending shift the IS curve to the left and reduce equilibrium real GDP (if interest rates are held constant).\n", "\n", "For example, two kinds of changes in government fiscal policy directly affect the position of the IS curve. A shift in tax rates changes both the position and the slope of the IS curve. And a change in the level of government purchases changes the position but not the slope of the IS curve; it shifts the IS curve to the right or the left. The government’s fiscal policy thus increases or decreases the equilibrium level of real GDP associated with each possible level of the real interest rate.\n", "\n", " \n", "\n", "#### 10.3.1.1 A Government Purchases Increase And The IS Curve: An Example\n", "\n", "Calculating the effect on the equilibrium level of real GDP of an increase in a component of baseline autonomous spending such as government purchases is straightforward. \n", "\n", "For example, suppose that in the economy the initial MPE is equal to 0.5, the baseline level of autonomous spending is 5000 billion, a 1-percentage-point decline in the real interest rate ($ {\\Delta}r = -0.01 $) raises investment spending by 110 billion and exports by 15 billion, and the real interest rate is fixed at 4 percent (r = 0.04). Then the initial equilibrium level of annual national income and product is:\n", "\n", "> $ Y = {\\mu}(A_o - (I_r + x_{\\epsilon}{\\epsilon}_r)r) = \\frac{A_o - (I_r + x_{\\epsilon}{\\epsilon}_r)r}{1 - MPE} $\n", "\n", "> $ Y = \\frac{5000 - (11000 + 1500)(0.04}{1 - 0.5} $\n", "\n", "> $ Y = (2)(5000 - (12500)(0.04) $\n", "\n", "> $ Y = 9000 $\n", "\n", "Now suppose that annual government purchases are then raised by AG = 200 billion. Government purchases are a component of baseline autonomous spending $ A_o $. The increase in the equilibrium level of real GDP is straightforward to calculate as long as the real interest rate r remaines unchanged:\n", "\n", "> $ {\\Delta}Y = {\\mu}{\\Delta}A_o = (2)(200) = 400 $\n", "\n", "Aggregate demand and national income and product rise by 400 billion.\n", "\n", " \n", "\n", "### 10.3.2 Moving Along the IS Curve\n", "\n", "Changes in the level of the real interest rate r will move the economy either left and upward or right and downward along the IS curve. A higher real interest rate will produce a lower level of planned expenditure. A lower real interest rate will produce a higher level of planned expenditure and equilibrium real GDP. The Federal Reserve can control— target—interest rates to a considerable degree. Such an interest-rate-targeting central bank can stimulate the economy by cutting interest rates, and can contract the economy by raising interest rates.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**Cutting Target Interest Rates and Raising Real GDP**: The IS curve shows us what happens to real GDP when the central bank changes the real interest rate._\n", "\n", " \n", "\n", "How does the Federal Reserve control interest rates? It does so by buying and selling short-term government bonds for cash in open-market operations, so called because they are carried out in the “open market” and the Federal Reserve really does not care whom it buys from or sells to. Whenever the Federal Reserve buys government bonds in return for cash, it increases the total amount of cash in the hands of the public and reserves in the hands of the banking system. Banks with the extra reserves use them to try to increase their deposits. Thus such an expansionary open-market operation increases the economy’s stock of money: It increases the quantity of assets—checking account deposits and cash—that are readily spendable purchasing power.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**Open-Market Operations**: The Federal Reserve changes interest rates by changing the quantity of liquid money in the economy through open-market operations: purchases or sales of U.S. government bills, notes, and bonds for cash on the open market._\n", "\n", " \n", "\n", "Banks, businesses, and households take a look at the larger quantity of money—wealth in the form of readily spendable purchasing power—that they hold. At the previous level of interest rates this is more money than they want to hold in their portfolios. So households, businesses, and banks try to use this money to buy assets, such as bonds, that pay higher yields than cash. As they do so, they push the price of bonds up and the interest rate down. Thus an expansionary open-market opera­ tion reduces interest rates in the economy. The same process works in reverse to push interest rates up when the Federal Reserve sells bonds for cash on the open market. Box 10.4 shows how central bankers would go about trying to calculate the size of the change in interest rates needed to properly manage the economy.\n", "\n", "#### 10.3.2.1 Moving Along The IS Curve: An Example\n", "\n", "Suppose that the staff projections of the Federal Reserve predict that if current policies are continued, real GDP will be only 18 trillion at a time for which estimates of potential output are 19 trillion. The Federal Open Market Committee (FOMC) might well decide that it is time to lower interest rates to close such a “deflationary gap.”\n", "\n", "Suppose further that the staff estimates that the marginal propensity to expend MPE is 0.5, that a 1-percentage-point fall in the real interest rate (${\\Delta}r = -0.01$) generates an extra 110 billion in annual investment spending and a 5-point rise in the real exchange rate. And that each 1 percentage point rise in the real exchange rate—the value of foreign currency—raises exports by 3 billion.\n", "\n", "Such estimates of the structure of the economy imply that the slope of the IS curve is:\n", "\n", "> IS slope = $ - {\\mu}(I_r + x_{\\epsilon}{\\epsilon}_r) = (2)(11000 + 1500) = 25000 $\n", "\n", "So to boost equilibrium national income and product by 500 billion by moving the economy along the IS curve, the real interest rate has to be reduced by 0.02—by 2 percentage points.\n", "\n", " \n", "\n", "#### 10.3.2.2 Difficulties\n", "\n", "Attempts to control aggregate by manipulating interest rates encounter certain difficulties. \n", "\n", "First, our knowledge of the structure of the economy is imperfect. Perhaps at any particular moment the slope of the IS curve is half what the Federal Reserve staff believes or is twice what the Federal Reserve staff believes. Second, even when policies do have their expected effects, these effects do not necessarily arrive on schedule. As economist Milton Friedman often said, economic policy works with long and _variable_ lags.\n", "\n", "Moreover, the interest rates that the Federal Reserve can control are short-term, nominal, safe interest rates. The interest rate that determines where the economy is in equilibrium on the IS curve is the long-term, real, risky interest rate. Even if the government and central bank attain their target interest rate and even if the effects of changes in the interest rate are exactly as predicted and arrive exactly on schedule, there is a lot of potential slippage: Changes in the term premium between short and long interest rates, changes in the rate of inflation, and changes in the risk premium will each carry the economy to a point on the IS curve other than the point that the Federal Reserve wanted.\n", "\n", "What determines the value of the term premium—the gap between short-term and long-term interest rates? A major determinant is expectations of future monetary policy. Long-term interest rates will be high relative to short-term interest rates if people expect short-term interest rates to be raised in the future; long-term interest rates will be low relative to short-term interest rates if people expect short-term rates to be lowered in the future.\n", "\n", " \n", "\n", "#### 10.3.2.2.1 An Example: Trumpenomics\n", "\n", "* An increase $ {\\Delta}I_o $ because of increased incentives for investment…\n", "* An increase $ {\\Delta}G $ in government purchases…\n", "* A Federal Reserve that has strong views about what the appropriate level of Y is—and that will move r in order to keep the rest of the government from disturbing that level\n", " * “Monetary offset”\n", "* What will the effect of these policy moves be on the interest rate r the Federal Reserve chooses?\n", "\n", "###### Pieces of the Model\n", "\n", "> $ I = I_o - I_rr $\n", "> $ GX = x_fY^f + x_{\\epsilon}{\\epsilon} $ \n", "> $ \\epsilon = \\epsilon_o + \\epsilon_r(r^f - r) $\n", "> $ IM = IM_yY $\n", "> $ C = c_o + c_y(1-t)Y $\n", "> $ Y = C + I + G + GX - IM $\n", "\n", "###### All of These Equations Will Hold\n", "\n", "(1) $ {\\Delta}I_o + {\\Delta}G - (I_r + x_{\\epsilon}{\\epsilon}_r){\\Delta}r = 0 $\n", "\n", "(2) $ {\\Delta}r = \\frac{{\\Delta}I_o + {\\Delta}G}{I_r + x_{\\epsilon}{\\epsilon}_r} $\n", "\n", "(3) $ {\\Delta}r = \\frac{{\\Delta}G + {\\Delta}I_o + x_{\\epsilon}{\\Delta}{\\epsilon}}{I_r} $\n", "\n", "Donald Trump:\n", "\n", ">The problem I have is with the Fed. The Fed is going wild. I mean, I don't know what their problem is that they are raising interest rates and it's ridiculous. \"The problem in my opinion is Treasury and the Fed. The Fed is going loco and there's no reason for them to do it. I'm not happy about it...\n", "\n", "Larry Kudlow:\n", "\n", ">The president has his own views, he's stated them many times, and there's nothing new here as far as i can tell. We know the Fed is independent. The president is not dictating policy to the Fed. He didn't say anything remotely like that. They are independent, and they're going to do what they're going to do…\n", "\n", "Steve Mnuchin:\n", "\n", ">We as an administration absolutely support the independence of the Fed…\n", "\n", "Kevin Hassett:\n", "\n", ">Part of President Trump’s brand is he says what he thinks, but he respects the independence of the Fed, and that’s clear from his nominations. I think our nominees have been absolutely first-rate…\n", "\n", "* Richard Clarida \n", "* Nellie Liang\n", "* Jay Powell\n", "* Randall Quarles\n", "* Michelle Bowman\n", "* Marvin Goodfriend" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 10.3.3 Economic Fluctuations in the United States: The IS Curve as a Lens\n", "\n", "How useful is the IS curve in understanding economic fluctuations in the United States over the past generation or so? If we plot on a graph the points corresponding to the long-term real interest rate and output relative to potential attained by the U.S. economy since 1960, we see that the economy has been all over the map—or at least all over the diagram. Yet we can make sense of what has happened using shifts in and movements along the IS curve. That in fact is what the IS curve is for. It is a useful tool, which is why we have spent so many pages developing it. In the following five subsections we will apply the IS curve to gain insight into business-cycle fluctuations in each of the past four decades as well as the current decade.\n", "\n", " \n", "\n", "#### 10.3.3.1 The 1960s\n", "\n", "The 1960s saw a substantial rightward shift of the IS curve. Increased optimism on the part of businesses, the Kennedy-Johnson cut in income taxes, and the extra government expenditures needed to fight the Vietnam War all increased planned expenditure. The IS curve shifted rightward by perhaps 3 percent of potential output in the 1960s.\n", "\n", "The late 1960s also saw a movement downward and to the right along the IS curve, as real interest rates declined. In large part real interest rates declined by accident. The Federal Reserve did not fully gauge the amount by which inflation was rising. Rising inflation increased the gap between the nominal interest rates directly controlled by monetary policy and the real interest rates that determine planned expenditure. The Federal Reserve did not recognize this as it was happening and thus allowed real interest rates to drift downward.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**Shifting Out and Moving along the IS Curve, 1960s**: The Vietnam War, the Kennedy-Johnson tax cut, and an increase in business optimism about\n", "the future all shifted the IS curve to the right between the start of the 1960s and the second half of the decade._\n", "\n", " \n", "\n", "#### 10.3.3.2 The 1970s\n", "\n", "The end of the 1970s saw the level of real GDP in the United States near the level of potential output. As Figure 10.16 shows, from 1977 to 1979 the U.S. economy moved down and to the right along the IS curve. However, the expansion of output beyond potential was accompanied by unexpectedly high and rising inflation. This rise in inflation was further fueled by a supply shock: the sudden rise in oil prices triggered by the Iranian revolution.\n", "\n", "A sudden shift in Federal Reserve policy occurred in 1979 when Paul Volcker became chair of the Federal Reserve, replacing G. William Miller. Under Miller fighting inflation had been a relatively low priority. Under Volcker fighting inflation became the highest priority of all. The Federal Reserve raised annual real interest rates step-by-step from 1979 to 1982 up to over 10 percent. The increase in real interest rates moved the economy up and to the left along the end-of- the-1970s position of the IS curve: The unemployment rate reached nearly 10 percent in 1982, and real GDP fell to only 94 percent of the economy’s potential output.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**Moving along the IS Curve, Late 1970s**: Sharp rises in real interest rates at the end of the 1970s after Paul Volcker became Chair of the Fed­ eral Reserve pushed the U.S. economy up and to the left along the IS curve._\n", "\n", " \n", "\n", "#### 10.3.3.3 The 1980s\n", "\n", "The election of Ronald Reagan in 1980 was followed by a massive fiscal expansion. Military spending was increased and income taxes were cut in a series of steps that became effective between 1982 and 1985. The result of these increases in government purchases and cuts in taxes was an enormous government deficit and an outward shift in the IS curve. A simultaneous increase in investor optimism triggered by falling inflation combined with the government’s fiscal stimulus to shift the IS curve outward relative to potential output by at least 4 percent.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**Shifting the IS Curve Out, Early 1980s**: The Reagan budget deficits of the 1980s shifted the economy's IS curve to the right._\n", "\n", " \n", "\n", "The Federal Reserve responded to this outward shift in the IS curve by maintaining high real interest rates. It sought in the first half of the 1980s to ensure that the success it had achieved in reducing inflation did not unravel. The Federal Reserve feared that a rapid return of real GDP to potential GDP would put upward pressure on inflation once more—hence the maintenance of high real interest rates to make sure that the large Reagan-era fiscal expansion did not have too great an effect.\n", "\n", "As inflation remained low throughout the mid and late 1980s, Federal Reserve policy makers gained confidence. They became increasingly optimistic that higher real GDP levels relative to potential would not reignite inflation. Between 1985 and 1990 successive step-by-step reductions in real interest rates carried the U.S. economy back to full employment, and carried it down and to the right along the IS curve.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**Moving along the IS Curve, Late 1980s**: With the inflation of the 1970s broken and no longer a threat, the Federal Reserve gradually reduced interest rates in the late 1980s. As it did so, the economy moved down and to the right along its IS curve._\n", "\n", " \n", "\n", "#### 10.3.3.4 The 1990s\n", "\n", "The principal maker of economic policy from the late 1980s to the mid 2000s was Federal Reserve Chair Alan Greenspan, appointed and reappointed by four successive presidents: Reagan, George H. W. Bush, Clinton, and George W. Bush. \n", "\n", "Greenspan is somewhat of a paradox: a Federal Reserve chair whom all trust to be a ferocious inflation fighter, yet one who—in the policies that he has chosen—frequently seemed willing to risk higher inflation in order to achieve higher economic growth or to avoid a recession.\n", "\n", "Immediately after taking office Greenspan faced a challenge: the sudden stock market crash of October 1987. How large an effect would this crash have on planned expenditure? What would it do to investment spending? Would a leftward shift in the IS curve be generated by the sudden change in investors’ expectations about the future that triggered the stock market crash? No one knew If the crash turned out to be the harbinger of a large leftward shift in the IS curve, then an unchang­ ing monetary policy would lead to a significant recession. So the Greenspan-led FOMC lowered interest rates and expanded the monetary base, hoping that this shift in monetary policy would offset any leftward shift in the IS curve and avoid a recession.\n", "\n", "In point of fact, the stock market crash of 1987 had next to no effect on investment spending or planned expenditure. Economists have still not come up with a convincing story for why its effects were so small. The two years after 1987 saw higher output relative to potential and saw lower unemployment rates. The years between 1987 and 1990 did not see real interest rates rising—as they usually do in the latter stages of an expansion—but real interest rates that were stable or falling.\n", "\n", "As the unemployment rate fell, inflation accelerated. In 1988 and 1989, inflation moved up from 3 to 4 percent. The Federal Reserve found that it had successfully avoided any chance of a (big) recession in 1988 in the aftermath of the stock market crash, but only at the price of letting inflation rise above 4 percent per year. In the second half of 1990 there came a sudden leftward shift in the IS curve: The Iraqi invasion of Kuwait served as a trigger for firms to reduce investment, as they waited to see whether the world economy was about to experience another long-run upward spike in oil prices. The U.S. economy slid into recession at the end of 1990. The Federal Reserve, worried about the upward creep in inflation in the late 1980s, took no steps to reduce real interest rates as the economy slid into the recession.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**The 1990s**: A sharp inward shift in the IS curve triggered a reces­ sion at the beginning of the 1990s. Subsequent increases in autonomous investment shifted the IS curve to the right again._\n", "\n", " \n", "\n", "During the recession, inflation fell to 2 V2 percent. Unemployment rose to a peak of 7.6 percent—in the late spring of 1992, just in time to be salient for the 1992 presidential election. Recovery began in mid-1992.\n", "Soon thereafter Greenspan made another decision to risk higher inflation in order to accomplish other goals. In 1993 he signaled that if Congress and the president took significant steps to reduce the budget deficit, then the Federal Reserve would try as best as it could to maintain lower interest rates—a shift in the policy mix that would keep the target level of production and employment unchanged but that with lower interest rates would promise higher investment and faster pro­ ductivity growth: an “investment-led recovery.”\n", "\n", "This time the gamble turned out extremely well. As fiscal policy tightened in 1994 and beyond, interest rates remained significantly lower than they had been in the 1980s even though output recovered to potential. Moreover, this time there was no significant acceleration of inflation, even though by the end of the 1990s unemployment had fallen to the lowest level in a generation and it seemed as though the economy was above potential output.\n", "\n", " \n", "\n", "#### 10.3.3.5 The Early 2000s\n", "\n", "\n", "The end of the 1990s saw the end of the dot-com bubble. The crash of the stock market in 2000 was both cause and consequence of the recognition that investors and businesses had been overly optimistic not about the technology and productivity benefits of the computer revolution, but about the ability of businesses to make profits off of the computer boom. Investment fell sharply in 2000 and 2001, carrying real GDP relative to potential down with it. The recession was given a further impetus by the uncertainty created by the terror attack of September 11, 2001. While real GDP had been some 3 percent above potential output in 1999, by 2001 it was 1 percent below potential.\n", "\n", "The executive branch—the administration of George W. Bush—responded by proposing tax cuts that were poorly crafted to stimulate demand: The bulk of the money went to households for which the marginal propensity to consume was low. Fiscal policy thus did little to move the IS curve back to the right and expand output. The Federal Reserve responded by cutting interest rates severely. Observers even began to fear that the Federal Reserve would run out of room to cut interest rates further, since short-term nominal interest rates cannot fall below zero. But during 2002 and 2003 the Federal Reserve’s easy-money policies were neutralized by further falls in business and investor confidence and a further move to the left in the IS curve. In spite of remarkably expansionary monetary policy, it was only after 2004 that there were signs that the economy was beginning to close the output gap.\n", "\n", " \n", "\n", "\"DeLong\n", "\n", ">>_**The 2000s**: The collapse of the dot-com stock-market bubble in 2000 and the September 11, 2001, attacks were large shocks to the U.S. economy: Output fell from about 3 percent above to perhaps 1 percent below potential in response. The Federal Reserve waited to respond, believing that the economy in 2000 had been running at a rate unsustainable without ris­ ing inflation. But when the Federal Reserve did move, it moved rapidly to reduce interest rates. Before 2004, however, few signs suggested that the reduc­ tion in interest rates and concomitant stimulative budget deficits had done much to keep output from falling even further below potential._\n", "\n", " \n", "\n", "#### 10.3.3.6 The Crash\n", "\n", "In the mid-2000s the U.S. economy moved toward full employment, largely as a result of a construction boom fueled by the housing bubble.\n", "\n", " \n", "\n", "#### 10.3.3.7 The 2010s\n", "\n", " \n", "\n", "### RECAP: Using the IS Curve to Understand the Economy\n", "\n", "We have seen that anything that affects the non-interest-dependent components $ A_o $ of autonomous spending shifts the position of the IS curve. Changes that increase baseline autonomous spending shift the IS curve to the right and raise equilibrium national income and product. Changes that reduce baseline autonomous spending shift the IS curve to the left and reduce real natinal income and product.\n", "\n", "Change in the size of the multiplier—the interest sensitivity of investment or gross exports—and the responsiveness of the real exchange rate to changes in the interest rate change the slope of the IS curve. Changes in the level of the real interest rate will move the economy either left and upward or right and downward along the IS curve: A higher real interest rate will produce a lower level of planned expenditure. A lower real interest rate will produce a higher level of planned expenditure and equilibrium real GDP. The Federal Reserve can control—target—interest rates to a considerable degree. Such an interest rate-targeting central bank can stimulate the economy by cutting interest rates and can contract the economy by raising interest rates.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## Catch Our Breath\n", "\n", "* Ask me two questions…\n", "* Make two comments…\n", "* Further reading…\n", "\n", "
\n", "\n", "----\n", "\n", "Lecture Support: \n", "Keynote File: \n", "\n", " \n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The IS Curve: Investment, Net Exports, and Interest Rates: PRESENTATION SLIDES" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Multiplier\n", "\n", "> $ Y = C + I + G + NX $ \n", "$ Y = c_o + c_y(1-t)Y + I + G + GX - im_yY $ \n", "$ (1 - c_y(1-t)+ im_y)Y = c_o + I + G + GX $ \n", "     $ A = c_o + I + G + GX $ \n", "$ Y = \\frac{c_o + I + G + GX}{1 - c_y(1-t)+ im_y} = \\frac{A}{1 - c_y(1-t)+ im_y} $ \n", "$ Y = {\\mu}A $ \n", " $ {\\mu} = \\frac{1}{1 - c_y(1-t)+ im_y} $\n", "\n", "* A: autonomous spending—\"autonomous\" because it does not depend on the level of national income\n", "* $ \\mu $: the multiplier\n", "* What is the multiplier? $ c_y = 0.67 $, $ im_y = 0.17 $ $ t = 0.25 $\n", "* What is the multiplier? > 1.5 (investment accelerator?)\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Autonomous Spending, the Real Interest Rate, and the IS-Curve\n", "\n", "$ A = c_o + I + G + GX $\n", "\n", "$ \\mu = \\frac{1}{1 - c_y(1-t) + IM_Y} $\n", "\n", "$ Y = {\\mu}A $\n", "\n", " \n", "\n", "$ I = I_o - I_{r}r $\n", "\n", "$ GX = x_{f}Y^f + x_{\\epsilon}{\\epsilon} $ ; $ \\epsilon = \\epsilon_o + \\epsilon_{r}\\left(r^f - r\\right) $\n", "\n", "> $ GX = x_{f}Y^f + x_{\\epsilon}{\\epsilon}_o + x_{\\epsilon}{\\epsilon}_rr^f - x_{\\epsilon}\\epsilon_{r}r $\n", "\n", " \n", "\n", "$ A = c_o + G + (I_o - I_rr) + x_{f}Y^f + x_{\\epsilon}{\\epsilon}_o + x_{\\epsilon}{\\epsilon}_rr^f - x_{\\epsilon}\\epsilon_{r}r $\n", "\n", "$ A = c_o + G + I_o + x_{f}Y^f + x_{\\epsilon}{\\epsilon}_o + x_{\\epsilon}{\\epsilon}_rr^f - (I_rr + x_{\\epsilon}\\epsilon_{r}r) $\n", "\n", "> $ A_o = A = (c_o + G + I_o) + (x_{f}Y^f + x_{\\epsilon}{\\epsilon}_o + x_{\\epsilon}{\\epsilon}_rr^f) $\n", "\n", "$ A = A_o - (I_r + x_{\\epsilon}\\epsilon_{r})r $\n", "\n", " \n", "\n", "$ Y = {\\mu}A_o - {\\mu}(I_r + x_{\\epsilon}\\epsilon_{r})r $\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving using $\\Delta$s\n", "\n", "* Start at some equilibrium\n", "* $ \\Delta $: deviations from that equilibrium—either dynamic or counterfactual...\n", "* Hence: \n", "\n", "         \n", "$ {\\Delta}C = {\\Delta}c_o + {c_y}(1-t){\\Delta}Y $ :: consumption\n", "\n", "         \n", "$ {\\Delta}I = {\\Delta}I_o - {I_r}{\\Delta}r $ :: investment \n", "\n", "         \n", "$ {\\Delta}G $ :: government \n", "\n", "         \n", "$ {\\Delta}NX = x_f{\\Delta}Y^f + {x_{\\epsilon}}{\\Delta}{\\epsilon} - im_y{\\Delta}Y $ :: international\n", "\n", "         \n", "$ {\\Delta}\\epsilon = {\\Delta}{\\epsilon}_o + {\\epsilon}_r\\left({\\Delta}r^f - {\\Delta}r\\right) $ :: exchange rate\n", "\n", "         \n", "$ {\\Delta}Y = {\\Delta}C + {\\Delta}I + {\\Delta}C + {\\Delta}NX $ :: demand-determined national income and product\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $\\Delta$s: Autonomous Spending, the Real Interest Rate, and the IS-Curve\n", "\n", " \n", "\n", "$ {\\Delta}A_o = ({\\Delta}c_o + {\\Delta}G + {\\Delta}I_o) + (x_{f}{\\Delta}Y^f + x_{\\epsilon}{\\Delta}{\\epsilon}_o + x_{\\epsilon}{\\epsilon}_r{\\Delta}r^f) $\n", "\n", " \n", "\n", "$ {\\Delta}A = {\\Delta}A_o - (I_r + x_{\\epsilon}\\epsilon_{r}){\\Delta}r $\n", "\n", " \n", "\n", "$ \\mu = \\frac{1}{1 - c_y(1-t) + im_y} $\n", "\n", " \n", "\n", "$ {\\Delta}Y = {\\mu}{\\Delta}A = {\\mu}{\\Delta}A_o - {\\mu}(I_r + x_{\\epsilon}\\epsilon_{r}){\\Delta}r $\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Now to Your iClickers...\n", "\n", "…with the marginal propensity to consume $ c_y = 0.67 $, the tax rate $ t = 0.25 $, and the marginal propensity to import $ im_y = 0.17 $, then a 500 billion dollar increase in government purchases holding the real interest rate fixed would…\n", "\n", "1. ...raise real national income and product by an amount in billions: $ {\\Delta}Y = 500 $\n", "2. ...raise real national income and product by an amount in billions: $ {\\Delta}Y = 1250 $\n", "3. ...raise real national income and product by an amount in billions: $ {\\Delta}Y = 1000 $\n", "4. ...raise real national income and product by an amount in billions: $ {\\Delta}Y = 750 $\n", "5. ...None of the above/not enough information\n", "\n", "----\n", "\n", " \n", "\n", "## Now to Your iClickers...\n", "\n", "…with the marginal propensity to consume $ c_y = 0.75 $, the tax rate $ t = 0.2 $, and the marginal propensity to import $ im_y = 0.0 $, then a 500 billion dollar increase in government purchases holding the real interest rate fixed would…\n", "\n", "1. ...raise real national income and product by an amount in billions: $ {\\Delta}Y = 500 $\n", "2. ...raise real national income and product by an amount in billions: $ {\\Delta}Y = 1250 $\n", "3. ...raise real national income and product by an amount in billions: $ {\\Delta}Y = 1000 $\n", "4. ...raise real national income and product by an amount in billions: $ {\\Delta}Y = 750 $\n", "5. ...None of the above/not enough information\n", "\n", "----\n", "\n", " \n", "\n", "## Now to Your iClickers...\n", "\n", "…with the multiplier μ = 2.0, the interest sensitivity of investment spending Ir = 10 (trillions/magnitude) and with the international parameters xε = 1 and εr = 5, respectively, a 2 percentage point boost in the real interest rate r would reduce real national income and product by...\n", "\n", "1. …an amount in billions: ΔY= - 300\n", "2. …an amount in billions: ΔY= - 600\n", "3. …an amount in billions: ΔY= - 400\n", "4. …an amount in billions: ΔY= - 200\n", "5. ...None of the above/not enough information\n", "\n", "----\n", "\n", " \n", "\n", "\n", "## Now to Your iClickers...\n", "\n", "…with an Okun’s Law coefficient of 2 and a real GDP level of 20 trillion per year, a ΔY = -400 billion would be expected to raise three unemployment rate u by…\n", "\n", "1. …1 percentage point: Δu = + 0.01\n", "2. …2 percentage points: Δu = + 0.02\n", "3. …half a percentage point: Δu= +0.005\n", "4. …4 percentage points: Δu = + 0.04\n", "5. ...None of the above/not enough information\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## Catch Our Breath\n", "\n", "* Ask me two questions…\n", "* Make two comments…\n", "* Further reading…\n", "\n", "
\n", "\n", "----\n", "\n", "Lecture Support: \n", "Keynote File: \n", "\n", " \n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Savings and Investment Functions\n", "\n", " \n", "\n", "**The private savings function**\n", "\n", "         \n", "$ Y - C - T = S_p $\n", "\n", "         \n", "$ Y - (c_o + c_y(1-t)Y) - T = S_p $\n", "\n", "         \n", "$ Y - (c_o + c_y(1-t)Y) - tY = S_p $\n", "\n", "         \n", "$ (1 - c_y - t + c_{y}t)Y - c_o = S_p $\n", "\n", " \n", "\n", "**Government savings**\n", "\n", "         \n", "$ S_g = T - G = tY - G $\n", "\n", " \n", "\n", "**Foreign Savings**\n", "\n", "         \n", "$ S_f = - NX = IM - GX $\n", "\n", "         \n", "$ S_f = im_{y}Y - x_fY^f - {x_{\\epsilon}}{\\epsilon} $\n", "\n", "         \n", "$ S_f = im_{y}Y - x_fY^f -$ \n", "             \n", "$ {x_{\\epsilon}}\\left({\\epsilon}_o + {\\epsilon}_r\\left(r^f - r\\right)\\right) $ \n", "\n", " \n", "\n", "**Investment**\n", "\n", "         \n", "$ I = I_o - {I_r}r $\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## An Increase in Government Purchases of ΔG...\n", "\n", "* Start at full employment\n", "* $ \\Delta $: deviations from full-employment\n", "* Hence: \n", "\n", "         \n", "$ {\\Delta}G = {\\Delta}G $ \n", "\n", "         \n", "$ {\\Delta}Y = 0 $\n", "\n", "         \n", "$ {\\Delta}S_p + {\\Delta}S_f + {\\Delta}S_g = {\\Delta}I $\n", "\n", "         \n", "$ {\\Delta}S_p + {\\Delta}S_f - {\\Delta}G = {\\Delta}I $\n", "\n", "         \n", "$ {\\Delta}S_p = (1 - c_y - t + c_{y}t){\\Delta}Y - {\\Delta}c_o = 0 $\n", "\n", "         \n", "$ 0 + {\\Delta}S_f - {\\Delta}G = {\\Delta}I $\n", "\n", "         \n", "$ {\\Delta}S_f = im_{y}{\\Delta}Y - x_f{\\Delta}Y^f - {x_{\\epsilon}}\\left({\\Delta}{\\epsilon}_o + {\\epsilon}_r\\left({\\Delta}r^f - {\\Delta}r\\right)\\right) $\n", "\n", "         \n", "$ {\\Delta}S_f = x_{\\epsilon}{\\epsilon}_r{\\Delta}r $\n", "\n", "         \n", "$ {\\Delta}I = {\\Delta}I_o - {I_r}{\\Delta}r $\n", "\n", "         \n", "$ 0 + x_{\\epsilon}{\\epsilon}_r{\\Delta}r - {\\Delta}G = -{I_r}{\\Delta}r $\n", "\n", "         \n", "$ -{\\Delta}G = -\\left({I_r} + x_{\\epsilon}{\\epsilon}_r\\right){\\Delta}r $\n", "\n", "         \n", "$ {\\Delta}r = \\frac{{\\Delta}G}{{I_r} + x_{\\epsilon}{\\epsilon}_r} $\n", "\n", "         \n", "$ {\\Delta}I = -I_{r}{\\Delta}r = \\frac{-I_{r}{\\Delta}G}{{I_r} + x_{\\epsilon}{\\epsilon}_r} $\n", "\n", "         \n", "$ {\\Delta}GX = {\\Delta}NX = -{x_{\\epsilon}}{\\epsilon}_r{\\Delta}r = \\frac{-{x_{\\epsilon}}{\\epsilon}_{r}{\\Delta}G}{{I_r} + x_{\\epsilon}{\\epsilon}_r} $\n", "\n", "         \n", "$ {\\Delta}I + {\\Delta}GX = -{\\Delta}G $\n", "\n", " \n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A Decrease in Animal Spirits ${\\Delta}I_o $... \n", "\n", "* Start at full employment\n", "* $ \\Delta $: deviations from full-employment\n", "* Hence: \n", "\n", "         \n", "$ {\\Delta}I = {\\Delta}I_o - I_r{\\Delta}r $ :: investment\n", "\n", "         \n", "$ {\\Delta}Y = 0 $ :: full employment is maintained\n", "\n", "         \n", "$ {\\Delta}S_p + {\\Delta}S_f + {\\Delta}S_g = {\\Delta}I $ :: flow-of-funds\n", "\n", " \n", "\n", "         \n", "$ {\\Delta}S_g = t{\\Delta}Y - {\\Delta}G = 0 $ :: government savings \n", "\n", "         \n", "$ {\\Delta}S_p + {\\Delta}S_f + 0 = {\\Delta}I_o - I_r{\\Delta}r $ :: it's a zero...\n", "\n", "         \n", "$ {\\Delta}S_p = (1 - c_y - t + c_{y}t){\\Delta}Y - {\\Delta}c_o = 0 $ :: pvt dom svgs\n", "\n", "         \n", "$ 0 + {\\Delta}S_f + 0 = {\\Delta}I_o - I_r{\\Delta}r $ :: it's a zero\n", "\n", " \n", "\n", "         \n", "$ {\\Delta}S_f = im_{y}{\\Delta}Y - x_f{\\Delta}Y^f - x_{\\epsilon}{\\Delta}{\\epsilon}_o - {x_{\\epsilon}}{\\epsilon}_r\\left({\\Delta}r^f - {\\Delta}r\\right) $ :: foreigners \n", "\n", "         \n", "$ {\\Delta}S_f = 0 - 0 - 0 - x_{\\epsilon}{\\epsilon}_r\\left(0 - {\\Delta}r\\right) $ :: one term nonzero\n", "\n", "         \n", "$ x_{\\epsilon}{\\epsilon}_r{\\Delta}r = {\\Delta}I_o - I_r{\\Delta}r $ :: flow-of-funds\n", "\n", " \n", "\n", "         \n", "$ \\left(I_r + x_{\\epsilon}{\\epsilon}_r\\right){\\Delta}r = {\\Delta}I_o $\n", "\n", "         \n", "$ {\\Delta}r = \\frac{{\\Delta}I_o}{I_r + x_{\\epsilon}{\\epsilon}_r} $ :: Change in r\n", "\n", "         \n", "$ {\\Delta}I = \n", "{\\Delta}I_o - I_r{\\Delta}r = \n", "{\\Delta}I_o - \\frac{I_r{\\Delta}I_o}{I_r + x_{\\epsilon}{\\epsilon}_r} = \n", "\\frac{x_{\\epsilon}{\\epsilon}_r{\\Delta}I_o}{I_r + x_{\\epsilon}{\\epsilon}_r} $ :: Change in I\n", "\n", "         \n", "$ {\\Delta}GX = - {\\Delta}S_f - x_{\\epsilon}{\\epsilon}_r{\\Delta}r = -\\frac{x_{\\epsilon}{\\epsilon}_r{\\Delta}I_o}{I_r + x_{\\epsilon}{\\epsilon}_r} $ :: Change in GX" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "         \n", "$ {\\Delta}S_p + {\\Delta}S_f - {\\Delta}G = {\\Delta}I $\n", "\n", "         \n", "$ {\\Delta}S_p = (1 - c_y - t + c_{y}t){\\Delta}Y - {\\Delta}c_o = 0 $\n", "\n", "         \n", "$ 0 + {\\Delta}S_f - {\\Delta}G = {\\Delta}I $\n", "\n", "         \n", "$ {\\Delta}S_f = im_{y}{\\Delta}Y - x_f{\\Delta}Y^f - {x_{\\epsilon}}\\left({\\Delta}{\\epsilon}_o + {\\epsilon}_r\\left({\\Delta}r^f - {\\Delta}r\\right)\\right) $\n", "\n", "         \n", "$ {\\Delta}S_f = x_{\\epsilon}{\\epsilon}_r{\\Delta}r $\n", "\n", "         \n", "$ {\\Delta}I = {\\Delta}I_o - {I_r}{\\Delta}r $\n", "\n", "         \n", "$ 0 + x_{\\epsilon}{\\epsilon}_r{\\Delta}r - {\\Delta}G = -{I_r}{\\Delta}r $\n", "\n", "         \n", "$ -{\\Delta}G = -\\left({I_r} + x_{\\epsilon}{\\epsilon}_r\\right){\\Delta}r $\n", "\n", "         \n", "$ {\\Delta}r = \\frac{{\\Delta}G}{{I_r} + x_{\\epsilon}{\\epsilon}_r} $\n", "\n", "         \n", "$ {\\Delta}I = -I_{r}{\\Delta}r = \\frac{-I_{r}{\\Delta}G}{{I_r} + x_{\\epsilon}{\\epsilon}_r} $\n", "\n", "         \n", "$ {\\Delta}GX = {\\Delta}NX = -{x_{\\epsilon}}{\\epsilon}_r{\\Delta}r = \\frac{-{x_{\\epsilon}}{\\epsilon}_{r}{\\Delta}G}{{I_r} + x_{\\epsilon}{\\epsilon}_r} $\n", "\n", "         \n", "$ {\\Delta}I + {\\Delta}GX = -{\\Delta}G $\n", "\n", " \n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implications\n", "\n", "* ΔIo is negative here…\n", " * So the interest rate r falls…\n", " * So investment spending I falls—but not by as much as the fall in ΔIo here…\n", "* Consumption C, government spending G, and national income Y are unaffected…\n", "* Imports IM are unaffected…\n", "* So something must go up when I goes down? What is that something?\n", "* GX:\n", " * A lower interest rate produced by less optimism about their investments by businesses here at home discourages the inflow of foreign saving…\n", " * And raises the value of foreign currency—the exchange rate…\n", " * Hence U.S. exports look more tempting to foreigners…\n", " *And so they grow when r falls\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implications\n", "\n", "* ΔIo is negative here…\n", " * So the interest rate r falls…\n", " * So investment spending I falls—but not by as much as the fall in ΔIo here…\n", "* Consumption C, government spending G, and national income Y are unaffected…\n", "* Imports IM are unaffected…\n", "* So something must go up when I goes down? What is that something?\n", "* GX:\n", " * A lower interest rate produced by less optimism about their investments by businesses here at home discourages the inflow of foreign saving…\n", " * And raises the value of foreign currency—the exchange rate…\n", " * Hence U.S. exports look more tempting to foreigners…\n", " *And so they grow when r falls\n", "\n", "----\n", "\n", " \n", "\n", "## Look at the U.S. Between 1999 and 2017…\n", "\n", "----\n", "\n", " \n", "\n", "## Look at the U.S. Between 1999 and 2005…\n", "----\n", "\n", " \n", "\n", "## Look at the U.S. Between 2005 and the Start of 2008…\n", "\n", "----\n", "\n", " \n", "\n", "## Look at the U.S. Between 2008 and 2010…\n", "\n", "----\n", "\n", " \n", "\n", "## Look at the U.S. Between 2010 and Today…\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## Catch Our Breath\n", "\n", "* Ask me two questions…\n", "* Make two comments…\n", "* Further reading…\n", "\n", "
\n", "\n", "----\n", "\n", "Lecture Support: \n", "The Multiplier and the IS Curve: \n", "\n", " \n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Flexprice Model Solution Strategy\n", "\n", "* Set up the flow-of-funds equation\n", "* Solve for the equilibrium real interest rate r (or Δr)\n", "* Plug the r (or Δr) back into the equations for the components of real GDP\n", "* Take advantage of the fact that in the flexprice model ΔY = 0\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Calibration\n", "\n", "$ Y = Y^* = 20 $\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise: A Fall $ {\\Delta}I_0 $ in Investment Spending\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spending on Domestically-Produced Goods\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Course of the Business Cycle\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## National Income and Components\n", "\n", "**Real GDP**: \n", "\"Real\n", "\n", "**Real GDP per Worker**: \n", "\"Real \n", "\n", "**Investment as a Share of Potential GDP**: \n", "\"Investment\n", "\n", "**Consumption as a Share of Potential GDP**: \n", "\"Consumption\n", "\n", "**Gross Exports as a Share of Potential GDP**: \n", "\"Gross\n", "\n", "**Imports as a Share of Potential GDP**: \n", "\"Gross\n", "\n", "**Net Exports as a Share of Potential GDP**: \n", "\"Net\n", "\n", "----\n", "\n", " \n", "\n", "## Monetary\n", "\n", "**Price Level**: \n", "\"Price\n", "\n", "**Inflation Rate**: \n", "\"Inflation\n", "\n", "----\n", "\n", " \n", "\n", "## Interest and Exchange Rates\n", "\n", "**Nominal Short-Term Safe Rate**: \n", "\"Short\n", "\n", "**Long-Term Real Safe Rate**: \n", "\"Long\n", "\n", "**Long-Term Risky Real Rate**: \n", "\"Long\n", "\n", "**Real Exchange Rate** (Value of Foreign Goods/Currency): \n", "\"Real \n", "\n", "----\n", "\n", " \n", "\n", "## The Output Gap\n", "\n", "\"The\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Medium Run Cometh\n", "\n", "----\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Notes on Figures\n", "\n", "Real GDP\n", "\n", "* Real GDP: labor productivity times employment\n", "* The principal aspect of this graph is long-run growth: the American economy today is eight times the size of the economy of 1950\n", " * 2.5 times as many workers\n", " * 3.1 times output per worker\n", "* The secondary aspect is the business cycle\n", "* The tertiary aspect is speedup and slowdown in the growth trend\n", "\n", " \n", "\n", "Real GDP per Worker\n", "\n", "* Real GDP per worker (in 2009 dollars) was $45,000 per year in 1950 and is $115,000 today\n", "* Note the productivity growth speedup of the mid-1990s\n", "* And note the productivity growth collapse since 2000\n", "\n", " \n", "\n", "Investment Spending as a Share of Potential GDP\n", "\n", "* The major driver of the business cycle is fluctuating investment spending\n", "* This is investment spending as a share of potential GDP\n", "* In our simple macro model, I/Y☆ \n", "* These waves are the business cycles\n", "* Note the anemic investment recovery of 2009-present\n", "\n", " \n", "\n", "Personal Consumption Expenditures as a Share of Potential GDP\n", "\n", "* In the language of our simple macro model, this is C/Y☆\n", "* When Y is low relative to Y☆, C/☆ is low as well\n", "* C/Y☆ was low in the business cycle troughs of 2009, 1992, 1982, 1975, 1970, 1960, etc.\n", "* The medium-term rise in C/Y☆ as the U.S. becomes a save-and-invest-less country\n", "\n", " \n", "\n", "Gross Exports\n", "\n", "* Demand for U.S. exports has risen massively since 1950: from 5% to 13% of national income and product\n", "* When the value of foreign currency/bonds is high, exports boom\n", "* When the value of foreign currency/goods is low, exports are depressed\n", "\n", " \n", "\n", "Gross Imports\n", "\n", "* Imports have risen from 4% to 16% of national income and product since 1950\n", "* “Globalization” and “hyperglobalization”\n", " * The coming of the container ship\n", " * The tripling of world oil prices in the 1970s a big moment\n", " * As is the great expansion of world trade with the coming of the internet\n", " * Value chains\n", " * The China shock\n", "\n", " \n", "\n", "The Trade Balance\n", "\n", "* Net exports are a balancing item: you have to add them to C+I+G to get total spending on domestically-produced goods\n", "* The high interest rates of the 1980s that drove the value of foreign currency up led to a large negative swing in net exports\n", "* So did the optimism about America of the dot-com boom, and the so-called “strong dollar policy”\n", "* Most of all, however, the medium-term shift in the trade balance is due to the savings shortfall\n", " * Largely induced by large government deficits\n", "\n", " \n", "\n", "Short-Term Safe Nominal Interest Rate: Treasury Bills\n", "\n", "* The interest rate the Federal Reserve can nail: the short-term safe nominal interest rate\n", "* Note the regular cycles as the Federal Reserve tries to “lean against the wind”\n", "* Note the impact of the inflationary wave of the 1970s on the Treasury bill rate the Fed thought was appropriate\n", "* Note the extended time at the zero lower bound in the 2010s\n", "\n", " \n", "\n", "Long-Term Safe Real Interest Rate\n", "\n", "* Subtract the current inflation rate and add on the term premium—the difference between the 3-mo. T-bill and the 10-yr. T-bond rate—and get what current and expected future Federal Reserve policy have on incentives for investment\n", "* Note the:\n", " * Substantial tightening of the early 1970s\n", " * Loosening of the mid 1960s\n", " * Volcker disinflation of the early 1980s\n", " * The Greenspan preemption of the mid 1990s\n", " * The great easing of policy at the end of the 2000s\n", "\n", " \n", "\n", "Long-Term Risky Real Interest Rate\n", "\n", "* But the interest rate that actually matters for the determination of investment is the long-term real risky interest rate\n", "* The safe rate plus the risk premium assigned by financial markets\n", "* See the sharp tightenings coming from Federal Reserve policy and the financial system in:\n", " * the late 2000s, \n", " * the early 1980s, and\n", " * the early 1970s\n", "\n", " \n", "\n", "Real Exchange Rate\n", "\n", "* Dollar pegged to other currencies under the Bretton Woods system until the early 1970s\n", "* Since then, three major dollar cycles\n", "* Exports drop (and manufacturing hammered) when the value of foreign currency/goods falls\n", " * Reagan deficits\n", " * Internet/China\n", " * “Taper tantrum”\n", " * Trumpenomics\n", "\n", " \n", "\n", "Price Level\n", "\n", "* Headline and core\n", "* Cumulative and compounded 7.5-fold inflation since 1950\n", " * Consumer prices today 2.5 times what they were in 1984\n", " * Consumer prices in 1950 1/3 what they were in 1984\n", "* 2.5% per year\n", "\n", " \n", "\n", "Inflation Rate\n", "\n", "* Consumer Price Index\n", " * Not PCE…\n", "* “Headline” and “core”\n", " * Current core a better forecast of future headline than current headline is\n", "* Korean War \n", "* Mid-50s to late 60s\n", "* The 70s inflation\n", "* “Opportunistic” disinflation\n", "* The era of the zero lower bound" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 6 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# To Your iClickers...\n", "\n", "(A) The primary reason we are making the flexprice assumption right now is:\n", "\n", "1. While it is not good for analysis for today, for next year, or even for the next three years, it is almost invariably the case that the effects of all disturbances on the unemployment rate and the level of production relative to potential die out within five years, so it is a good medium-run analysis.\n", "2. We want to distract attention from market failures lest people begin agitating for socialism\n", "3. It serves as a useful benchmark—what would happen if the macroeconomy were functioning efficiently\n", "4. It rests on Say’s Law—the economic principal that supply creates its own demand. And even though Say’s Law is a false theory, the Federal Reserve is skillful and does a good job of making it true in practice almost always. (_This might be a good answer if not for the “almost always” at the end—it would have to be “most of the time” or “much of the time” or “some of the time”_.)\n", "5. None of the above/not enough information\n", "\n", "----\n", " \n", " \n", "\n", "## S = I\n", "\n", "The easiest way to solve the flexprice model is through examining the flow-of-funds through financial markets because:\n", "\n", "1. the savings equation is simpler than the consumption function, which we would have to use if we were to solve the flexprice model using the national income identity C + I + G + NX = Y\n", "2. the price of what is traded in financial markets is the real interest rate r, and r is the thing that moves to ensure that disturbances to one component of spending do not push the economy out of its flexprice full-employment equilibrium\n", "3. it allows us to easily incorporate international trade and finance, and it is long past time that we stopped pretending that the United States was a closed economy in macroeconomics\n", "4. it is most important to link the medium-run flexprice model to the long-run Solow growth model, and so we focus on the determinants of investment\n", "5. none of the above/not enough information" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# To Your iClickers...\n", "\n", "(A) The primary reason we are making the sticky price-wages-debt assumption right now is:\n", "\n", "1. We are sure that it corresponds to reality\n", "2. There is a lot of evidence that prices, wages, and debt are sticky, and that in the short run it is aggregate demand that determines the level of national income and product.\n", "3. It is the simplest way to break the flexprice model conclusion that national income and product must always be close to potential output, and we know that conclusion must be broken in any good model.\n", "4. It is a legacy left behind from the economics of the 1940s that ought to be dropped.\n", "5. None of the above/not enough information\n", "\n", "----\n", " \n", " \n", "\n", "## (B) When We Made the Flexprice Assumption…\n", "\n", "…it was because:\n", "\n", "1. While it is not good for analysis for today, for next year, or even for the next three years, it is almost invariably the case that the effects of all disturbances on the unemployment rate and the level of production relative to potential die out within five years, so it is a good medium-run analysis.\n", "2. We want to distract attention from market failures lest people begin agitating for socialism\n", "3. It serves as a useful benchmark—what would happen if the macroeconomy were functioning efficiently\n", "4. It rests on Say’s Law—the economic principal that supply creates its own demand. And even though Say’s Law is a false theory, the Federal Reserve is skillful and does a good job of making it true in practice almost always.\n", "5. None of the above/not enough information\n", "\n", "----\n", " \n", " \n", "\n", "## (C) In the Flexprice Model…\n", "\n", "…suppose foreign exchange speculators become more pessimistic about the dollar so that the parameter εo goes up by an amount Δεo. The relevant pieces of the flexprice model are:\n", "\n", "         \n", "$ {\\Delta}{\\epsilon} = {\\Delta}{\\epsilon}_o - {\\epsilon}_r\\left({\\Delta}r\\right) $\n", "\n", "         \n", "$ {\\Delta}I = - I_r\\left({\\Delta}r\\right) $\n", "\n", "         \n", "$ {\\Delta}NX = - x_{\\epsilon}{\\epsilon}_r\\left({\\Delta}r\\right) $\n", "\n", "This increased pessimism leads:\n", "\n", "1. investment spending to go up and net exports to go up\n", "2. investment spending to go up and net exports to go down\n", "3. investment spending to go down and net exports to go up\n", "4. investment spending to go down and net exports to go down\n", "5. none of the above/not enough information\n", "\n", "----\n", " \n", " \n", "\n", "## (D) In the Sticky-Price Model…\n", "\n", "…an increase in consumer confidence co leads to:\n", "\n", "1. an increase in Y, an increase in C, and no change in NX and I\n", "2. an increase in Y, an increase in C, and reductions in NX and I\n", "3. no increase in Y, an increase in C, and a fall in NX and I.\n", "4. no increase in Y, an increase in C, a fall in I, and no change in NX\n", "5. none of the above/not enough information\n", "\n", "----\n", " \n", " \n", "\n", "## (E) In the Sticky-Price Model…\n", "\n", "…an increase in the marginal propensity to consume cy leads to:\n", "\n", "an increase in the multiplier μ\n", "a decrease in the multiplier μ\n", "no change in the multiplier μ\n", "not enough information to tell…\n", "\n", "----\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# To Your iClickers...\n", "\n", "We study business cycles because:\n", "\n", "1. They almost invariably have decisive influence on the long run trend of economic growth\n", "2. A five percent rise or fall in production and a two percent fall or rise in the unemployment rate is a bigger deal in the short run in which we live than most other things affecting the economy\n", "3. They pose a great intellectual puzzle\n", "4. They demonstrate the optimality of a market economy\n", "5. None of the above/not enough information\n", "\n", "----\n", "\n", " \n", "\n", "## In the Real World…\n", "\n", "…to the extent that production and national income are equal to potential output, it is primarily because…\n", "\n", "1. …the real interest rate adjusts to balance demand among the broad categories of spending: C, I, G, GX, and IM\n", "2. …clever monetary and fiscal policy make Say’s Law—the idea that supply creates its own demand, that the act of setting production in motion automatically creates enough income to purchase an equivalent amount of production elsewhere in the economy\n", "3. …the nominal price level P adjusts—with inflation if aggregate demand is too high and deflation if aggregate demand is too low—to match nominal spending to actual production\n", "4. …the real wage W/P adjusts so that supply and demand balance in the labor market and so, minor frictional and structural unemployment aside, everyone who wants a job gets to work\n", "5. None of the above/not enough information\n", "\n", "----\n", "\n", " \n", "\n", "## In the Flexprice Medium-Run Model…\n", "\n", "…we would expect that a cut in tax rates would lead to…\n", "\n", "1. ...no change in Y, an increase in C, an increase in r, and a decrease in G, I, and NX\n", "2. ...no change in Y, no change in G, an increase in C, an decrease in r, and an increase in I and NX\n", "3. ...no change in Y, no change in G, an increase in C, an increase in r, and a decrease in I and NX\n", "4. ...no change in Y, no change in G, an increase in C, and a decrease in r, I, and NX\n", "5. ...None of the above/not enough information\n", "\n", "----\n", "\n", " \n", "\n", "## In the Flexprice Medium-Run Model…\n", "\n", "…when you solve it you frequently find terms like (Ir + xεεr) appearing in your calculations because…\n", "\n", "1. …it is the change in foreign savings that appears in response to a one unit increase in investment demand\n", "2. …it is the amount by which a gap between investment and savings in the flow-of-funds is decreased by a one-unit increase in the real interest rate r\n", "3. …it determines the value of the multiplier in a flexible price economy\n", "4. …it determines the increase or the decrease in the real wage necessary in order to keep actual national income and product Y equal to potential output Y*\n", "5. ...None of the above/not enough information\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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }