{ "cells": [ { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%%javascript\n", "\n", "IPython.OutputArea.prototype._should_scroll = function(lines) {\n", " return false;}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Phillips Curve, Expectations, and Monetary Policy\n", "\n", "### Ideal Types of Inflation Expectations\n", "\n", "* Static: $ {\\pi}^e = {\\pi}^* $\n", "* Adaptive: $ {\\pi_t}^e = {\\pi}_{t-1} $\n", "* Rational: $ {\\pi_t}^e = E_{t-1}\\left({\\pi}_{t}\\right) $\n", "* Panglossian $ {\\pi_t}^e = min({\\pi_t}^a, {\\pi_t}^b, {\\pi_t}^c, {\\pi_t}^d) $\n", "* Eeyorian $ {\\pi_t}^e = max({\\pi_t}^a, {\\pi_t}^b, {\\pi_t}^c, {\\pi_t}^d) $\n", "* Diagnostic $ {\\pi_t}^e = (1+\\theta)\\left(E_{t-1}\\left({\\pi}_{t}\\right) - E_{t-2}\\left({\\pi}_{t}\\right)\\right) + E_{t-2}\\left({\\pi}_{t}\\right) $\n", "\n", " \n", "\n", "### Phillips Curve\n", "\n", "* $ {\\pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) $\n", "\n", "\n", " \n", "\n", "\"Https\n", "\n", "\"Https\n", "\n", "**Olivier Blanchard**: _[The US Phillips Curve: Back to the 60s?](https://piie.com/publications/pb/pb16-1.pdf)_\n", "\n", "\"Preview\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Static Expectations\n", "\n", "* $ {\\pi}^e = {\\pi}^* $\n", "* $ {\\pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) $\n", "* $ {\\pi}_t = {\\pi}^* - {\\beta}(u_t - {u_t}^*) $\n", " * Push the unemployment rate down, the inflation rate goes up\n", " * Push the unemployment rate up, the inflation rate down\n", " * Costs of inflation are (within limits) low; costs of unemployment high...\n", " * Why not attempt to systematically exploit this?\n", " \n", " \n", "\n", "### Static Expectations: An Example\n", "\n", "* $ {\\pi}^e = {\\pi}^* $\n", "* $ {\\pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) $\n", "* $ {\\pi}_t = {\\pi}^* - {\\beta}(u_t - {u_t}^*) $\n", "* $ {\\beta} = 0.2 :: {\\pi}^* = 0.02 :: u^* = 0.04 $\n", "* If $ u_t = 0.04 $ then $ {\\pi}_t = 0.02 $\n", "* If $ u_t = 0.01 $ then what is $ {\\pi}_t $?\n", "\n", "To your iClickers...\n", "\n", ">A. 0.02 \n", "B. 0.022 \n", "C. 0.026 \n", "B. 0.04 \n", "E. None of the above\n", "\n", " \n", "\n", "### Why Not Attempt to Exploit This?\n", "\n", "WELL, WHAT MADE EXPECTATIONS STATIC IN THE FIRST PLACE?\n", "\n", " \n", "\n", "### Adaptive Expectations\n", "\n", "* $ {\\pi_t}^e = \\pi_{t-1} $\n", "* $ {\\pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) $\n", "* $ {\\pi}_t = {\\pi}_{t-1} - {\\beta}(u_t - {u_t}^*) $\n", "* $ \\Delta{pi}_t = - {\\beta}(u_t - {u_t}^*) $\n", " * If you push unemployment down—thus running a high pressure economy—you push inflation up, and up, and up...\n", " * If you want to keep unemployment below its natural rate, you have to accept an accelerating price level...\n", " * If you want to keep inflaiton constant, you have to make it the case that the average unemployment rate equals $ u^* $...\n", " * Hence no benefit to worrying about unemployment: what you lose one year you will gain back in another...\n", " \n", " \n", " \n", "### Adaptive Expectations: An Example\n", "\n", "* $ \\Delta{pi}_t = - {\\beta}(u_t - {u_t}^*) $\n", "* $ {\\beta} = 0.2 :: u^* = 0.04 :: {\\pi_1}^e = {\\pi}_o $\n", "* If $ u_o = 0.04 $ then $ {\\pi}_o = 0.02 $\n", "* If $ u_1 = 0.02 $ then what is $ {\\pi}_5 $?\n", "\n", "To your iClickers...\n", "\n", ">A. 0.02 \n", "B. 0.022 \n", "C. 0.026 \n", "B. 0.04 \n", "E. None of the above\n", "\n", " \n", "\n", "### Perfect Foresight\n", "\n", "* $ {\\pi_t}^e = \\pi_{t} $\n", "* $ {\\pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) + SS_t $ :: complicate the Phillips Curve with supply shocks\n", "* $ {\\pi}_t = {\\pi}_t - {\\beta}(u_t - {u_t}^*) + SS_t $\n", "* $ 0 = - {\\beta}(u_t - {u_t}^*) + SS_t $\n", "* $ u_t = {u_t}^* + \\frac{SS_t}{\\beta} $\n", "\n", " \n", "\n", "### Rational Expectations\n", "\n", "* $ {\\pi_t}^e = E_{t-1}\\left(\\pi_{t}\\right) $\n", "* $ {\\pi_t} = {\\pi_t}^e + \\epsilon_t $ (unforecastable)\n", "* $ {pi}_t = {\\pi}^e - {\\beta}(u_t - {u_t}^*) + SS_t $ :: complicate the Phillips Curve with supply shocks\n", "* $ {pi}_t = {\\pi}_t + \\epsilon_t - {\\beta}(u_t - {u_t}^*) + SS_t $\n", "* $ 0 = - {\\beta}(u_t - {u_t}^*) + \\epsilon_t + SS_t $\n", "* $ u_t = {u_t}^* + \\frac{\\epsilon_t + SS_t}{\\beta} $\n", " * $ SS_t $ :: things that temporarily push the natural rate around\n", " * $ \\epsilon_t $ :: surprises\n", " * No room for policy...\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Intermediate Cases\n", "\n", "* $ \\pi_t = (1-\\lambda)\\pi^* + \\lambda\\pi_{t-1} - \\beta(u_t - {u_t}^*) + SS_t $\n", "\n", " \n", "\n", "* Here we have something we can estimate!\n", "\n", " \n", "\n", "### Here Is Our $ \\lambda $...\n", "\n", "\"Expectations\n", "\n", " \n", "\n", "### Here Is Our $ \\beta $...\n", "\n", "\"Expectations\n", "\n", " \n", "\n", "### Here Is Our $ \\beta $...\n", "\n", "* Where are the supply shock terms in the regression?\n", "* What happens if you leave out an important variable from the right hand side?\n", "\n", ">A. It’s OK: your estimates of the variables will still be unbiased—the missing variables go into the regression error ε, and your estimates will be less precise… \n", "B. It’s not OK: the missing variables are highly likely to be correlated with the stuff you have on the RHS, and the computer will attribute as much of the effect of the missing variable it can to the variable it sees…\n", "\n", "* Implications for their estimates of λ…\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### To Your iClickers\n", "\n", "The Keynesian multiplier is:\n", "\n", ">A. A process that amplifies a shock to autonomous spending and leads it to have a multiplied effect on the level of real national income and product in the sticky-price model \n", "B. A force that keeps national income and product equal to potential output in the flexprice model \n", "C. The process by which a change in bank reserves produces an amplified change in the money stock \n", "D. None of the above\n", "\n", " \n", "\n", "The IS-Curve relationship is primarily:\n", "\n", ">A. The relationship between national income and product Y and the long-term real risky interest rate r \n", "B. The relationship between national income and product Y and the multiplier μ \n", "C. The relationship between national income and product Y and the marginal propensity to consume $ c_y $ \n", "D. The relationship between national income and product Y and the money stock M \n", "E. None of the above\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Why Do We Care About Inflation?\n", "\n", "* Quite clear why we care about production…\n", "* Quite clear why we care about unemployment/employment…\n", "* But why do we care about inflation?\n", " * It’s zero sum…\n", " * Yet we do…\n", " \n", "\"Expectations\n", "\n", " \n", "\n", "### John Maynard Keynes on Inflation\n", "\n", "* Lenin is said to have declared that the best way to destroy the Capitalist System was to debauch the currency. By a continuing process of inflation, governments can confiscate, secretly and unobserved, an important part of the wealth of their citizens. By this method they not only confiscate, but they confiscate arbitrarily; and, while the process impoverishes many, it actually enriches some…\n", "\n", "\"John\n", "\n", " \n", "\n", "### Costs of Inflation\n", "\n", "* But that is inflation of 25% per year or so…\n", "* Inflation of less than 10% per year?\n", "Paul Volcker and Alan Greenspan think inflation above 5% per year\n", " * Causes confusion…\n", " * Distracts businessmen from what it would be more productive for them to think about…\n", " * Thus slows productivity growth\n", "* Inflation of less than 5% per year?\n", " * Volcker was happy with it…\n", " * Greenspan pushed for 2%…\n", " * Greenspan did not push for 0%…\n", " \n", " \n", "\n", "### Costs of Low Inflation\n", "\n", "* Limited running room on the part of the Federal Reserve\n", "* DeLong and Summers (1988) at Jackson Hole, WY…\n", "\n", " \n", "\n", "### But We Keep Inflation Very Low, Even So?\n", "\n", "* Why? Because voters hate it!\n", " * Money illusion?\n", " * Evidence of governmental incompetence?\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Monetary Policy: The Federal Reserve and Its \"Reaction Function\"\n", " \n", "* The policy rate—the short-term safe nominal interest rate: i\n", "* The long-term safe interest rate: $ i + {\\rho}_T $ (T for \"term risk premium\")\n", "* On top of this, we pile:\n", " * The rest of the risk premium: $ i + {\\rho}_T + {\\rho}_D $ (D for \"default risk premium\")\n", " * Whole risk premium: $ \\rho = \\rho_T + \\rho_D $\n", " Subtract the inflation rate $ \\pi $\n", "* Trying to alter the term risk premium via: “forward guidance” and “quantitative easing”\n", " * Not very powerful tools\n", "\n", " \n", "\n", "* Does the Federal Reserve's pattern of behavior makes sense?\n", "* Applied math optimal control tells us:\n", " * Bang-bang…\n", " * Minor course corrections…\n", "* The Fed does neither...\n", "\n", "\"10\n", "\n", " \n", "\n", "### Monetary Policy: The Federal Reserve and Its \"Reaction Function\"\n", " \n", "* The zero lower bound—purple line: $ -\\pi $\n", " * The Fed cannot push any interest rate below the negative of the inflation rate\n", "* The real policy rate, the short-term safe real interest rate—blue line: $ i - \\pi $\n", "* The long-term real safe Treasury rate—red line: $ i - \\pi + \\rho_T $\n", "* The long-term risky real interest rate—green line: $ i - \\pi + \\rho_T + \\rho_D = i - \\pi + \\rho $\n", "\n", "\"Expectations\n", "\n", " \n", "\n", "### Understanding the Recent History of the Federal Reserve\n", "\n", "* The Volcker disinflation 1979-83\n", "* Post-1983 “policy easing” (Volcker)\n", " * Trying to make Say’s Law true in practice\n", "* The 1987 shock (caused by Haas)\n", " * Greenspan’s reaction 1987-1989\n", "* “Overheating” 1990-2 (Greenspan)\n", "* Accomodating fiscal contraction 1992-4 (Greenspan)\n", "* Monetary tightening 1994-5 (Greenpan)\n", "* Accommodating the dot-com boom 1995-9 (Greenspan)\n", "\n", " \n", "\n", "* Slow to react 2000-2 (Greenspan)\n", "Keeping rates low (2002-5) and encouraging housing and derivatives bubbles (Greenspan)\n", "* Raising (2005-7) (Bernanke)\n", "* Slow to cut (2007-8) (Bernanke)\n", "* The crisis (2008-10) (Bernanke)\n", "* Declaring victory (2010-12) (Bernanke)\n", "* Fiscal headwinds (2012-16) (Yellen)\n", "* Tightening cycle (2016-present) (Yellen, Powell)\n", "\n", " \n", "\n", "### Implications for the Output Gap\n", "\n", "\"Expectations\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interest Rate Rules\n", "\n", "#### $ r = r_o + r_π(π - π^t) - r_u(u - u*) $\n", "\n", "* (also McKibben and Henderson)\n", "\n", " \n", "\n", "### The Atlanta Fed's Interest Rate Rule Calculator\n", "\n", "$ r = r_o + r_π(π - π^t) - r_u(u - u*) $\n", "\n", "* Taylor: r = 0.03 + (0.5)(π - 0.02) - (0.25)(u - 0.06)\n", "\n", "\n", "\n", "\"Expectations\n", "\n", " \n", "\n", "### r*\n", "\n", "\"Expectations\n", "\n", " \n", "\n", "### The Bernanke Letter\n", "\n", "\n", "\n", "* We believe the Federal Reserve’s large-scale asset purchase plan (so-called “quantitative easing”) should be reconsidered and discontinued…. The planned asset purchases risk currency debasement and inflation…\n", "* We do not think they will achieve the Fed’s objective of promoting employment…\n", "* We disagree with the view that inflation needs to be pushed higher…\n", "* Another round of asset purchases, with interest rates still near zero over a year into the recovery, will distort financial markets and greatly complicate future Fed efforts to normalize monetary policy…\n", "* Quantitative easing by the Fed is neither warranted nor helpful…\n", "\n", " \n", "\n", "### Enough Inside Baseball!\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Monetary Policy Reaction Function\n", "\n", "\"Expectations\n", "\n", "* $ r = r_o + r_π(π - π^t) - r_u(u - u*) $\n", "* $ u = u_o + {\\phi}(π - π^t) $\n", "\n", "The MPRF brings together three relationships at once:\n", "\n", "1. Interest rate rule: $ r = r_o + r_π(π - π^t) - r_u(u - u*) $\n", "2. IS Curve: $ Y = AD = \\mu(A_o - (I_rr_\\epsilon)r $\n", "3. Okun's Law; $ u = u^* - 0.4\\left(\\frac{Y - Y^*}{}Y^*\\right) $\n", "\n", " \n", "\n", "### The Monetary Policy Reaction Function: An Example\n", "\n", "Suppose:\n", "\n", ">$ {\\pi}^t = 0.02 $ \n", "$ \\pi = 0.05 $ \n", "$ r_{\\pi} = \\frac{1}{3} $ \n", "$ r_o = .025 $\n", "\n", "Then by the interest rate rule:\n", "\n", ">$ r = 0.025 + \\frac{1}{3}(0.05 - 0.02) = 0.035 $\n", "\n", "The central bank will conduct monetary policy so that the real interest rate is 3.5%.\n", "\n", "Suppose further that:\n", "\n", ">$ MPE = 0.5 $ \n", "$ A_o = 2.15 $ trillion \n", "$ I_r = 8 $ \n", "$ x_{\\epsilon}{\\epsilon}_r = 2 $\n", "\n", "Then the IS Curve tells us that when the interest rate is 3.5 percent:\n", "\n", ">$ \\mu = \\frac{1}{1 - MPE} = 2 $ \n", "$ Y = \\mu(A_o) - \\mu(I_r + x_{\\epsilon}{\\epsilon}_r)r = 4.3 - (2)(10)(.035) = 3.6 $ trillion\n", "\n", "Planned expenditure will equal real output and national income when they are 3.6 trillion.\n", "\n", "Finally, supppose that:\n", "\n", ">$ u^* = 0.05 $ \n", "$ Y^* = 4 $ trillion\n", "\n", "Then Okun's Law tells us that when output is 3.6 trillion:\n", "\n", ">$ u = 0.05 - 0.4\\frac{3.6-4}{4} = 0.05 + 0.04 = 0.09 $\n", "\n", "The unemploymente rate is then 9 percent.\n", "\n", "When the inflation rate is 5 percent rather than the central bank's target of 2 percent, the central bank will raise the real interst rate from its normal baseline rate of 2.5 percent to 3.5 percent, which will cause output to fall to 3.6 trillion and generate an unemployment rate of 9 percent.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Monetary Policy Reaction II Function\n", "\n", "\"Expectations\n", "\n", "* $ π = π^e - {\\beta}(u - u^*) + SS $\n", "* $ r = r_o + r_π(π - π^t) - r_u(u - u*) $\n", "* $ u = u_o + {\\phi}(π - π^t) $\n", "\n", "Nomenclature:\n", "\n", ">r :: real risky interest rate \n", "$r^*$ :: neutral rate \n", "$r_π$ :: reaction of central bank to higher (or lower) inflation \n", "$π^t$ :: central bank’s inflation target \n", "$r_u$ :: reaction of central bank to higher (or lower) unemployment \n", "u :: unemployment rate \n", "$u^*$ :: NAIRU: unemployment rate at which inflation equals expectations \n", "π :: inflation \n", "$π^e$ :: expected inflation \n", "β :: slope of Phillips Curve: relationship of inflation to unemployment \n", "SS :: supply shock to inflation \n", "φ :: a combination of Okun’s Law, the multiplier, and interest sensitivity of investment and exports \n", "δ :: demand shock\n", "\n", " \n", "\n", "### Add Lags\n", "\n", ">$ r_t = r^* + r_π(π_t - π^t) - r_u(u_t - u*) $\n", "\n", ">$ π_t = π^e - β(u_{t-1} - u*) + SS_t $\n", "\n", ">$ u_t = u* + φ(r_t - r*) + δ_t $\n", "\n", " \n", "\n", ">$ u_t - u^* = +{\\phi}r_{\\pi}(\\pi_t - \\pi^t) - {\\phi}r_u(u_t - u*) + \\delta_t $ \n", "\n", ">$ (u_t - u^*) = \\frac{{\\phi}r_{\\pi}(\\pi_t - \\pi^t) + \\delta_t}{1 + {\\phi}r_u} $\n", "\n", "With adaptive expectations:\n", "\n", ">$ π_t = π_{t-1} - β(u_{t-1} - u*) + SS_t $\n", "\n", ">$ (π_t - π^t) = (π_{t-1} - π^t) - \\beta\\left(\\frac{{\\phi}r_{\\pi}(\\pi_{t-1} - \\pi^t) + \\delta_{t-1}}{1 + {\\phi}r_u}\\right) + SS_t $\n", "\n", ">$ (π_t - π^t) = \\left(\\frac{1 + {\\phi}r_u -\\beta{\\phi}r_{\\pi}}{1 + {\\phi}r_u}\\right)(\\pi_{t-1} - \\pi^t) - \\beta\\left(\\frac{\\delta_{t-1}}{1 + {\\phi}r_u}\\right) + SS_t $\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Alternatively: They Could Try to Get Ahead of the Curve\n", "\n", ">$ (u_t - u^*) = {\\phi}(r_t - r^*) + \\delta_t $\n", "\n", ">$ π_t = π_{t-1} - β(u_{t-1} - u*) + SS_t $\n", "\n", " \n", "\n", ">$ (π_t - π^t) = (π_{t-1} - π^t) - β{\\phi}(r_{t-1} - r^*) - β\\delta_t + SS_t $\n", "\n", "Try to stabilize inflation:\n", "\n", ">$ 0 = (π_{t-1} - π^t) - β{\\phi}(r_{t-1} - r^*) - β\\delta_t + SS_t $\n", "\n", ">$ β{\\phi}(r_{t-1} - r^*) = (π_{t-1} - π^t) - β\\delta_t + SS_t $\n", "\n", ">$ r_{t-1} = r^* + \\frac{(π_{t-1} - π^t)}{β{\\phi}} - \\frac{\\delta_t}{\\phi} + \\frac{SS_t}{β{\\phi}} $\n", "\n", "Then:\n", "\n", ">$ \\pi_t = \\pi^t $\n", "\n", " \n", "\n", "### Why Doesn't the Federal Reserve Try Harder to Get Ahead of the Curve?\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### To Your iClickers...\n", "\n", "The interest rate rule is:\n", "\n", ">A. A way of capturing how the Federal Reserve and other central banks typically react to the changing economic environment \n", "B. The rule that higher interest rates reduce investment spending \n", "C. The fact that higher interest rates make the future look “cheaper” relative to the present \n", "D. Required by Congress that the Federal Reserve follow—or explain why it is not following \n", "E. None of the above\n", "\n", " \n", "\n", "The Keynesian multiplier is:\n", "\n", ">A. An amplified relationship between shifts in autonomous spending—exports, government purchases, investment, consumer confidence—and shifts in real national product \n", "B. The fact that the money supply expands by a multiplied factor times the expansion in the monetary base \n", "C. The fact that a sticky-price economy has multiple possible equilibrium positions for national income and product \n", "D. The fact that investment increases when production increases because investment depends largely on business-sector cash flow \n", "E. None of the above\n", "\n", " \n", "\n", "Living standards were more-or-less stagnant from 5000 BC to 1800 largely because of:\n", "\n", ">A. Keynesian factors \n", "B. Schumpeterian factors \n", "C. Ricardian factors \n", "D. Malthusian factors \n", "E. None of the above\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Catch Our Breath\n", "\n", "\n", "\n", "* Ask me two questions…\n", "* Make two comments…\n", "\n", " \n", "\n", "* Further reading…\n", "\n", "
\n", "\n", "----\n", "\n", "Lecture Support: \n", "The Phillips Curve and Expectations, and Monetary Policy: \n", "Expectations and Monetary Policy: \n", "The Monetary Policy Reaction Function: \n", "\n", " \n", "\n", "----" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }