{
 "metadata": {
  "name": "",
  "signature": "sha256:6f30cd257aa9ac10585ead728649fb253b01d95e78019f8727a0deda1c3aeb57"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Inflation, money velocity, and interest rates"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We examine and attempt to replicate the results of two interesting articles by **Yi Wen**, Economist at the St. Louis Federal Reserve Bank, and **Maria A. Arias**:\n",
      "\n",
      "*What Does Money Velocity Tell Us about Low Inflation in the U.S.?*, 9/1/14 http://www.stlouisfed.org/on-the-economy/what-does-money-velocity-tell-us-about-low-inflation-in-the-u-s/\n",
      "\n",
      "*The Liquidity Trap: An Alternative Explanation for Today's Low Inflation*, April 2014, http://www.stlouisfed.org/publications/re/articles/?id=2505\n",
      "\n",
      "from which we shall quote and edit extensively. \n",
      "\n",
      "Along the way, we take a detour and explore the connection between money velocity and bond rates. This will tie together their relationship with GDP and the money supply in a fitted equation."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Dependencies:*\n",
      "\n",
      "    - Linux, bash [not crucial, cross-platform prefered]\n",
      "    - Python: matplotlib, pandas [recommend Anaconda distribution]\n",
      "    - Modules: yi_1tools, yi_plot, yi_timeseries, yi_fred\n",
      "     \n",
      "*CHANGE LOG*\n",
      "\n",
      "    2015-05-15  Code review and revision.\n",
      "    2014-09-03  First version."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  NOTEBOOK settings and system details:   [00-tpl v14.09.28]\n",
      "\n",
      "#  Assume that the backend is LINUX (our particular distro is Ubuntu, running bash shell):\n",
      "print '\\n ::  TIMESTAMP of last notebook execution:'\n",
      "!date\n",
      "print '\\n ::  IPython version:'\n",
      "!ipython --version\n",
      "\n",
      "#  Automatically reload modified modules:\n",
      "%load_ext autoreload\n",
      "%autoreload 2   \n",
      "#           0 will disable autoreload.\n",
      "#  Generate plots inside notebook:\n",
      "%matplotlib inline\n",
      "\n",
      "#  DISPLAY options\n",
      "from IPython.display import Image \n",
      "#  e.g. Image(filename='holt-winters-equations.png', embed=True)\n",
      "from IPython.display import YouTubeVideo\n",
      "#  e.g. YouTubeVideo('1j_HxD4iLn8')\n",
      "from IPython.display import HTML # useful for snippets\n",
      "#  e.g. HTML('<iframe src=http://en.mobile.wikipedia.org/?useformat=mobile width=700 height=350></iframe>')\n",
      "import pandas as pd\n",
      "print '\\n ::  pandas version:'\n",
      "print pd.__version__\n",
      "#      pandas DataFrames are represented as text by default; enable HTML representation:\n",
      "#      [Deprecated: pd.core.format.set_printoptions( notebook_repr_html=True ) ]\n",
      "pd.set_option( 'display.notebook_repr_html', False )\n",
      "\n",
      "#  MATH display, use %%latex, rather than the following:\n",
      "#                from IPython.display import Math\n",
      "#                from IPython.display import Latex\n",
      "\n",
      "print '\\n ::  Working directory (set as $workd):'\n",
      "workd, = !pwd\n",
      "print workd + '\\n'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " ::  TIMESTAMP of last notebook execution:\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Fri May 15 14:37:44 PDT 2015\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " ::  IPython version:\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "2.3.0\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " ::  pandas version:\n",
        "0.15.0\n",
        "\n",
        " ::  Working directory (set as $workd):\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "/home/yaya/Dropbox/ipy/fecon235/nb\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from yi_1tools import *\n",
      "from yi_fred import *\n",
      "from yi_plot import *\n",
      "from yi_timeseries import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Quick intro to monetarist theory"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One of the most important theories to explain inflation is the monetarist view: according to Milton Friedman, \u201cInflation is always and everywhere a monetary phenomenon.\u201d In other words, inflation occurs because there is too much money available to buy the same amount of goods and services produced in the economy. This view can also be represented by the so-called \u201c**quantity theory of money**,\u201d which relates the general price level, the total goods and services produced in a given period, the total money supply and the speed (velocity) at which money circulates in the economy in facilitating transactions in the following equation:\n",
      "\n",
      "    M V = P Q\n",
      "\n",
      "where:\n",
      "\n",
      "    M stands for money.\n",
      "    V stands for the velocity of money (or the rate at which people spend money).\n",
      "    P stands for the general price level (not the rate of its growth).\n",
      "    Q stands for the quantity of goods and services produced (in real terms, e.g. real GDP).\n",
      "\n",
      "Based on this equation, *holding the money velocity constant,* if the money supply (M) increases at a faster rate than real economic output (Q), the price level (P) must increase to make up the difference.\n",
      "\n",
      "[See details in David Colander, 2010, *Macroeconomics*, pp. 387ff for theories of inflation where the tautological equation becomes interpreted as bi-causal given added assumptions.]\n",
      "\n",
      "[For small percentage changes, we can thus write the so-called *inflation identity*:\n",
      "\n",
      "$ \\Delta P = \\Delta M + \\Delta V - \\Delta Q $ \n",
      "\n",
      "where \u0394P represents the inflation rate. This equation is only useful if \u0394V follows regular behavior (studied below). It also loses usefulness if the central bank lacks control over \u0394M.]\n",
      "\n",
      "In equilibrium, real money demand is understood to be Q/V."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Money expanded enormously due to QE \"quantitative easing\" during the Great Recession, yet inflation did not rage upwards\n",
      "\n",
      "From January 2009 to December 2013, the Federal Reserve's balance sheet grew by approximately $3.5 trillion due to the large-scale asset purchase (LSAP) policies implemented to aid the ailing economy after the Great Recession. These unconventional monetary policies, also known as quantitative easing (QE), increased credit availability in the private lending markets and put downward pressure on real interest rates.\n",
      "\n",
      "*According to the monetarist view, inflation in the U.S. should have been about 31 percent per year between 2008 and 2013, when the money supply grew at an average pace of 33 percent per year and output grew at an average pace around 2 percent.* \n",
      "\n",
      "# Question:  **Why, then, has inflation remained persistently low (below 2%) during this period (\"Great Recession\")?** \n",
      "\n",
      "[\"Normal times\" (1960-2007) shall refer to the postwar period prior to the Great Recession.]"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Define our start of the Great Recession:\n",
      "recession = '2006-12-31'\n",
      "#                ^this would include 2007-Q1 data.\n",
      "\n",
      "#  According to the U.S. National Bureau of Economic Research \n",
      "#  (the official arbiter) the US recession began in December 2007. \n",
      "#  But the emergence of sub-prime loan losses in 2007 \n",
      "#  began the global crisis. \n",
      "#  Lehman Brothers went bankrupt during September 2008."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Let us look at headline price levels averaged, including core versions:\n",
      "P = getfred( m4infl )\n",
      "\n",
      "#  Compute YoY percentage change for INFLATION:\n",
      "Prate = pcent(P, 12)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Plot INFLATION rate:\n",
      "plotfred( Prate, 'Infl rate' )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAW0AAAEYCAYAAACX7qdQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLMO7b3zpqwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad29f88c>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  Finished: plotdf-Infl_rate.png\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Before Great Recession, our so-called \"normal times\":\n",
      "georet( P[:recession], 12 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "[3.8, 3.8, 0.79, 12]"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Great Recession through the present:\n",
      "georet( P[recession:], 12 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "[1.65, 1.66, 0.57, 12]"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2015-03-21 The geometric mean return for prices is more than double for \"normal times\" 3.78% vs. \"Great Recession\" 1.64%. \n",
      "\n",
      "**Several reasons have been provided for the persistently low inflation.** For example, Janet Yellen said in 2009 that inflation would not take hold during a recession because of *little pressure for prices and wages to increase given that resources through the economy were underused.* \n",
      "\n",
      "Others say the unusually low inflation stems from the weakening of the money multiplier, as *banks continue to hold excess reserves instead of extending more credit through loans.* \n",
      "\n",
      "While others point to the FOMC's increased communications and forward guidance in anchoring future inflation expectations, as well as to the knowledge that the LSAPs will eventually be reversed.\n",
      "\n",
      "Andolfatto and Li note when describing the effect of QE in Japan during the 2000s, **\"even large changes in the monetary base are not likely to have any inflationary consequences if people generally believe the program will be reversed at some future date.\"** (*\"Quantitative Easing in Japan: Past and Present.\"* Federal Reserve Bank of St. Louis Economic Synopses, 2014, No. 1, Jan. 10, 2014. See http://research.stlouisfed.org/publications/es/article/10024 )"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Answer: Velocity has not been constant, in fact, declining...\n",
      "\n",
      "The issue has to do with the velocity of money, which has never been constant, as can be seen below. **If for some reason the money velocity declines rapidly during an expansionary monetary policy period, it can offset the increase in money supply and even lead to deflation instead of inflation.**\n",
      "\n",
      "*The velocity of money can be calculated as the ratio of nominal gross domestic product (GDP) to the money supply (V=PQ/M), which can be used to gauge the economy\u2019s strength or people\u2019s willingness to spend money.* When there are more transactions being made throughout the economy, velocity increases, and the economy is likely to expand. The opposite is also true: Money velocity decreases when fewer transactions are being made; therefore the economy is likely to shrink.\n",
      "\n",
      "    G := P*Q i.e. nominal GDP \n",
      "    \n",
      "To measure money supply, we use the monetary base which includes notes and coins in circulation as well as bank reserves.    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  M used in the article is the St. Louis Adjusted Monetary Base:\n",
      "M = getfred( m4baseus )\n",
      "\n",
      "#  Monetary base is traditionally the most liquid measure of the money supply.\n",
      "#  Note that bank reserves are not included in \"M1\" \n",
      "#  which is another measure of the money supply.\n",
      "#  Ref: https://en.wikipedia.org/wiki/Money_supply"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Data for M goes back to 1918:\n",
      "plotfred( M['1960':], 'Mbase' )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEYCAYAAAC5q4bCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUs+TvHPOVTBP8s45V8E8yTvnXAX7/2lhip1g5GIkAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad167b4c>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  Finished: plotdf-Mbase.png\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Plot for log( M ):\n",
      "plotfred( np.log( M['1960':] ))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWYAAAEYCAYAAABvDlynAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/wMkVajYcqqb0QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad24196c>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  M goes parabolic after the Great Recession due to quantitative easing:\n",
      "georet( M[recession:], 12)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "[19.15, 20.44, 16.04, 12]"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2015-03-22: As of the Great Recession, the money supply, per M the monetary base, has exploded at an annual geometric rate of 19%"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "\"How The Economic Machine Works\""
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For background information, we embed a 30-minute video by Ray Dalio (founder of the largest hedge fund, Bridgewater), which shows the fundamental importance of *transactions* both from the money and credit standpoint. This sets the stage for **velocity** which is a way of quantifying transactional turnovers in the economy."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "YouTubeVideo( 'PHe0bXAIuk0' )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "        <iframe\n",
        "            width=\"400\"\n",
        "            height=300\"\n",
        "            src=\"https://www.youtube.com/embed/PHe0bXAIuk0\"\n",
        "            frameborder=\"0\"\n",
        "            allowfullscreen\n",
        "        ></iframe>\n",
        "        "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "<IPython.lib.display.YouTubeVideo at 0xad1f262c>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Velocity computed and plotted"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Nominal GDP, resampled monthly:\n",
      "G = getfred( m4gdpus )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "V = todf( G / M )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plotfred( V, 'Velocity Mbase' )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWwAAAEYCAYAAAB4LMxuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncQqE/wcJC51qmLKXLgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad205a0c>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  Finished: plotdf-Velocity_Mbase.png\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Clearly velocity is not constant over time. The plunge after 2008 Q1 is very dramatic and  significant.**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stats( V )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                Y\n",
        "count  817.000000\n",
        "mean    15.458331\n",
        "std      4.587706\n",
        "min      4.304107\n",
        "25%     12.502377\n",
        "50%     16.727152\n",
        "75%     18.523686\n",
        "max     22.257864\n",
        "\n",
        " ::  Index on min:\n",
        "Y   2014-08-01\n",
        "dtype: datetime64[ns]\n",
        "\n",
        " ::  Index on max:\n",
        "Y   1981-07-01\n",
        "dtype: datetime64[ns]\n",
        "\n",
        " ::  Head:\n",
        "                   Y\n",
        "T                   \n",
        "1947-01-01  7.212152\n",
        "1947-02-01  7.336959\n",
        "1947-03-01  7.368347\n",
        "1947-04-01  7.429192\n",
        "1947-05-01  7.471004\n",
        "1947-06-01  7.473595\n",
        "1947-07-01  7.486007\n",
        "\n",
        " ::  Tail:\n",
        "                   Y\n",
        "T                   \n",
        "2014-07-01  4.390173\n",
        "2014-08-01  4.304107\n",
        "2014-09-01  4.339132\n",
        "2014-10-01  4.380710\n",
        "2014-11-01  4.601357\n",
        "2014-12-01  4.542387\n",
        "2015-01-01  4.405736\n",
        "\n",
        " ::  Correlation matrix:\n",
        "   Y\n",
        "Y  1"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "During the second quarter of 2014, the velocity of the monetary base was at 4.4, its slowest pace on record. This means that every dollar in the monetary base was spent only 4.4 times in the economy, severely down from 17.2 times just prior to the Great Recession. \n",
      "\n",
      "This implies that the unprecedented monetary base increase driven by the Fed\u2019s large money injections through its large-scale [QE] asset purchase programs has failed to cause at least a one-for-one proportional increase in nominal GDP. Thus, **it is precisely the sharp decline in velocity that has offset the sharp increase in money supply, leading to the almost no change in nominal GDP** (either P or Q)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Okay, so let's look at nominal GDP:\n",
      "plotfred( G[recession:] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEYCAYAAABcGYHrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb63ff48c>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Well, their research needs correction, for there's is indeed change in nominal GDP. \n",
      "\n",
      "georet( G[recession:], 12 )\n",
      "\n",
      "#  2015-03-22: about +2.8% per annum since 2007:"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "[2.73, 2.74, 0.92, 12]"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  So where is velocity heading in the next 12 months?\n",
      "holtfred( V, 12 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "    Forecast\n",
        "0   4.405736\n",
        "1   4.376337\n",
        "2   4.385083\n",
        "3   4.393830\n",
        "4   4.402577\n",
        "5   4.411323\n",
        "6   4.420070\n",
        "7   4.428816\n",
        "8   4.437563\n",
        "9   4.446309\n",
        "10  4.455056\n",
        "11  4.463802\n",
        "12  4.472549"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  If M and Q are held fixed, then the \n",
      "#  change in V should predict the change in P,\n",
      "#  i.e. the inflation rate:\n",
      "\n",
      "(3.87 / 4.38) - 1\n",
      "#  as of 2015-03-23 = -11.6% which is very deflationary, \n",
      "#  even given modest GDP growth. M probably will stabilize \n",
      "#  since QE has ceased."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "-0.11643835616438347"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Near zero rates lead many to hoard money, thus the decline in velocity\n",
      "\n",
      "So why did the monetary base increase not cause a proportionate increase in either the general price level or GDP? The answer lies in the private sector\u2019s dramatic increase in their willingness to hoard money instead of spend it. **Why would people suddenly decide to hoard money instead of spending it?** A possible answer lies in the combination of two issues:\n",
      "\n",
      "- **A glooming economy after the financial crisis**\n",
      "    \n",
      "- **The dramatic decrease in interest rates (to zero) that has forced investors to readjust their portfolios toward liquid money and away from interest-bearing assets such as government bonds**\n",
      "\n",
      "In this regard, the unconventional monetary policy has reinforced the recession by stimulating the private sector\u2019s money demand through pursuing an excessively low interest rate policy (i.e., the zero-interest rate policy, ZIRP). Indeed, during the pre-recession period, for every 1 percentage point decrease in 10-year Treasury note interest rates, the velocity of the monetary base decreased 0.17 points, based on a linear regression model of the velocity onto interest rates. Since 10-year interest rates declined by about 0.5 percentage points between 2008 and 2013, the velocity of the monetary base should have decreased by about 0.085 points. But the actual velocity has gone down by 5.85 points, 69 times larger than predicted. This happened because *the nominal interest rate on short-term bonds has declined essentially to zero, and, in this case, **the best form of risk-free liquid asset is no longer the short-term government bonds, but money.** * \n",
      "\n",
      "*Notes:*\n",
      "\n",
      "- [Bond rates can be expected to drop *ceteris paribus* if economic transactions decline. But the numbers provided in the last paragraph need to be double-checked -- which we will do next. ]\n",
      "\n",
      "- [In a negative interest rate environment, there's even talk of starting ETFs which buys currency notes and stores them in a vault as an investment. Such notes can be considered as zero-coupon perpetual bearer bonds at 0%.] \n",
      "\n",
      "- [Since the Great Recession, qualification for credit has become extremely strict, which would of course diminish consumer spending. The financial instruments used to manage credit risk have become heavily regulated and discouraged under the Volker rule.]"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Velocity as a function of bond rates?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  We try replicate the findings above:\n",
      "bond = getfred( m4bond10 )\n",
      "#  Yields for 10-year Treasuries, resampled monthly."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Actual yields (not the model):\n",
      "plotfred( bond )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWwAAAEYCAYAAAB4LMxuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJztnXmYVNXRuN9il3UAWQbZFRQVxZ0o6rjEEDc0aqKJieQz\nLokmRj938xON0RhN3DWfJipqlMS4Je4aZVyjIoqAgAgCgiA7wgCy1u+P6mv39PQ+vd3pep+nn9v3\nnrtU9e2uPrdOnSpRVRzHcZzyp1mpBXAcx3Eyww224zhOSHCD7TiOExLcYDuO44QEN9iO4zghwQ22\n4zhOSHCD7dRDRLaKyMBSy+E4TkPcYJcYEZkrIocW+Zq9RGR+Ac9fKyKnp2gfLCL/EpElIrJcRF4Q\nkcFx+5wvIotE5CsRuVdEWsW0nSsi74vI1yJyf9xx/SN/OmtiXlekkfcwEZkhImtF5FUR6Ztgn1Yi\nMj2Tz01E/iAiyyKv6+ParhGRKSKySUTGZHCuVJ9DFxF5UkTqIt+jUxqjZyq5E5yrv4iMj5xruogc\nFtf+QxGZF5HtSRHpnE5XJz1usEuPAlLkax4JPF/A86ebjdUJeAoYDPQA3gP+FTSKyHeAS4BDgX7A\nQODqmOO/AK4B7ktxjY6q2iHyujbZTiKyLfA4cAXQGXgf+EeCXS8ClqTTTUTOAkYBu0Vex0S2BXwa\nOdezGZwr3edwJ/A10B34EfBnEdk5Fz0zkDueccBEoEvknI9FroGI7AL8X0SmHsA64K5UujoZoqr+\nKtELeAjYgn2h1wAXAv2BrcBo4HNgOXA2sA8wGVgJ3B5zjtHAW8DtwCpgOnBomus+ARyXpG0rMDDy\n/ijgQ+CriCxjYvZrA/wNWBaR6T3McFwLbAbWR3S6LYPPoUvkup0j648Av4tpPwRYlOC4a4D747YF\nn1/zDO/BmcCbMettI/djcMy2AcA0YCQwP8353gZ+FrP+U+C/Se79mDTnSvo5AO2ADcAOMe0PAL/P\nRc9M5Y60Dcb+KNrFbHsNOCvy/jrgbzFtAyOytkulr7/Sv7yHXUJU9ceYITxarSf4x5jmfYEdgJOB\nW4HLsZ7WLsD3ReSguH1nAV2BMcATyR5BRaQlcCDwcgYi1gGnqmonzHj/XERGRdpOAzoCvTGDexaw\nXlWvAN4Azono9KsMrnMQZohWRtZ3Bj6KaZ8M9EigU6onk3kiMl9E7hORrin22yX2Wqq6Dvssd43Z\n53bgMsxIpSOR7LtkcFym5wo+h8HAZlWdFdP+Uey1RGSliOwfWU2mZ7B/SrlF5GkRuTjmXJ+p6tok\n146/1meYwa7n9nKyxw12+XKNqm5U1ZexnuojqrpMVRdiBnGPmH2XqOqtqrpFVR8FPsEMbCIOAj6K\n+7ElRFVfU9WPI++nAH8HDo40b8T+IAap8aGqrok5PCM3j4j0Bu4ALojZ3B7r1Qesjiw7xIuY4JRL\ngb2BvsBekWMeTiFCu5jzx16vfUS+4wFR1X/FH5iERLK3z/DYTM4FplN7Gsq9hpjPSFU7q+rbkdVk\negb7p5RbVY9R1RuS7BtcO9i/XYL22Gs5OeIGu3xZHPN+fYL1djHrX8QdOw/oleS8R2L+07SIyH6R\ngaUlIrIK60UHvdWHgBeBv4vIF5EBqxYxh6fNKiYi3YCXgDtVNdZvXIf13gM6RZaxfwiQ4E9BVdeq\n6gequlVVlwDnAkeISDsR6RszEBkYr/hrBddbIyLtgBuA85LIf3nM+QIfbSLZ6xIdnwGpPoekcmd4\nrvj9s5E7k3N1StHu5Igb7NKTj3SJ28Wt96OhEQ/4LvBchud9BBsc7K2qVdhAUjMAVd2sqr9V1V2A\n/YGjgZ9EjsvEWHfGjPVTqvr7uOaPgWEx67sDi2NcJgHZfHbNVPVzjQ5EBgbn48j5A7naAdtHtg/C\nPss3RGQRNmhXHYna6Kuq18Wc7xcpZJ+aRKZ08qf6HGYCLURkhwyvlUrPbOX+GBgoIu3j9o89V+y1\ntgdaRWR2GoEb7NKzGPvhZEts77K7iPxKRFqKyEnAjiQwyiIyAGitqp9keI32wEpV3Sgi+wI/JGJk\nRKRGRIaKSHOs57QJG0BNq5OIdMR652+q6uUJdnkQOF1EhkQM+/8D7o85vrmItAFaAM1FpHVEDkRk\nXxHZUUSaRXzXtwHj49w1sTwJ7Coi34uccwwwSVVnAlMwH/3ukdfPIrrtDixIcr4HgQvEQie3w1w9\nY2NkbxG5TnOgpYi0EZFkv8Okn0PEpfUE8FsRaSsiI4BjsCefbPVMK3cskWMmAWMi8n8P8/k/Htnl\nYSzKZETkj+Ea4PFM3HBOGko96lnpL+BYzIWxEvuR9McMX7OYfeYDB8WsPwRcHnk/GniTaJTIDODw\nJNc6lzRRG5FrB1EiJwBzMf/j05jxezDSdnLkWnXAl8AtgczAcMyPvgK4JcE1TsMiOeowY78mco3e\nMfucHznvV8C9QMuYtqsix8e+royR67PIuRdiRqd7Gp0Pw6Jr1gGvAn2T7FcDfJ7BPf0DFt2zHLg+\nrm1sAtl/kuJcqT6Hzpghrovcp5Pjjl0DHJCpnmnkfg64NGa9HzA+cq4GkUnAKdj3ui4iY1Wpf2tN\n4SWRDzchInIfNni1RFWHxmz/JfAL7Mf9rKpekvQkTkERkdHA6ap6YAb7PouFBL5QcMEcx8k76Vwi\n92Oxp98gIodgvcLdVHVX4I+JDnTKktrIy3GcEJLSYKvqG9ijeiw/x4LzN0X2WVog2ZzMUDIcfFPV\nG1U1k1hix3HKkFwGHQcBB4nIO2I5I/bOt1BO5qjqA6p6UPo9HccJOy3S75LwmM6qOlxE9gEexaae\nOo7jOAUkF4O9AAsnQlUniGVG66qqy2N3EhEvx+44jpMDqppwpnAuLpGnsJwWiKXEbBVvrGMuWvav\nMWPGlFwG18v1cr3C9SqkXqlI2cMWkXFY7oiuYnmAr8RSWt4nIlOwfBI/SXGKsmfu3LmlFqEguF7h\nwvUKF6XSK6XBVtVkCdF/XABZHMdxnBRU/NT00aNHl1qEguB6hQvXK1yUSq+UMx0bdWIRLdS5Hcdx\nmioiguZx0LFJUVtbW2oRCoLrFS5cr3BRKr0q3mA7juOEBXeJOKFl4UKorgYpdgljxykg7hJxmiTb\nbQfPZlQ7x3GaBhVvsN3HFi7i9Zo2rTRy5JtKuV9NBfdhO04WrF9vy88/L60cjlNM3IfthJLPP4d+\n/eC002Ds2FJL4zj5w33YTpNjyRJbbtpUWjkcp5hUvMF2H1u4CPRqaga7qd+vpob7sB0nC9asgWbN\nYPPmUkviOMXDfdhOKLnvPrjoIth/f3j66VJL4zj5w33YTpNj7Vqoqmo6LhHHyYSKN9juYwsXgV6x\nBrspPMg19fvV1HAftuNkQV2dGey1a82XvXFjqSVynMLjPmwnlJx/vsViT50KM2fCBx/AHnuUWirH\naTzuw3aaHGvXQufOsHq1rX/wQWnlcZxiUPEG231s4SLWh92pE3z1lW1furR0MuWDpn6/mhpl6cMW\nkftEZHGk4G582/+KyFYR6VI48RwnMYEPO8gpsmaNpVl9/fXSyuU4hSRdD/t+YGT8RhHpA3wbmFcI\noYpJTU1NqUUoCE1dryBKJCBwjUycWHyZ8kFTv19NjVLpldJgq+obwMoETTcBFxdEIsdJw8qV9urc\nObptzRpbrl1bGpkcpxhk7cMWkVHAAlWdXAB5io772MJFbW0tv/iFDTLG9rADg11XVxq5GktTvl9N\nkVLp1SKbnUWkLXA55g75ZnNeJXKcNASJnzp1ii6DwUfvYTtNmawMNrA90B/4SKyQXm9goojsq6pL\n4ncePXo0/fv3B6Cqqophw4Z94/sJ/qF8vTDrwbZykSef6xdcAFDLp58C1NCjB8yebe3Ll5devlzW\ng23lIo+vp14PtuXjfLW1tYyNJHUP7GUy0k6cEZH+wNOqOjRB2xxgL1VdkaDNJ844BWHAAJg7F+bP\nhz594PDD4T//sbZjj4V//auk4jlOo8h54oyIjAPeBgaLyHwR+WncLqG3yME/XVOjKeu1ItI9CFwi\nQ4fCfvvZ+3XrSiNXY2nK96spUiq9UrpEVPWUNO0D8yuO46Rmy5ZoCF/r1rZs1w623x7efdd92E7T\nxnOJOKFi5UroEpmqtWULNG8Ot95qLpKbb4bdd4dJk0oqouM0Cs8l4jQZVsbMCmgW+fZ27w5jxsAd\nd2TWw966Fc4805aOEyYq3mC7jy1cvPxybYNt225r/uxRozLzYX/6KfzlLzZoWS401fvleuWXijfY\nTrioq7M0qn/+c3Rb1662bNs2M4P9zju2nD49//I5TiGpeIMdG1fZlGiqevXtW8OAAXD22bZ+0kmw\n0072vl27zFwiX3xhy08+KYyMudBU75frlV+ynTjjOCUlPofIo49G37dqZQORmzZBy5bJz7Funfm/\nVybKkuM4ZUzF97DdxxYufv/72m/ir+MRsV52OrfI2rXQo0c0/0g50FTvl+uVXyreYDvhYetWC9+b\nPTv5Ppn4sdetKz+D7TiZ4HHYTmhYvdqiQWbPhoFJpmxtvz28+CLssEPy85x6Kixfbtn+xo0rjKyO\nkyseh+00Cdasgerq5MYaMu9h9+zpPWwnfFS8wXYfW3hYvRpatKhNuU8mkSKBwQ6muJcDTfF+geuV\nbyreYDvh4cILbSp6KjLpYZfjoKPjZELFG2yPEy1f3n03+n7dOnjuOVi6tCblMZn2sMvNYDeF+5UI\n1yu/VLzBdsqTrVth+PBorPRHH9kynTHOtIfdq5fHYTvho+INtvvYypPly225ebMt584NWmpTHpdp\nHHb//nbuZctylzGfhP1+JcP1yi8Vb7Cd8mTxYltu3GjL9ettWV2d+ri2bVP3wlVh6VLL8Lfzzp5P\nxAkXFW+w3cdWngQGe8MGW65fD2ecAXPm1KQ8Ll0Pe/lyM+rbbAODB8PMmfmRt7GE/X4lw/XKLxVv\nsJ3yJFEPu0OHaJWZZKTrYX/xBWy3nb3v2TN6HccJAxVvsN3HVp4ERjfWYG+zTXq90kWJxBrsHj1g\nyZLGy5oPwn6/kuF65Ze0BltE7hORxSIyJWbbjSIyXUQ+EpEnRCRJOh7HyY3AUMe6RLbZJv1xrVtH\nj03E4sVmqMH82N7DdsJEJj3s+4GRcdteAnZR1d2BmcBl+RasWLiPrTzZtMmW8T3sdHq1apXaYK9a\nFU3PWk497LDfr2S4XvklrcFW1TeAlXHbXlbVoCLeu0DvAsjmVDCBwc62h92yZWqDHZtPu1s3ixhx\nnLCQDx/2/wDP5eE8JcF9bOVJsh52Or1atYoem4hVqyxLH1jmv3LJJxL2+5UM1yu/NMpgi8gVwEZV\nfSRP8jgOkNiH3bZt+uPSuURie9idOsFXXzVOTscpJjmXCBOR0cCRwGHJ9hk9ejT9+/cHoKqqimHD\nhn3j+wn+oXy9MOvBtnKRJ9v1WbNsfeNGW58/v5ZZs+D73099fKtWNWzcmLx91aoaqqpsffNmWL26\nBlV47bXS6htsK5fP39dTrwfb8nG+2tpaxo4dC/CNvUxGRgUMRKQ/8LSqDo2sjwT+BBysqgkn93oB\nA6cxXHwx3HgjPPSQFRw4/HC49FJbpuLZZ+Guu2wZ8Mc/Wq97993hl7+EsWPhoIOsrW1b82O3b28V\n2du1K5hKjpMRjSpgICLjgLeBHUVkvoj8D3A70B54WUQ+FJG78ipxEQn+6ZoaYderMT7seJfItdfC\nFVfA0UfDnDkwaFC0rVMnWLTI3pcyr0jY71cyXK/8ktYloqqnJNh8XwFkcZxvCIxusFy2DLp0SR83\nnchgV1fbYGPsekDHjjBrlr1fvhz69Wuc3I5TSHL2YTcVYn1STYmw67Vpk02C2bABtmyBefNgwAAY\nMqQm5XEtWzaMEqmutiRP3bvDmWfWb4s12KXsYYf9fiXD9covFT813SlPNm0yf/LGjbBwIXTtCm3a\npD8uUQ87MOBDhsA119Rv69oVPvjA3gcpXR2nXKl4g+0+tvJk0yYbCNywwXrXweB5Lj7slSttIPLe\nexvuf/LJcP/99t592PnH9covFe8SccqTjRvNYG/caNPHu3fP7LhWCSbOrFwJRx0Fffs23H/UKFt2\n7+49bKf8ySisL6cTe1if0wiOP94y6x1yCAwcCBMnwj33pD9u9mw44ghbBrRrZ4OV7dsnPub00y1a\nBOCmmxovu+M0hkaF9TlOKQhcIhs3mqti220zOy7eJbJxY9Qfnox774UddyyvoryOk4iKN9juYytP\nAiO7YYNNbOnWzbZn4sOOdYmsXGm5QyRhfyVKhw6lNdhhv1/JcL3yS8UbbKc8ifVhZ9PDjs/WF5s7\nJBWlNtiOkwkVb7A9TrQ8iXWJxOawTqdXvEskLAY77PcrGa5Xfql4g+2UJ7FhfevWZZ7jI5FLJAwG\n23EyoeINtvvYypPYiTPr1kWLF6TTK5jpGAQohcVgh/1+JcP1yi8Vb7Cd8iTwYQc97ExyYYMNLnbq\nZIYawmOwHScTKt5gu4+tPFm/3gxv0MMODHYmevXoEU0SFRaDHfb7lQzXK79UvMF2yo8tWywypFev\n7HvYYAb7ySett52pwQ5CCDdvzl1uxyk0FW+w3cdWfrRoYbUWu3dv2MPORK+ePeHtt+398uWZGWyR\naBGDUhDm+5UK1yu/VLzBdsqXNm1y62FXV0crzkyZkpnBhtK7RRwnHZ5LxCk7glmJU6fCccdZlZhN\nm9LPVgxYtMjcKQHjx0MmLschQ+Dxx2HnnbMW2XHyhucScULDunXR961bW1XzbbbJ3FiD9bCfeQbO\nPtvWs+1hey/bKVcq3mC7j628WLzYYqmfecYmwaxcWd8dkqleRx0F110HP/85bL99Ztdu1w5GjrQq\nNMUmrPcrHa5XfklpsEXkPhFZLCJTYrZ1EZGXRWSmiLwkIlWFF9OpFJYtg6FDzeC2bm1RG9n4r2Pp\n3NkKFyRLqxrPlCnR2o+eG9spR1L6sEXkQKAOeFBVh0a23QAsU9UbROQSoLOqXprgWPdhO1nz+utW\n4fyNN6x33aWLGfDJkwt/bRHrXe+yC9xwA4wYUfhrOk48OfuwVfUNYGXc5mOBByLvHwCOa7SEjhPh\n66+j09CDnnFVkZ7hrr/ecmN36RKdKek45UQuPuweqhqZR8ZioEce5Sk67mMrL9avjxbbbdmyYXsh\n9brkEjjxRHOlFNtgh/V+pcP1yi+NqumoqioiSf0eo0ePpn+kempVVRXDhg37ZkpnoHCp1wPKRZ58\nrU+aNKms5Ml0/euva2jTJvb+1LB5c3HvV+fOMGFCLX37+v3y31fi9Xzer9raWsaOHQvwjb1MRto4\nbBHpDzwd48OeAdSo6pciUg2MV9WdEhznPmwnax54AF591ZZgfuV994V33y2eDFdeCc2bw5gxxbum\n4wTkOw7738BpkfenAU/lKpjjxBPrEgkodn6PUrhEHCcT0oX1jQPeBnYUkfki8lPgeuDbIjITODSy\nHlriH92aCmHVK3bQEWDwYDjwwOh6MfRyH3b+cL3yS0oftqqekqTp8ALI4jh8/XX9HvYnnxRfBu9h\nO+WK5xJxyooxY8xvfdVVpZMhNhbccYqN5xJxQkO8S6QUZNPDnjq1sLI4TiwVb7Ddx1ZexLtE4ikn\nH/acOTYLM7bob66E9X6lw/XKLxVvsJ3yYv368PSwX3jBlsmKHqh6BRsnv1S8wQ4C2ZsaYdUrUVhf\nLMXQq21b6zVv2JB6v6VLbZksHetvfwtdu2Z2zbDer3S4XvmlUTMdHSdffPCBlQNbuhS6dSutLCKW\nT2TJEujTJ/l+gaGONdiPPQZbt8L3vw/vv2+lzhwnX1R8D9t9bKVHFc48E8aOhQULoHfv5PsWS68j\nj4RHHkm9T+AKiTXYJ50EP/iBvQ+CpDKpExmm+5UNrld+qXiD7ZSWujq46CL46CMr7ZXOYBeLESNg\nxozU+wSGOjDIH39sy/bt4aGHrK5k+/bw+eeFk9OpLCreYLuPrbT89a/w/POW1nTmTPMdp0qnWiy9\nMhl4jHeJ7LqrLdu3h1//Gk49FfbZBxYuTH+9sNyvbHG98kvFG2yntDz9NPzhD3DwwdajHT48u/qN\nhSIbg/2970XdH2Blztavtz+h6mp7cnCcfFDxBtt9bKVlyhTYYw/oEcmqftllqfcvll6ZGOxY3/SK\nFbbcYQcz3lVVVpOyV6/kBnvlSngqkjotLPcrW1yv/FLxBtspHYsXW5xyr14WyrdyJRxeJllqMu1h\nf/e79n7yZDPWM2faehBL3qMHfPll/eM2bTK9b7oJjj8+v3I7TZuKN9juYysdU6bYTMHABZJJKbBy\n82HffTfsuSd8+KEZZxG47TZ7gekUH9p3/vnm5/7iC1tftSoc9ysXXK/84nHYTskIDHY50qGDTZPf\ntClxqbKtW6Mx4716WRx54Nb55S+j+3XsCF99Vf/YuXNtUk6kaAnTp8O3vlUQNZwmRsX3sN3HVny2\nbLGe6H//axXKs6FYeomYW2P9+oZtCxZYVZoOHcyV06OH/fn0SFDdtFOnhj3sIFzwww/Nf79wYXnf\nr8bgeuWXijfYTvGZNcuWzz0HO+5YWllSsc021suO55FH4NprYbvtbL1LF+slJzLY8T3sFStsBuXw\n4ba+996Zhf05DrjBdh9bI8g1S92UKbZcu9YG6rKhmPerTZvEPeyePW3Zvbstu3SxzyKTHvabb5qx\nrq629X79zGD79zBceBy2Eyp+9rNoDzNbxo+HZpFvXjnMakxGmzaJe9jBH1UwUSZI8JRJD3vGDNht\nN4vRnjjR/N/ew3YypeINtvvYcuO556LZ6rLlpZfMf/3VV1HDnSnFvF/JDHZdHRxzDNx4o6136WLL\nRImiOnas38OeMwf697colD33jBps/x6Gi9D5sEXkMhH5WESmiMgjItI6n4I55cnixeaDDULxtmzJ\n7vj162H+fDNWHTvmX758ksyHXVdn0S0tIjFW7drZMuhxx9K+vZ1j40ZbnzsXBgyItsdOrJkyxT7X\nIJbbceLJyWCLSH/gDGBPVR0KNAdOzp9YxcN9bNlx663w+9/b4FmHDma8s2HmTNh++6ixy5Zy8GHX\n1ZnuAYFrKFEe72bNrP3ii+2pYt486Ns32l5dHfVhf/ihbQt8/E0B/33ll1zjsFcDm4C2IrIFaAt8\nkTepnLJl+XLzvbZqZT3KqVOjA2iZMGEC7L574eTLJ6lcIrH++6FD6+cSiadfP/uj69jRZj3Gfl5d\nu9oEnRtvhMcft22LF+dHfqfpkVMPW1VXAH8CPgcWAqtU9T/5FKxYuI8tNevXw49+FJ3ksWqVGezq\najjxRMu2lymrV8Mtt1iu6VwpBx/2mjXm6siUfv3MbTJxoh0b+LzBXCA77AAXX1zLu+/Cfvtl/9RS\nzvjvK7/k1MMWke2BXwP9ga+Af4rIj1T14dj9Ro8eTf/+/QGoqqpi2LBh3zxKBAqXej2gXOTJ1/qk\niIVt7Pk6daqJJPKv5YwzYOVKa2/WrJaddoJrr61hwQKYNSv9+R55BPr2reEHPwjH/VqzBr7+umF7\nXR3Mm1dLbW1m5xs9Gvr0qeX3v4cePWpo1qx++z33wKGHTuLss2HXXWuYOrXx8l9zTS277grHH1+4\nzyeT9YBS/x7K9fdVU1NDbW0tY8eOBfjGXiZFVbN+AT8A/hqz/mPgzrh91CkO69apdumiun59/s/9\n+OOqbdqoHnywre+9tyqo7rOPrY8YoVpbq/rAA6qvvZb6XEceqfrUU/mXsVCcdprqffc13P6d76g+\n/3x259q61T63zp0bts2bZ22ffqr6z3+qHndcTuLWA1R//vPGn8cpPhHbmdD25holMgMYLiLbiIgA\nhwPTcjyX0whWrLDwuhUr4Mkn83/+OXMshC2YTh1k1Dv3XFvv39/cJQ8/bC6SVDHF8+bZ/mGhTRvz\nVweVZALq6rJziYC5Po47LnFR3iAWvXdvG5BsbIWawJ++YEHjzuOUH7n6sD8CHgTeByZHNt+TL6GK\nSfyjW5hQNQPw8su2PmdOtC1fen32Gey/v/mf16wxgz1uHPzkJ9beooVVV3npJTjgALjgguSyzptn\n/tzGUMz71bYtjBnTMFwvPkokU554oqHxB4skGT++ljZtLOQv9j7mQpCb+7//hU8/bdy5GkuYf1+p\nKJVeOcdhq+oNqrqLqg5V1dNUNceJyk6uzJtnyyCqINeJLKmYM8fC8AYOtBwgq1fXT4P6m9/At79t\n7y+80IxEIpYtg+bNM0uhWi5UVSVOsZrtoGOAiEXXpGLbbW0m5apV2Z8/YM4cGDbMEkvNnp37eZzy\no+JnOgaDAGFkcuTZJjDcsdEF+dBrzRqLbBgwwIz2e++ZEYuNod5+e/j5z+39vvta7y6RsXn1VTjw\nwEaLVNT7FRvNEUsuLpF0BHqJwJAhVpQ4V+bMsXvWu3c053apCPPvKxWl0qviDXaYCXp/8+aZcXnk\nkYbVTRrDySfbn0D//maYX301mvAolmHDbNmypbkPEk38uPtuOOGE/MlWDDp3jr7fvDn6vhAGO5Yj\njoAXX7Sp+5dckjrGOxGxBtv92E2LijfYYfaxBT3ZefPMZQFw++22zIdeb70Fr79uxqm6Gh59NJoa\nNZYBA6JGZbfdrOe/ejXccIP5u5cts576qac2WqSi3q/YHvbjj5seW7ZYbHZQAixfxOo1ciS88AK8\n+659hv/JcoZDYLC32670BjvMv69UlEovrzgTYmIN9rnn2gzCqVNzP9+zz1ollWOOMYO7aROMGGFt\nhxxiyyAnRjJ2392M89q11jsE2Hln65nnOh29VAQ97F697Gnj2982w922bfZJq7Jh+HCbwv/++7b+\nwAPRcYJMmDULRo2yP5d//aswMjqloeJ72GH2sa1aZSWq1q83o/KnP8Hbb5sBz0Wvf//bsvCBJWjq\n0yea5Gnvvc09kijKIZaDDzbXyVtvRQvqTpuWfd7rZBTzfgWlwYJQvNmzc48QSUesXi1aWO+4ttYi\ncF580f5IM2HhQhv4HTy4PHrYYf59pcJ92E7WrFoVDZPr1cuS5e+yS+6RAXPmRAepAoMdS7du1ltO\nxc47m+/T5ja4AAAgAElEQVT1P/+BO++0rHz//jc880xuMpWSIUPgV7+y6BawaJyxYzM3no2hutry\nrhxwgP1BfPJJZscdeKA93fTrVx6Djk5+qXiDHVYf25Qp9ugbFLHt1cuWXbrYYGQuesUb7Niscpki\nYj7vdetsoHLiRHOxBEavsRQ7DvvWW81wgw2uXn11dNJQPonXq7ra/pC3287GJzLpKb/+usXNX3qp\nfd5du5q/Pb6mZDEJ6+8rHaGLw3ZKy957W7mpUaNsPba+YDBxIhu2bDFXSqoedqYEfu58GelSc/vt\n8Npr9plv2ACnnVb4awYZ/bbbzgzv8uXpj7noIlv+7//aUsRkfuedwsjoFJ+QDQPln7D62Pbc0x5/\njz0WWreO/sA7dzaDna1eCxdGj920yQx2MOCYLbnWesyEUtyvrl3hoIMsvHHjxsKUNYvX61vfgptv\ntvu67bYWoZKOzp3hrLNs/4Dhwy1+/ogj8itvpoT195UO92E7WfH11xa5IGLvg+T5gUskW+bMsYHB\n7t1t4HHs2NwNUyENdinp2xfuuis6EFtITjwR3njDBj4z7WF/+mnD1ADV1U0rXWulU/EGO6w+thUr\n6k/sCAh6ydnqNXmy+Uq32w6ef97ieINQvmxJF/rXGMJ6v9IRr5dI9Amna1frYS9YkHpi1NKlDYtJ\nJDP2s2aZy2vt2ui2++5LHGffGCrlfhWLijfYYWXFisRTp3PtYd98sz1Ob7ed9ex+/OP0eS+S8eST\n8NRTuR3rNKRbNzPGNTXRAdB4Nm+2gd74GZhduyYe03jjDfsDaN8+mh3w9NPh2mvzKrqTZyreYIfR\nx7Z4scUDJypiGww6Bnq9917iuoSxLF1q59x/f5v4Mm1a/UKx2fLd70YHQ/NNGO9XJqTSq18/K967\nzTYWOZJoqvrq1RbWGe+u6dIlcQ87qB8JlrckKKac7TT4dFTi/SokFW+ww8j3v2/LRL7UwCUSsN9+\ncNNNyc+1dav5rdeutdl7551nYWGFMrhO9gQpV4Oom0Sx1StXJs6EmKyHPX06DBpk71evjiYQmz8/\nNxlfe63pjl2UExVvsMPoY1u2zGJuExEbhx30mlIlxP/wQ/tRv/eerVdVWVX0RP7xciCM9ysTUunV\ns6cZ1enTYa+96veOA1atsh52PMl82LNnw/nn2/uFC202Zb9+do1cqKmBhx5quL0S71chqfiwvrDx\n9df2Yxs+PHF7bA876DXNndtwv7/8BcaPh0MPhaOOgn32KYi4Th5o1sz+iBcutHC/zz5ruM+qVYl7\n2J06WZrczZujuVw2bbJe+umnm7vso4/gwQetOPJrryU/VzICN0q6tAVO46n4HnbYfGxz59rofpDn\nIp6OHW3w6YADapgwwXpniXpYb75pmfQmTLAMe2EhbPcrU9LpFSSb6tUrcRm2ZEa2eXMz2i1bRivc\nz5tn52nVypZB0Ylly2DHHTOfBh9QV2fLOXPggw/qt1Xq/SoUFW+ww8Znn0VTqSaiWTP74a5YYb2l\nE09MbLADA/DQQ9llgnNKw9lnww9/aAZ20aKG7al6xUHyqiCT46xZljYA7HxBGbHjj7fJQdnWlAzi\nvN9/31w2xci1UqlUvMEOk49t2TILl0sXwbHzzvDQQ7V8/rkNOiYy2F9+aT2sQYPC1cMO0/3KhnR6\nXXGFFTrOtocN0dzdgUtk9uyowQ5SGpx9tg029+1rec+D8Y9MCIpcBAOWsbMyK/V+FYqcDbaIVInI\nYyIyXUSmiUgSr6qTL845x3zPu++eer8RIyw51OrVNltx/fqGk1kWLYLRoy0bnRMecjHYQeKo4Li5\nc6NPacFEmyCJGMBjj1kBhUxZtMiOb906uu4Uhsb0sG8FnlPVIcBuQI7jy6UlTD62YJbbnnum3m/E\nCFiwoIavvrIfcWxCqNGj4R//MH/jddfZwFOYCNP9yoZM9crFYAf3PqjGvmxZNN9I27a2POooW/7o\nR9aWTeGDuXPtqS/I7hg7G7PS71e+yclgi0gn4EBVvQ9AVTer6ld5lcypx5YtNpo/blz6iI7997cw\nvZUrbRCyRw/r9cyebdVLTj7ZekSBb9MJD1VVljFw3br621MZ7KlTLVxvyhT7Hq1cWT9sUzWaV33v\nveHppy0tbiYsWGDZAQcMiJ4jiE5y8k+uPewBwFIRuV9EPhCRv4hI23wKVizC4mO76y6L+Dj55PTl\nqaqqQKSW+fMtQmDQIBtY+sUvLKfztGnwxBPFkTvfhOV+ZUumeomYG+OII+pPoEllsHfZBXbayY6b\nNq2hwY5nt93MwGeSE+a112xZVWUGu08f+L//i7ZX+v3KN7nGYbcA9gTOVdUJInILcClwZexOo0eP\npn///gBUVVUxbNiwbx4lAoVLvR5QLvIkW//rX2s58USAzPZv1WoSAB071rDjjvDoo7W8+SZ8+mkN\nvXrZ/tOmlY9+Te1+Zbs+adKkjPevroa33qrl8svhgQesfc6c2ojLI/nxQ4bAiy/WsHIlzJ5di0ji\n87dtCz161PLAA3DGGcnPpwp3313Dd78LPXvW0rkzXHRRDRddBK+8UlsvH3qpP99S3q9067W1tYwd\nOxbgG3uZFFXN+gX0BObErI8AnonbR53G8cYbqps22fvBg1WnTcv82F13VQ1uwSOP2Puf/CT/MjrF\np65O9e9/V91//+i26mrVzz9Pfdxjj6kefbRq796q8+al3vfHP1a9557k7Vu22HcKVF96qX7bgAGq\nM2emPr+TnIjtTGh7c3KJqOqXwHwRGRzZdDjg85zyzIEHWj1EMB90fOrMTDnsMFued15+5HJKS7t2\ncPTRNqbx9dc2kzEoJ5aKnXYy11iy1LyxHH104qnmAcFA5oABDeP4d97Z/OBO/mlMlMgvgYdF5CMs\nSuS6/IhUXOIftUvNU0/B3/8Of/6zrX/yiSVm2rQpca6IZMyYUfvN++7d4dlnzX8ddsrtfuWLbPVq\n184M8IQJVnji66/Tj21sv719n1q3bpiGNZ5jj4V3300+CWbxYlvecUfDtptugt/9zv5Q/H7ll5xz\niajqR4BnoMgzV1xhA0MBH31k4Vh9+mRX6eSAA+ob6COPzJ+MTnlwwAFw//32vZg9O/3+QVWidevS\nf5fatLFe+Esv2fT2ww6r/4eweLElfEr0vRo8GC68EMaMgV//OmN1nAyo+ORPwSBAuRBblCB4hH31\nVaspmA21tTV5latcKLf7lS9y0WvwYIseGjw48/zlr76aPj96QO/eltsc4K23LFw0YPFie3JLxogR\nVrnI71d+qfip6eVGEMPaoYP9SD79FF5+2fN9OA3p1cuexrp1y/yYQw7J/GmrZUsbNznnnIaV1xcv\ntvj+ZFRV5Vb5yElNxRvscvKxbdhgP4QZM8wN0qWLPbo+80x04DBTykmvfOJ6RenVy5aperqN4YUX\nbBbj0UfDnXfa9zMgncHu3Dmal70pUiq9Kt5glxMzZtjA0I47RmchXn215fsIphI7TkBgsLPpYWdD\np06WIGzkSPs+BmlYIXODDXDrrZbO12k8ovku4hacWEQLde6myh13WHHUf/yj1JI4YWDzZnNb3HJL\n4UM2L7nEIkv+3/+z9aOOsgx/xxyTeH9VM/Z1dTaAudNO9avZrFsXzWPi1EdEUNWEw8Lewy4BGzbA\nzJn1t23cCL/5DZxxRmlkcsJHixb2vTnnnMJfq7o6mjZ16VJ47rnUPWwR62UHx8yYEZ1KP3OmJYpK\nVGvSSU3FG+xS+KIeftjcHrfdFo1zfecdi6c9/PD8XMN9h+EiV71atozmuS4kVVU2OQeicwQCl0wy\nDj8crrqqllatrCf+9tu2fcECy9H+hz8UTt5C4z7sCiKImT3vvGh1jzfesLhWxylHYg326tVw0UUW\n9peKSy6xsmQ9eljo4Zw55hZ5+WULQ3z++fzL+fvfWxRMfO/9+usTV5sPGxVvsEsRTzljRvR98CWa\nMAH23Td/1/D413BR7nrFGux586wUWDqs0EYNzZubgZ4zx9x+119vlZBmz85vOTFVGweaNMmqwMdy\n2WV23XzhcdgVxIwZ8MgjNogTlFWaMMErlzvlS1UVfBXJeD93bjT3dSZs2RI12EG005o1Ntcgn9Vp\nFiywa511FkyeHN0exD4EtSvDTMUb7GL6oiZPtiK6n30Gxx1nA4wLFlgve+NGq4uXL9zXGy7KXa/4\nHnamBnubbWoZMCBqsIP6onvtZWXKPvssfzLOmWNhsbvtZsUaAtasqb/MB6HLJeJkx9at9og4aJCN\nuG+zjfkA582zfCF77JFdrhDHKSZVVfZdbdbMwvVSRYjEMm6cza5s2dLGa6qr4ZVX4NBDLRFV8ISZ\nD4I/kqFD6xvsoGRZotJqYaNietjvvZfYX1YsX1Tgq54925LigCV0WrAgWhMvn5S7TzRXXK/S0LGj\nLVXNrZEuM2DAqFE1dOxoHZSqKitXFuTL6dMnM4O9dKkVn043rSMw2AMH2p/DE09YaOH48VYHddGi\n9OfIFPdhF4jzzoMLLrBBjvffL50cM2daFMiCBXDaabatd28z1nPn5tcd4jj5JtZAp0vNmoyddjKX\nSDCLN1OD/Ze/wJlnwpIlqfebPt2iUZo1g1NOgR/+0Nw4Z59t7sc2bcIf+93kDfZtt8HNN9v7RCko\ni+WLOvxwmywQW4SgTx/44AO48cbsBnEyodx9orniepWeZ5/NfN9YvYKak4E7pVevzELtgtzbs2al\n3i924P7uu+vnPjnhBKtt+dFHmcmdDo/DLjCDBmWWM7gQLFli//rxyd579YKTTrL3hx5afLkcJ1uO\nOsoG9nLhoousuEGrVrbevbu5O9KxZImN78RGecTOFH7+efje98zlMWSIbevQwWaAnn++dYa6dYPh\nw63nHeaMGU06l8jXX9vj2zPPmLGeOBHuu6/4crz0Elx3HST7U/a8Ck4YWLTIKt0E/uzGMmMGjBpl\ng4+x/Pe/VmEpyAF/2GEWRXXQQXDttTYW1by5RZgMGAAHHwyvv25GOZXbZN48cz1mUiKtlFRsLpHf\n/MYSsI8caf+8s2fbLK1iY4nck7e7sXbCQHV1/ow1JDewI0eaEQ5YvNiq6wQ97CAL4Acf2PKzz2yc\n6tJLU1+vXz970k7nCy9nmqzBfvVVKyIa9KgHDrR/4U6dLMtZQKF9UV9+aZNkTjmloJdpQJh8otng\neoWLVHp17mzZ/DZurL89mPL+4IPmvli2DL71ragPO/BpT5xoPfHFi20W4wUXpJene/f8GOxQ+rBF\npLmIfCgiZVcj+YknLJdBkCu4T59oWz6D9Zcvt3y/q1ZZ6aUtWyxA/7//tdcPfwinn27JnhzHidKs\nmYUIBhn9AoLq71dcAY89Zr+t4cPNbz13Llx1lbXPmGG/q02bLM47E/JlsEtFYyfOnAdMAzrkQZa8\n8vHH5h8LaN7cBjhGj7a2wYNte2PiKadMsS9Su3ZWbLRFC+u9d+pkvYSWLa3tyisbpUpOlHtcb664\nXuEinV7dutnvMjbz34YNFjs9dap1vFTN0PbrZ1EggYF/5RVzcY4Ykbk83btHe+iNIXRx2CLSGzgS\n+CtQVnP0tm41Y7rrrvW3b7ut/SPH56KOZe3a6Jck1flPP92+KN/5jn2x3nnHHu/uuccGF6dOhQ8/\ntEobQbVqx3Hqk6jHu2KFTa4ZNQr+/neLEBGxcaBly+ypNhiPOvBAy3SZKQcdBH/7m71/6y17Og4V\nqprTC/gnsAdwMPB0gnYtBcuWqV58ser22yduv/121bPPjq6PHz9eVVXffVf15z9XvegiVVB98EHV\nL79UHT9edevW6P5r16qOHKk6cKBqXV3B1Gg0gV5NDdcrXKTT6+STVXv0sN/cuHG2rVcv1fnz7X3P\nntamqrpxo+qnn0aPBdW99spOnnXrVFu1st/0CSfYObZsye4cqoW9XxHbmdDu5uQSEZGjgSWq+qGI\n1CTbb/To0fSPTOGrqqpi2LBh3zxKBE77bNeHDavhn/+ECy6o5amn4LDD6rd/8kkNN9wAJ5xQS21t\nw+MHDKjh2Wfh2WdrWbUq6i+78cZaHnsMoIZzzoG//KWWp5+Gf/6zhuOOg7POquX55+G222oYMgR+\n9rNaJkzIXv5irU+aNKms5MnXekC5yOP3K/V6QLL2bt1qWLwYdt21lksvhXffrWHlSpgypZZZs6BL\nlxq+/DLx8RdeCEcfnb18rVvDM8/URmY91jBpEqxenZ1++bxftbW1jB07FuAbe5mUZJY81Qu4DpgP\nzAEWAWuBB7UIPewbb1Tt2NH+GefMadh+zjmq55+vumlT4uOnT1ft31912DA7x+bNqosX27/8ddep\n/vSnqgsXqnbqZP/u77yjethhqt262eukk1SXLi2Iao5TcZx0kv0O33vPlqDarFn0qXb//aM97Hwx\naJDZgT33VN1vP9Xrr0+9/+rV9ioWpOhh5+wS0ahhLqpL5OijVR99VPWgg1RfeaV+2yuvqLZtq/rW\nW8mP37rVjDGoDhigeuSRqjffrHrssfX3O+MM1XvusfdffWVfojvvzK8ujlPpzJxpnaItW6IGu0OH\naPvVV6t26ZLfa44YEbUVt99u10xlM/r0MXtTLIphsP+dYHtBlOnVy3rWo0er/vWv0e11ddEbvnFj\n6nO89prqCy+obtig2rr1eAXzX6diy5b6vuxyp1J9omHF9VJ99VX7/fbqFd22dWv+f3fHH686ZIhq\nv36qEybYNWMNcqzI48ZZ+/Dh9c8RKh92nEvlNeC1xp4nE1atsqoXffua7zk2cczMmZbc5amn0sdk\nBlNewSbXvPsunHpq6mOaNdkpRo5THgS/y222iW4rRI74Cy+0mZNHHx3NPRJM1tmwwfJ3f/GFhRwG\nE96Csa5SEwoz9PbbFh43bZqlaGzWrH7JIrB8BEOGWOXxbDjppBr++EcYNiy/MpeaYHCjqeF6hYts\n9Gre3JaxWfYKwbe+Zct+/WyexAsvREMLg2RUP/uZ1YYcOtSKBsenZa2rqylJEqlQGOwDDrB4y9df\nt/dQv2QRWJ6BQYNKI5/jOPmj0Pl+gl57kBelTx8reABRg/388zZTea+9LH93UNoMLJfJMcdYbvti\nU/YGO8gz0KyZTWj5zndsPd5gL1wYfazJhvjwo6aC6xUuXC+jWbPiJGj797/NNQJmuIN6j0uXWu76\nXXeFxx83N2u8wf74Y4Badtut8HLGU9YGWxVOPNGmeg8ZYh9aMoO9aBH07FkaOR3HyQ/duxfnOscc\nEy1V1qZN1A2zdKn5rvfbz57o99nHZFq2LJo0LhKCzapVljuomJS1wX71VXj6aZsG/tOfwjXXRP1c\nnTs3NNix1VwyxX2H4cL1ChfZ6nXKKcUfT2rdur7B3nZbuOsuq8J+8MFm0KurbR34ZkJdKRJJlXXV\n9MmT4Ze/hD/9qWFbfA/7yy9zM9iO45QPN91U/GvGG+xu3awqTuykwyFDLDvgoEGWI2jECHPBfvFF\nce1OWfawly83g/zJJ8nTkvbsaVm31q2zx5LFi3NzibjvMFy4XuEiDHq1bGk2ZMuWqMGOZ6edrMiv\nqnUUJ0+upXfv6GBlsSiowf71r3M7bto0C9n7xz+SG+x27WCPPeDFF63ycrdunhXPcZzsEYn2slMZ\n7BkzrOxg8+bWA995Z8vKWUwKarDvvDO344L0p6tWRWMmE3HZZVZk85NPci8M6r7DcOF6hYuw6JXO\nYA8ZYj3sVassCKKmpoY99oCHH7bCJcWioD7szZstnvG7302/76hR9oG1amWFc3/5Swutadcu+TFH\nHmlukGuusQB3x3GcXGjTxnrPyQz2wIFW7earr8xgg82InDnTJvYddlhx5CxoD3vUqMzcItOnWzLx\nF1+0Edhx4+D44+HMM9Mfe8opdvwVV+QmYxh8bLngeoUL16u0tG4NY8eaAe7bt2F7jx4W2rd0qY2v\n1dbW0q0bHHusFS7JhqOOgjFjcpOzoAb7iSdsNlC6QPinn4YTTrAqMbNn2xz/VK6QWM4+GyZMyG3S\njOM4DpjBvvxye5/oqb5FC4vHnjEj2sMO9s3UYK9bB+ecA889B7/9bW5yihZoQryIqKoybBjce69N\n8UzELbfA1VfDM89Ep507juMUk6FDbQBx7lzLMZKIffe1CTVLllhABJgXYK+94Kyz0l/j7rutgxlw\n221w7rkNE1yJCKqaMO1VwcP6unSBvfdOXCNx9my49lqbs+/G2nGcUhFMyEv1pL777nDHHfUTzLVv\nn3kPe/z46Ps//hEuucS8CtlQcIN99922jBcsmHb+299ayEypCIuPLVtcr3DhepWWwG0bGO5EXHaZ\nLXfYIapXNgb7/ffN6F99Nfzv/9osyt13z84HXnCDPWgQXHAB/POf9bdPnGgTZGIfERzHcUpBbHKn\nZAwcaMvYEOJMDfbmzTBvnhntK6+0bb/6lS07dDC/diYU3IcNlixlr72sUMDee8PatbDbbjZS+pOf\nFOTyjuM4GSNi0SHz5qXeT7W+z/muu8x78Oc/pz5u4UKzgYsW1d/+5JPwve/BaadZlIrJktyHXZRc\nIsOG2ePExRdb5YZ162D//d1YO45THlx9NWQyxyd+gDDTHvbChYlzjgTx25lWtCpaLpGTTzan+9/+\nBi+9lPssyHwTFh9btrhe4cL1Ki1XXlm/dGA6Yn3YQS7tVCxaBL16NdzesSO88grcf79lJ01HzgZb\nRPqIyHgR+VhEporIr1Ltv+uuZqynTrWp5EG1B8dxnLCy7bY2oSYdyXrYYNW0vv1tePbZ9OfJ2Yct\nIj2Bnqo6SUTaAxOB41R1eqRdC+UfdxzHKQdmzbLAirfeskHJH/3IeszxXHWV+b+vvjrxeV55BX73\nO/NCFCQOW1W/VNVJkfd1wHQgQaffcRynaRK4OQ44wCLfXn3VcvPHk67ASq9eDQckE5EXH7aI9Af2\nAN7Nx/mKSVh8bNnieoUL1ytcBHq1bRvdNmGCLd96q/6+dXXmEknkww6orjZXcfygZjyNjhKJuEMe\nA86L9LS/YfTo0fSPlG2oqqpi2LBh36RbDBQu9XpAuciTr/VJkcJz5SKP36/U636/wrUee78GDoTq\n6lquvho6darhs8+i+2/YUMPIkdCyZS1HHQXQ8Hy1tbXcf//YyCfVn1Q0Kg5bRFoCzwDPq+otcW3u\nw3Ycp2JQtanrM2ZEo+BOPjmadySoF5kMEfjFL+CuuwrgwxYRAe4FpsUba8dxnEpDxOpAfvZZdNuU\nKTbnBFIba7Aiv3fckXqfxviwDwBOBQ4RkQ8jr5GNOF9JiH90ayq4XuHC9QoXyfQaMsRKHE6daiUM\np02zKei77JL+nP37F9CHrapvUqZFfB3HcUrBwIGwYgUceqi5QJo3hx/8wF75oCi5RBzHcSqFgQPN\nvfHxx1byMDYdayaUNB+24zhOJTFqlFWi2Xnn7I11OireYFeajy3suF7hohL1+uMfYfHiwly34g22\n4zhOPmnePHFdyHzgPmzHcZwywn3YjuM4TYCKN9iV6GMLM65XuHC98kvFG2zHcZyw4D5sx3GcMsJ9\n2I7jOE2AijfY7mMLF65XuHC98kvFG2zHcZyw4D5sx3GcMsJ92I7jOE2AijfY7mMLF65XuHC98kvF\nG2zHcZyw4D5sx3GcMsJ92I7jOE2AxhThHSkiM0TkUxG5JJ9CFRP3sYUL1ytcuF75JSeDLSLNgTuA\nkcDOwCkiMiSfghWLSZMmlVqEguB6hQvXK1yUSq9ce9j7ArNUda6qbgL+DozKn1jFY9WqVaUWoSC4\nXuHC9QoXpdIrV4O9HTA/Zn1BZJvjOI5TIHI12E0m/GPu3LmlFqEguF7hwvUKF6XSK6ewPhEZDlyl\nqiMj65cBW1X1DzH7NBmj7jiOU0yShfXlarBbAJ8AhwELgfeAU1R1emOEdBzHcZLTIpeDVHWziJwL\nvAg0B+51Y+04jlNYCjbT0XEcx8kvPtPRcRwnJLjBdhynoIjIlaWWoRCUQi832PgXKmy4XqHjjFIL\nUCCKrpf7sAERma+qfUotR75xvcJFmPUSkTUpmrdR1ZwCHEpNuekVyg8xF9J98EUTJM+4XuGiqeoF\nrAT2VdUv4xtEZH6C/cNCWelVMQabMvvg84jrFS6aql4PAX2BBnoB44osSz4pK70qyWCX1QefR5qy\nXv1omno1ufulqlekaLu4mLLkk3LTy33YjuPkBRERYD8sEZwCXwDvNdXSUyKyk6rOKOo1m+hn2QAR\naQVsVtWtkfVDgT2Bj1X1+ZIK1whEZDdVnVxqOQqBiPQFVqvqKhEZAOwNTFfVqSUWrdGIyD5Ab2AL\nMLPYP/x8IyJHAHcBs7DsnWD6DQJ+oaovlkq2QlGKQeJKMtiTgYNVdaWIXAQcDzwHHAxMVNVLSypg\njojIFuAzLCf5OFWdVmKR8oKIXAqcBWwEbgQuBN4ChgP3qeqfSihezojIwcCfgFXAXsDbQBWwCfix\nqobSjy0iM4CRqjo3bvsA4HlV3akkgjUSEbk9RfNoVe1QNGGoLIM9VVV3jbyfCIxQ1fWRRFYfqurQ\n0kqYGyLyIfBj4IfA94F1wCPA3+N/PGFCRKZhBq0dMBcYoKpLRaQd9pi9SynlyxURmQR8O6LLAOBm\nVT1ORL4NXKSqR5RYxJwQkU+BnSMFTWK3twKmqeoOpZGscUSiei4ENlA/rbQAf1LVrsWUp5IGHdeI\nyFBVnQIsxUKo1gMtsQ8/tERcBJcDl4vIfsDJwJsi8rmq7l9a6XJmc+QPdSP2J7QCQFXXisjW0orW\nKJqp6tLI+8+xgVVU9WURubV0YjWa+4AJIjKOqEukD/ZdvK9kUjWe94GpqvpWfIOIXFVsYSqph70b\nNkI/GfunHAG8DgwFblLVh0soXs6IyIequkeC7c2Ag1S1tvhSNZ7IDx+sh70a+4N9EjgUaKWqp5ZK\ntsYgIvcDW4HxwLHAAlW9IPLkMDGsrgMAEdkZKxXYK7LpC+DfYXbTiUgX4GtVXVdqWaCCDDZ8k8f7\nCFOy73UAAAJYSURBVGAw9nQxH3hRVUNbeE5EfhTWP5tUiEgbrHe2SFVfFJFTgf2BGcDdqrqhpALm\nSMRFcAYwBPgI88dvEZFtgB5hdmM5haeiDLbjOIVBRKqAS4HjgB7YU+wS4Cng+rB2ispNr4pJ/iQi\nHUTktyLysYisFpFlIvKuiIwutWyNocL0eqeJ6hX6+wU8is3irAG6qGoX4BAsGubREsrVWMpKr4rp\nYYvIvzEf6H+Ak4D2WCjcbzA/4uUlFC9nXK9w0YT1mqmqg7NtK3fKTa9KMtiTVXW3mPX3VXXvyODc\ndFXdsYTi5YzrFS6asF4vAy8DD6jq4si2nsBpWBjj4aWUL1fKTa+KcYkAa0XkQAARGQUsBwhmPoYY\n1ytcNFW9fgBsC7wmIitFZCVQC3TF5geElfLSS1Ur4gXsDkzAfE9vATtGtncDflVq+Vwv1yvMekV0\nGAIcDnSI2z6y1LI1Fb0qxiWSChH5H1UNc3B/QlyvcBFmvUTkV8A5wHRgD+A8VX0q0pZwrkAYKDe9\n3GAT7kofqXC9wkWY9RKRqcBwVa0Tkf7A48BDqnpLyA12WelVMVPTRWRKiuYeRRMkz7he4aKp6oV1\n/uoAVHVuJMnV4yLSj3CnfigrvSrGYAPdgZFYTGU8bxdZlnzieoWLpqrXEhEZpqqTACI90qOBe4Hd\nUh9a1pSVXpVksJ8F2qvqh/ENIvJaCeTJF65XuGiqev0ESxH7Daq6SUROA+4pjUh5oaz0ch+24zhO\nSKikOGzHcZxQ4wbbcRwnJLjBdhzHCQlusB3HcUKCG2zHcZyQ8P8BRBMNDQAaONAAAAAASUVORK5C\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xac1ecf8c>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#   First before the Great Recession:\n",
      "stat2( V['Y'][:recession], bond['Y'][:recession] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  FIRST variable:\n",
        "count    720.000000\n",
        "mean      16.372415\n",
        "std        3.738999\n",
        "min        7.212152\n",
        "25%       14.536636\n",
        "50%       16.976360\n",
        "75%       19.204933\n",
        "max       22.257864\n",
        "Name: Y, dtype: float64"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " ::  SECOND variable:\n",
        "count    645.000000\n",
        "mean       6.496310\n",
        "std        2.693331\n",
        "min        2.290000\n",
        "25%        4.260000\n",
        "50%        6.110000\n",
        "75%        7.900000\n",
        "max       15.320000\n",
        "Name: Y, dtype: float64"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " ::  CORRELATION\n",
        "0.900602164492\n",
        "\n",
        "-------------------------Summary of Regression Analysis-------------------------\n",
        "\n",
        "Formula: Y ~ <x> + <intercept>\n",
        "\n",
        "Number of Observations:         645\n",
        "Number of Degrees of Freedom:   2\n",
        "\n",
        "R-squared:         0.8111\n",
        "Adj R-squared:     0.8108\n",
        "\n",
        "Rmse:              1.2711\n",
        "\n",
        "F-stat (1, 643):  2760.6338, p-value:     0.0000\n",
        "\n",
        "Degrees of Freedom: model 1, resid 643\n",
        "\n",
        "-----------------------Summary of Estimated Coefficients------------------------\n",
        "      Variable       Coef    Std Err     t-stat    p-value    CI 2.5%   CI 97.5%\n",
        "--------------------------------------------------------------------------------\n",
        "             x     0.9771     0.0186      52.54     0.0000     0.9407     1.0136\n",
        "     intercept    10.8727     0.1308      83.14     0.0000    10.6164    11.1290\n",
        "---------------------------------End of Summary---------------------------------\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For 55 years before the Great Recession, there is nice relationship between bond rates and velocity ($R^2 = 0.80$). A 100 basis point change in yield translated to 0.97 velocity points. \n",
      "\n",
      "$ V = 0.97 B + 10.96 $\n",
      "\n",
      "The bond rate B can be approximated as follows (before QE):\n",
      "\n",
      "$ B \\approx (PQ/M) - 10.72 $\n",
      "\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Bond rates in terms of money supply and nominal GDP"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we can see how the ratio of nominal GDP to money supply influences bond rates.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Recall that P*Q is our variable G for nominal GDP.\n",
      "bondmodel = todf((G / M) - 10.7242)\n",
      "\n",
      "#  We plot the DEVIATIONS for our bond rate model:\n",
      "#  (actual - model) through today.\n",
      "bonddev = todf( bond - bondmodel )\n",
      "\n",
      "plotfred( bonddev )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAEYCAYAAAB82RxTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/0jrE56YCAWUAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xac21930c>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Let's plot the model itself, i.e. bond rate approximations:\n",
      "plotfred( bondmodel )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEYCAYAAABMVQ1yAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLk94g+6cc3nCG3TnnMsT3qA751ye+H9jP46fHqLTBwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad2b19ac>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Deviations before the Great Recession\n",
      "bonddev[:recession].describe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "                Y\n",
        "count  645.000000\n",
        "mean    -0.000021\n",
        "std      1.271619\n",
        "min     -3.132862\n",
        "25%     -0.897922\n",
        "50%     -0.209418\n",
        "75%      0.805700\n",
        "max      3.839600"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**The bond rate model seems to work $\\pm$ 128 basis points per one standard deviation for almost six decades until the Great Recession wacks it out-of-order.** It was a very broad-stroke model anyways, not fine enough for trading bonds -- but adequate to show a definite change in interest rate regime.\n",
      "\n",
      "(The constant 10.7242 was adjusted until we got *zero mean* for bonddev before the Great Recession.)\n",
      "\n",
      "2015-03-23: The \"normal\" bond rate model estimates a 10-year Treasury rate 900 basis points *below* the current yield of +2%, i.e. a negative yield around -7%. This of course is due to the upward explosion in the monetary base M in a dampened inflation environment. (Notice the negative rates during the 1950's as projected by the the model.)\n",
      "\n",
      "*Next we look at the relationship since the Great Recession:*"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#   Since the Great Recession:\n",
      "stat2( V['Y'][recession:], bond['Y'][recession:] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ::  FIRST variable:\n",
        "count    97.000000\n",
        "mean      8.673375\n",
        "std       4.627410\n",
        "min       4.304107\n",
        "25%       5.765366\n",
        "50%       6.857381\n",
        "75%       8.650080\n",
        "max      17.317375\n",
        "Name: Y, dtype: float64\n",
        "\n",
        " ::  SECOND variable:\n",
        "count    100.000000\n",
        "mean       2.988000\n",
        "std        0.913625\n",
        "min        1.530000\n",
        "25%        2.200000\n",
        "50%        2.840000\n",
        "75%        3.682500\n",
        "max        5.100000\n",
        "Name: Y, dtype: float64"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " ::  CORRELATION\n",
        "0.790552012441\n",
        "\n",
        "-------------------------Summary of Regression Analysis-------------------------\n",
        "\n",
        "Formula: Y ~ <x> + <intercept>\n",
        "\n",
        "Number of Observations:         97\n",
        "Number of Degrees of Freedom:   2\n",
        "\n",
        "R-squared:         0.6250\n",
        "Adj R-squared:     0.6210\n",
        "\n",
        "Rmse:              2.8487\n",
        "\n",
        "F-stat (1, 95):   158.3147, p-value:     0.0000\n",
        "\n",
        "Degrees of Freedom: model 1, resid 95\n",
        "\n",
        "-----------------------Summary of Estimated Coefficients------------------------\n",
        "      Variable       Coef    Std Err     t-stat    p-value    CI 2.5%   CI 97.5%\n",
        "--------------------------------------------------------------------------------\n",
        "             x     4.0192     0.3194      12.58     0.0000     3.3931     4.6453\n",
        "     intercept    -3.4604     1.0068      -3.44     0.0009    -5.4337    -1.4871\n",
        "---------------------------------End of Summary---------------------------------\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2015-03-23: Since the Great Recession, the relationship between bond rates and velocity has deteriorated ($R^2 = 0.61$). A 100 basis point change in yield now translates to 4.00 velocity points -- which is about four times \"normal.\" But the relationship in this period is not very significant, and **also QE obviously distorted market yields for bonds**. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Alternative explanation for low inflation: the *liquidity trap*"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Conventionally, the expansion of the money supply will generate inflation as more money is chasing after the same amount of goods available. **During a liquidity trap, however, increases in money supply are fully absorbed by excess demand for money (liquidity); investors hoard the increased money instead of spending it because the opportunity cost of holding cash \u2014 the forgone earnings from interest \u2014 is zero when the nominal interest rate is zero.** *Even worse, if the increased money supply is through LSAPs on long-term debts (as is the case under QE), investors are prompted to further shift their portfolio holdings from interest-bearing assets to cash.*\n",
      "\n",
      "On one hand, if the increase in money demand is proportional to the increase in money supply, inflation remains stable. On the other hand, if money demand increases more than proportionally to the change in money supply due to the downward pressure LSAPs exert on the interest rate, the price level must fall to absorb the difference between the supply and demand of money. That is, *the increase in aggregate demand for real money balances then has to be accommodated by an overall decrease in the price level for any given money supply in the goods market. Therefore, the lower the interest rate through LSAPs, the lower the price level (due to the disproportionately higher money demand). The Fed's policy to pay positive interest rates on reserves can only reinforce the problem by making cash more attractive as a store of value.*\n",
      "\n",
      "Yi Wen showed in 2013 that large-scale asset purchases by the Fed could reduce the real interest rate by 2 percentage points, but would have an insignificant effect on aggregate employment and fixed capital investment, would reduce the aggregate price level significantly, and would put severe downward pressure on the inflation rate \u2014 thanks to firms' portfolio adjustments between cash and financial assets in a liquidity trap.\n",
      "\n",
      "### Risks of Declining Inflation\n",
      "\n",
      "Not only high inflation, but low inflation can be bad for the economy. Low inflation makes cash more attractive to investors as a store of value, everything else being equal. This makes the liquidity trap easier to occur and gives the Fed less room to reduce the real interest rate as desired during a recession. Furthermore, quantitative easing through LSAPs can reinforce the liquidity trap by further reducing the long-term interest rate. In other words, *more monetary injections during a liquidity trap can only reinforce the liquidity trap by keeping the inflation rate low* (or the real return to money high).\n",
      "\n",
      "Therefore, the correct monetary policy during a liquidity trap is not to further increase money supply or reduce the interest rate but to *raise inflation expectations by raising the nominal interest rate.* If LSAP policies are reversed and the money supply decreases as the Fed sells assets in the marketplace, the nominal interest rate will increase and investors will be more likely to shift their portfolios away from cash toward interest-bearing assets. If demand for money decreases more than proportional to the decrease in money supply due to upward pressure on the interest rate, inflation will increase. In other words, **only when financial assets become more attractive than cash can the aggregate price level increase.**\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Notes*\n",
      "\n",
      "- [Keynesians have pointed to a major example of ineffectiveness of Fed's open market operations on managing the money supply during the Great Recession. Short-term interest rates went as low as they could go in nominal terms, but no more monetary stimulus could occur. This zero bound problem has been called the liquidity trap or *\"pushing on a string\"* (the pusher being the central bank and the string being the real economy).]"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Flow has obviously shifted to equities (record highs), \n",
      "#  but let's look at the classic risk-free financial asset:\n",
      "#  90-day T-bills\n",
      "bills = getfred( m4bills )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plotfred( bills[recession:] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWYAAAEYCAYAAABvDlynAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/H/N8NAM0feu4wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xac9b86ec>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  T-bill stats since 2010:\n",
      "stats(bills['2010':])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "               Y\n",
        "count  64.000000\n",
        "mean    0.070156\n",
        "std     0.046067\n",
        "min     0.010000\n",
        "25%     0.030000\n",
        "50%     0.060000\n",
        "75%     0.100000\n",
        "max     0.160000\n",
        "\n",
        " ::  Index on min:\n",
        "Y   2011-09-01\n",
        "dtype: datetime64[ns]\n",
        "\n",
        " ::  Index on max:\n",
        "Y   2010-04-01\n",
        "dtype: datetime64[ns]\n",
        "\n",
        " ::  Head:\n",
        "               Y\n",
        "T               \n",
        "2010-01-01  0.06\n",
        "2010-02-01  0.11\n",
        "2010-03-01  0.15\n",
        "2010-04-01  0.16\n",
        "2010-05-01  0.16\n",
        "2010-06-01  0.12\n",
        "2010-07-01  0.16\n",
        "\n",
        " ::  Tail:\n",
        "               Y\n",
        "T               \n",
        "2014-10-01  0.02\n",
        "2014-11-01  0.02\n",
        "2014-12-01  0.03\n",
        "2015-01-01  0.03\n",
        "2015-02-01  0.02\n",
        "2015-03-01  0.03\n",
        "2015-04-01  0.02"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " ::  Correlation matrix:\n",
        "   Y\n",
        "Y  1\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2015-03-22: The annual average return for Treasury bills since 2010 is a mere 7 basis points. (So \\$100,000 only yields \\$70 annually -- and, any reasonable fees would certainly wipe out interest income!)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Concluding remarks"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Of course, this type of *policy-reinforced liquidity trap would take place only if the economy is in a deep recession in the first place. If the economy is not in a recession, monetary injections should lead to more inflation instead of less inflation because a lower interest rate generally reduces people's incentive to save and increases their incentive to spend.*\n",
      "\n",
      "The irony is that expansionary monetary policy is often called for only when the economy is in a recession. This policy dilemma makes economics a dismal science. One way to escape from it is to use expansionary fiscal policy (as suggested by the economist John Maynard Keynes). However, with the already high level of government debt across industrial countries, it takes courage and vision to implement bold expansionary fiscal policies."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Addendum"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- **On 29 October 2014, the Federal Reserve announced it would stop its sprawling six-year-old stimulus program, known as quantitative easing (a.k.a. QE or LSAP).** The Fed\u2019s balance sheet was under \\$1 trillion when it started buying bonds through QE -- currently its balance sheet is over \\$4 trillion. To get back to \"normal,\" the Fed will need find an orderly way to sell lots of bonds (without market panic). "
     ]
    }
   ],
   "metadata": {}
  }
 ]
}