Produce graphs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute Welfares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the various scenarios\n",
    "N = 100\n",
    "experiments = [\n",
    "    dict(name='ces', param='xi', range=(0.2,1.0,N)),\n",
    "    dict(name='exponential', param='alpha', range=(1,10,N)),\n",
    "    dict(name='translog', param='alpha', range=(1,10,N))\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def compute_case(expm):\n",
    "    '''Evaluates welfare for the planner and the competitive equilibrium for various values of a specified parameter.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    expm: dict\n",
    "        Description of the experiment to perform. Contains several fields:\n",
    "        - name: name of the experiment, the corresponding model file is expected to be model_*name*.yaml\n",
    "        - param: name of the parameter to change\n",
    "        - range: set of parameter values (min value, max value, N values)\n",
    "    Returns\n",
    "    -------\n",
    "    df: pandas.DataFrame\n",
    "        Each line contains:\n",
    "        - parameter value\n",
    "        - welfare for the planner optimum\n",
    "        - welfare for the competitive equilibrium\n",
    "    '''\n",
    "        \n",
    "    \n",
    "    import pandas\n",
    "    from dolo import yaml_import\n",
    "    from dolo.algos.dtcscc.steady_state import find_deterministic_equilibrium\n",
    "    from dolo.algos.dtcscc.perturbations_higher_order import approximate_controls\n",
    "    from numpy import exp, array, linspace, column_stack\n",
    "\n",
    "    \n",
    "    case = expm['name']\n",
    "    param = expm['param']\n",
    "    range = expm['range']\n",
    "    \n",
    "    # create parameter range\n",
    "    parm_vec = linspace(*range)\n",
    "        \n",
    "    # import model and get discount rate\n",
    "    model = yaml_import('model_{}.yaml'.format(case))\n",
    "    beta = model.get_calibration('beta')\n",
    "    \n",
    "    values_ce = []\n",
    "    values_po = []\n",
    "    \n",
    "    # solve all calibrations\n",
    "    for i in parm_vec:\n",
    "        \n",
    "        # Set calibrated parater value\n",
    "        pp = {param:i}\n",
    "        model.set_calibration(**pp)\n",
    "        \n",
    "        # Solve for the competitive equilibrium\n",
    "        model.set_calibration(po=0)\n",
    "        calib = find_deterministic_equilibrium(model)\n",
    "        dr_ce = approximate_controls(model, order=2, steady_state=calib, verbose=False)\n",
    "\n",
    "        # Solve for the social planner equilibrium\n",
    "        model.set_calibration(po=1)\n",
    "        calib = find_deterministic_equilibrium(model)\n",
    "        dr_po = approximate_controls(model, order=2, steady_state=calib, verbose=False)     \n",
    "        \n",
    "                    \n",
    "            \n",
    "        # Initial point at which to evaluate the welfare\n",
    "        eval_point = calib['states'].copy()\n",
    "        # Change initial value of N\n",
    "        eval_point[1]*=0.5 # to 50 % of its of its steady-state value\n",
    "#         eval_point[1]=1    # to 1\n",
    "\n",
    "        # Evalueate welfare\n",
    "        w_ce = dr_ce(eval_point)[1]\n",
    "        w_po = dr_po(eval_point)[1]\n",
    "        \n",
    "        # Convert to consumption equivalent\n",
    "        v_ce = exp((1-beta)*w_ce)\n",
    "        v_po = exp((1-beta)*w_po)\n",
    "        \n",
    "        # Add to list of values\n",
    "        values_ce.append(v_ce)\n",
    "        values_po.append(v_po)\n",
    "    \n",
    "   \n",
    "    # Construct dataframe\n",
    "    columns = [h.format(case) for h in ['{}_'+param, '{}_po', '{}_ce']]\n",
    "    df = pandas.DataFrame( column_stack([parm_vec, values_po, values_ce]), columns=columns)\n",
    "    \n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# parrallel evaluation (needs 3 workers)\n",
    "# from IPython.parallel import Client\n",
    "# rc = Client()\n",
    "# dviews = rc[:3]\n",
    "# all_welfares = dviews.map_sync(compute_case, experiments)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[33mwarning\u001b[0m: 32, 1 : Symbol e_Z has no calibrated value.\n",
      "\u001b[33mwarning\u001b[0m: 32, 1 : Symbol xi_theta has no calibrated value.\n",
      "\u001b[33mwarning\u001b[0m: 31, 1 : Symbol e_Z has no calibrated value.\n",
      "\u001b[31merror\u001b[0m: 1, 1  : Missing field: 'model_type'.\n",
      "Missing `model_type` field. Set to `dtcscc`\n"
     ]
    }
   ],
   "source": [
    "# serial evaluation\n",
    "all_welfares = [compute_case(exp) for exp in experiments]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ces_xi</th>\n",
       "      <th>ces_po</th>\n",
       "      <th>ces_ce</th>\n",
       "      <th>exponential_alpha</th>\n",
       "      <th>exponential_po</th>\n",
       "      <th>exponential_ce</th>\n",
       "      <th>translog_alpha</th>\n",
       "      <th>translog_po</th>\n",
       "      <th>translog_ce</th>\n",
       "      <th>ces_gain</th>\n",
       "      <th>exponential_gain</th>\n",
       "      <th>translog_gain</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.200000</td>\n",
       "      <td>1.164332</td>\n",
       "      <td>1.132897</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.690079</td>\n",
       "      <td>0.690052</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.772007</td>\n",
       "      <td>0.762135</td>\n",
       "      <td>2.774785</td>\n",
       "      <td>0.003981</td>\n",
       "      <td>1.295232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.208081</td>\n",
       "      <td>1.180358</td>\n",
       "      <td>1.152172</td>\n",
       "      <td>1.090909</td>\n",
       "      <td>0.701552</td>\n",
       "      <td>0.701526</td>\n",
       "      <td>1.090909</td>\n",
       "      <td>0.780831</td>\n",
       "      <td>0.771209</td>\n",
       "      <td>2.446277</td>\n",
       "      <td>0.003623</td>\n",
       "      <td>1.247621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.216162</td>\n",
       "      <td>1.196917</td>\n",
       "      <td>1.171797</td>\n",
       "      <td>1.181818</td>\n",
       "      <td>0.711795</td>\n",
       "      <td>0.711771</td>\n",
       "      <td>1.181818</td>\n",
       "      <td>0.788680</td>\n",
       "      <td>0.779288</td>\n",
       "      <td>2.143679</td>\n",
       "      <td>0.003320</td>\n",
       "      <td>1.205182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.224242</td>\n",
       "      <td>1.214013</td>\n",
       "      <td>1.191778</td>\n",
       "      <td>1.272727</td>\n",
       "      <td>0.721017</td>\n",
       "      <td>0.720995</td>\n",
       "      <td>1.272727</td>\n",
       "      <td>0.795723</td>\n",
       "      <td>0.786544</td>\n",
       "      <td>1.865649</td>\n",
       "      <td>0.003062</td>\n",
       "      <td>1.167024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.232323</td>\n",
       "      <td>1.231648</td>\n",
       "      <td>1.212122</td>\n",
       "      <td>1.363636</td>\n",
       "      <td>0.729379</td>\n",
       "      <td>0.729358</td>\n",
       "      <td>1.363636</td>\n",
       "      <td>0.802090</td>\n",
       "      <td>0.793108</td>\n",
       "      <td>1.610960</td>\n",
       "      <td>0.002839</td>\n",
       "      <td>1.132462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.240404</td>\n",
       "      <td>1.249828</td>\n",
       "      <td>1.232834</td>\n",
       "      <td>1.454545</td>\n",
       "      <td>0.737008</td>\n",
       "      <td>0.736989</td>\n",
       "      <td>1.454545</td>\n",
       "      <td>0.807883</td>\n",
       "      <td>0.799086</td>\n",
       "      <td>1.378487</td>\n",
       "      <td>0.002645</td>\n",
       "      <td>1.100954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.248485</td>\n",
       "      <td>1.268557</td>\n",
       "      <td>1.253921</td>\n",
       "      <td>1.545455</td>\n",
       "      <td>0.744007</td>\n",
       "      <td>0.743989</td>\n",
       "      <td>1.545455</td>\n",
       "      <td>0.813185</td>\n",
       "      <td>0.804560</td>\n",
       "      <td>1.167196</td>\n",
       "      <td>0.002474</td>\n",
       "      <td>1.072068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.256566</td>\n",
       "      <td>1.287840</td>\n",
       "      <td>1.275390</td>\n",
       "      <td>1.636364</td>\n",
       "      <td>0.750459</td>\n",
       "      <td>0.750441</td>\n",
       "      <td>1.636364</td>\n",
       "      <td>0.818062</td>\n",
       "      <td>0.809598</td>\n",
       "      <td>0.976134</td>\n",
       "      <td>0.002323</td>\n",
       "      <td>1.045454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.264646</td>\n",
       "      <td>1.307684</td>\n",
       "      <td>1.297248</td>\n",
       "      <td>1.727273</td>\n",
       "      <td>0.756432</td>\n",
       "      <td>0.756416</td>\n",
       "      <td>1.727273</td>\n",
       "      <td>0.822568</td>\n",
       "      <td>0.814256</td>\n",
       "      <td>0.804422</td>\n",
       "      <td>0.002188</td>\n",
       "      <td>1.020823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.272727</td>\n",
       "      <td>1.328095</td>\n",
       "      <td>1.319502</td>\n",
       "      <td>1.818182</td>\n",
       "      <td>0.761984</td>\n",
       "      <td>0.761968</td>\n",
       "      <td>1.818182</td>\n",
       "      <td>0.826748</td>\n",
       "      <td>0.818579</td>\n",
       "      <td>0.651247</td>\n",
       "      <td>0.002067</td>\n",
       "      <td>0.997938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.280808</td>\n",
       "      <td>1.349082</td>\n",
       "      <td>1.342159</td>\n",
       "      <td>1.909091</td>\n",
       "      <td>0.767162</td>\n",
       "      <td>0.767147</td>\n",
       "      <td>1.909091</td>\n",
       "      <td>0.830641</td>\n",
       "      <td>0.822607</td>\n",
       "      <td>0.515855</td>\n",
       "      <td>0.001958</td>\n",
       "      <td>0.976598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.288889</td>\n",
       "      <td>1.370652</td>\n",
       "      <td>1.365225</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.772007</td>\n",
       "      <td>0.771993</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.834277</td>\n",
       "      <td>0.826372</td>\n",
       "      <td>0.397548</td>\n",
       "      <td>0.001859</td>\n",
       "      <td>0.956634</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.296970</td>\n",
       "      <td>1.392815</td>\n",
       "      <td>1.388709</td>\n",
       "      <td>2.090909</td>\n",
       "      <td>0.776553</td>\n",
       "      <td>0.776540</td>\n",
       "      <td>2.090909</td>\n",
       "      <td>0.837684</td>\n",
       "      <td>0.829901</td>\n",
       "      <td>0.295676</td>\n",
       "      <td>0.001769</td>\n",
       "      <td>0.937901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.305051</td>\n",
       "      <td>1.415578</td>\n",
       "      <td>1.412617</td>\n",
       "      <td>2.181818</td>\n",
       "      <td>0.780831</td>\n",
       "      <td>0.780818</td>\n",
       "      <td>2.181818</td>\n",
       "      <td>0.840886</td>\n",
       "      <td>0.833218</td>\n",
       "      <td>0.209633</td>\n",
       "      <td>0.001687</td>\n",
       "      <td>0.920278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.313131</td>\n",
       "      <td>1.438953</td>\n",
       "      <td>1.436957</td>\n",
       "      <td>2.272727</td>\n",
       "      <td>0.784866</td>\n",
       "      <td>0.784853</td>\n",
       "      <td>2.272727</td>\n",
       "      <td>0.843902</td>\n",
       "      <td>0.836344</td>\n",
       "      <td>0.138855</td>\n",
       "      <td>0.001612</td>\n",
       "      <td>0.903655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.321212</td>\n",
       "      <td>1.462949</td>\n",
       "      <td>1.461738</td>\n",
       "      <td>2.363636</td>\n",
       "      <td>0.788680</td>\n",
       "      <td>0.788668</td>\n",
       "      <td>2.363636</td>\n",
       "      <td>0.846749</td>\n",
       "      <td>0.839297</td>\n",
       "      <td>0.082817</td>\n",
       "      <td>0.001543</td>\n",
       "      <td>0.887942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.329293</td>\n",
       "      <td>1.487576</td>\n",
       "      <td>1.486966</td>\n",
       "      <td>2.454545</td>\n",
       "      <td>0.792294</td>\n",
       "      <td>0.792282</td>\n",
       "      <td>2.454545</td>\n",
       "      <td>0.849444</td>\n",
       "      <td>0.842092</td>\n",
       "      <td>0.041026</td>\n",
       "      <td>0.001479</td>\n",
       "      <td>0.873056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.337374</td>\n",
       "      <td>1.512847</td>\n",
       "      <td>1.512650</td>\n",
       "      <td>2.545455</td>\n",
       "      <td>0.795723</td>\n",
       "      <td>0.795712</td>\n",
       "      <td>2.545455</td>\n",
       "      <td>0.851999</td>\n",
       "      <td>0.844743</td>\n",
       "      <td>0.013022</td>\n",
       "      <td>0.001420</td>\n",
       "      <td>0.858927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.345455</td>\n",
       "      <td>1.538774</td>\n",
       "      <td>1.538799</td>\n",
       "      <td>2.636364</td>\n",
       "      <td>0.798984</td>\n",
       "      <td>0.798973</td>\n",
       "      <td>2.636364</td>\n",
       "      <td>0.854425</td>\n",
       "      <td>0.847262</td>\n",
       "      <td>-0.001626</td>\n",
       "      <td>0.001365</td>\n",
       "      <td>0.845491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.353535</td>\n",
       "      <td>1.565367</td>\n",
       "      <td>1.565419</td>\n",
       "      <td>2.727273</td>\n",
       "      <td>0.802090</td>\n",
       "      <td>0.802079</td>\n",
       "      <td>2.727273</td>\n",
       "      <td>0.856735</td>\n",
       "      <td>0.849660</td>\n",
       "      <td>-0.003323</td>\n",
       "      <td>0.001314</td>\n",
       "      <td>0.832692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.361616</td>\n",
       "      <td>1.592640</td>\n",
       "      <td>1.592520</td>\n",
       "      <td>2.818182</td>\n",
       "      <td>0.805053</td>\n",
       "      <td>0.805043</td>\n",
       "      <td>2.818182</td>\n",
       "      <td>0.858935</td>\n",
       "      <td>0.851945</td>\n",
       "      <td>0.007552</td>\n",
       "      <td>0.001266</td>\n",
       "      <td>0.820482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.369697</td>\n",
       "      <td>1.620607</td>\n",
       "      <td>1.620111</td>\n",
       "      <td>2.909091</td>\n",
       "      <td>0.807883</td>\n",
       "      <td>0.807873</td>\n",
       "      <td>2.909091</td>\n",
       "      <td>0.861036</td>\n",
       "      <td>0.854128</td>\n",
       "      <td>0.030643</td>\n",
       "      <td>0.001222</td>\n",
       "      <td>0.808816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.377778</td>\n",
       "      <td>1.649281</td>\n",
       "      <td>1.648199</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.810591</td>\n",
       "      <td>0.810582</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.863044</td>\n",
       "      <td>0.856215</td>\n",
       "      <td>0.065614</td>\n",
       "      <td>0.001180</td>\n",
       "      <td>0.797654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.385859</td>\n",
       "      <td>1.678675</td>\n",
       "      <td>1.676795</td>\n",
       "      <td>3.090909</td>\n",
       "      <td>0.813185</td>\n",
       "      <td>0.813176</td>\n",
       "      <td>3.090909</td>\n",
       "      <td>0.864967</td>\n",
       "      <td>0.858213</td>\n",
       "      <td>0.112150</td>\n",
       "      <td>0.001141</td>\n",
       "      <td>0.786960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.393939</td>\n",
       "      <td>1.708805</td>\n",
       "      <td>1.705906</td>\n",
       "      <td>3.181818</td>\n",
       "      <td>0.815673</td>\n",
       "      <td>0.815664</td>\n",
       "      <td>3.181818</td>\n",
       "      <td>0.866809</td>\n",
       "      <td>0.860128</td>\n",
       "      <td>0.169955</td>\n",
       "      <td>0.001104</td>\n",
       "      <td>0.776703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.402020</td>\n",
       "      <td>1.739686</td>\n",
       "      <td>1.735543</td>\n",
       "      <td>3.272727</td>\n",
       "      <td>0.818062</td>\n",
       "      <td>0.818053</td>\n",
       "      <td>3.272727</td>\n",
       "      <td>0.868576</td>\n",
       "      <td>0.861966</td>\n",
       "      <td>0.238748</td>\n",
       "      <td>0.001069</td>\n",
       "      <td>0.766851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.410101</td>\n",
       "      <td>1.771334</td>\n",
       "      <td>1.765714</td>\n",
       "      <td>3.363636</td>\n",
       "      <td>0.820358</td>\n",
       "      <td>0.820350</td>\n",
       "      <td>3.363636</td>\n",
       "      <td>0.870274</td>\n",
       "      <td>0.863733</td>\n",
       "      <td>0.318267</td>\n",
       "      <td>0.001037</td>\n",
       "      <td>0.757381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.418182</td>\n",
       "      <td>1.803764</td>\n",
       "      <td>1.796430</td>\n",
       "      <td>3.454545</td>\n",
       "      <td>0.822568</td>\n",
       "      <td>0.822560</td>\n",
       "      <td>3.454545</td>\n",
       "      <td>0.871907</td>\n",
       "      <td>0.865432</td>\n",
       "      <td>0.408261</td>\n",
       "      <td>0.001006</td>\n",
       "      <td>0.748266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.426263</td>\n",
       "      <td>1.836994</td>\n",
       "      <td>1.827700</td>\n",
       "      <td>3.545455</td>\n",
       "      <td>0.824696</td>\n",
       "      <td>0.824688</td>\n",
       "      <td>3.545455</td>\n",
       "      <td>0.873479</td>\n",
       "      <td>0.867067</td>\n",
       "      <td>0.508497</td>\n",
       "      <td>0.000977</td>\n",
       "      <td>0.739485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.434343</td>\n",
       "      <td>1.871040</td>\n",
       "      <td>1.859534</td>\n",
       "      <td>3.636364</td>\n",
       "      <td>0.826748</td>\n",
       "      <td>0.826741</td>\n",
       "      <td>3.636364</td>\n",
       "      <td>0.874994</td>\n",
       "      <td>0.868644</td>\n",
       "      <td>0.618753</td>\n",
       "      <td>0.000949</td>\n",
       "      <td>0.731018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>0.765657</td>\n",
       "      <td>4.263043</td>\n",
       "      <td>3.801219</td>\n",
       "      <td>7.363636</td>\n",
       "      <td>0.875730</td>\n",
       "      <td>0.875727</td>\n",
       "      <td>7.363636</td>\n",
       "      <td>0.910890</td>\n",
       "      <td>0.906103</td>\n",
       "      <td>12.149377</td>\n",
       "      <td>0.000424</td>\n",
       "      <td>0.528298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>0.773737</td>\n",
       "      <td>4.355257</td>\n",
       "      <td>3.868598</td>\n",
       "      <td>7.454545</td>\n",
       "      <td>0.876454</td>\n",
       "      <td>0.876450</td>\n",
       "      <td>7.454545</td>\n",
       "      <td>0.911417</td>\n",
       "      <td>0.906655</td>\n",
       "      <td>12.579724</td>\n",
       "      <td>0.000418</td>\n",
       "      <td>0.525291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>0.781818</td>\n",
       "      <td>4.449683</td>\n",
       "      <td>3.937191</td>\n",
       "      <td>7.545455</td>\n",
       "      <td>0.877165</td>\n",
       "      <td>0.877162</td>\n",
       "      <td>7.545455</td>\n",
       "      <td>0.911935</td>\n",
       "      <td>0.907196</td>\n",
       "      <td>13.016681</td>\n",
       "      <td>0.000412</td>\n",
       "      <td>0.522336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>0.789899</td>\n",
       "      <td>4.546374</td>\n",
       "      <td>4.007019</td>\n",
       "      <td>7.636364</td>\n",
       "      <td>0.877864</td>\n",
       "      <td>0.877860</td>\n",
       "      <td>7.636364</td>\n",
       "      <td>0.912443</td>\n",
       "      <td>0.907728</td>\n",
       "      <td>13.460242</td>\n",
       "      <td>0.000407</td>\n",
       "      <td>0.519432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>0.797980</td>\n",
       "      <td>4.645385</td>\n",
       "      <td>4.078104</td>\n",
       "      <td>7.727273</td>\n",
       "      <td>0.878551</td>\n",
       "      <td>0.878547</td>\n",
       "      <td>7.727273</td>\n",
       "      <td>0.912943</td>\n",
       "      <td>0.908251</td>\n",
       "      <td>13.910398</td>\n",
       "      <td>0.000401</td>\n",
       "      <td>0.516577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>0.806061</td>\n",
       "      <td>4.746773</td>\n",
       "      <td>4.150469</td>\n",
       "      <td>7.818182</td>\n",
       "      <td>0.879226</td>\n",
       "      <td>0.879222</td>\n",
       "      <td>7.818182</td>\n",
       "      <td>0.913434</td>\n",
       "      <td>0.908765</td>\n",
       "      <td>14.367147</td>\n",
       "      <td>0.000396</td>\n",
       "      <td>0.513771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>0.814141</td>\n",
       "      <td>4.850597</td>\n",
       "      <td>4.224137</td>\n",
       "      <td>7.909091</td>\n",
       "      <td>0.879890</td>\n",
       "      <td>0.879886</td>\n",
       "      <td>7.909091</td>\n",
       "      <td>0.913917</td>\n",
       "      <td>0.909270</td>\n",
       "      <td>14.830484</td>\n",
       "      <td>0.000391</td>\n",
       "      <td>0.511011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>0.822222</td>\n",
       "      <td>4.956916</td>\n",
       "      <td>4.299132</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>0.880543</td>\n",
       "      <td>0.880539</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>0.914391</td>\n",
       "      <td>0.909767</td>\n",
       "      <td>15.300408</td>\n",
       "      <td>0.000385</td>\n",
       "      <td>0.508296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>0.830303</td>\n",
       "      <td>5.065792</td>\n",
       "      <td>4.375476</td>\n",
       "      <td>8.090909</td>\n",
       "      <td>0.881185</td>\n",
       "      <td>0.881181</td>\n",
       "      <td>8.090909</td>\n",
       "      <td>0.914858</td>\n",
       "      <td>0.910256</td>\n",
       "      <td>15.776919</td>\n",
       "      <td>0.000380</td>\n",
       "      <td>0.505625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>0.838384</td>\n",
       "      <td>5.177286</td>\n",
       "      <td>4.453195</td>\n",
       "      <td>8.181818</td>\n",
       "      <td>0.881817</td>\n",
       "      <td>0.881813</td>\n",
       "      <td>8.181818</td>\n",
       "      <td>0.915318</td>\n",
       "      <td>0.910737</td>\n",
       "      <td>16.260018</td>\n",
       "      <td>0.000376</td>\n",
       "      <td>0.502997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>0.846465</td>\n",
       "      <td>5.291464</td>\n",
       "      <td>4.532314</td>\n",
       "      <td>8.272727</td>\n",
       "      <td>0.882438</td>\n",
       "      <td>0.882435</td>\n",
       "      <td>8.272727</td>\n",
       "      <td>0.915769</td>\n",
       "      <td>0.911210</td>\n",
       "      <td>16.749709</td>\n",
       "      <td>0.000371</td>\n",
       "      <td>0.500411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>0.854545</td>\n",
       "      <td>5.408390</td>\n",
       "      <td>4.612857</td>\n",
       "      <td>8.363636</td>\n",
       "      <td>0.883050</td>\n",
       "      <td>0.883047</td>\n",
       "      <td>8.363636</td>\n",
       "      <td>0.916214</td>\n",
       "      <td>0.911675</td>\n",
       "      <td>17.245995</td>\n",
       "      <td>0.000366</td>\n",
       "      <td>0.497865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>0.862626</td>\n",
       "      <td>5.528134</td>\n",
       "      <td>4.694851</td>\n",
       "      <td>8.454545</td>\n",
       "      <td>0.883652</td>\n",
       "      <td>0.883649</td>\n",
       "      <td>8.454545</td>\n",
       "      <td>0.916652</td>\n",
       "      <td>0.912133</td>\n",
       "      <td>17.748882</td>\n",
       "      <td>0.000362</td>\n",
       "      <td>0.495359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>0.870707</td>\n",
       "      <td>5.650764</td>\n",
       "      <td>4.778320</td>\n",
       "      <td>8.545455</td>\n",
       "      <td>0.884245</td>\n",
       "      <td>0.884242</td>\n",
       "      <td>8.545455</td>\n",
       "      <td>0.917082</td>\n",
       "      <td>0.912584</td>\n",
       "      <td>18.258377</td>\n",
       "      <td>0.000357</td>\n",
       "      <td>0.492891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>0.878788</td>\n",
       "      <td>5.776352</td>\n",
       "      <td>4.863293</td>\n",
       "      <td>8.636364</td>\n",
       "      <td>0.884829</td>\n",
       "      <td>0.884826</td>\n",
       "      <td>8.636364</td>\n",
       "      <td>0.917506</td>\n",
       "      <td>0.913028</td>\n",
       "      <td>18.774489</td>\n",
       "      <td>0.000353</td>\n",
       "      <td>0.490461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>0.886869</td>\n",
       "      <td>5.904969</td>\n",
       "      <td>4.949796</td>\n",
       "      <td>8.727273</td>\n",
       "      <td>0.885404</td>\n",
       "      <td>0.885401</td>\n",
       "      <td>8.727273</td>\n",
       "      <td>0.917924</td>\n",
       "      <td>0.913466</td>\n",
       "      <td>19.297225</td>\n",
       "      <td>0.000349</td>\n",
       "      <td>0.488068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>0.894949</td>\n",
       "      <td>6.036692</td>\n",
       "      <td>5.037856</td>\n",
       "      <td>8.818182</td>\n",
       "      <td>0.885970</td>\n",
       "      <td>0.885967</td>\n",
       "      <td>8.818182</td>\n",
       "      <td>0.918335</td>\n",
       "      <td>0.913896</td>\n",
       "      <td>19.826598</td>\n",
       "      <td>0.000345</td>\n",
       "      <td>0.485710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>0.903030</td>\n",
       "      <td>6.171596</td>\n",
       "      <td>5.127502</td>\n",
       "      <td>8.909091</td>\n",
       "      <td>0.886528</td>\n",
       "      <td>0.886525</td>\n",
       "      <td>8.909091</td>\n",
       "      <td>0.918740</td>\n",
       "      <td>0.914320</td>\n",
       "      <td>20.362619</td>\n",
       "      <td>0.000341</td>\n",
       "      <td>0.483388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>0.911111</td>\n",
       "      <td>6.309760</td>\n",
       "      <td>5.218762</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>0.887078</td>\n",
       "      <td>0.887075</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>0.919139</td>\n",
       "      <td>0.914738</td>\n",
       "      <td>20.905301</td>\n",
       "      <td>0.000337</td>\n",
       "      <td>0.481099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>0.919192</td>\n",
       "      <td>6.451266</td>\n",
       "      <td>5.311666</td>\n",
       "      <td>9.090909</td>\n",
       "      <td>0.887620</td>\n",
       "      <td>0.887617</td>\n",
       "      <td>9.090909</td>\n",
       "      <td>0.919532</td>\n",
       "      <td>0.915150</td>\n",
       "      <td>21.454658</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>0.478843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>0.927273</td>\n",
       "      <td>6.596194</td>\n",
       "      <td>5.406242</td>\n",
       "      <td>9.181818</td>\n",
       "      <td>0.888153</td>\n",
       "      <td>0.888150</td>\n",
       "      <td>9.181818</td>\n",
       "      <td>0.919920</td>\n",
       "      <td>0.915556</td>\n",
       "      <td>22.010706</td>\n",
       "      <td>0.000329</td>\n",
       "      <td>0.476619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>0.935354</td>\n",
       "      <td>6.744631</td>\n",
       "      <td>5.502522</td>\n",
       "      <td>9.272727</td>\n",
       "      <td>0.888680</td>\n",
       "      <td>0.888677</td>\n",
       "      <td>9.272727</td>\n",
       "      <td>0.920301</td>\n",
       "      <td>0.915956</td>\n",
       "      <td>22.573461</td>\n",
       "      <td>0.000325</td>\n",
       "      <td>0.474427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>0.943434</td>\n",
       "      <td>6.896664</td>\n",
       "      <td>5.600535</td>\n",
       "      <td>9.363636</td>\n",
       "      <td>0.889198</td>\n",
       "      <td>0.889195</td>\n",
       "      <td>9.363636</td>\n",
       "      <td>0.920678</td>\n",
       "      <td>0.916350</td>\n",
       "      <td>23.142940</td>\n",
       "      <td>0.000322</td>\n",
       "      <td>0.472266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>0.951515</td>\n",
       "      <td>7.052380</td>\n",
       "      <td>5.700313</td>\n",
       "      <td>9.454545</td>\n",
       "      <td>0.889710</td>\n",
       "      <td>0.889707</td>\n",
       "      <td>9.454545</td>\n",
       "      <td>0.921049</td>\n",
       "      <td>0.916739</td>\n",
       "      <td>23.719164</td>\n",
       "      <td>0.000318</td>\n",
       "      <td>0.470135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>0.959596</td>\n",
       "      <td>7.211872</td>\n",
       "      <td>5.801888</td>\n",
       "      <td>9.545455</td>\n",
       "      <td>0.890214</td>\n",
       "      <td>0.890211</td>\n",
       "      <td>9.545455</td>\n",
       "      <td>0.921415</td>\n",
       "      <td>0.917122</td>\n",
       "      <td>24.302150</td>\n",
       "      <td>0.000315</td>\n",
       "      <td>0.468033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>0.967677</td>\n",
       "      <td>7.375233</td>\n",
       "      <td>5.905293</td>\n",
       "      <td>9.636364</td>\n",
       "      <td>0.890711</td>\n",
       "      <td>0.890709</td>\n",
       "      <td>9.636364</td>\n",
       "      <td>0.921775</td>\n",
       "      <td>0.917500</td>\n",
       "      <td>24.891920</td>\n",
       "      <td>0.000311</td>\n",
       "      <td>0.465960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.975758</td>\n",
       "      <td>7.542560</td>\n",
       "      <td>6.010559</td>\n",
       "      <td>9.727273</td>\n",
       "      <td>0.891202</td>\n",
       "      <td>0.891199</td>\n",
       "      <td>9.727273</td>\n",
       "      <td>0.922131</td>\n",
       "      <td>0.917873</td>\n",
       "      <td>25.488495</td>\n",
       "      <td>0.000308</td>\n",
       "      <td>0.463915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.983838</td>\n",
       "      <td>7.713950</td>\n",
       "      <td>6.117721</td>\n",
       "      <td>9.818182</td>\n",
       "      <td>0.891686</td>\n",
       "      <td>0.891683</td>\n",
       "      <td>9.818182</td>\n",
       "      <td>0.922482</td>\n",
       "      <td>0.918241</td>\n",
       "      <td>26.091899</td>\n",
       "      <td>0.000304</td>\n",
       "      <td>0.461897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.991919</td>\n",
       "      <td>7.889506</td>\n",
       "      <td>6.226813</td>\n",
       "      <td>9.909091</td>\n",
       "      <td>0.892163</td>\n",
       "      <td>0.892161</td>\n",
       "      <td>9.909091</td>\n",
       "      <td>0.922828</td>\n",
       "      <td>0.918603</td>\n",
       "      <td>26.702154</td>\n",
       "      <td>0.000301</td>\n",
       "      <td>0.459907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.069330</td>\n",
       "      <td>6.337869</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.892635</td>\n",
       "      <td>0.892632</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.923170</td>\n",
       "      <td>0.918961</td>\n",
       "      <td>27.319287</td>\n",
       "      <td>0.000298</td>\n",
       "      <td>0.457942</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      ces_xi    ces_po    ces_ce  exponential_alpha  exponential_po  \\\n",
       "0   0.200000  1.164332  1.132897           1.000000        0.690079   \n",
       "1   0.208081  1.180358  1.152172           1.090909        0.701552   \n",
       "2   0.216162  1.196917  1.171797           1.181818        0.711795   \n",
       "3   0.224242  1.214013  1.191778           1.272727        0.721017   \n",
       "4   0.232323  1.231648  1.212122           1.363636        0.729379   \n",
       "5   0.240404  1.249828  1.232834           1.454545        0.737008   \n",
       "6   0.248485  1.268557  1.253921           1.545455        0.744007   \n",
       "7   0.256566  1.287840  1.275390           1.636364        0.750459   \n",
       "8   0.264646  1.307684  1.297248           1.727273        0.756432   \n",
       "9   0.272727  1.328095  1.319502           1.818182        0.761984   \n",
       "10  0.280808  1.349082  1.342159           1.909091        0.767162   \n",
       "11  0.288889  1.370652  1.365225           2.000000        0.772007   \n",
       "12  0.296970  1.392815  1.388709           2.090909        0.776553   \n",
       "13  0.305051  1.415578  1.412617           2.181818        0.780831   \n",
       "14  0.313131  1.438953  1.436957           2.272727        0.784866   \n",
       "15  0.321212  1.462949  1.461738           2.363636        0.788680   \n",
       "16  0.329293  1.487576  1.486966           2.454545        0.792294   \n",
       "17  0.337374  1.512847  1.512650           2.545455        0.795723   \n",
       "18  0.345455  1.538774  1.538799           2.636364        0.798984   \n",
       "19  0.353535  1.565367  1.565419           2.727273        0.802090   \n",
       "20  0.361616  1.592640  1.592520           2.818182        0.805053   \n",
       "21  0.369697  1.620607  1.620111           2.909091        0.807883   \n",
       "22  0.377778  1.649281  1.648199           3.000000        0.810591   \n",
       "23  0.385859  1.678675  1.676795           3.090909        0.813185   \n",
       "24  0.393939  1.708805  1.705906           3.181818        0.815673   \n",
       "25  0.402020  1.739686  1.735543           3.272727        0.818062   \n",
       "26  0.410101  1.771334  1.765714           3.363636        0.820358   \n",
       "27  0.418182  1.803764  1.796430           3.454545        0.822568   \n",
       "28  0.426263  1.836994  1.827700           3.545455        0.824696   \n",
       "29  0.434343  1.871040  1.859534           3.636364        0.826748   \n",
       "..       ...       ...       ...                ...             ...   \n",
       "70  0.765657  4.263043  3.801219           7.363636        0.875730   \n",
       "71  0.773737  4.355257  3.868598           7.454545        0.876454   \n",
       "72  0.781818  4.449683  3.937191           7.545455        0.877165   \n",
       "73  0.789899  4.546374  4.007019           7.636364        0.877864   \n",
       "74  0.797980  4.645385  4.078104           7.727273        0.878551   \n",
       "75  0.806061  4.746773  4.150469           7.818182        0.879226   \n",
       "76  0.814141  4.850597  4.224137           7.909091        0.879890   \n",
       "77  0.822222  4.956916  4.299132           8.000000        0.880543   \n",
       "78  0.830303  5.065792  4.375476           8.090909        0.881185   \n",
       "79  0.838384  5.177286  4.453195           8.181818        0.881817   \n",
       "80  0.846465  5.291464  4.532314           8.272727        0.882438   \n",
       "81  0.854545  5.408390  4.612857           8.363636        0.883050   \n",
       "82  0.862626  5.528134  4.694851           8.454545        0.883652   \n",
       "83  0.870707  5.650764  4.778320           8.545455        0.884245   \n",
       "84  0.878788  5.776352  4.863293           8.636364        0.884829   \n",
       "85  0.886869  5.904969  4.949796           8.727273        0.885404   \n",
       "86  0.894949  6.036692  5.037856           8.818182        0.885970   \n",
       "87  0.903030  6.171596  5.127502           8.909091        0.886528   \n",
       "88  0.911111  6.309760  5.218762           9.000000        0.887078   \n",
       "89  0.919192  6.451266  5.311666           9.090909        0.887620   \n",
       "90  0.927273  6.596194  5.406242           9.181818        0.888153   \n",
       "91  0.935354  6.744631  5.502522           9.272727        0.888680   \n",
       "92  0.943434  6.896664  5.600535           9.363636        0.889198   \n",
       "93  0.951515  7.052380  5.700313           9.454545        0.889710   \n",
       "94  0.959596  7.211872  5.801888           9.545455        0.890214   \n",
       "95  0.967677  7.375233  5.905293           9.636364        0.890711   \n",
       "96  0.975758  7.542560  6.010559           9.727273        0.891202   \n",
       "97  0.983838  7.713950  6.117721           9.818182        0.891686   \n",
       "98  0.991919  7.889506  6.226813           9.909091        0.892163   \n",
       "99  1.000000  8.069330  6.337869          10.000000        0.892635   \n",
       "\n",
       "    exponential_ce  translog_alpha  translog_po  translog_ce   ces_gain  \\\n",
       "0         0.690052        1.000000     0.772007     0.762135   2.774785   \n",
       "1         0.701526        1.090909     0.780831     0.771209   2.446277   \n",
       "2         0.711771        1.181818     0.788680     0.779288   2.143679   \n",
       "3         0.720995        1.272727     0.795723     0.786544   1.865649   \n",
       "4         0.729358        1.363636     0.802090     0.793108   1.610960   \n",
       "5         0.736989        1.454545     0.807883     0.799086   1.378487   \n",
       "6         0.743989        1.545455     0.813185     0.804560   1.167196   \n",
       "7         0.750441        1.636364     0.818062     0.809598   0.976134   \n",
       "8         0.756416        1.727273     0.822568     0.814256   0.804422   \n",
       "9         0.761968        1.818182     0.826748     0.818579   0.651247   \n",
       "10        0.767147        1.909091     0.830641     0.822607   0.515855   \n",
       "11        0.771993        2.000000     0.834277     0.826372   0.397548   \n",
       "12        0.776540        2.090909     0.837684     0.829901   0.295676   \n",
       "13        0.780818        2.181818     0.840886     0.833218   0.209633   \n",
       "14        0.784853        2.272727     0.843902     0.836344   0.138855   \n",
       "15        0.788668        2.363636     0.846749     0.839297   0.082817   \n",
       "16        0.792282        2.454545     0.849444     0.842092   0.041026   \n",
       "17        0.795712        2.545455     0.851999     0.844743   0.013022   \n",
       "18        0.798973        2.636364     0.854425     0.847262  -0.001626   \n",
       "19        0.802079        2.727273     0.856735     0.849660  -0.003323   \n",
       "20        0.805043        2.818182     0.858935     0.851945   0.007552   \n",
       "21        0.807873        2.909091     0.861036     0.854128   0.030643   \n",
       "22        0.810582        3.000000     0.863044     0.856215   0.065614   \n",
       "23        0.813176        3.090909     0.864967     0.858213   0.112150   \n",
       "24        0.815664        3.181818     0.866809     0.860128   0.169955   \n",
       "25        0.818053        3.272727     0.868576     0.861966   0.238748   \n",
       "26        0.820350        3.363636     0.870274     0.863733   0.318267   \n",
       "27        0.822560        3.454545     0.871907     0.865432   0.408261   \n",
       "28        0.824688        3.545455     0.873479     0.867067   0.508497   \n",
       "29        0.826741        3.636364     0.874994     0.868644   0.618753   \n",
       "..             ...             ...          ...          ...        ...   \n",
       "70        0.875727        7.363636     0.910890     0.906103  12.149377   \n",
       "71        0.876450        7.454545     0.911417     0.906655  12.579724   \n",
       "72        0.877162        7.545455     0.911935     0.907196  13.016681   \n",
       "73        0.877860        7.636364     0.912443     0.907728  13.460242   \n",
       "74        0.878547        7.727273     0.912943     0.908251  13.910398   \n",
       "75        0.879222        7.818182     0.913434     0.908765  14.367147   \n",
       "76        0.879886        7.909091     0.913917     0.909270  14.830484   \n",
       "77        0.880539        8.000000     0.914391     0.909767  15.300408   \n",
       "78        0.881181        8.090909     0.914858     0.910256  15.776919   \n",
       "79        0.881813        8.181818     0.915318     0.910737  16.260018   \n",
       "80        0.882435        8.272727     0.915769     0.911210  16.749709   \n",
       "81        0.883047        8.363636     0.916214     0.911675  17.245995   \n",
       "82        0.883649        8.454545     0.916652     0.912133  17.748882   \n",
       "83        0.884242        8.545455     0.917082     0.912584  18.258377   \n",
       "84        0.884826        8.636364     0.917506     0.913028  18.774489   \n",
       "85        0.885401        8.727273     0.917924     0.913466  19.297225   \n",
       "86        0.885967        8.818182     0.918335     0.913896  19.826598   \n",
       "87        0.886525        8.909091     0.918740     0.914320  20.362619   \n",
       "88        0.887075        9.000000     0.919139     0.914738  20.905301   \n",
       "89        0.887617        9.090909     0.919532     0.915150  21.454658   \n",
       "90        0.888150        9.181818     0.919920     0.915556  22.010706   \n",
       "91        0.888677        9.272727     0.920301     0.915956  22.573461   \n",
       "92        0.889195        9.363636     0.920678     0.916350  23.142940   \n",
       "93        0.889707        9.454545     0.921049     0.916739  23.719164   \n",
       "94        0.890211        9.545455     0.921415     0.917122  24.302150   \n",
       "95        0.890709        9.636364     0.921775     0.917500  24.891920   \n",
       "96        0.891199        9.727273     0.922131     0.917873  25.488495   \n",
       "97        0.891683        9.818182     0.922482     0.918241  26.091899   \n",
       "98        0.892161        9.909091     0.922828     0.918603  26.702154   \n",
       "99        0.892632       10.000000     0.923170     0.918961  27.319287   \n",
       "\n",
       "    exponential_gain  translog_gain  \n",
       "0           0.003981       1.295232  \n",
       "1           0.003623       1.247621  \n",
       "2           0.003320       1.205182  \n",
       "3           0.003062       1.167024  \n",
       "4           0.002839       1.132462  \n",
       "5           0.002645       1.100954  \n",
       "6           0.002474       1.072068  \n",
       "7           0.002323       1.045454  \n",
       "8           0.002188       1.020823  \n",
       "9           0.002067       0.997938  \n",
       "10          0.001958       0.976598  \n",
       "11          0.001859       0.956634  \n",
       "12          0.001769       0.937901  \n",
       "13          0.001687       0.920278  \n",
       "14          0.001612       0.903655  \n",
       "15          0.001543       0.887942  \n",
       "16          0.001479       0.873056  \n",
       "17          0.001420       0.858927  \n",
       "18          0.001365       0.845491  \n",
       "19          0.001314       0.832692  \n",
       "20          0.001266       0.820482  \n",
       "21          0.001222       0.808816  \n",
       "22          0.001180       0.797654  \n",
       "23          0.001141       0.786960  \n",
       "24          0.001104       0.776703  \n",
       "25          0.001069       0.766851  \n",
       "26          0.001037       0.757381  \n",
       "27          0.001006       0.748266  \n",
       "28          0.000977       0.739485  \n",
       "29          0.000949       0.731018  \n",
       "..               ...            ...  \n",
       "70          0.000424       0.528298  \n",
       "71          0.000418       0.525291  \n",
       "72          0.000412       0.522336  \n",
       "73          0.000407       0.519432  \n",
       "74          0.000401       0.516577  \n",
       "75          0.000396       0.513771  \n",
       "76          0.000391       0.511011  \n",
       "77          0.000385       0.508296  \n",
       "78          0.000380       0.505625  \n",
       "79          0.000376       0.502997  \n",
       "80          0.000371       0.500411  \n",
       "81          0.000366       0.497865  \n",
       "82          0.000362       0.495359  \n",
       "83          0.000357       0.492891  \n",
       "84          0.000353       0.490461  \n",
       "85          0.000349       0.488068  \n",
       "86          0.000345       0.485710  \n",
       "87          0.000341       0.483388  \n",
       "88          0.000337       0.481099  \n",
       "89          0.000333       0.478843  \n",
       "90          0.000329       0.476619  \n",
       "91          0.000325       0.474427  \n",
       "92          0.000322       0.472266  \n",
       "93          0.000318       0.470135  \n",
       "94          0.000315       0.468033  \n",
       "95          0.000311       0.465960  \n",
       "96          0.000308       0.463915  \n",
       "97          0.000304       0.461897  \n",
       "98          0.000301       0.459907  \n",
       "99          0.000298       0.457942  \n",
       "\n",
       "[100 rows x 12 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add welfare gains to dataframe\n",
    "import pandas\n",
    "df = pandas.concat(all_welfares, axis=1)\n",
    "# compute gains\n",
    "for exp in experiments:\n",
    "    case = exp['name']\n",
    "    df['{}_gain'.format(case)] = (df['{}_po'.format(case)]/df['{}_ce'.format(case)]-1)*100\n",
    "# save to Excel\n",
    "df.to_excel('welfare_gains.xls')\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FJ57IfAW2WPXoEe4kpEsc36W4vr/F8lo9ZmHFdOlRVlbGCSfAvffCEUeEFi3Z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\nRLkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb8843ac518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,3))\n",
    "plt.subplot(131)\n",
    "plt.plot(df['ces_xi'],df['ces_gain'])\n",
    "plt.ylabel('Welfare gains (%)')\n",
    "plt.xlabel(\"$\\\\xi$\")\n",
    "yl = plt.ylim()\n",
    "plt.ylim(0,yl[1])\n",
    "plt.title(\"CES-Benassy\")\n",
    "plt.grid()\n",
    "# xlim(4,8)\n",
    "# ylim(0,0.2)\n",
    "plt.subplot(132)\n",
    "plt.plot(df['exponential_alpha'],df['exponential_gain'])\n",
    "plt.grid()\n",
    "yl = plt.ylim()\n",
    "plt.ylim(0,yl[1])\n",
    "plt.title(\"Exponential\")\n",
    "plt.xlabel(\"$\\\\alpha$\")\n",
    "plt.subplot(133)\n",
    "plt.plot(df['translog_alpha'],df['translog_gain'])\n",
    "plt.grid()\n",
    "yl = plt.ylim()\n",
    "plt.ylim(0,yl[1])\n",
    "plt.title(\"Translog\")\n",
    "plt.xlabel(\"$\\\\alpha$\")\n",
    "plt.savefig('BGM_welfare_gains.png')\n",
    "plt.savefig('BGM_welfare_gains.pdf')\n",
    "plt.savefig('BGM_welfare_gains.svg')\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": "3.5.1"
  },
  "widgets": {
   "state": {},
   "version": "1.0.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}