development_accounting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intro to Development Accounting\n",
    "In this note, we produce some results which conceptually replicates [Caselli 2005](https://personal.lse.ac.uk/casellif/papers/handbook.pdf) (see also [Caselli 2016](https://documents1.worldbank.org/curated/ru/199521487336202705/pdf/112882-WP-PUBLIC-WDR17BPAccountingforCrossCountryDifferencesTenYearsLater.pdf)). However, we use Penn World Table 10 with a different and improved treatment of both capital and human capital.\n",
    "\n",
    "## Loading modules\n",
    "\n",
    "First, we load Python modules (informally: collections of functions and capabilities):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np #numerical stuff (i.e., taking logarithms)\n",
    "import pandas as pd #good for handling datasets\n",
    "import plotly.express as px #good for plotting\n",
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading the dataset and constructing variables\n",
    "\n",
    "Then we load the dataset from the website."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Download data from Penn World Table\n",
    "url = \"https://www.rug.nl/ggdc/docs/pwt100.xlsx\"\n",
    "data_in = pd.read_excel(url, sheet_name='Data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What does the dataset look like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>countrycode</th>\n",
       "      <th>country</th>\n",
       "      <th>currency_unit</th>\n",
       "      <th>year</th>\n",
       "      <th>rgdpe</th>\n",
       "      <th>rgdpo</th>\n",
       "      <th>pop</th>\n",
       "      <th>emp</th>\n",
       "      <th>avh</th>\n",
       "      <th>hc</th>\n",
       "      <th>...</th>\n",
       "      <th>csh_x</th>\n",
       "      <th>csh_m</th>\n",
       "      <th>csh_r</th>\n",
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       "      <td>ABW</td>\n",
       "      <td>Aruba</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>Aruba</td>\n",
       "      <td>Aruban Guilder</td>\n",
       "      <td>1953</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>Zimbabwe</td>\n",
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       "      <td>2015</td>\n",
       "      <td>40141.617188</td>\n",
       "      <td>39798.644531</td>\n",
       "      <td>13.814629</td>\n",
       "      <td>6.393752</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.584653</td>\n",
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       "      <td>0.140172</td>\n",
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       "      <td>-0.051930</td>\n",
       "      <td>0.479228</td>\n",
       "      <td>0.651287</td>\n",
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       "      <td>0.533235</td>\n",
       "      <td>0.422764</td>\n",
       "      <td>1.533909</td>\n",
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       "    <tr>\n",
       "      <th>12806</th>\n",
       "      <td>ZWE</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>US Dollar</td>\n",
       "      <td>2016</td>\n",
       "      <td>41875.203125</td>\n",
       "      <td>40963.191406</td>\n",
       "      <td>14.030331</td>\n",
       "      <td>6.504374</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.616257</td>\n",
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       "      <td>0.131920</td>\n",
       "      <td>-0.251232</td>\n",
       "      <td>-0.016258</td>\n",
       "      <td>0.470640</td>\n",
       "      <td>0.651027</td>\n",
       "      <td>0.539631</td>\n",
       "      <td>0.619789</td>\n",
       "      <td>0.519718</td>\n",
       "      <td>0.416510</td>\n",
       "      <td>1.491724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12807</th>\n",
       "      <td>ZWE</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>US Dollar</td>\n",
       "      <td>2017</td>\n",
       "      <td>44672.175781</td>\n",
       "      <td>44316.742188</td>\n",
       "      <td>14.236595</td>\n",
       "      <td>6.611773</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.648248</td>\n",
       "      <td>...</td>\n",
       "      <td>0.126722</td>\n",
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       "      <td>-0.039897</td>\n",
       "      <td>0.473560</td>\n",
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       "      <td>0.519956</td>\n",
       "      <td>0.619739</td>\n",
       "      <td>0.552042</td>\n",
       "      <td>0.415592</td>\n",
       "      <td>1.514525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12808</th>\n",
       "      <td>ZWE</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>US Dollar</td>\n",
       "      <td>2018</td>\n",
       "      <td>44325.109375</td>\n",
       "      <td>43420.898438</td>\n",
       "      <td>14.438802</td>\n",
       "      <td>6.714952</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.680630</td>\n",
       "      <td>...</td>\n",
       "      <td>0.144485</td>\n",
       "      <td>-0.263658</td>\n",
       "      <td>-0.020791</td>\n",
       "      <td>0.543757</td>\n",
       "      <td>0.655473</td>\n",
       "      <td>0.529867</td>\n",
       "      <td>0.641361</td>\n",
       "      <td>0.561526</td>\n",
       "      <td>0.425143</td>\n",
       "      <td>1.590120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12809</th>\n",
       "      <td>ZWE</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>US Dollar</td>\n",
       "      <td>2019</td>\n",
       "      <td>42296.062500</td>\n",
       "      <td>40826.570312</td>\n",
       "      <td>14.645468</td>\n",
       "      <td>6.831017</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.713408</td>\n",
       "      <td>...</td>\n",
       "      <td>0.213562</td>\n",
       "      <td>-0.270959</td>\n",
       "      <td>-0.089798</td>\n",
       "      <td>0.494755</td>\n",
       "      <td>0.652439</td>\n",
       "      <td>0.500927</td>\n",
       "      <td>0.487763</td>\n",
       "      <td>0.430082</td>\n",
       "      <td>0.420675</td>\n",
       "      <td>1.384068</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>12810 rows × 52 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      countrycode   country   currency_unit  year         rgdpe         rgdpo  \\\n",
       "0             ABW     Aruba  Aruban Guilder  1950           NaN           NaN   \n",
       "1             ABW     Aruba  Aruban Guilder  1951           NaN           NaN   \n",
       "2             ABW     Aruba  Aruban Guilder  1952           NaN           NaN   \n",
       "3             ABW     Aruba  Aruban Guilder  1953           NaN           NaN   \n",
       "4             ABW     Aruba  Aruban Guilder  1954           NaN           NaN   \n",
       "...           ...       ...             ...   ...           ...           ...   \n",
       "12805         ZWE  Zimbabwe       US Dollar  2015  40141.617188  39798.644531   \n",
       "12806         ZWE  Zimbabwe       US Dollar  2016  41875.203125  40963.191406   \n",
       "12807         ZWE  Zimbabwe       US Dollar  2017  44672.175781  44316.742188   \n",
       "12808         ZWE  Zimbabwe       US Dollar  2018  44325.109375  43420.898438   \n",
       "12809         ZWE  Zimbabwe       US Dollar  2019  42296.062500  40826.570312   \n",
       "\n",
       "             pop       emp  avh        hc  ...     csh_x     csh_m     csh_r  \\\n",
       "0            NaN       NaN  NaN       NaN  ...       NaN       NaN       NaN   \n",
       "1            NaN       NaN  NaN       NaN  ...       NaN       NaN       NaN   \n",
       "2            NaN       NaN  NaN       NaN  ...       NaN       NaN       NaN   \n",
       "3            NaN       NaN  NaN       NaN  ...       NaN       NaN       NaN   \n",
       "4            NaN       NaN  NaN       NaN  ...       NaN       NaN       NaN   \n",
       "...          ...       ...  ...       ...  ...       ...       ...       ...   \n",
       "12805  13.814629  6.393752  NaN  2.584653  ...  0.140172 -0.287693 -0.051930   \n",
       "12806  14.030331  6.504374  NaN  2.616257  ...  0.131920 -0.251232 -0.016258   \n",
       "12807  14.236595  6.611773  NaN  2.648248  ...  0.126722 -0.202827 -0.039897   \n",
       "12808  14.438802  6.714952  NaN  2.680630  ...  0.144485 -0.263658 -0.020791   \n",
       "12809  14.645468  6.831017  NaN  2.713408  ...  0.213562 -0.270959 -0.089798   \n",
       "\n",
       "           pl_c      pl_i      pl_g      pl_x      pl_m      pl_n      pl_k  \n",
       "0           NaN       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "1           NaN       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "2           NaN       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "3           NaN       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "4           NaN       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "...         ...       ...       ...       ...       ...       ...       ...  \n",
       "12805  0.479228  0.651287  0.541446  0.616689  0.533235  0.422764  1.533909  \n",
       "12806  0.470640  0.651027  0.539631  0.619789  0.519718  0.416510  1.491724  \n",
       "12807  0.473560  0.639560  0.519956  0.619739  0.552042  0.415592  1.514525  \n",
       "12808  0.543757  0.655473  0.529867  0.641361  0.561526  0.425143  1.590120  \n",
       "12809  0.494755  0.652439  0.500927  0.487763  0.430082  0.420675  1.384068  \n",
       "\n",
       "[12810 rows x 52 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = data_in.copy()\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Development accounting\n",
    "\n",
    "As organizing framework for our development accounting exercise, we employ an aggregate production function $Y=AK^\\alpha(hL)^{1-\\alpha}$ where $Y$ is real output, $K$ is the stock of capital, $L$ is the number of workers,$h$ is a measure of the human capital of the workers and $A$ is total-factor productivity. Dividing by $L$, we express the production function in per capita terms, arriving at\n",
    "$$ y = Ak^\\alpha h^{1-\\alpha}.$$\n",
    "\n",
    "To perform our accounting exercise, we need cross-country comparable measures of $y$, $k$, and $h$, as well as a calibrated value for $\\alpha$. The Penn World Table provides us with $y$, $k$, and $h$. We set $\\alpha=1/3$, to match the capital share in, e.g., the US.\n",
    "\n",
    "_Note that our approach here is dangerous. We are using someone else's data set and crossing our fingers that whatever they did to construct $y$, $k$, and $h$ is the best we can do. Research on development accounting is all about figuring out conceptual problems with our ways of measuring variables, and on improving on estimates or at the very least cast some doubt on previous estimates._\n",
    "\n",
    "### Constructing our per capita variables for 2015\n",
    "\n",
    "First, we choose `country` as our index and restrict our data to 2015. For this sample, we choose our variables for output, capital, human capital (per capita), and the labor force."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/3891126883.py:5: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['output'] = data['cgdpo']\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/3891126883.py:6: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['capital'] = data['cn']\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/3891126883.py:7: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['human_capital_per_capita'] = data['hc']#*data['avh']\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/3891126883.py:8: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['labor'] = data['emp']\n"
     ]
    }
   ],
   "source": [
    "data.index = data['country']\n",
    "restriction = (data['year']==2015)\n",
    "data = data[restriction]\n",
    "\n",
    "data['output'] = data['cgdpo']\n",
    "data['capital'] = data['cn']\n",
    "data['human_capital_per_capita'] = data['hc']#*data['avh']\n",
    "data['labor'] = data['emp']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this variable definitions, we construct our per capita measures and back out total-factor productivity relative to the US. For this, we need our calibrated value of $\\alpha$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/1483562494.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['output_per_capita'] = data['output']/data['emp']\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/1483562494.py:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['capital_per_capita'] = data['capital']/data['emp']\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/1483562494.py:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['output_per_capita_implied'] = data['capital_per_capita']**alpha*data['human_capital_per_capita']**(1-alpha)\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/1483562494.py:5: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['TFP'] = data['output_per_capita']/data['output_per_capita_implied']\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/1483562494.py:6: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['TFP_rel_US'] = data['TFP']/data['TFP'].loc['United States']\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/1483562494.py:7: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['TFP_rel_DE'] = data['TFP']/data['TFP'].loc['Germany']\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.33\n",
    "data['output_per_capita'] = data['output']/data['emp']\n",
    "data['capital_per_capita'] = data['capital']/data['emp']\n",
    "data['output_per_capita_implied'] = data['capital_per_capita']**alpha*data['human_capital_per_capita']**(1-alpha)\n",
    "data['TFP'] = data['output_per_capita']/data['output_per_capita_implied']\n",
    "data['TFP_rel_US'] = data['TFP']/data['TFP'].loc['United States']\n",
    "data['TFP_rel_DE'] = data['TFP']/data['TFP'].loc['Germany']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like with growth accounting, \"this is it\". After having chosen our measures of capital, human capital, etc., the analysis is very simple.\n",
    "\n",
    "Below, we plot output per capita relative to the US and total-factor productivity relative to the US. The main takeaway is that TFP lines up well with GDP per capita. I.e., high income countries have higher TFP and that GDP per capita."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/3916804488.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['output_per_capita_rel_US'] = data['output_per_capita']/data['output_per_capita'].loc['United States']\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/3916804488.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['output_per_capita_implied_rel_US'] = data['output_per_capita_implied']/data['output_per_capita_implied'].loc['United States']\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/3916804488.py:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['output_per_capita_rel_DE'] = data['output_per_capita']/data['output_per_capita'].loc['Germany']\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/3916804488.py:5: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  data['output_per_capita_implied_rel_DE'] = data['output_per_capita_implied']/data['output_per_capita_implied'].loc['Germany']\n"
     ]
    },
    {
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          "title": {
           "x": 0.05
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           "linecolor": "rgb(36,36,36)",
           "showgrid": false,
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           "title": {
            "standoff": 15
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            "standoff": 15
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           "zeroline": false,
           "zerolinecolor": "rgb(36,36,36)"
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        },
        "title": {
         "text": "TFP is higher in rich countries"
        },
        "width": 800,
        "xaxis": {
         "anchor": "y",
         "domain": [
          0,
          1
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         "ticktext": [
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          "text": "GDP per capita"
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         "type": "log"
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        "yaxis": {
         "anchor": "x",
         "domain": [
          0,
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         "ticktext": [
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     "metadata": {},
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   ],
   "source": [
    "\n",
    "data['output_per_capita_rel_US'] = data['output_per_capita']/data['output_per_capita'].loc['United States']\n",
    "data['output_per_capita_implied_rel_US'] = data['output_per_capita_implied']/data['output_per_capita_implied'].loc['United States']\n",
    "\n",
    "data['output_per_capita_rel_DE'] = data['output_per_capita']/data['output_per_capita'].loc['Germany']\n",
    "data['output_per_capita_implied_rel_DE'] = data['output_per_capita_implied']/data['output_per_capita_implied'].loc['Germany']\n",
    "\n",
    "fig = px.scatter(data, 'output_per_capita_rel_US', 'TFP_rel_US', text = data.index,\n",
    "                 log_x = True, log_y=True)\n",
    "fig.update_traces(mode='text')\n",
    "#fig2 = px.line(x=[1/32,1.4],y=[1/32,1.4], log_x = True, log_y=True)\n",
    "#fig = go.Figure(data = fig1.data + fig2.data, log_x=True)\n",
    "\n",
    "fig.update_layout(template = 'simple_white',\n",
    "                  width = 800, height = 600,\n",
    "                  xaxis_title = 'GDP per capita',\n",
    "                  yaxis_title = 'TFP',\n",
    "                  title = 'TFP is higher in rich countries')\n",
    "\n",
    "fig.update_xaxes(tickvals = [1/32, 1/16, 1/8, 1/4, 1/2, 1],\n",
    "                 ticktext = [\"1/32\", \"1/16\", \"1/8\", \"1/4\", \"1/2\", \"1\"])\n",
    "fig.update_yaxes(tickvals = [1/32, 1/16, 1/8, 1/4, 1/2, 1],\n",
    "                 ticktext = [\"1/32\", \"1/16\", \"1/8\", \"1/4\", \"1/2\", \"1\"])\n"
   ]
  },
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    "For the poorer countries, TFP is closer to the US than GDP per capita, indicative of the fact that also a shortage of capital and human capital goes some way to account for the income differences with the US. Part of this is, arguably, mechanical since higher productivity, in itself, leads to greater capital accumulation. Following Klenow and Rodriguez-Clare (1997) and Hall and Jones (1999), we can rewrite the accounting identity as\n",
    "$$ y = (k/y)^{\\alpha/(1-\\alpha)}h A^{1/(1-\\alpha)}. $$\n",
    "Setting $A$ constant across countries with this accounting identity assumes that the capital-output ratio remains stable in the thought experiment, something which is consistent with, e.g the Solow model. This formulation takes into account that an increase in productivity endogenously leads to an increase in the capital stock."
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      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/2410153740.py:1: SettingWithCopyWarning:\n",
      "\n",
      "\n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "\n",
      "/var/folders/s0/3g1gb_9s56x9hxnb2d1npjc80000gn/T/ipykernel_53630/2410153740.py:2: SettingWithCopyWarning:\n",
      "\n",
      "\n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "\n"
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    "data['capital_to_output'] = data['capital']/data['output']\n",
    "data['output_per_capita_implied_KR'] = data['capital_to_output']**(alpha/(1-alpha))*data['human_capital_per_capita']\n"
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    "\n",
    "To quantify how large share of the variation is accounted for by factor inputs, following Table 1 in Caselli 2005, we compute the variance in log GDP per capita and the variance in log GDP per capita which would result if all countries kept their factor inputs but total-factor productivity was equalized across countries."
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   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kalle/opt/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning:\n",
      "\n",
      "invalid value encountered in log\n",
      "\n"
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       "      <th>success_1</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Baseline success of the factor-only model</th>\n",
       "      <td>1.081702</td>\n",
       "      <td>0.366579</td>\n",
       "      <td>0.338891</td>\n",
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       "                                           var[log(y)]  var[log(y_KH)]  \\\n",
       "Baseline success of the factor-only model     1.081702        0.366579   \n",
       "\n",
       "                                           success_1  \n",
       "Baseline success of the factor-only model   0.338891  "
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    "table = pd.DataFrame([np.var(np.log(data['output_per_capita'])), np.var(np.log(data['output_per_capita_implied'])), np.var(np.log(data['output_per_capita_implied']))/np.var(np.log(data['output_per_capita']))]).transpose()\n",
    "table.columns = ['var[log(y)]', 'var[log(y_KH)]', 'success_1']\n",
    "table.index = ['Baseline success of the factor-only model']\n",
    "table"
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    "The factor-only model is only able to account for 34 percent of the variation in GDP per capita. If we use Klenow and Rodriguez-Clare's formulation, the success of the factor-only model is even poorer. See Caselli for the intuition behind this result."
   ]
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  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kalle/opt/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:397: RuntimeWarning:\n",
      "\n",
      "invalid value encountered in log\n",
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       "      <th>success_1</th>\n",
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       "      <th>Baseline success of the factor-only model with Klenow-Rodriguez-Clare formulation</th>\n",
       "      <td>1.081702</td>\n",
       "      <td>0.185329</td>\n",
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       "                                                    var[log(y)]  \\\n",
       "Baseline success of the factor-only model with ...     1.081702   \n",
       "\n",
       "                                                    var[log(y_KH)]  success_1  \n",
       "Baseline success of the factor-only model with ...        0.185329   0.171331  "
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    "table = pd.DataFrame([np.var(np.log(data['output_per_capita'])), np.var(np.log(data['output_per_capita_implied_KR'])), np.var(np.log(data['output_per_capita_implied_KR']))/np.var(np.log(data['output_per_capita']))]).transpose()\n",
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   "source": [
    "## Focusing on the EU\n",
    "\n",
    "One may be interested in a more narrow question. Rather than studying the global dispersion of income, we now focus on the European Union."
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    "eu = ['Austria', 'Belgium', 'Bulgaria', 'Croatia', 'Cyprus', 'Czech Republic', \n",
    "      'Denmark', 'Estonia', 'Finland', 'France', 'Germany', 'Greece', 'Hungary', \n",
    "       'Italy', 'Latvia', 'Lithuania', 'Luxembourg', 'Malta', 'Netherlands',\n",
    "      'Poland', 'Portugal', 'Romania', 'Slovakia', 'Slovenia', 'Spain', \n",
    "        'Sweden']\n",
    "\n",
    "eu_90s = ['Austria', 'Belgium', 'Denmark', 'Finland', 'France', 'Germany', 'Greece',\n",
    "          'Ireland', 'Italy', 'Luxembourg', 'Netherlands', 'Portugal', 'Spain', 'Sweden']\n",
    "\n",
    "\n",
    "fig = px.scatter(data.loc[eu], 'output_per_capita_rel_DE', 'TFP_rel_DE', text = data.loc[eu].index,\n",
    "                 log_x = True, log_y=True)\n",
    "fig.update_traces(mode='text')\n",
    "\n",
    "\n",
    "fig.update_layout(template = 'simple_white',\n",
    "                  width = 800, height = 600,\n",
    "                  xaxis_title = 'GDP per capita',\n",
    "                  yaxis_title = 'TFP',\n",
    "                  title = 'European Union excluding Ireland')\n",
    "\n",
    "\n"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we compute how much the variance of log income is decreased if all countries have the same TFP:"
   ]
  },
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   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "      <th></th>\n",
       "      <th>var[log(y)]</th>\n",
       "      <th>var[log(y_KH)]</th>\n",
       "      <th>success_1</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Baseline success of the factor-only model</th>\n",
       "      <td>0.073353</td>\n",
       "      <td>0.022376</td>\n",
       "      <td>0.305051</td>\n",
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       "                                           var[log(y)]  var[log(y_KH)]  \\\n",
       "Baseline success of the factor-only model     0.073353        0.022376   \n",
       "\n",
       "                                           success_1  \n",
       "Baseline success of the factor-only model   0.305051  "
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    "table = pd.DataFrame([\n",
    "    np.var(np.log(data.loc[eu]['output_per_capita'])), np.var(np.log(data.loc[eu]['output_per_capita_implied'])), np.var(np.log(data.loc[eu]['output_per_capita_implied']))/np.var(np.log(data.loc[eu]['output_per_capita']))\n",
    "]).transpose()\n",
    "table.columns = ['var[log(y)]', 'var[log(y_KH)]', 'success_1']\n",
    "table.index = ['Baseline success of the factor-only model']\n",
    "table\n",
    "\n"
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   "source": [
    "## Focusing on the OECD\n",
    "\n",
    "Let's do the same analysis for the OECD because why not?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
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   "source": [
    "oecd = ['Australia', 'Austria', 'Belgium', 'Canada', 'Chile', 'Colombia', 'Costa Rica', 'Czech Republic', \n",
    "        'Denmark', 'Estonia', 'Finland', 'France', 'Germany', 'Greece', 'Hungary', 'Iceland',  \n",
    "        'Israel', 'Italy', 'Japan', 'Republic of Korea', 'Latvia', 'Lithuania', 'Luxembourg', 'Mexico',\n",
    "        'Netherlands', 'New Zealand', 'Norway', 'Poland', 'Portugal', 'Slovakia', 'Slovenia', 'Spain', \n",
    "        'Sweden', 'Switzerland', 'Turkey', 'United Kingdom', 'United States'] #'Ireland',\n",
    "\n",
    "fig = px.scatter(data.loc[oecd], 'output_per_capita_rel_DE', 'TFP_rel_DE', text = data.loc[oecd].index,\n",
    "                 trendline = \"ols\")\n",
    "fig.update_traces(mode='text')\n",
    "\n",
    "fig.update_layout(template = 'simple_white',\n",
    "                  width = 800, height = 600,\n",
    "                  xaxis_title = 'GDP per capita',\n",
    "                  yaxis_title = 'TFP',\n",
    "                  title = 'OECD excluding Ireland')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>var[log(y)]</th>\n",
       "      <th>var[log(y_KH)]</th>\n",
       "      <th>success_1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Baseline success of the factor-only model</th>\n",
       "      <td>0.105484</td>\n",
       "      <td>0.041043</td>\n",
       "      <td>0.389096</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "                                           var[log(y)]  var[log(y_KH)]  \\\n",
       "Baseline success of the factor-only model     0.105484        0.041043   \n",
       "\n",
       "                                           success_1  \n",
       "Baseline success of the factor-only model   0.389096  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = pd.DataFrame([\n",
    "    np.var(np.log(data.loc[oecd]['output_per_capita'])), np.var(np.log(data.loc[oecd]['output_per_capita_implied'])), np.var(np.log(data.loc[oecd]['output_per_capita_implied']))/np.var(np.log(data.loc[oecd]['output_per_capita']))]).transpose()\n",
    "table.columns = ['var[log(y)]', 'var[log(y_KH)]', 'success_1']\n",
    "table.index = ['Baseline success of the factor-only model']\n",
    "table"
   ]
  }
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