{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "3c8f084c-5a77-45ca-8606-ada243fffc96",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import statsmodels.api as sm\n",
    "import pandas_datareader as pdr\n",
    "import datetime as dt\n",
    "from Ipython import markdown as md"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edd97b79-e45d-4924-b160-3375f0b00ea1",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\">Functional Forms</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e46469af-5bae-4f09-9990-dd0a649e2831",
   "metadata": {},
   "source": [
    "Linear regression requires parameters to be linear rather than variables, for instance an exponential form is nonlinear\n",
    "$$\n",
    "Y_{i}=\\beta_{1} X_{i}^{\\beta_{2}} e^{u_{i}}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5126451f-9590-4746-8029-3e1ada793c0c",
   "metadata": {},
   "source": [
    "Many of you might wonder what if variables are nonlinear, such as\n",
    "$$\n",
    "Y=\\beta_{1}+\\beta_{2} X_{2}^{3}+\\beta_{3} \\sqrt{X_{3}}+\\beta_{4} \\log X_{4} + u_i\n",
    "$$\n",
    "Actually, it doesn't matter, they are essentially linear after nonlinear operation performed. \n",
    "$$\n",
    "Y=\\beta_{1}+\\beta_{2} Z_2+\\beta_{3}Z_3+\\beta_{4}Z_4+u_i\n",
    "$$\n",
    "where $Z_2 = X_{2}^{3}$, $Z_3 = \\sqrt{X_{3}}$ and $Z_4 =\\log X_{4}$.\n",
    "\n",
    "But interpretation of parameters not the same anymore."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c8722c5-bd99-40ce-adcc-7726666a1ba0",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\">Log Form Transformation</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0038241-2a3a-4877-99a4-4e67bf936541",
   "metadata": {},
   "source": [
    "We will explain how log form transformation is used through an economics example.\n",
    "\n",
    "If you have studied microeconomics, you probably remember the concept of elasticity, it is a unitless measurement of relative changes of two variables. For example, the price elasticity of demand is defined as\n",
    "$$\n",
    "\\frac{\\Delta C/C}{\\Delta P/P} = \\frac{d C/d P}{C/P}\n",
    "$$\n",
    "If price elasticity of demand is $.3$, it means one percent of price change would cause $.3%$ percent change of demand."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab85cbec-ff2d-4782-a8b2-b580fd6a904c",
   "metadata": {},
   "source": [
    "If $C$ and $P$ takes the form of $C = \\beta_1 P^{\\beta_2}$, then\n",
    "$$\n",
    "\\frac{d C}{d P}=\\beta_1 \\beta_2 P^{\\beta_2-1}= \\beta_2\\frac{C}{P}\n",
    "$$\n",
    "Substitute the result back in elasticity of consumption to price\n",
    "$$\n",
    "\\frac{\\Delta C/C}{\\Delta P/P} = \\beta_2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "455d5ef7-cf19-4981-a32a-4d90559d9180",
   "metadata": {},
   "source": [
    "$\\beta_2$ is the elasticity, and this is also why we prefer using exponential form in estimating elasticities. Taking natural log on $C = \\beta_1 P^{\\beta_2}u$\n",
    "$$\n",
    "\\ln{C} = \\ln{\\beta_1}+\\beta_2\\ln{P}+\\ln{u}\n",
    "$$\n",
    "This, again, back to linear regression form. With cosmetic substitution, the model becomes\n",
    "$$\n",
    "C' = \\beta_1'+\\beta_2 P'+u'\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "576651b7-c362-4cf9-8199-3fc1d81a084b",
   "metadata": {},
   "source": [
    "Here is the estimation procedure:\n",
    "1. Take natural log of $C$ and $P$.\n",
    "2. Estimate the regression by OLS.\n",
    "3. $\\beta_2$ has the direct interpretation of elasticity.\n",
    "4. To obtain $\\beta_1$, take $\\exp{\\beta_1'}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41df40d1-2809-4f94-be50-1cd9fa5ba20a",
   "metadata": {},
   "source": [
    "We will retrieve _Consumer Price Index_ and _Expenditure of Durable Good_ from FRED. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "6f61d915-cb57-4cfe-88b5-b4533916576c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "start = dt.datetime(1950, 1, 1)\n",
    "end = dt.datetime(2021, 1, 1)\n",
    "df_exp = pdr.data.DataReader([\"PCEDG\", \"PCE\"], \"fred\", start, end)\n",
    "df_exp.columns = [\"Exp_Dur\", \"Tot_Exp\"]\n",
    "df_exp = df_exp.dropna()\n",
    "(df_exp / df_exp.iloc[0]).plot(\n",
    "    grid=True,\n",
    "    figsize=(12, 7),\n",
    "    title=\"Total Exp. and Exp. on Durables (Normalised at 1.2010)\",\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "58598cde-633d-4948-a919-407849140ac2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Exp_Dur   R-squared:                       0.995\n",
      "Model:                            OLS   Adj. R-squared:                  0.995\n",
      "Method:                 Least Squares   F-statistic:                 1.398e+05\n",
      "Date:                Sat, 24 Jul 2021   Prob (F-statistic):               0.00\n",
      "Time:                        18:20:51   Log-Likelihood:                 805.70\n",
      "No. Observations:                 745   AIC:                            -1607.\n",
      "Df Residuals:                     743   BIC:                            -1598.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         -1.4413      0.020    -72.514      0.000      -1.480      -1.402\n",
      "Tot_Exp        0.9242      0.002    373.902      0.000       0.919       0.929\n",
      "==============================================================================\n",
      "Omnibus:                      163.607   Durbin-Watson:                   0.076\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               35.463\n",
      "Skew:                          -0.182   Prob(JB):                     1.99e-08\n",
      "Kurtosis:                       1.995   Cond. No.                         53.9\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "X = np.log(df_exp[\"Tot_Exp\"])\n",
    "Y = np.log(df_exp[\"Exp_Dur\"])\n",
    "\n",
    "X = sm.add_constant(X)  # adding a constant\n",
    "\n",
    "model = sm.OLS(Y, X).fit()\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "16131011-9178-4a6e-85f0-62e5ba3fe49f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "That means every $1\\%$ increase of total expenditure will bring up 0.9242\\% of durable good consumption."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "md(\n",
    "    \"That means every $1\\%$ increase of total expenditure will bring up {:.4f}\\% of durable good consumption.\".format(\n",
    "        model.params[1]\n",
    "    )\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}