{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Asymptotic Efficiency Simulation\n\nLearning goal: Compare OLS with an alternative consistent estimator.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Dataset check\nThis cell confirms the dataset file is available. Simulation notebooks mount a harmless CSV so public file delivery is still validated.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "import os\n",
        "DATASET = \"WAGE1.csv\"\n",
        "VARIABLES = [\"x\",\"z\",\"variance\"]\n",
        "if not os.path.exists(DATASET):\n",
        "    raise FileNotFoundError(\n",
        "        \"Dataset file not installed yet\\n\"\n",
        "        \"Dataset: SIMULATION\\n\"\n",
        "        \"Variables needed: x, z, variance\\n\"\n",
        "        \"Course data folder: https://drive.google.com/drive/folders/1_STdcydIcst-opcbwOKRFzUXsgxQgBoS?usp=sharing\\n\"\n",
        "        \"Admin upload instruction: upload the dataset in Admin -> Datasets, publish it, and make the file available to the notebook runner.\"\n",
        "    )\n",
        "print(\"Ready:\", DATASET)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Run the lab\nRun the code, inspect the table or graph, and connect the result to the formula in the lesson.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import statsmodels.api as sm\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "np.random.seed(70)\n",
        "beta1 = 2\n",
        "rows = []\n",
        "for _ in range(600):\n",
        "    n = 300\n",
        "    x = np.random.uniform(0.2, 2.5, size=n)\n",
        "    u = np.random.normal(size=n)\n",
        "    y = 1 + beta1 * x + u\n",
        "    ols = sm.OLS(y, sm.add_constant(x)).fit().params[1]\n",
        "    z = np.log1p(x**2)\n",
        "    alt = np.sum((z - z.mean()) * y) / np.sum((z - z.mean()) * x)\n",
        "    rows.append({\"OLS\": ols, \"alternative\": alt})\n",
        "result = pd.DataFrame(rows)\n",
        "print(result.agg([\"mean\", \"std\"]))\n",
        "result.hist(bins=30)\n",
        "plt.suptitle(\"Consistent estimators can have different spread\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Formula explanation\nExplain the probability limit, asymptotic approximation, standard-error pattern, or LM statistic in words. Do not treat output as automatic causal evidence.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Short exercise\nChange one sample size, regressor, or restriction. Write two sentences: what changed mechanically, and what assumption still matters?\n\n## Check your understanding\nDoes increasing n fix nonnormality, endogeneity, heteroskedasticity, or omitted variables? Explain.\n"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "name": "python",
      "version": "3.11"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}