{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# Example usage"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Here we will demonstrate how to use `ivxj` package to compute the IVXJ estimates and the corresponding \\\\(t\\\\)-statistics for unbalanced panel data under a simple regression specification."
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We use the baseline sample of [Greenwood et al. (2022)](https://onlinelibrary.wiley.com/doi/full/10.1111/jofi.13105), which is an unbalanced panel that covers 42 countries from 1950 to 2016 annually. They investigate the empirical association via the panel local projection:\n"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "```{math}\n",
                "y_{i,t+h} = \\mu_{y,i}^{(h)} + \\beta^{(h)*} \\cdot x_{i,t}^{\\mathrm{diff}} + e_{i,t+h},\\quad h=1,2,3.\n",
                "```\n"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "\n",
                "The dependent variable \\\\(y_{i,t+h}\\\\) is a binary indicator of financial crisis occurring in country \\\\(i\\\\) in any year between year \\\\(t+1\\\\) and year \\\\(t+h\\\\), and the regressor \\\\(x_{i,t}^{\\mathrm{diff}}\\\\) is the three-year debt growth relative to either GDP or CPI. And we run the regression when \\\\(h = 1\\\\) in this example.\n",
                "\n",
                "Four measures of normalized debt are used, and in this example, we use this measure:\n",
                "Ratio of private debt to GDP (\\\\(\\mathit{Debt}^{\\mathit{Priv}}/\\mathit{GDP}\\\\)).\n",
                "\n",
                "\n",
                "For IVX we set  \\\\(c_{z}=-1\\\\)  and  \\\\(\\theta=0.95\\\\)  as in our paper, thereby \\\\(\\rho_{z}=1-1 / \\max_{i \\leq n} T_{i}^{0.95}\\\\), where \\\\(T_{i}\\\\) is the time span of country  \\\\(i\\\\)  in this unbalanced panel.\n"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Import"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "0.1.0\n"
                    ]
                }
            ],
            "source": [
                "import ivxj\n",
                "\n",
                "print(ivxj.__version__)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Data Processing"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The data is downloaded from [here](https://onlinelibrary.wiley.com/action/downloadSupplement?doi=10.1111%2Fjofi.13105&file=jofi13105-sup-0002-ReplicationCode.zip). The Data.csv can be found in this folder."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": [
                "import pandas as pd\n",
                "data = pd.read_csv('Data.csv')"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The dependent variable is `crisis_ind_bvx` and the regressor is `debt_to_gdp_private_d3`."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "metadata": {},
            "outputs": [],
            "source": [
                "data_selected = data[[\"country\", \"year\", \"crisis_ind_bvx\", \"debt_to_gdp_private_d3\"]].dropna()\n",
                "\n",
                "# delete individual time series less than 3 observations\n",
                "country_counts = data_selected[\"country\"].value_counts()\n",
                "valid_countries = country_counts[country_counts > 2].index\n",
                "data_filtered = data_selected[data_selected[\"country\"].isin(valid_countries)]"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Estimation"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "metadata": {},
            "outputs": [],
            "source": [
                "import numpy as np\n",
                "rhoz = np.float64(0.980174328998269)\n",
                "btaHat, btaHatDebias, se, rhoHat = ivxj.ivxj(data_filtered, rhoz)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "`btaHat` is the IVX estimate for \\\\(\\beta^{(h)*}\\\\)."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "np.float64(0.0029654842208844436)"
                        ]
                    },
                    "execution_count": 5,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "btaHat"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The IVXJ estimate is `btaHatDebias`. Below, we print both the IVXJ estimate and its corresponding standard error `se`."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "IVXJ Estimate: 0.003058926878738318\n",
                        "Standard Error: 0.0007471981592453964\n"
                    ]
                }
            ],
            "source": [
                "print(\"IVXJ Estimate:\", btaHatDebias)\n",
                "print(\"Standard Error:\", se)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Finally, we calculate the \\\\(t\\\\)-statistic for the hypothesis test."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 7,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "t-statistics: 4.093862974485325\n"
                    ]
                }
            ],
            "source": [
                "print(\"t-statistics:\", btaHatDebias / se)"
            ]
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": "ivxjenv",
            "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": "3.12.7"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 4
}