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<title data-rh="true">Econometrics - Intros - Usage | OpenBB SDK Docs</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" property="og:image" content="https://docs.openbb.co/img/banner.png"><meta data-rh="true" name="twitter:image" content="https://docs.openbb.co/img/banner.png"><meta data-rh="true" property="og:url" content="https://docs.openbb.co/sdk/data-available/econometrics"><meta data-rh="true" property="og:locale" content="en"><meta data-rh="true" name="docusaurus_locale" content="en"><meta data-rh="true" name="docsearch:language" content="en"><meta data-rh="true" name="docusaurus_version" content="current"><meta data-rh="true" name="docusaurus_tag" content="docs-default-current"><meta data-rh="true" name="docsearch:version" content="current"><meta data-rh="true" name="docsearch:docusaurus_tag" content="docs-default-current"><meta data-rh="true" property="og:title" content="Econometrics | OpenBB Docs"><meta data-rh="true" name="description" content="This documentation page guides users in the usage of the openbb Terminal's Econometrics menu that allows users to load, modify, and perform statistical tests on their datasets via a powerful SDK. The article explains the process of running various regression models, performing tests on residuals, and how to overcome potential errors during the process."><meta data-rh="true" property="og:description" content="This documentation page guides users in the usage of the openbb Terminal's Econometrics menu that allows users to load, modify, and perform statistical tests on their datasets via a powerful SDK. The article explains the process of running various regression models, performing tests on residuals, and how to overcome potential errors during the process."><meta data-rh="true" name="keywords" content="openbb Terminal,Econometrics menu,statistical tests,regression models,OLS regression,Panel regression,Custom datasets,Descriptive Statistics,Unit root,Multicollinearity"><link data-rh="true" rel="icon" href="/img/favicon.ico"><link data-rh="true" rel="canonical" href="https://docs.openbb.co/sdk/data-available/econometrics"><link data-rh="true" rel="alternate" href="https://docs.openbb.co/sdk/data-available/econometrics" hreflang="en"><link data-rh="true" rel="alternate" href="https://docs.openbb.co/sdk/data-available/econometrics" hreflang="x-default"><link data-rh="true" rel="preconnect" href="https://7D1HQ0IXAS-dsn.algolia.net" crossorigin="anonymous"><link rel="search" type="application/opensearchdescription+xml" title="OpenBB Docs" href="/opensearch.xml">
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tocCollapsibleButton_TO0P">On this page</button></div><div class="theme-doc-markdown markdown"><header><h1>Econometrics</h1></header>
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<p>The capabilities of the <a href="/terminal/menus/econometrics">Econometrics menu</a> in the OpenBB Terminal are wrapped into a powerful SDK, enabling users to work with the data in a flexible environment that can be fully customized to meet the needs of any user. The Econometrics menu's purpose is to provide the user the ability to perform statistical research on custom datasets. The menu allows the user to load in his/her own dataset(s), modify the data by adding columns or setting indices, apply statistical tests (e.g. <a href="https://en.wikipedia.org/wiki/Breusch%E2%80%93Godfrey_test" target="_blank" rel="noreferrer noopener">Breusch-Godfrey autocorrelation tests</a>) as well as OLS regressions and Panel regressions (e.g. <a href="https://en.wikipedia.org/wiki/Random_effects_model" target="_blank" rel="noreferrer noopener">Random Effects</a> and <a href="https://en.wikipedia.org/wiki/Fixed_effects_model" target="_blank" rel="noreferrer noopener">Fixed Effects</a>)</p>
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id="how-to-use">How to use<a href="#how-to-use" class="hash-link" aria-label="Direct link to How to use" title="Direct link to How to use"></a></h2>
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<p>Start a Python script or Notebook file and import the SDK module:</p>
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<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token keyword" style="color:rgb(86, 156, 214)">from</span><span class="token plain"> openbb_terminal</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">sdk </span><span class="token keyword" style="color:rgb(86, 156, 214)">import</span><span class="token plain"> openbb</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
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<p>Below is a brief description of each function within the Portfolio module:</p>
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<table><thead><tr><th style="text-align:left">Path</th><th style="text-align:center">Type</th><th style="text-align:right">Description</th></tr></thead><tbody><tr><td style="text-align:left">openbb.econometrics.granger</td><td style="text-align:center">Function</td><td style="text-align:right">Check time-series for Granger causality (X causes Y)</td></tr><tr><td style="text-align:left">openbb.econometrics.granger_chart</td><td style="text-align:center">Function</td><td style="text-align:right">Obtain a nice table of Granger causality</td></tr><tr><td style="text-align:left">openbb.econometrics.fe</td><td style="text-align:center">Function</td><td style="text-align:right">Perform a Fixed Effects (fe) regression on Panel data</td></tr><tr><td style="text-align:left">openbb.econometrics.options</td><td style="text-align:center">Function</td><td style="text-align:right">Obtain all options that can be used for regression techniques</td></tr><tr><td style="text-align:left">openbb.econometrics.options_chart</td><td style="text-align:center">Function</td><td style="text-align:right">Get a nice table of the options</td></tr><tr><td style="text-align:left">openbb.econometrics.dwat</td><td style="text-align:center">Function</td><td style="text-align:right">Check for auto-correlation with Durbin Watson</td></tr><tr><td style="text-align:left">openbb.econometrics.dwat_chart</td><td style="text-align:center">Function</td><td style="text-align:right">Plot the residuals of the OLS model</td></tr><tr><td style="text-align:left">openbb.econometrics.coint</td><td style="text-align:center">Function</td><td style="text-align:right">Check whether time-series are cointegrated</td></tr><tr><td style="text-align:left">openbb.econometrics.coint_chart</td><td style="text-align:center">Function</td><td style="text-align:right">Show the error-correction terms plot</td></tr><tr><td style="text-align:left">openbb.econometrics.pols</td><td style="text-align:center">Function</td><td style="text-align:right">Perform a Pooled OLS (pols) regression on Panel data</td></tr><tr><td style="text-align:left">openbb.econometrics.root</td><td style="text-align:center">Function</td><td style="text-align:right">Check for unit root in the timeseries</td></tr><tr><td style="text-align:left">openbb.econometrics.root_chart</td><td style="text-align:center">Function</td><td style="text-align:right">Show a nice table of the unit root test results</td></tr><tr><td style="text-align:left">openbb.econometrics.bgod</td><td style="text-align:center">Function</td><td style="text-align:right">Check for autocorrelation with Breusch Godfrey</td></tr><tr><td style="text-align:left">openbb.econometrics.bgod_chart</td><td style="text-align:center">Function</td><td style="text-align:right">Show a nice table of the autocorrelation test results</td></tr><tr><td style="text-align:left">openbb.econometrics.re</td><td style="text-align:center">Function</td><td style="text-align:right">Perform a Random Effects (re) regression on Panel data</td></tr><tr><td style="text-align:left">openbb.econometrics.bols</td><td style="text-align:center">Function</td><td style="text-align:right">Perform a Between OLS (bols) regression on Panel data</td></tr><tr><td style="text-align:left">openbb.econometrics.panel</td><td style="text-align:center">Function</td><td style="text-align:right">Obtain the regression results wrapper</td></tr><tr><td style="text-align:left">openbb.econometrics.get_regression_data</td><td style="text-align:center">Function</td><td style="text-align:right">Obtain an OLS model wrapper</td></tr><tr><td style="text-align:left">openbb.econometrics.norm</td><td style="text-align:center">Function</td><td style="text-align:right">Check whether the time-series is normally distributed</td></tr><tr><td style="text-align:left">openbb.econometrics.norm_chart</td><td style="text-align:center">Function</td><td style="text-align:right">Show a histogram of the time-series</td></tr><tr><td style="text-align:left">openbb.econometrics.clean</td><td style="text-align:center">Function</td><td style="text-align:right">Apply either a fill or drop method to clean the data</td></tr><tr><td style="text-align:left">openbb.econometrics.bpag</td><td style="text-align:center">Function</td><td style="text-align:right">Test for heteroskedasticity with a Breusch-Pagan test</td></tr><tr><td style="text-align:left">openbb.econometrics.bpag_chart</td><td style="text-align:center">Function</td><td style="text-align:right">Get a nice table with Breusch-Pagan test results</td></tr><tr><td style="text-align:left">openbb.econometrics.fdols</td><td style="text-align:center">Function</td><td style="text-align:right">Perform a First Difference OLS (fdols) regression on Panel data</td></tr><tr><td style="text-align:left">openbb.econometrics.load</td><td style="text-align:center">Function</td><td style="text-align:right">Load in a dataset to be used within other functionalities</td></tr><tr><td style="text-align:left">openbb.econometrics.ols</td><td style="text-align:center">Function</td><td style="text-align:right">Perform an Ordinary Least Squares (ols) regression on time-series data</td></tr><tr><td style="text-align:left">openbb.econometrics.comparison</td><td style="text-align:center">Function</td><td style="text-align:right">Compare different regression models in one table</td></tr></tbody></table>
|
||
<p>Alternatively you can print the contents of the Econometrics SDK with:</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token builtin" style="color:rgb(86, 156, 214)">help</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token plain">openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometrics</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id="examples">Examples<a href="#examples" class="hash-link" aria-label="Direct link to Examples" title="Direct link to Examples"></a></h2>
|
||
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="loading-a-dataset">Loading a dataset<a href="#loading-a-dataset" class="hash-link" aria-label="Direct link to Loading a dataset" title="Direct link to Loading a dataset"></a></h3>
|
||
<p>The first step in using this menu is loading a dataset. This can be either an example dataset, see the list below, or any locally stored Excel file. To demonstrate the usage of the menu, the <a href="https://www.statsmodels.org/dev/datasets/generated/longley.html" target="_blank" rel="noreferrer noopener">longley</a>
|
||
dataset is loaded in. This can be done with the following</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain">example_load </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometrics</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">load</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token string" style="color:rgb(206, 145, 120)">"anes96"</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">file_load </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometric</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">load</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token string" style="color:rgb(206, 145, 120)">"PATH_TO_FILE/FILE.xlsx"</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<table><thead><tr><th style="text-align:left">File</th><th style="text-align:right">Description</th></tr></thead><tbody><tr><td style="text-align:left">anes96</td><td style="text-align:right">American National Election Survey 1996</td></tr><tr><td style="text-align:left">cancer</td><td style="text-align:right">Breast Cancer Data</td></tr><tr><td style="text-align:left">ccard</td><td style="text-align:right">Bill Greene’s credit scoring data.</td></tr><tr><td style="text-align:left">cancer_china</td><td style="text-align:right">Smoking and lung cancer in eight cities in China.</td></tr><tr><td style="text-align:left">co2</td><td style="text-align:right">Mauna Loa Weekly Atmospheric CO2 Data</td></tr><tr><td style="text-align:left">committee</td><td style="text-align:right">First 100 days of the US House of Representatives 1995</td></tr><tr><td style="text-align:left">copper</td><td style="text-align:right">World Copper Market 1951-1975 Dataset</td></tr><tr><td style="text-align:left">cpunish</td><td style="text-align:right">US Capital Punishment dataset.</td></tr><tr><td style="text-align:left">danish_data</td><td style="text-align:right">Danish Money Demand Data</td></tr><tr><td style="text-align:left">elnino</td><td style="text-align:right">El Nino - Sea Surface Temperatures</td></tr><tr><td style="text-align:left">engel</td><td style="text-align:right">Engel (1857) food expenditure data</td></tr><tr><td style="text-align:left">fair</td><td style="text-align:right">Affairs dataset</td></tr><tr><td style="text-align:left">fertility</td><td style="text-align:right">World Bank Fertility Data</td></tr><tr><td style="text-align:left">grunfeld</td><td style="text-align:right">Grunfeld (1950) Investment Data</td></tr><tr><td style="text-align:left">heart</td><td style="text-align:right">Transplant Survival Data</td></tr><tr><td style="text-align:left">interest_inflation</td><td style="text-align:right">(West) German interest and inflation rate 1972-1998</td></tr><tr><td style="text-align:left">longley</td><td style="text-align:right">Longley dataset</td></tr><tr><td style="text-align:left">macrodata</td><td style="text-align:right">United States Macroeconomic data</td></tr><tr><td style="text-align:left">modechoice</td><td style="text-align:right">Travel Mode Choice</td></tr><tr><td style="text-align:left">nile</td><td style="text-align:right">Nile River flows at Ashwan 1871-1970</td></tr><tr><td style="text-align:left">randhie</td><td style="text-align:right">RAND Health Insurance Experiment Data</td></tr><tr><td style="text-align:left">scotland</td><td style="text-align:right">Taxation Powers Vote for the Scottish Parliament 1997</td></tr><tr><td style="text-align:left">spector</td><td style="text-align:right">Spector and Mazzeo (1980) - Program Effectiveness Data</td></tr><tr><td style="text-align:left">stackloss</td><td style="text-align:right">Stack loss data</td></tr><tr><td style="text-align:left">star98</td><td style="text-align:right">Star98 Educational Dataset</td></tr><tr><td style="text-align:left">statecrim</td><td style="text-align:right">Statewide Crime Data 2009</td></tr><tr><td style="text-align:left">strikes</td><td style="text-align:right">U.S. Strike Duration Data</td></tr><tr><td style="text-align:left">sunspots</td><td style="text-align:right">Yearly sunspots data 1700-2008</td></tr><tr><td style="text-align:left">wage_panel</td><td style="text-align:right">Veila and M. Verbeek (1998): Whose Wages Do Unions Raise?</td></tr></tbody></table>
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||
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="working-with-time-series-data">Working with Time Series data<a href="#working-with-time-series-data" class="hash-link" aria-label="Direct link to Working with Time Series data" title="Direct link to Working with Time Series data"></a></h3>
|
||
<p>To demonstrate the usage of the Econometrics SDK for time series data, the
|
||
<a href="https://www.statsmodels.org/dev/datasets/generated/longley.html" target="_blank" rel="noreferrer noopener">longley</a> dataset is loaded in.</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token comment" style="color:rgb(106, 153, 85)"># Load the data</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">longley </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometrics</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">load</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token string" style="color:rgb(206, 145, 120)">"longley"</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"></span><span class="token comment" style="color:rgb(106, 153, 85)"># Show the data</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">longley</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<table><thead><tr><th style="text-align:right"></th><th style="text-align:right">TOTEMP</th><th style="text-align:right">GNPDEFL</th><th style="text-align:right">GNP</th><th style="text-align:right">UNEMP</th><th style="text-align:right">ARMED</th><th style="text-align:right">POP</th><th style="text-align:right">YEAR</th></tr></thead><tbody><tr><td style="text-align:right">0</td><td style="text-align:right">60323</td><td style="text-align:right">83</td><td style="text-align:right">234289</td><td style="text-align:right">2356</td><td style="text-align:right">1590</td><td style="text-align:right">107608</td><td style="text-align:right">1947</td></tr><tr><td style="text-align:right">1</td><td style="text-align:right">61122</td><td style="text-align:right">88.5</td><td style="text-align:right">259426</td><td style="text-align:right">2325</td><td style="text-align:right">1456</td><td style="text-align:right">108632</td><td style="text-align:right">1948</td></tr><tr><td style="text-align:right">2</td><td style="text-align:right">60171</td><td style="text-align:right">88.2</td><td style="text-align:right">258054</td><td style="text-align:right">3682</td><td style="text-align:right">1616</td><td style="text-align:right">109773</td><td style="text-align:right">1949</td></tr><tr><td style="text-align:right">3</td><td style="text-align:right">61187</td><td style="text-align:right">89.5</td><td style="text-align:right">284599</td><td style="text-align:right">3351</td><td style="text-align:right">1650</td><td style="text-align:right">110929</td><td style="text-align:right">1950</td></tr><tr><td style="text-align:right">4</td><td style="text-align:right">63221</td><td style="text-align:right">96.2</td><td style="text-align:right">328975</td><td style="text-align:right">2099</td><td style="text-align:right">3099</td><td style="text-align:right">112075</td><td style="text-align:right">1951</td></tr><tr><td style="text-align:right">5</td><td style="text-align:right">63639</td><td style="text-align:right">98.1</td><td style="text-align:right">346999</td><td style="text-align:right">1932</td><td style="text-align:right">3594</td><td style="text-align:right">113270</td><td style="text-align:right">1952</td></tr><tr><td style="text-align:right">6</td><td style="text-align:right">64989</td><td style="text-align:right">99</td><td style="text-align:right">365385</td><td style="text-align:right">1870</td><td style="text-align:right">3547</td><td style="text-align:right">115094</td><td style="text-align:right">1953</td></tr><tr><td style="text-align:right">7</td><td style="text-align:right">63761</td><td style="text-align:right">100</td><td style="text-align:right">363112</td><td style="text-align:right">3578</td><td style="text-align:right">3350</td><td style="text-align:right">116219</td><td style="text-align:right">1954</td></tr><tr><td style="text-align:right">8</td><td style="text-align:right">66019</td><td style="text-align:right">101.2</td><td style="text-align:right">397469</td><td style="text-align:right">2904</td><td style="text-align:right">3048</td><td style="text-align:right">117388</td><td style="text-align:right">1955</td></tr><tr><td style="text-align:right">9</td><td style="text-align:right">67857</td><td style="text-align:right">104.6</td><td style="text-align:right">419180</td><td style="text-align:right">2822</td><td style="text-align:right">2857</td><td style="text-align:right">118734</td><td style="text-align:right">1956</td></tr><tr><td style="text-align:right">10</td><td style="text-align:right">68169</td><td style="text-align:right">108.4</td><td style="text-align:right">442769</td><td style="text-align:right">2936</td><td style="text-align:right">2798</td><td style="text-align:right">120445</td><td style="text-align:right">1957</td></tr><tr><td style="text-align:right">11</td><td style="text-align:right">66513</td><td style="text-align:right">110.8</td><td style="text-align:right">444546</td><td style="text-align:right">4681</td><td style="text-align:right">2637</td><td style="text-align:right">121950</td><td style="text-align:right">1958</td></tr><tr><td style="text-align:right">12</td><td style="text-align:right">68655</td><td style="text-align:right">112.6</td><td style="text-align:right">482704</td><td style="text-align:right">3813</td><td style="text-align:right">2552</td><td style="text-align:right">123366</td><td style="text-align:right">1959</td></tr><tr><td style="text-align:right">13</td><td style="text-align:right">69564</td><td style="text-align:right">114.2</td><td style="text-align:right">502601</td><td style="text-align:right">3931</td><td style="text-align:right">2514</td><td style="text-align:right">125368</td><td style="text-align:right">1960</td></tr><tr><td style="text-align:right">14</td><td style="text-align:right">69331</td><td style="text-align:right">115.7</td><td style="text-align:right">518173</td><td style="text-align:right">4806</td><td style="text-align:right">2572</td><td style="text-align:right">127852</td><td style="text-align:right">1961</td></tr><tr><td style="text-align:right">15</td><td style="text-align:right">70551</td><td style="text-align:right">116.9</td><td style="text-align:right">554894</td><td style="text-align:right">4007</td><td style="text-align:right">2827</td><td style="text-align:right">130081</td><td style="text-align:right">1962</td></tr></tbody></table>
|
||
<p>This can be extended by also showing the descriptive statistics, this can be
|
||
done with a native command from Pandas as follows:</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain">longley</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">describe</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<table><thead><tr><th style="text-align:left"></th><th style="text-align:right">TOTEMP</th><th style="text-align:right">GNPDEFL</th><th style="text-align:right">GNP</th><th style="text-align:right">UNEMP</th><th style="text-align:right">ARMED</th><th style="text-align:right">POP</th><th style="text-align:right">YEAR</th></tr></thead><tbody><tr><td style="text-align:left">count</td><td style="text-align:right">16</td><td style="text-align:right">16</td><td style="text-align:right">16</td><td style="text-align:right">16</td><td style="text-align:right">16</td><td style="text-align:right">16</td><td style="text-align:right">16</td></tr><tr><td style="text-align:left">mean</td><td style="text-align:right">65317</td><td style="text-align:right">101.681</td><td style="text-align:right">387698</td><td style="text-align:right">3193.31</td><td style="text-align:right">2606.69</td><td style="text-align:right">117424</td><td style="text-align:right">1954.5</td></tr><tr><td style="text-align:left">std</td><td style="text-align:right">3511.97</td><td style="text-align:right">10.7916</td><td style="text-align:right">99394.9</td><td style="text-align:right">934.464</td><td style="text-align:right">695.92</td><td style="text-align:right">6956.1</td><td style="text-align:right">4.76095</td></tr><tr><td style="text-align:left">min</td><td style="text-align:right">60171</td><td style="text-align:right">83</td><td style="text-align:right">234289</td><td style="text-align:right">1870</td><td style="text-align:right">1456</td><td style="text-align:right">107608</td><td style="text-align:right">1947</td></tr><tr><td style="text-align:left">25%</td><td style="text-align:right">62712.5</td><td style="text-align:right">94.525</td><td style="text-align:right">317881</td><td style="text-align:right">2348.25</td><td style="text-align:right">2298</td><td style="text-align:right">111788</td><td style="text-align:right">1950.75</td></tr><tr><td style="text-align:left">50%</td><td style="text-align:right">65504</td><td style="text-align:right">100.6</td><td style="text-align:right">381427</td><td style="text-align:right">3143.5</td><td style="text-align:right">2717.5</td><td style="text-align:right">116804</td><td style="text-align:right">1954.5</td></tr><tr><td style="text-align:left">75%</td><td style="text-align:right">68290.5</td><td style="text-align:right">111.25</td><td style="text-align:right">454086</td><td style="text-align:right">3842.5</td><td style="text-align:right">3060.75</td><td style="text-align:right">122304</td><td style="text-align:right">1958.25</td></tr><tr><td style="text-align:left">max</td><td style="text-align:right">70551</td><td style="text-align:right">116.9</td><td style="text-align:right">554894</td><td style="text-align:right">4806</td><td style="text-align:right">3594</td><td style="text-align:right">130081</td><td style="text-align:right">1962</td></tr></tbody></table>
|
||
<p>It is possible to check for a variety of assumptions, e.g. normality, unit root,
|
||
granger and co-integration. The functions <code>openbb.econometric.norm</code> and <code>openb.econometrics.root</code> are shown below. Note
|
||
that due to the small size of the dataset, many of these tests are not
|
||
statistically significant.</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain">openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometrics</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">norm</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token plain">longley</span><span class="token punctuation" style="color:rgb(212, 212, 212)">[</span><span class="token string" style="color:rgb(206, 145, 120)">'GNP'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">]</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<table><thead><tr><th style="text-align:left"></th><th style="text-align:right">Kurtosis</th><th style="text-align:right">Skewness</th><th style="text-align:right">Jarque-Bera</th><th style="text-align:right">Shapiro-Wilk</th><th style="text-align:right">Kolmogorov-Smirnov</th></tr></thead><tbody><tr><td style="text-align:left">Statistic</td><td style="text-align:right">-1.1944</td><td style="text-align:right">0.0525317</td><td style="text-align:right">0.835092</td><td style="text-align:right">0.962593</td><td style="text-align:right">1</td></tr><tr><td style="text-align:left">p-value</td><td style="text-align:right">0.23232</td><td style="text-align:right">0.95811</td><td style="text-align:right">0.65866</td><td style="text-align:right">0.709</td><td style="text-align:right">0</td></tr></tbody></table>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain">openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometrics</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">root</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token plain">longley</span><span class="token punctuation" style="color:rgb(212, 212, 212)">[</span><span class="token string" style="color:rgb(206, 145, 120)">'POP'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">]</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<table><thead><tr><th style="text-align:left"></th><th style="text-align:right">ADF</th><th style="text-align:right">KPSS</th></tr></thead><tbody><tr><td style="text-align:left">Test Statistic</td><td style="text-align:right">2.35204</td><td style="text-align:right">0.324887</td></tr><tr><td style="text-align:left">P-Value</td><td style="text-align:right">0.998986</td><td style="text-align:right">0.1</td></tr><tr><td style="text-align:left">NLags</td><td style="text-align:right">6</td><td style="text-align:right">0</td></tr><tr><td style="text-align:left">Nobs</td><td style="text-align:right">9</td><td style="text-align:right">0</td></tr><tr><td style="text-align:left">ICBest</td><td style="text-align:right">113.054</td><td style="text-align:right">0</td></tr></tbody></table>
|
||
<p>The longley dataset is known for the ability to create an OLS regression that results in a <a href="https://www.investopedia.com/terms/r/r-squared.asp" target="_blank" rel="noreferrer noopener">R-squared</a> of 1.0 due to the fact that the US macroeconomic variables are known to be highly collinear. See the following regression performed with <code>openbb.econometrics.ols</code> as follows:</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token comment" style="color:rgb(106, 153, 85)"># Perform the regression technique. TOTEMP is dependent, all others independent</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">ols_regression </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometrics</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">ols</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token plain">longley</span><span class="token punctuation" style="color:rgb(212, 212, 212)">[</span><span class="token string" style="color:rgb(206, 145, 120)">'TOTEMP'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">]</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> longley</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">drop</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token string" style="color:rgb(206, 145, 120)">'TOTEMP'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> axis</span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token number" style="color:rgb(181, 206, 168)">1</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"></span><span class="token comment" style="color:rgb(106, 153, 85)"># Show the model summary</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">ols_regression</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">summary</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-text codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain"> OLS Regression Results</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">=======================================================================================</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Dep. Variable: TOTEMP R-squared (uncentered): 1.000</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Model: OLS Adj. R-squared (uncentered): 1.000</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Method: Least Squares F-statistic: 5.052e+04</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Date: Mon, 21 Nov 2022 Prob (F-statistic): 8.20e-22</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Time: 10:54:19 Log-Likelihood: -117.56</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">No. Observations: 16 AIC: 247.1</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Df Residuals: 10 BIC: 251.8</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Df Model: 6</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Covariance Type: nonrobust</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">==============================================================================</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> coef std err t P>|t| [0.025 0.975]</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">------------------------------------------------------------------------------</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">GNPDEFL -52.9936 129.545 -0.409 0.691 -341.638 235.650</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">GNP 0.0711 0.030 2.356 0.040 0.004 0.138</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">UNEMP -0.4235 0.418 -1.014 0.335 -1.354 0.507</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">ARMED -0.5726 0.279 -2.052 0.067 -1.194 0.049</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">POP -0.4142 0.321 -1.289 0.226 -1.130 0.302</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">YEAR 48.4179 17.689 2.737 0.021 9.003 87.832</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">==============================================================================</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Omnibus: 1.443 Durbin-Watson: 1.277</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Prob(Omnibus): 0.486 Jarque-Bera (JB): 0.605</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Skew: 0.476 Prob(JB): 0.739</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Kurtosis: 3.031 Cond. No. 4.56e+05</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">==============================================================================</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Notes:</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">[1] R² is computed without centering (uncentered) since the model does not contain a constant.</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">[3] The condition number is large, 4.56e+05. This might indicate that there are</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">strong multicollinearity or other numerical problems.</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<p>After running the regression estimation, it is possible to perform tests on the residuals of the model. E.g. for autocorrelation and heteroscedasity as shown below with the <code>openbb.econometrics.bgod</code> and <code>openbb.econometrics.bpag</code> functions.</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token comment" style="color:rgb(106, 153, 85)"># Perform Breusch Goodfrey auto-correlation test</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometrics</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">bgod</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token plain">ols_regression</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<table><thead><tr><th style="text-align:left"></th><th style="text-align:right">0</th></tr></thead><tbody><tr><td style="text-align:left">lm-stat</td><td style="text-align:right">10.3471</td></tr><tr><td style="text-align:left">p-value</td><td style="text-align:right">0.0158347</td></tr><tr><td style="text-align:left">f-stat</td><td style="text-align:right">0.0970889</td></tr><tr><td style="text-align:left">fp-value</td><td style="text-align:right">0.958799</td></tr></tbody></table>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token comment" style="color:rgb(106, 153, 85)"># Perform Breusch Pagan heteroskedacity test</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometrics</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">bpag</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token plain">ols_regression</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<table><thead><tr><th style="text-align:left"></th><th style="text-align:right">0</th></tr></thead><tbody><tr><td style="text-align:left">lm-stat</td><td style="text-align:right">7.90331</td></tr><tr><td style="text-align:left">p-value</td><td style="text-align:right">0.161645</td></tr><tr><td style="text-align:left">f-stat</td><td style="text-align:right">1.62686</td></tr><tr><td style="text-align:left">fp-value</td><td style="text-align:right">0.236596</td></tr></tbody></table>
|
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<h3 class="anchor anchorWithStickyNavbar_LWe7" id="working-with-panel-data">Working with Panel data<a href="#working-with-panel-data" class="hash-link" aria-label="Direct link to Working with Panel data" title="Direct link to Working with Panel data"></a></h3>
|
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<p>Within the examples there is one panel dataset available named <code>wage_panel</code>. This is a dataset from the paper by Vella and M. Verbeek (1998), “Whose Wages Do Unions Raise? A Dynamic Model of Unionism and Wage Rate Determination for Young Men,” Journal of Applied Econometrics 13, 163-183. This is a well-known dataset also used within Chapter 14 of <a href="https://www.amazon.com/Introductory-Econometrics-Modern-Approach-Economics/dp/1111531048" target="_blank" rel="noreferrer noopener">Introduction to Econometrics by Jeffrey Wooldridge</a>.</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token comment" style="color:rgb(106, 153, 85)"># Load the data</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">wage_panel </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometrics</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">load</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token string" style="color:rgb(206, 145, 120)">"wage_panel"</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"></span><span class="token comment" style="color:rgb(106, 153, 85)"># Show the data</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">wage_panel</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<table><thead><tr><th style="text-align:right"></th><th style="text-align:right">nr</th><th style="text-align:right">year</th><th style="text-align:right">black</th><th style="text-align:right">exper</th><th style="text-align:right">hisp</th><th style="text-align:right">hours</th><th style="text-align:right">married</th><th style="text-align:right">educ</th><th style="text-align:right">union</th><th style="text-align:right">lwage</th><th style="text-align:right">expersq</th><th style="text-align:right">occupation</th></tr></thead><tbody><tr><td style="text-align:right">0</td><td style="text-align:right">13</td><td style="text-align:right">1980</td><td style="text-align:right">0</td><td style="text-align:right">1</td><td style="text-align:right">0</td><td style="text-align:right">2672</td><td style="text-align:right">0</td><td style="text-align:right">14</td><td style="text-align:right">0</td><td style="text-align:right">1.19754</td><td style="text-align:right">1</td><td style="text-align:right">9</td></tr><tr><td style="text-align:right">1</td><td style="text-align:right">13</td><td style="text-align:right">1981</td><td style="text-align:right">0</td><td style="text-align:right">2</td><td style="text-align:right">0</td><td style="text-align:right">2320</td><td style="text-align:right">0</td><td style="text-align:right">14</td><td style="text-align:right">1</td><td style="text-align:right">1.85306</td><td style="text-align:right">4</td><td style="text-align:right">9</td></tr><tr><td style="text-align:right">2</td><td style="text-align:right">13</td><td style="text-align:right">1982</td><td style="text-align:right">0</td><td style="text-align:right">3</td><td style="text-align:right">0</td><td style="text-align:right">2940</td><td style="text-align:right">0</td><td style="text-align:right">14</td><td style="text-align:right">0</td><td style="text-align:right">1.34446</td><td style="text-align:right">9</td><td style="text-align:right">9</td></tr><tr><td style="text-align:right">3</td><td style="text-align:right">13</td><td style="text-align:right">1983</td><td style="text-align:right">0</td><td style="text-align:right">4</td><td style="text-align:right">0</td><td style="text-align:right">2960</td><td style="text-align:right">0</td><td style="text-align:right">14</td><td style="text-align:right">0</td><td style="text-align:right">1.43321</td><td style="text-align:right">16</td><td style="text-align:right">9</td></tr><tr><td style="text-align:right">4</td><td style="text-align:right">13</td><td style="text-align:right">1984</td><td style="text-align:right">0</td><td style="text-align:right">5</td><td style="text-align:right">0</td><td style="text-align:right">3071</td><td style="text-align:right">0</td><td style="text-align:right">14</td><td style="text-align:right">0</td><td style="text-align:right">1.56812</td><td style="text-align:right">25</td><td style="text-align:right">5</td></tr></tbody></table>
|
||
<p>4360 rows × 12 columns</p>
|
||
<p>To run panel regressions, it is important to define both <em>entity</em> (e.g. company) and <em>time</em> (e.g. year).
|
||
Trying to run the <code>openbb.econometrics.re</code> function would right now result in the following:</p>
|
||
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-text codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain">openbb.econometrics.re(wage_panel['black'], wage_panel.drop('black', axis=1))</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Error: Series can only be used with a 2-level MultiIndex</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<p>This can be corrected by setting a multi-index, this can be done with the following:</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain">wage_panel </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> wage_panel</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">set_index</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token punctuation" style="color:rgb(212, 212, 212)">[</span><span class="token string" style="color:rgb(206, 145, 120)">'nr'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> </span><span class="token string" style="color:rgb(206, 145, 120)">'year'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">]</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> drop</span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token boolean">False</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<p>The columns <code>nr</code> and <code>year</code> still exists within the dataset and could have been dropped with the if desired. However, in this case the <code>year</code> column is relevant for generating time effects in Pooled OLS, Fixed Effects and Random Effects estimations. To be able to do this, the type of the year column needs to be changed accordingly to 'category' so it is perceived as categorical data. This can be done with the following:</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token comment" style="color:rgb(106, 153, 85)"># Observe the current types</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">wage_panel</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">dtypes</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<table><thead><tr><th style="text-align:left"></th><th style="text-align:left">0</th></tr></thead><tbody><tr><td style="text-align:left">nr</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">year</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">black</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">exper</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">hisp</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">hours</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">married</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">educ</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">union</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">lwage</td><td style="text-align:left">float64</td></tr><tr><td style="text-align:left">expersq</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">occupation</td><td style="text-align:left">int64</td></tr></tbody></table>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token comment" style="color:rgb(106, 153, 85)"># Change the type of year to categorical</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">wage_panel</span><span class="token punctuation" style="color:rgb(212, 212, 212)">[</span><span class="token string" style="color:rgb(206, 145, 120)">'year'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">]</span><span class="token plain"> </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> wage_panel</span><span class="token punctuation" style="color:rgb(212, 212, 212)">[</span><span class="token string" style="color:rgb(206, 145, 120)">'year'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">]</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">astype</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token string" style="color:rgb(206, 145, 120)">'category'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"></span><span class="token comment" style="color:rgb(106, 153, 85)"># Observe the changed types</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">wage_panel</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">dtypes</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<table><thead><tr><th style="text-align:left"></th><th style="text-align:left">0</th></tr></thead><tbody><tr><td style="text-align:left">nr</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">year</td><td style="text-align:left">category</td></tr><tr><td style="text-align:left">black</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">exper</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">hisp</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">hours</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">married</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">educ</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">union</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">lwage</td><td style="text-align:left">float64</td></tr><tr><td style="text-align:left">expersq</td><td style="text-align:left">int64</td></tr><tr><td style="text-align:left">occupation</td><td style="text-align:left">int64</td></tr></tbody></table>
|
||
<p>The dataset is now properly configured to allow for proper panel regressions. The Econometrics SDK supports the following regression techniques.</p>
|
||
<table><thead><tr><th style="text-align:left">Path</th><th style="text-align:right">Description</th></tr></thead><tbody><tr><td style="text-align:left">openbb.econometrics.ols</td><td style="text-align:right">Perform an Ordinary Least Squares (ols) regression on time-series data</td></tr><tr><td style="text-align:left">openbb.econometrics.pols</td><td style="text-align:right">Perform a Pooled OLS (pols) regression on Panel data</td></tr><tr><td style="text-align:left">openbb.econometrics.bols</td><td style="text-align:right">Perform a Between OLS (bols) regression on Panel data</td></tr><tr><td style="text-align:left">openbb.econometrics.fdols</td><td style="text-align:right">Perform a First Difference OLS (fdols) regression on Panel data</td></tr><tr><td style="text-align:left">openbb.econometrics.fe</td><td style="text-align:right">Perform a Fixed Effects (fe) regression on Panel data</td></tr><tr><td style="text-align:left">openbb.econometrics.re</td><td style="text-align:right">Perform a Random Effects (re) regression on Panel data</td></tr></tbody></table>
|
||
<p>As an example, a <strong>Random Effects</strong> regression is performed. This can be done as follows:</p>
|
||
<div class="language-python codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-python codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token comment" style="color:rgb(106, 153, 85)"># Perform the Random Effects regression technique</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">random_effects_regression </span><span class="token operator" style="color:rgb(212, 212, 212)">=</span><span class="token plain"> openbb</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">econometrics</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">re</span><span class="token punctuation" style="color:rgb(212, 212, 212)">(</span><span class="token plain">wage_panel</span><span class="token punctuation" style="color:rgb(212, 212, 212)">[</span><span class="token string" style="color:rgb(206, 145, 120)">'lwage'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">]</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> wage_panel</span><span class="token punctuation" style="color:rgb(212, 212, 212)">[</span><span class="token punctuation" style="color:rgb(212, 212, 212)">[</span><span class="token string" style="color:rgb(206, 145, 120)">'black'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> </span><span class="token string" style="color:rgb(206, 145, 120)">'hisp'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> </span><span class="token string" style="color:rgb(206, 145, 120)">'exper'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> </span><span class="token string" style="color:rgb(206, 145, 120)">'expersq'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> </span><span class="token string" style="color:rgb(206, 145, 120)">'married'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> </span><span class="token string" style="color:rgb(206, 145, 120)">'educ'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token plain"> </span><span class="token string" style="color:rgb(206, 145, 120)">'union'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">,</span><span class="token string" style="color:rgb(206, 145, 120)">'year'</span><span class="token punctuation" style="color:rgb(212, 212, 212)">]</span><span class="token punctuation" style="color:rgb(212, 212, 212)">]</span><span class="token punctuation" style="color:rgb(212, 212, 212)">)</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"></span><span class="token comment" style="color:rgb(106, 153, 85)"># Show the results</span><span class="token plain"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">random_effects_regression</span><span class="token punctuation" style="color:rgb(212, 212, 212)">.</span><span class="token plain">summary</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" d="M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z"></path></svg></span></button></div></div></div>
|
||
<div class="codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#9CDCFE;--prism-background-color:#1E1E1E"><div class="codeBlockContent_m3Ux"><pre tabindex="0" class="prism-code language-text codeBlock_qGQc thin-scrollbar"><code class="codeBlockLines_p187"><span class="token-line" style="color:#9CDCFE"><span class="token plain"> RandomEffects Estimation Summary</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">================================================================================</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Dep. Variable: lwage R-squared: 0.1806</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Estimator: RandomEffects R-squared (Between): 0.1853</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">No. Observations: 4360 R-squared (Within): 0.1799</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Date: Mon, Nov 21 2022 R-squared (Overall): 0.1828</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Time: 11:13:36 Log-likelihood -1622.5</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Cov. Estimator: Unadjusted</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> F-statistic: 68.409</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Entities: 545 P-value 0.0000</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Avg Obs: 8.0000 Distribution: F(14,4345)</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Min Obs: 8.0000</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Max Obs: 8.0000 F-statistic (robust): 68.409</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> P-value 0.0000</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Time periods: 8 Distribution: F(14,4345)</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Avg Obs: 545.00</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Min Obs: 545.00</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">Max Obs: 545.00</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain" style="display:inline-block"></span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> Parameter Estimates</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">==============================================================================</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain"> Parameter Std. Err. T-stat P-value Lower CI Upper CI</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">------------------------------------------------------------------------------</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">const 0.0234 0.1514 0.1546 0.8771 -0.2735 0.3203</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">black -0.1394 0.0480 -2.9054 0.0037 -0.2334 -0.0453</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">hisp 0.0217 0.0428 0.5078 0.6116 -0.0622 0.1057</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">exper 0.1058 0.0154 6.8706 0.0000 0.0756 0.1361</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">expersq -0.0047 0.0007 -6.8623 0.0000 -0.0061 -0.0034</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">married 0.0638 0.0168 3.8035 0.0001 0.0309 0.0967</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">educ 0.0919 0.0107 8.5744 0.0000 0.0709 0.1129</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">union 0.1059 0.0179 5.9289 0.0000 0.0709 0.1409</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">year.1981 0.0404 0.0247 1.6362 0.1019 -0.0080 0.0889</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">year.1982 0.0309 0.0324 0.9519 0.3412 -0.0327 0.0944</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">year.1983 0.0202 0.0417 0.4840 0.6284 -0.0616 0.1020</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">year.1984 0.0430 0.0515 0.8350 0.4037 -0.0580 0.1440</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">year.1985 0.0577 0.0615 0.9383 0.3482 -0.0629 0.1782</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">year.1986 0.0918 0.0716 1.2834 0.1994 -0.0485 0.2321</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">year.1987 0.1348 0.0817 1.6504 0.0989 -0.0253 0.2950</span><br></span><span class="token-line" style="color:#9CDCFE"><span class="token plain">==============================================================================</span><br></span></code></pre><div class="buttonGroup_6DOT"><button type="button" aria-label="Copy code to clipboard" title="Copy" class="clean-btn"><span class="copyButtonIcons_eSgA" aria-hidden="true"><svg viewBox="0 0 24 24" class="copyButtonIcon_y97N"><path fill="currentColor" d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"></path></svg><svg viewBox="0 0 24 24" class="copyButtonSuccessIcon_LjdS"><path fill="currentColor" 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