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<!DOCTYPE html>
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<title>15 Dummy Variables Part 1 | R Programming Guidebook Project</title>
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<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>About</a></li>
<li class="part"><span><b>I DataCamp</b></span></li>
<li class="chapter" data-level="1" data-path="introduction-to-r.html"><a href="introduction-to-r.html"><i class="fa fa-check"></i><b>1</b> Introduction to R</a>
<ul>
<li class="chapter" data-level="1.1" data-path="introduction-to-r.html"><a href="introduction-to-r.html#intro-to-basics"><i class="fa fa-check"></i><b>1.1</b> Intro to basics</a></li>
<li class="chapter" data-level="1.2" data-path="introduction-to-r.html"><a href="introduction-to-r.html#vectors"><i class="fa fa-check"></i><b>1.2</b> Vectors</a></li>
<li class="chapter" data-level="1.3" data-path="introduction-to-r.html"><a href="introduction-to-r.html#matrices"><i class="fa fa-check"></i><b>1.3</b> Matrices</a></li>
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<li class="chapter" data-level="1.5" data-path="introduction-to-r.html"><a href="introduction-to-r.html#data-frames"><i class="fa fa-check"></i><b>1.5</b> Data frames</a></li>
<li class="chapter" data-level="1.6" data-path="introduction-to-r.html"><a href="introduction-to-r.html#lists"><i class="fa fa-check"></i><b>1.6</b> Lists</a></li>
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<ul>
<li class="chapter" data-level="2.1" data-path="intermediate-r.html"><a href="intermediate-r.html#conditionals-and-control-flow"><i class="fa fa-check"></i><b>2.1</b> Conditionals And Control Flow</a></li>
<li class="chapter" data-level="2.2" data-path="intermediate-r.html"><a href="intermediate-r.html#loops"><i class="fa fa-check"></i><b>2.2</b> Loops</a></li>
<li class="chapter" data-level="2.3" data-path="intermediate-r.html"><a href="intermediate-r.html#functions"><i class="fa fa-check"></i><b>2.3</b> Functions</a></li>
<li class="chapter" data-level="2.4" data-path="intermediate-r.html"><a href="intermediate-r.html#the-apply-family"><i class="fa fa-check"></i><b>2.4</b> The apply family</a></li>
<li class="chapter" data-level="2.5" data-path="intermediate-r.html"><a href="intermediate-r.html#utilities"><i class="fa fa-check"></i><b>2.5</b> Utilities</a></li>
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<li class="chapter" data-level="3" data-path="intro-to-the-tidyverse.html"><a href="intro-to-the-tidyverse.html"><i class="fa fa-check"></i><b>3</b> Intro to the Tidyverse</a>
<ul>
<li class="chapter" data-level="3.1" data-path="intro-to-the-tidyverse.html"><a href="intro-to-the-tidyverse.html#data-wrangling"><i class="fa fa-check"></i><b>3.1</b> Data wrangling</a></li>
<li class="chapter" data-level="3.2" data-path="intro-to-the-tidyverse.html"><a href="intro-to-the-tidyverse.html#data-visualization"><i class="fa fa-check"></i><b>3.2</b> Data visualization</a></li>
<li class="chapter" data-level="3.3" data-path="intro-to-the-tidyverse.html"><a href="intro-to-the-tidyverse.html#grouping-and-summarizing"><i class="fa fa-check"></i><b>3.3</b> Grouping and summarizing</a></li>
<li class="chapter" data-level="3.4" data-path="intro-to-the-tidyverse.html"><a href="intro-to-the-tidyverse.html#types-of-visualizations"><i class="fa fa-check"></i><b>3.4</b> Types of visualizations</a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="intro-to-data-visualization-with-ggplot2.html"><a href="intro-to-data-visualization-with-ggplot2.html"><i class="fa fa-check"></i><b>4</b> Intro to Data Visualization with ggplot2</a>
<ul>
<li class="chapter" data-level="4.1" data-path="intro-to-data-visualization-with-ggplot2.html"><a href="intro-to-data-visualization-with-ggplot2.html#introduction"><i class="fa fa-check"></i><b>4.1</b> Introduction</a></li>
<li class="chapter" data-level="4.2" data-path="intro-to-data-visualization-with-ggplot2.html"><a href="intro-to-data-visualization-with-ggplot2.html#aesthetics"><i class="fa fa-check"></i><b>4.2</b> Aesthetics</a></li>
<li class="chapter" data-level="4.3" data-path="intro-to-data-visualization-with-ggplot2.html"><a href="intro-to-data-visualization-with-ggplot2.html#geometries"><i class="fa fa-check"></i><b>4.3</b> Geometries</a></li>
<li class="chapter" data-level="4.4" data-path="intro-to-data-visualization-with-ggplot2.html"><a href="intro-to-data-visualization-with-ggplot2.html#themes"><i class="fa fa-check"></i><b>4.4</b> Themes</a></li>
</ul></li>
<li class="chapter" data-level="5" data-path="working-with-data-in-the-tidyverse.html"><a href="working-with-data-in-the-tidyverse.html"><i class="fa fa-check"></i><b>5</b> Working with Data in the Tidyverse</a>
<ul>
<li class="chapter" data-level="5.1" data-path="working-with-data-in-the-tidyverse.html"><a href="working-with-data-in-the-tidyverse.html#explore-your-data"><i class="fa fa-check"></i><b>5.1</b> Explore your data</a></li>
<li class="chapter" data-level="5.2" data-path="working-with-data-in-the-tidyverse.html"><a href="working-with-data-in-the-tidyverse.html#tame-your-data"><i class="fa fa-check"></i><b>5.2</b> Tame your data</a></li>
<li class="chapter" data-level="5.3" data-path="working-with-data-in-the-tidyverse.html"><a href="working-with-data-in-the-tidyverse.html#tidy-your-data"><i class="fa fa-check"></i><b>5.3</b> Tidy your data</a></li>
<li class="chapter" data-level="5.4" data-path="working-with-data-in-the-tidyverse.html"><a href="working-with-data-in-the-tidyverse.html#transform-your-data"><i class="fa fa-check"></i><b>5.4</b> Transform your data</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="categorical-data-in-the-tidyverse.html"><a href="categorical-data-in-the-tidyverse.html"><i class="fa fa-check"></i><b>6</b> Categorical Data in the Tidyverse</a>
<ul>
<li class="chapter" data-level="6.1" data-path="categorical-data-in-the-tidyverse.html"><a href="categorical-data-in-the-tidyverse.html#introduction-to-factor-variables"><i class="fa fa-check"></i><b>6.1</b> Introduction to Factor Variables</a></li>
<li class="chapter" data-level="6.2" data-path="categorical-data-in-the-tidyverse.html"><a href="categorical-data-in-the-tidyverse.html#manipulating-factor-variables"><i class="fa fa-check"></i><b>6.2</b> Manipulating Factor Variables</a></li>
<li class="chapter" data-level="6.3" data-path="categorical-data-in-the-tidyverse.html"><a href="categorical-data-in-the-tidyverse.html#creating-factor-variables"><i class="fa fa-check"></i><b>6.3</b> Creating Factor Variables</a></li>
<li class="chapter" data-level="6.4" data-path="categorical-data-in-the-tidyverse.html"><a href="categorical-data-in-the-tidyverse.html#case-study-on-flight-etiquette"><i class="fa fa-check"></i><b>6.4</b> Case Study on Flight Etiquette</a></li>
</ul></li>
<li class="chapter" data-level="7" data-path="data-manipulation-with-dplyr.html"><a href="data-manipulation-with-dplyr.html"><i class="fa fa-check"></i><b>7</b> Data Manipulation with dplyr</a>
<ul>
<li class="chapter" data-level="7.1" data-path="data-manipulation-with-dplyr.html"><a href="data-manipulation-with-dplyr.html#transforming-data-with-dplyr"><i class="fa fa-check"></i><b>7.1</b> Transforming Data with dplyr</a></li>
<li class="chapter" data-level="7.2" data-path="data-manipulation-with-dplyr.html"><a href="data-manipulation-with-dplyr.html#aggregating-data"><i class="fa fa-check"></i><b>7.2</b> Aggregating Data</a></li>
<li class="chapter" data-level="7.3" data-path="data-manipulation-with-dplyr.html"><a href="data-manipulation-with-dplyr.html#selecting-and-transforming-data"><i class="fa fa-check"></i><b>7.3</b> Selecting and Transforming Data</a></li>
<li class="chapter" data-level="7.4" data-path="data-manipulation-with-dplyr.html"><a href="data-manipulation-with-dplyr.html#case-study-the-babynames-dataset"><i class="fa fa-check"></i><b>7.4</b> Case Study: The babynames Dataset</a></li>
</ul></li>
<li class="chapter" data-level="8" data-path="joining-data-with-dplyr.html"><a href="joining-data-with-dplyr.html"><i class="fa fa-check"></i><b>8</b> Joining Data with dplyr</a>
<ul>
<li class="chapter" data-level="8.1" data-path="joining-data-with-dplyr.html"><a href="joining-data-with-dplyr.html#joining-tables"><i class="fa fa-check"></i><b>8.1</b> Joining Tables</a></li>
<li class="chapter" data-level="8.2" data-path="joining-data-with-dplyr.html"><a href="joining-data-with-dplyr.html#left-and-right-joins"><i class="fa fa-check"></i><b>8.2</b> Left and Right Joins</a></li>
<li class="chapter" data-level="8.3" data-path="joining-data-with-dplyr.html"><a href="joining-data-with-dplyr.html#full-semi-and-anti-joins"><i class="fa fa-check"></i><b>8.3</b> Full, Semi, and Anti Joins</a></li>
<li class="chapter" data-level="8.4" data-path="joining-data-with-dplyr.html"><a href="joining-data-with-dplyr.html#case-study-joins-on-stack-overflow-data"><i class="fa fa-check"></i><b>8.4</b> Case Study: Joins on Stack Overflow Data</a></li>
</ul></li>
<li class="chapter" data-level="9" data-path="cleaning-data-in-r.html"><a href="cleaning-data-in-r.html"><i class="fa fa-check"></i><b>9</b> Cleaning Data in R</a>
<ul>
<li class="chapter" data-level="9.1" data-path="cleaning-data-in-r.html"><a href="cleaning-data-in-r.html#common-data-problems"><i class="fa fa-check"></i><b>9.1</b> Common Data Problems</a></li>
<li class="chapter" data-level="9.2" data-path="cleaning-data-in-r.html"><a href="cleaning-data-in-r.html#categorical-and-text-data"><i class="fa fa-check"></i><b>9.2</b> Categorical and Text Data</a></li>
<li class="chapter" data-level="9.3" data-path="cleaning-data-in-r.html"><a href="cleaning-data-in-r.html#advanced-data-problems"><i class="fa fa-check"></i><b>9.3</b> Advanced Data Problems</a></li>
<li class="chapter" data-level="9.4" data-path="cleaning-data-in-r.html"><a href="cleaning-data-in-r.html#record-linkage"><i class="fa fa-check"></i><b>9.4</b> Record Linkage</a></li>
</ul></li>
<li class="chapter" data-level="10" data-path="introduction-to-sql.html"><a href="introduction-to-sql.html"><i class="fa fa-check"></i><b>10</b> Introduction to SQL</a>
<ul>
<li class="chapter" data-level="10.1" data-path="introduction-to-sql.html"><a href="introduction-to-sql.html#selecting-columns"><i class="fa fa-check"></i><b>10.1</b> Selecting columns</a></li>
<li class="chapter" data-level="10.2" data-path="introduction-to-sql.html"><a href="introduction-to-sql.html#filtering-rows"><i class="fa fa-check"></i><b>10.2</b> Filtering rows</a></li>
<li class="chapter" data-level="10.3" data-path="introduction-to-sql.html"><a href="introduction-to-sql.html#aggregate-functions"><i class="fa fa-check"></i><b>10.3</b> Aggregate Functions</a></li>
<li class="chapter" data-level="10.4" data-path="introduction-to-sql.html"><a href="introduction-to-sql.html#sorting-and-grouping"><i class="fa fa-check"></i><b>10.4</b> Sorting and grouping</a></li>
</ul></li>
<li class="chapter" data-level="11" data-path="joining-data-in-sql.html"><a href="joining-data-in-sql.html"><i class="fa fa-check"></i><b>11</b> Joining Data in SQL</a>
<ul>
<li class="chapter" data-level="11.1" data-path="joining-data-in-sql.html"><a href="joining-data-in-sql.html#introduction-to-joins"><i class="fa fa-check"></i><b>11.1</b> Introduction to joins</a></li>
<li class="chapter" data-level="11.2" data-path="joining-data-in-sql.html"><a href="joining-data-in-sql.html#outer-joins-and-cross-joins"><i class="fa fa-check"></i><b>11.2</b> Outer joins and cross joins</a></li>
<li class="chapter" data-level="11.3" data-path="joining-data-in-sql.html"><a href="joining-data-in-sql.html#set-theory-clauses"><i class="fa fa-check"></i><b>11.3</b> Set theory clauses</a></li>
<li class="chapter" data-level="11.4" data-path="joining-data-in-sql.html"><a href="joining-data-in-sql.html#subqueries"><i class="fa fa-check"></i><b>11.4</b> Subqueries</a></li>
</ul></li>
<li class="chapter" data-level="12" data-path="web-scraping-in-r.html"><a href="web-scraping-in-r.html"><i class="fa fa-check"></i><b>12</b> Web Scraping in R</a>
<ul>
<li class="chapter" data-level="12.1" data-path="web-scraping-in-r.html"><a href="web-scraping-in-r.html#introduction-to-html-and-web-scraping"><i class="fa fa-check"></i><b>12.1</b> Introduction to HTML and Web Scraping</a></li>
<li class="chapter" data-level="12.2" data-path="web-scraping-in-r.html"><a href="web-scraping-in-r.html#navigation-and-selection-with-css"><i class="fa fa-check"></i><b>12.2</b> Navigation and Selection with CSS</a></li>
<li class="chapter" data-level="12.3" data-path="web-scraping-in-r.html"><a href="web-scraping-in-r.html#advanced-selection-with-xpath"><i class="fa fa-check"></i><b>12.3</b> Advanced Selection with XPATH</a></li>
<li class="chapter" data-level="12.4" data-path="web-scraping-in-r.html"><a href="web-scraping-in-r.html#scraping-best-practices"><i class="fa fa-check"></i><b>12.4</b> Scraping Best Practices</a></li>
</ul></li>
<li class="part"><span><b>II Econometrics</b></span></li>
<li class="chapter" data-level="13" data-path="ch-2---slr.html"><a href="ch-2---slr.html"><i class="fa fa-check"></i><b>13</b> Ch 2 - SLR</a>
<ul>
<li class="chapter" data-level="13.1" data-path="ch-2---slr.html"><a href="ch-2---slr.html#notes"><i class="fa fa-check"></i><b>13.1</b> Notes</a></li>
<li class="chapter" data-level="13.2" data-path="ch-2---slr.html"><a href="ch-2---slr.html#example-2.3-ceo-salary-and-return-on-equity"><i class="fa fa-check"></i><b>13.2</b> Example 2.3: CEO Salary and Return on Equity</a></li>
<li class="chapter" data-level="13.3" data-path="ch-2---slr.html"><a href="ch-2---slr.html#example-2.4-wage-and-education"><i class="fa fa-check"></i><b>13.3</b> Example 2.4: Wage and Education</a></li>
<li class="chapter" data-level="13.4" data-path="ch-2---slr.html"><a href="ch-2---slr.html#example-2.5-voting-outcomes-and-campaign-expenditures"><i class="fa fa-check"></i><b>13.4</b> Example 2.5: Voting Outcomes and Campaign Expenditures</a></li>
<li class="chapter" data-level="13.5" data-path="ch-2---slr.html"><a href="ch-2---slr.html#example-of-fitted-values-haty"><i class="fa fa-check"></i><b>13.5</b> Example of Fitted Values (<span class="math inline">\(\hat{y}\)</span>)</a></li>
</ul></li>
<li class="chapter" data-level="14" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html"><i class="fa fa-check"></i><b>14</b> Ch 3 - MLR</a>
<ul>
<li class="chapter" data-level="14.1" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#data"><i class="fa fa-check"></i><b>14.1</b> Data</a>
<ul>
<li class="chapter" data-level="14.1.1" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#summary-statistics"><i class="fa fa-check"></i><b>14.1.1</b> Summary Statistics</a></li>
</ul></li>
<li class="chapter" data-level="14.2" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#regression-model-comparisons"><i class="fa fa-check"></i><b>14.2</b> Regression model comparisons</a></li>
<li class="chapter" data-level="14.3" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#adjusted-r-squared"><i class="fa fa-check"></i><b>14.3</b> Adjusted R-Squared</a></li>
<li class="chapter" data-level="14.4" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#multicollinearity"><i class="fa fa-check"></i><b>14.4</b> Multicollinearity</a>
<ul>
<li class="chapter" data-level="14.4.1" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#variance-inflation-factor-vif"><i class="fa fa-check"></i><b>14.4.1</b> Variance Inflation Factor (VIF)</a></li>
<li class="chapter" data-level="14.4.2" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#joint-hypotheses-test"><i class="fa fa-check"></i><b>14.4.2</b> Joint hypotheses test</a></li>
</ul></li>
<li class="chapter" data-level="14.5" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#testing-linear-combinations-of-parameters"><i class="fa fa-check"></i><b>14.5</b> Testing linear combinations of parameters</a></li>
<li class="chapter" data-level="14.6" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#a-note-on-presentation"><i class="fa fa-check"></i><b>14.6</b> A note on presentation</a></li>
<li class="chapter" data-level="14.7" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#log-transformations"><i class="fa fa-check"></i><b>14.7</b> Log transformations</a>
<ul>
<li class="chapter" data-level="14.7.1" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#histograms"><i class="fa fa-check"></i><b>14.7.1</b> Histograms</a></li>
<li class="chapter" data-level="14.7.2" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#scatter-plots"><i class="fa fa-check"></i><b>14.7.2</b> Scatter plots</a></li>
<li class="chapter" data-level="14.7.3" data-path="ch-3---mlr.html"><a href="ch-3---mlr.html#regression-models-with-levels-and-logs"><i class="fa fa-check"></i><b>14.7.3</b> Regression models with levels and logs</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="15" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html"><i class="fa fa-check"></i><b>15</b> Dummy Variables Part 1</a>
<ul>
<li class="chapter" data-level="15.1" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html#obtain-and-prepare-data"><i class="fa fa-check"></i><b>15.1</b> Obtain and prepare data</a></li>
<li class="chapter" data-level="15.2" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html#define-dummy-variables"><i class="fa fa-check"></i><b>15.2</b> Define dummy variables</a>
<ul>
<li class="chapter" data-level="15.2.1" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html#alpha-model"><i class="fa fa-check"></i><b>15.2.1</b> Alpha Model</a></li>
<li class="chapter" data-level="15.2.2" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html#beta-model"><i class="fa fa-check"></i><b>15.2.2</b> Beta Model</a></li>
</ul></li>
<li class="chapter" data-level="15.3" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html#compare-the-regressions-side-by-side"><i class="fa fa-check"></i><b>15.3</b> Compare the regressions side-by-side</a></li>
<li class="chapter" data-level="15.4" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html#compare-the-predictions-of-each-model"><i class="fa fa-check"></i><b>15.4</b> Compare the predictions of each model</a>
<ul>
<li class="chapter" data-level="15.4.1" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html#group-averages"><i class="fa fa-check"></i><b>15.4.1</b> Group averages</a></li>
<li class="chapter" data-level="15.4.2" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html#causal-estimates"><i class="fa fa-check"></i><b>15.4.2</b> Causal estimates?</a></li>
<li class="chapter" data-level="15.4.3" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html#what-about-age"><i class="fa fa-check"></i><b>15.4.3</b> What about age?</a></li>
<li class="chapter" data-level="15.4.4" data-path="dummy-variables-part-1.html"><a href="dummy-variables-part-1.html#what-about-sex"><i class="fa fa-check"></i><b>15.4.4</b> What about sex?</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="16" data-path="dummy-variables-part-2.html"><a href="dummy-variables-part-2.html"><i class="fa fa-check"></i><b>16</b> Dummy Variables Part 2</a>
<ul>
<li class="chapter" data-level="16.1" data-path="dummy-variables-part-2.html"><a href="dummy-variables-part-2.html#size-only"><i class="fa fa-check"></i><b>16.1</b> Size only</a></li>
<li class="chapter" data-level="16.2" data-path="dummy-variables-part-2.html"><a href="dummy-variables-part-2.html#number-of-bathrooms-and-size"><i class="fa fa-check"></i><b>16.2</b> Number of bathrooms and size</a></li>
<li class="chapter" data-level="16.3" data-path="dummy-variables-part-2.html"><a href="dummy-variables-part-2.html#slope-dummy"><i class="fa fa-check"></i><b>16.3</b> Slope dummy</a></li>
<li class="chapter" data-level="16.4" data-path="dummy-variables-part-2.html"><a href="dummy-variables-part-2.html#intercept-and-slope-dummies"><i class="fa fa-check"></i><b>16.4</b> Intercept and slope dummies</a></li>
<li class="chapter" data-level="16.5" data-path="dummy-variables-part-2.html"><a href="dummy-variables-part-2.html#models-with-the-number-of-bedrooms"><i class="fa fa-check"></i><b>16.5</b> Models with the number of bedrooms</a></li>
</ul></li>
<li class="chapter" data-level="17" data-path="fixed-effects.html"><a href="fixed-effects.html"><i class="fa fa-check"></i><b>17</b> Fixed Effects</a>
<ul>
<li class="chapter" data-level="17.1" data-path="fixed-effects.html"><a href="fixed-effects.html#variables"><i class="fa fa-check"></i><b>17.1</b> Variables</a></li>
<li class="chapter" data-level="17.2" data-path="fixed-effects.html"><a href="fixed-effects.html#ols"><i class="fa fa-check"></i><b>17.2</b> OLS</a></li>
<li class="chapter" data-level="17.3" data-path="fixed-effects.html"><a href="fixed-effects.html#country-fixed-effects"><i class="fa fa-check"></i><b>17.3</b> Country Fixed Effects</a></li>
<li class="chapter" data-level="17.4" data-path="fixed-effects.html"><a href="fixed-effects.html#year-fixed-effects"><i class="fa fa-check"></i><b>17.4</b> Year Fixed Effects</a></li>
<li class="chapter" data-level="17.5" data-path="fixed-effects.html"><a href="fixed-effects.html#country-and-year-fixed-effects"><i class="fa fa-check"></i><b>17.5</b> Country and Year Fixed Effects</a></li>
<li class="chapter" data-level="17.6" data-path="fixed-effects.html"><a href="fixed-effects.html#comparison-of-all-models"><i class="fa fa-check"></i><b>17.6</b> Comparison of all models</a>
<ul>
<li class="chapter" data-level="17.6.1" data-path="fixed-effects.html"><a href="fixed-effects.html#within-transformation"><i class="fa fa-check"></i><b>17.6.1</b> Within Transformation</a></li>
<li class="chapter" data-level="17.6.2" data-path="fixed-effects.html"><a href="fixed-effects.html#plm-package"><i class="fa fa-check"></i><b>17.6.2</b> PLM Package</a></li>
<li class="chapter" data-level="17.6.3" data-path="fixed-effects.html"><a href="fixed-effects.html#dummy-variables"><i class="fa fa-check"></i><b>17.6.3</b> Dummy Variables</a></li>
</ul></li>
<li class="chapter" data-level="17.7" data-path="fixed-effects.html"><a href="fixed-effects.html#data-summary-by-country"><i class="fa fa-check"></i><b>17.7</b> Data Summary by Country</a>
<ul>
<li class="chapter" data-level="17.7.1" data-path="fixed-effects.html"><a href="fixed-effects.html#average-values-for-each-country"><i class="fa fa-check"></i><b>17.7.1</b> Average Values for Each Country</a></li>
<li class="chapter" data-level="17.7.2" data-path="fixed-effects.html"><a href="fixed-effects.html#variable-specific-values-and-within-transformation-for-each-country"><i class="fa fa-check"></i><b>17.7.2</b> Variable-Specific Values and Within Transformation for Each Country</a></li>
<li class="chapter" data-level="17.7.3" data-path="fixed-effects.html"><a href="fixed-effects.html#life-expectancy"><i class="fa fa-check"></i><b>17.7.3</b> Life expectancy</a></li>
<li class="chapter" data-level="17.7.4" data-path="fixed-effects.html"><a href="fixed-effects.html#gdp-per-capita"><i class="fa fa-check"></i><b>17.7.4</b> GDP per capita</a></li>
<li class="chapter" data-level="17.7.5" data-path="fixed-effects.html"><a href="fixed-effects.html#population"><i class="fa fa-check"></i><b>17.7.5</b> Population</a></li>
<li class="chapter" data-level="17.7.6" data-path="fixed-effects.html"><a href="fixed-effects.html#percent-female"><i class="fa fa-check"></i><b>17.7.6</b> Percent female</a></li>
<li class="chapter" data-level="17.7.7" data-path="fixed-effects.html"><a href="fixed-effects.html#percent-rural"><i class="fa fa-check"></i><b>17.7.7</b> Percent rural</a></li>
</ul></li>
<li class="chapter" data-level="17.8" data-path="fixed-effects.html"><a href="fixed-effects.html#bookdown-style-note"><i class="fa fa-check"></i><b>17.8</b> Bookdown Style Note</a></li>
</ul></li>
<li class="chapter" data-level="18" data-path="difference-in-differences.html"><a href="difference-in-differences.html"><i class="fa fa-check"></i><b>18</b> Difference-in-Differences</a>
<ul>
<li class="chapter" data-level="18.1" data-path="difference-in-differences.html"><a href="difference-in-differences.html#data-1"><i class="fa fa-check"></i><b>18.1</b> Data</a></li>
<li class="chapter" data-level="18.2" data-path="difference-in-differences.html"><a href="difference-in-differences.html#model-1"><i class="fa fa-check"></i><b>18.2</b> Model 1</a>
<ul>
<li class="chapter" data-level="18.2.1" data-path="difference-in-differences.html"><a href="difference-in-differences.html#equivalent-model-1"><i class="fa fa-check"></i><b>18.2.1</b> Equivalent model 1</a></li>
</ul></li>
<li class="chapter" data-level="18.3" data-path="difference-in-differences.html"><a href="difference-in-differences.html#model-2"><i class="fa fa-check"></i><b>18.3</b> Model 2</a></li>
<li class="chapter" data-level="18.4" data-path="difference-in-differences.html"><a href="difference-in-differences.html#comparison-of-models"><i class="fa fa-check"></i><b>18.4</b> Comparison of models</a></li>
<li class="chapter" data-level="18.5" data-path="difference-in-differences.html"><a href="difference-in-differences.html#additional-questions"><i class="fa fa-check"></i><b>18.5</b> Additional questions</a>
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<li class="chapter" data-level="18.5.1" data-path="difference-in-differences.html"><a href="difference-in-differences.html#question-1"><i class="fa fa-check"></i><b>18.5.1</b> Question 1</a></li>
<li class="chapter" data-level="18.5.2" data-path="difference-in-differences.html"><a href="difference-in-differences.html#question-2"><i class="fa fa-check"></i><b>18.5.2</b> Question 2</a></li>
<li class="chapter" data-level="18.5.3" data-path="difference-in-differences.html"><a href="difference-in-differences.html#question-3"><i class="fa fa-check"></i><b>18.5.3</b> Question 3</a></li>
<li class="chapter" data-level="18.5.4" data-path="difference-in-differences.html"><a href="difference-in-differences.html#question-4"><i class="fa fa-check"></i><b>18.5.4</b> Question 4</a></li>
</ul></li>
<li class="chapter" data-level="18.6" data-path="difference-in-differences.html"><a href="difference-in-differences.html#polynomials"><i class="fa fa-check"></i><b>18.6</b> Polynomials</a></li>
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<h1><span class="header-section-number">15</span> Dummy Variables Part 1<a href="dummy-variables-part-1.html#dummy-variables-part-1" class="anchor-section" aria-label="Anchor link to header"></a></h1>
<p>This chapter goes with LN4.1. In LN4.1 we examine two models of the relationship between education and wages. We examined two different ways we could define sets of dummy variables to represent people with a high school degree, a BA, a Master’s, or a PhD as their highest level of education. We saw how both models could be used to answer questions such as “what is the average wage for someone with a Master’s degree?” or “What is the expected difference in average wage for a person with a Master’s degree compared to a BA?” In this BP chapter you will explore these models empirically using micro-level data (i.e., data on individual people).</p>
<p>Specifically, the data we’ll use comes from the 2019 ACS 1-year Public Use <a href="https://www.census.gov/programs-surveys/acs/microdata.html">Microdata Sample (PUMS)</a>. This data has the responses of individuals that the Census Bureau uses to calculate the county- and state-level statistics they publish as part of the ACS (e.g., what you’re using for the CP). Formally to analyze this data properly we need to use survey weights to make calculates done using the individual responses representative of the population as a whole. We’re not going to worry about that. However, note that our calculations will be off somewhat from the true average wages for the groups we explore in this chapter. We’ll obtain our data using the tidycensus package, <a href="https://walker-data.com/tidycensus/articles/pums-data.html">as described here</a>.</p>
<div class="sourceCode" id="cb716"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb716-1"><a href="dummy-variables-part-1.html#cb716-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidyverse)</span>
<span id="cb716-2"><a href="dummy-variables-part-1.html#cb716-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidycensus)</span>
<span id="cb716-3"><a href="dummy-variables-part-1.html#cb716-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(stargazer)</span>
<span id="cb716-4"><a href="dummy-variables-part-1.html#cb716-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(pander)</span>
<span id="cb716-5"><a href="dummy-variables-part-1.html#cb716-5" aria-hidden="true" tabindex="-1"></a><span class="do">## This turns off scientific notation when there are fewer then 4 digits. Otherwise pander displays very small p values with way too many decimal places</span></span>
<span id="cb716-6"><a href="dummy-variables-part-1.html#cb716-6" aria-hidden="true" tabindex="-1"></a><span class="fu">options</span>(<span class="at">scipen =</span> <span class="dv">4</span>)</span></code></pre></div>
<div id="obtain-and-prepare-data" class="section level2 hasAnchor" number="15.1">
<h2><span class="header-section-number">15.1</span> Obtain and prepare data<a href="dummy-variables-part-1.html#obtain-and-prepare-data" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>To work with the PUMS data via tidycensus, you can pull the table of variables to find what variables are included. I’ve set this code chunk to not be evaluated (eval = FALSE) when you build because while doing this is helpful while you’re working with this data, it doesn’t belong in your HTML output</p>
<div class="sourceCode" id="cb717"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb717-1"><a href="dummy-variables-part-1.html#cb717-1" aria-hidden="true" tabindex="-1"></a><span class="do">## To work with the PUMS data via tidycensus, you can pull the table of variables to find what variables are included</span></span>
<span id="cb717-2"><a href="dummy-variables-part-1.html#cb717-2" aria-hidden="true" tabindex="-1"></a><span class="do">## I've set this code chunk to not be evaluated (eval = FALSE) when you build. You might want to do this on your own, but it doesn't belong in your HTML output</span></span>
<span id="cb717-3"><a href="dummy-variables-part-1.html#cb717-3" aria-hidden="true" tabindex="-1"></a>pums_vars_2018 <span class="ot"><-</span> pums_variables <span class="sc">%>%</span> </span>
<span id="cb717-4"><a href="dummy-variables-part-1.html#cb717-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(year <span class="sc">==</span> <span class="dv">2019</span>, survey <span class="sc">==</span> <span class="st">"acs1"</span>)</span></code></pre></div>
<style>
.variablesTable th {
text-align: left;
}
</style>
<p>Let’s pull the following variables from the 2019 ACS-1 year Public Use Microdata (i.e., data on individual people) for the state of Wisconsin (we’re limiting our sample to Wisconsin so that it doesn’t take too long to load or work with).</p>
<div class="variablesTable">
<table>
<thead>
<tr class="header">
<th>Variable</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><code>PUMA</code></td>
<td>Public Use Microdata Areas</td>
</tr>
<tr class="even">
<td><code>WAGP</code></td>
<td>WAGe of Person</td>
</tr>
<tr class="odd">
<td><code>AGEP</code></td>
<td>AGE of Person</td>
</tr>
<tr class="even">
<td><code>SCHL</code></td>
<td>educational attainment of person</td>
</tr>
<tr class="odd">
<td><code>sex</code></td>
<td>SEX of person</td>
</tr>
</tbody>
</table>
</div>
<p>The <code>results='hide'</code> code chunk option keeps it from displaying status updates while it downloads (which is sometimes about 100 lines of output, so you definitely don’t want it in your HTML output).</p>
<div class="sourceCode" id="cb718"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb718-1"><a href="dummy-variables-part-1.html#cb718-1" aria-hidden="true" tabindex="-1"></a><span class="do">## Download 2018 acs1 for Wisconsin.</span></span>
<span id="cb718-2"><a href="dummy-variables-part-1.html#cb718-2" aria-hidden="true" tabindex="-1"></a>wiPUMS <span class="ot"><-</span> <span class="fu">get_pums</span>(</span>
<span id="cb718-3"><a href="dummy-variables-part-1.html#cb718-3" aria-hidden="true" tabindex="-1"></a> <span class="at">variables =</span> <span class="fu">c</span>(<span class="st">"PUMA"</span>,<span class="st">"WAGP"</span>, <span class="st">"AGEP"</span>, <span class="st">"SCHL"</span>, <span class="st">"SEX"</span>),</span>
<span id="cb718-4"><a href="dummy-variables-part-1.html#cb718-4" aria-hidden="true" tabindex="-1"></a> <span class="at">state =</span> <span class="st">"wi"</span>,</span>
<span id="cb718-5"><a href="dummy-variables-part-1.html#cb718-5" aria-hidden="true" tabindex="-1"></a> <span class="at">survey =</span> <span class="st">"acs1"</span>,</span>
<span id="cb718-6"><a href="dummy-variables-part-1.html#cb718-6" aria-hidden="true" tabindex="-1"></a> <span class="at">year =</span> <span class="dv">2018</span>,</span>
<span id="cb718-7"><a href="dummy-variables-part-1.html#cb718-7" aria-hidden="true" tabindex="-1"></a> <span class="at">recode =</span> <span class="cn">TRUE</span></span>
<span id="cb718-8"><a href="dummy-variables-part-1.html#cb718-8" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<p>Let’s rename <code>WAGP</code> as <code>wage</code> so that we remember what it is.</p>
<div class="sourceCode" id="cb719"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb719-1"><a href="dummy-variables-part-1.html#cb719-1" aria-hidden="true" tabindex="-1"></a>wiPUMS <span class="ot"><-</span> <span class="fu">rename</span>(wiPUMS, <span class="at">wage =</span> WAGP)</span></code></pre></div>
<p>Let’s see what levels of education exist in our data, and how many observations we have for each</p>
<div class="sourceCode" id="cb720"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb720-1"><a href="dummy-variables-part-1.html#cb720-1" aria-hidden="true" tabindex="-1"></a>wiPUMS <span class="sc">%>%</span> <span class="fu">count</span>(SCHL,SCHL_label) <span class="sc">%>%</span> <span class="fu">pander</span>()</span></code></pre></div>
<table style="width:65%;">
<colgroup>
<col width="9%" />
<col width="44%" />
<col width="11%" />
</colgroup>
<thead>
<tr class="header">
<th align="center">SCHL</th>
<th align="center">SCHL_label</th>
<th align="center">n</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center">01</td>
<td align="center">No schooling completed</td>
<td align="center">1552</td>
</tr>
<tr class="even">
<td align="center">02</td>
<td align="center">Nursery school, preschool</td>
<td align="center">766</td>
</tr>
<tr class="odd">
<td align="center">03</td>
<td align="center">Kindergarten</td>
<td align="center">718</td>
</tr>
<tr class="even">
<td align="center">04</td>
<td align="center">Grade 1</td>
<td align="center">614</td>
</tr>
<tr class="odd">
<td align="center">05</td>
<td align="center">Grade 2</td>
<td align="center">650</td>
</tr>
<tr class="even">
<td align="center">06</td>
<td align="center">Grade 3</td>
<td align="center">722</td>
</tr>
<tr class="odd">
<td align="center">07</td>
<td align="center">Grade 4</td>
<td align="center">724</td>
</tr>
<tr class="even">
<td align="center">08</td>
<td align="center">Grade 5</td>
<td align="center">802</td>
</tr>
<tr class="odd">
<td align="center">09</td>
<td align="center">Grade 6</td>
<td align="center">793</td>
</tr>
<tr class="even">
<td align="center">10</td>
<td align="center">Grade 7</td>
<td align="center">796</td>
</tr>
<tr class="odd">
<td align="center">11</td>
<td align="center">Grade 8</td>
<td align="center">1306</td>
</tr>
<tr class="even">
<td align="center">12</td>
<td align="center">Grade 9</td>
<td align="center">1000</td>
</tr>
<tr class="odd">
<td align="center">13</td>
<td align="center">Grade 10</td>
<td align="center">1321</td>
</tr>
<tr class="even">
<td align="center">14</td>
<td align="center">Grade 11</td>
<td align="center">1511</td>
</tr>
<tr class="odd">
<td align="center">15</td>
<td align="center">12th grade - no diploma</td>
<td align="center">851</td>
</tr>
<tr class="even">
<td align="center">16</td>
<td align="center">Regular high school diploma</td>
<td align="center">14364</td>
</tr>
<tr class="odd">
<td align="center">17</td>
<td align="center">GED or alternative credential</td>
<td align="center">1619</td>
</tr>
<tr class="even">
<td align="center">18</td>
<td align="center">Some college, but less than 1
year</td>
<td align="center">3724</td>
</tr>
<tr class="odd">
<td align="center">19</td>
<td align="center">1 or more years of college
credit, no degree</td>
<td align="center">6867</td>
</tr>
<tr class="even">
<td align="center">20</td>
<td align="center">Associate’s degree</td>
<td align="center">5169</td>
</tr>
<tr class="odd">
<td align="center">21</td>
<td align="center">Bachelor’s degree</td>
<td align="center">8182</td>
</tr>
<tr class="even">
<td align="center">22</td>
<td align="center">Master’s degree</td>
<td align="center">2859</td>
</tr>
<tr class="odd">
<td align="center">23</td>
<td align="center">Professional degree beyond a
bachelor’s degree</td>
<td align="center">714</td>
</tr>
<tr class="even">
<td align="center">24</td>
<td align="center">Doctorate degree</td>
<td align="center">455</td>
</tr>
<tr class="odd">
<td align="center">bb</td>
<td align="center">N/A (less than 3 years old)</td>
<td align="center">1754</td>
</tr>
</tbody>
</table>
<p>We’re interested in examining how wages differ by educational attainment. We’d like to limit our data to people who are old enough to have completed high school (or equivalent) and college, and then be working. So, let’s limit our sample to people age 25 or older. Let’s also only examine people who have a wage.</p>
<div class="sourceCode" id="cb721"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb721-1"><a href="dummy-variables-part-1.html#cb721-1" aria-hidden="true" tabindex="-1"></a>wiPUMS <span class="ot"><-</span> wiPUMS <span class="sc">%>%</span> </span>
<span id="cb721-2"><a href="dummy-variables-part-1.html#cb721-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(AGEP <span class="sc">>=</span> <span class="dv">25</span> <span class="sc">&</span> wage <span class="sc">></span> <span class="dv">0</span>)</span></code></pre></div>
<p>We should look at what education levels (<code>SCHL</code>) remain after filtering</p>
<div class="sourceCode" id="cb722"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb722-1"><a href="dummy-variables-part-1.html#cb722-1" aria-hidden="true" tabindex="-1"></a>wiPUMS <span class="sc">%>%</span> <span class="fu">count</span>(SCHL,SCHL_label) <span class="sc">%>%</span> <span class="fu">pander</span>()</span></code></pre></div>
<table style="width:64%;">
<colgroup>
<col width="9%" />
<col width="44%" />
<col width="9%" />
</colgroup>
<thead>
<tr class="header">
<th align="center">SCHL</th>
<th align="center">SCHL_label</th>
<th align="center">n</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center">01</td>
<td align="center">No schooling completed</td>
<td align="center">133</td>
</tr>
<tr class="even">
<td align="center">02</td>
<td align="center">Nursery school, preschool</td>
<td align="center">4</td>
</tr>
<tr class="odd">
<td align="center">03</td>
<td align="center">Kindergarten</td>
<td align="center">5</td>
</tr>
<tr class="even">
<td align="center">04</td>
<td align="center">Grade 1</td>
<td align="center">1</td>
</tr>
<tr class="odd">
<td align="center">05</td>
<td align="center">Grade 2</td>
<td align="center">3</td>
</tr>
<tr class="even">
<td align="center">06</td>
<td align="center">Grade 3</td>
<td align="center">5</td>
</tr>
<tr class="odd">
<td align="center">07</td>
<td align="center">Grade 4</td>
<td align="center">4</td>
</tr>
<tr class="even">
<td align="center">08</td>
<td align="center">Grade 5</td>
<td align="center">8</td>
</tr>
<tr class="odd">
<td align="center">09</td>
<td align="center">Grade 6</td>
<td align="center">39</td>
</tr>
<tr class="even">
<td align="center">10</td>
<td align="center">Grade 7</td>
<td align="center">14</td>
</tr>
<tr class="odd">
<td align="center">11</td>
<td align="center">Grade 8</td>
<td align="center">92</td>
</tr>
<tr class="even">
<td align="center">12</td>
<td align="center">Grade 9</td>
<td align="center">95</td>
</tr>
<tr class="odd">
<td align="center">13</td>
<td align="center">Grade 10</td>
<td align="center">168</td>
</tr>
<tr class="even">
<td align="center">14</td>
<td align="center">Grade 11</td>
<td align="center">282</td>
</tr>
<tr class="odd">
<td align="center">15</td>
<td align="center">12th grade - no diploma</td>
<td align="center">349</td>
</tr>
<tr class="even">
<td align="center">16</td>
<td align="center">Regular high school diploma</td>
<td align="center">6826</td>
</tr>
<tr class="odd">
<td align="center">17</td>
<td align="center">GED or alternative credential</td>
<td align="center">824</td>
</tr>
<tr class="even">
<td align="center">18</td>
<td align="center">Some college, but less than 1
year</td>
<td align="center">1948</td>
</tr>
<tr class="odd">
<td align="center">19</td>
<td align="center">1 or more years of college
credit, no degree</td>
<td align="center">3579</td>
</tr>
<tr class="even">
<td align="center">20</td>
<td align="center">Associate’s degree</td>
<td align="center">3664</td>
</tr>
<tr class="odd">
<td align="center">21</td>
<td align="center">Bachelor’s degree</td>
<td align="center">5600</td>
</tr>
<tr class="even">
<td align="center">22</td>
<td align="center">Master’s degree</td>
<td align="center">2002</td>
</tr>
<tr class="odd">
<td align="center">23</td>
<td align="center">Professional degree beyond a
bachelor’s degree</td>
<td align="center">515</td>
</tr>
<tr class="even">
<td align="center">24</td>
<td align="center">Doctorate degree</td>
<td align="center">320</td>
</tr>
</tbody>
</table>
<p>After filtering, the value “bb” that indicates a person who is under 3 years old and thus can’t have any schooling is now gone. Now all of the levels of <code>SCHL</code> are numeric, which allows us to convert them from a character to a numeric data type. This will then allow us to use inequalities to define dummy variables (e.g., <code>SCHL <16</code>).</p>
<div class="sourceCode" id="cb723"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb723-1"><a href="dummy-variables-part-1.html#cb723-1" aria-hidden="true" tabindex="-1"></a>wiPUMS<span class="sc">$</span>SCHL <span class="ot"><-</span> <span class="fu">as.numeric</span>(wiPUMS<span class="sc">$</span>SCHL)</span></code></pre></div>
<p>We’re comparing wages of people who have a high school degree (or equivalent) or higher, so we also need to drop everyone who has less than a high school degree. Because <code>SCHL</code> is now numeric, we can do this using an inequality (rather than listing all of the options separately).</p>
<div class="sourceCode" id="cb724"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb724-1"><a href="dummy-variables-part-1.html#cb724-1" aria-hidden="true" tabindex="-1"></a>wiPUMS <span class="ot"><-</span> wiPUMS <span class="sc">%>%</span> <span class="fu">filter</span>(SCHL <span class="sc">>=</span> <span class="dv">16</span>)</span></code></pre></div>
<p>In order to match with LN4.1, we also need to drop people with a professional degree. In practice we would probably want to examine them too, but for the sake of matching with what is in LN4.1 we’re going to drop them.</p>
<div class="sourceCode" id="cb725"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb725-1"><a href="dummy-variables-part-1.html#cb725-1" aria-hidden="true" tabindex="-1"></a>wiPUMS <span class="ot"><-</span> wiPUMS <span class="sc">%>%</span> <span class="fu">filter</span>(SCHL <span class="sc">!=</span> <span class="dv">23</span>)</span></code></pre></div>
<p>Whenever you do something like filtering data, it’s a very good idea to look at the data and make sure it worked. In previous years of 380, students have wasted many hours trying to get models to work, only to finally go back and look at the data to find that they actually messed up an earlier step that seems easy. So even if it’s something easy you think you know how to do, look at the data. You can display summary measures as we’ll do here, but it’s also a good idea to click on it in the Environment tab and actually scroll through it quickly. Typically you don’t display the results in a paper, but for the purposes of the BP, I want to demonstrate what you might do (e.g., get a count by education levels). Here, we could just re-run this:</p>
<div class="sourceCode" id="cb726"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb726-1"><a href="dummy-variables-part-1.html#cb726-1" aria-hidden="true" tabindex="-1"></a>wiPUMS <span class="sc">%>%</span> <span class="fu">count</span>(SCHL,SCHL_label) <span class="sc">%>%</span> <span class="fu">pander</span>()</span></code></pre></div>
<table style="width:64%;">
<colgroup>
<col width="9%" />
<col width="44%" />
<col width="9%" />
</colgroup>
<thead>
<tr class="header">
<th align="center">SCHL</th>
<th align="center">SCHL_label</th>
<th align="center">n</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center">16</td>
<td align="center">Regular high school diploma</td>
<td align="center">6826</td>
</tr>
<tr class="even">
<td align="center">17</td>
<td align="center">GED or alternative credential</td>
<td align="center">824</td>
</tr>
<tr class="odd">
<td align="center">18</td>
<td align="center">Some college, but less than 1
year</td>
<td align="center">1948</td>
</tr>
<tr class="even">
<td align="center">19</td>
<td align="center">1 or more years of college
credit, no degree</td>
<td align="center">3579</td>
</tr>
<tr class="odd">
<td align="center">20</td>
<td align="center">Associate’s degree</td>
<td align="center">3664</td>
</tr>
<tr class="even">
<td align="center">21</td>
<td align="center">Bachelor’s degree</td>
<td align="center">5600</td>
</tr>
<tr class="odd">
<td align="center">22</td>
<td align="center">Master’s degree</td>
<td align="center">2002</td>
</tr>
<tr class="even">
<td align="center">24</td>
<td align="center">Doctorate degree</td>
<td align="center">320</td>
</tr>
</tbody>
</table>
</div>
<div id="define-dummy-variables" class="section level2 hasAnchor" number="15.2">
<h2><span class="header-section-number">15.2</span> Define dummy variables<a href="dummy-variables-part-1.html#define-dummy-variables" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>In LN4.1 we had an “alpha model” and “beta model” which defined education in different ways.</p>
<div class="variablesTable">
<table>
<colgroup>
<col width="13%" />
<col width="39%" />
<col width="47%" />
</colgroup>
<thead>
<tr class="header">
<th>Variable</th>
<th>Alpha Model Definition</th>
<th>Beta Model Definition</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><code>HS</code></td>
<td>N/A</td>
<td>=1 if highest degree is high school, <br>=0 otherwise</td>
</tr>
<tr class="even">
<td><code>BA</code></td>
<td>=1 if have B.A. degree, <br>=0 if don’t</td>
<td>=1 if highest degree is B.A. degree, <br>=0 otherwise</td>
</tr>
<tr class="odd">
<td><code>Masters</code></td>
<td>=1 if have Master’s degree, <br>=0 if don’t</td>
<td>=1 if highest degree is Master’s, <br>=0 otherwise</td>
</tr>
<tr class="even">
<td><code>PhD</code></td>
<td>=1 if have PhD, <br>==0 if don’t</td>
<td>=1 if highest degree is PhD, <br>=0 otherwise</td>
</tr>
</tbody>
</table>
</div>
<div id="alpha-model" class="section level3 hasAnchor" number="15.2.1">
<h3><span class="header-section-number">15.2.1</span> Alpha Model<a href="dummy-variables-part-1.html#alpha-model" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>In LN4.1, we defined the “Alpha Model” as</p>
<p><span class="math display">\[
wage = \alpha_0 + \alpha_1 BA + \alpha_2 Masters + \alpha_3 PhD + u
\]</span></p>
<p>We need to create the dummy variables used for the “Alpha Model”. We’ll prefix the variables with “a” for “Alpha”. Later you’ll define “Beta Model” variables and prefix them with “b”.</p>
<p>In our data, some people have some college or an Associates Degree. While we might be interested in differences between people with some college and a only a high school degree, for the purposes of what we’re doing here (learning about dummy variables), let’s classify anyone without a BA as having high school as their highest degree (even if they have some college or an Associates Degree).</p>
<div class="sourceCode" id="cb727"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb727-1"><a href="dummy-variables-part-1.html#cb727-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Create dummy variables for "alpha model" (starting with a)</span></span>
<span id="cb727-2"><a href="dummy-variables-part-1.html#cb727-2" aria-hidden="true" tabindex="-1"></a>wiPUMS <span class="ot"><-</span> wiPUMS <span class="sc">%>%</span></span>
<span id="cb727-3"><a href="dummy-variables-part-1.html#cb727-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">aBA =</span> <span class="fu">ifelse</span>(SCHL <span class="sc">>=</span> <span class="dv">21</span>, <span class="dv">1</span>, <span class="dv">0</span>),</span>
<span id="cb727-4"><a href="dummy-variables-part-1.html#cb727-4" aria-hidden="true" tabindex="-1"></a> <span class="at">aMasters =</span> <span class="fu">ifelse</span>(SCHL <span class="sc">>=</span> <span class="dv">22</span>, <span class="dv">1</span>, <span class="dv">0</span>),</span>
<span id="cb727-5"><a href="dummy-variables-part-1.html#cb727-5" aria-hidden="true" tabindex="-1"></a> <span class="at">aPhD =</span> <span class="fu">ifelse</span>(SCHL <span class="sc">==</span> <span class="dv">24</span>, <span class="dv">1</span>, <span class="dv">0</span>)</span>
<span id="cb727-6"><a href="dummy-variables-part-1.html#cb727-6" aria-hidden="true" tabindex="-1"></a> )</span></code></pre></div>
<p>Now let’s estimate the regression shown as “Alpha Model v1” in LN4</p>
<div class="sourceCode" id="cb728"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb728-1"><a href="dummy-variables-part-1.html#cb728-1" aria-hidden="true" tabindex="-1"></a>alphaModel <span class="ot"><-</span> <span class="fu">lm</span>(wage <span class="sc">~</span> aBA <span class="sc">+</span> aMasters <span class="sc">+</span> aPhD, <span class="at">data =</span> wiPUMS)</span>
<span id="cb728-2"><a href="dummy-variables-part-1.html#cb728-2" aria-hidden="true" tabindex="-1"></a><span class="fu">pander</span>(<span class="fu">summary</span>(alphaModel))</span></code></pre></div>
<table style="width:90%;">
<colgroup>
<col width="25%" />
<col width="15%" />
<col width="18%" />
<col width="13%" />
<col width="18%" />
</colgroup>
<thead>
<tr class="header">
<th align="center"> </th>
<th align="center">Estimate</th>
<th align="center">Std. Error</th>
<th align="center">t value</th>
<th align="center">Pr(>|t|)</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center"><strong>(Intercept)</strong></td>
<td align="center">40891</td>
<td align="center">357.2</td>
<td align="center">114.5</td>
<td align="center">0</td>
</tr>
<tr class="even">
<td align="center"><strong>aBA</strong></td>
<td align="center">21960</td>
<td align="center">715.1</td>
<td align="center">30.71</td>
<td align="center">2.893e-203</td>
</tr>
<tr class="odd">
<td align="center"><strong>aMasters</strong></td>
<td align="center">9235</td>
<td align="center">1207</td>
<td align="center">7.65</td>
<td align="center">2.08e-14</td>
</tr>
<tr class="even">
<td align="center"><strong>aPhD</strong></td>
<td align="center">34351</td>
<td align="center">2791</td>
<td align="center">12.31</td>
<td align="center">1.041e-34</td>
</tr>
</tbody>
</table>
<table style="width:89%;">
<caption>Fitting linear model: wage ~ aBA + aMasters + aPhD</caption>
<colgroup>
<col width="20%" />
<col width="30%" />
<col width="13%" />
<col width="23%" />
</colgroup>
<thead>
<tr class="header">
<th align="center">Observations</th>
<th align="center">Residual Std. Error</th>
<th align="center"><span class="math inline">\(R^2\)</span></th>
<th align="center">Adjusted <span class="math inline">\(R^2\)</span></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center">24763</td>
<td align="center">46360</td>
<td align="center">0.07482</td>
<td align="center">0.07471</td>
</tr>
</tbody>
</table>
</div>
<div id="beta-model" class="section level3 hasAnchor" number="15.2.2">
<h3><span class="header-section-number">15.2.2</span> Beta Model<a href="dummy-variables-part-1.html#beta-model" class="anchor-section" aria-label="Anchor link to header"></a></h3>
<p>In LN4.1, we defined the “Beta Model” (version 1) as:</p>
<p><span class="math display">\[
wage = \beta_0 + \beta_1 BA + \beta_2 Masters + \beta_3 PhD + u
\]</span></p>
<p>We need to create the dummy variables for the “Beta Model” from LN4.1. Use the same categories as you did for the Alpha Model (so we’re considering anyone with some college or an associates degree as having high school as their highest education). Prefix these variables with a “b” for “Beta”.</p>
<hr />
<p><strong>YOUR CODE GOES HERE: add variables bBA, bMasters, and bPhD to wiPUMS</strong></p>
<div class="sourceCode" id="cb729"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb729-1"><a href="dummy-variables-part-1.html#cb729-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Create dummy variables for "Beta Model" (prefix with b)</span></span>
<span id="cb729-2"><a href="dummy-variables-part-1.html#cb729-2" aria-hidden="true" tabindex="-1"></a>wiPUMS <span class="ot"><-</span> wiPUMS <span class="sc">%>%</span></span>
<span id="cb729-3"><a href="dummy-variables-part-1.html#cb729-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">bBA =</span> <span class="fu">ifelse</span>(SCHL <span class="sc">==</span> <span class="dv">21</span>, <span class="dv">1</span>, <span class="dv">0</span>),</span>
<span id="cb729-4"><a href="dummy-variables-part-1.html#cb729-4" aria-hidden="true" tabindex="-1"></a> <span class="at">bMasters =</span> <span class="fu">ifelse</span>(SCHL <span class="sc">==</span> <span class="dv">22</span>, <span class="dv">1</span>, <span class="dv">0</span>),</span>
<span id="cb729-5"><a href="dummy-variables-part-1.html#cb729-5" aria-hidden="true" tabindex="-1"></a> <span class="at">bPhD =</span> <span class="fu">ifelse</span>(SCHL <span class="sc">==</span> <span class="dv">24</span>, <span class="dv">1</span>, <span class="dv">0</span>)</span>
<span id="cb729-6"><a href="dummy-variables-part-1.html#cb729-6" aria-hidden="true" tabindex="-1"></a> )</span></code></pre></div>
<hr />
<p>Now let’s estimate the regression shown as “Beta Model v1” in LN4.1</p>
<hr />
<p><strong>UN-COMMENT-OUT the following code after you estimate the Beta Model v1</strong></p>
<div class="sourceCode" id="cb730"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb730-1"><a href="dummy-variables-part-1.html#cb730-1" aria-hidden="true" tabindex="-1"></a>betaModel <span class="ot"><-</span> <span class="fu">lm</span>(wage <span class="sc">~</span> bBA <span class="sc">+</span> bMasters <span class="sc">+</span> bPhD, <span class="at">data =</span> wiPUMS)</span>
<span id="cb730-2"><a href="dummy-variables-part-1.html#cb730-2" aria-hidden="true" tabindex="-1"></a><span class="fu">pander</span>(<span class="fu">summary</span>(betaModel))</span></code></pre></div>
<table style="width:90%;">
<colgroup>
<col width="25%" />
<col width="15%" />
<col width="18%" />
<col width="13%" />
<col width="18%" />
</colgroup>
<thead>
<tr class="header">
<th align="center"> </th>
<th align="center">Estimate</th>
<th align="center">Std. Error</th>
<th align="center">t value</th>
<th align="center">Pr(>|t|)</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center"><strong>(Intercept)</strong></td>
<td align="center">40891</td>
<td align="center">357.2</td>
<td align="center">114.5</td>
<td align="center">0</td>
</tr>
<tr class="even">
<td align="center"><strong>bBA</strong></td>
<td align="center">21960</td>
<td align="center">715.1</td>
<td align="center">30.71</td>
<td align="center">2.893e-203</td>
</tr>
<tr class="odd">
<td align="center"><strong>bMasters</strong></td>
<td align="center">31195</td>
<td align="center">1096</td>
<td align="center">28.46</td>
<td align="center">2.205e-175</td>
</tr>
<tr class="even">
<td align="center"><strong>bPhD</strong></td>
<td align="center">65546</td>
<td align="center">2616</td>
<td align="center">25.06</td>
<td align="center">7.787e-137</td>
</tr>
</tbody>
</table>
<table style="width:89%;">
<caption>Fitting linear model: wage ~ bBA + bMasters + bPhD</caption>
<colgroup>
<col width="20%" />
<col width="30%" />
<col width="13%" />
<col width="23%" />
</colgroup>
<thead>
<tr class="header">
<th align="center">Observations</th>
<th align="center">Residual Std. Error</th>
<th align="center"><span class="math inline">\(R^2\)</span></th>
<th align="center">Adjusted <span class="math inline">\(R^2\)</span></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center">24763</td>
<td align="center">46360</td>
<td align="center">0.07482</td>
<td align="center">0.07471</td>
</tr>
</tbody>
</table>
<hr />
</div>
</div>
<div id="compare-the-regressions-side-by-side" class="section level2 hasAnchor" number="15.3">
<h2><span class="header-section-number">15.3</span> Compare the regressions side-by-side<a href="dummy-variables-part-1.html#compare-the-regressions-side-by-side" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>In LN4.1 we talk about how different models can lead to equivalent results theoretically. Here we want to examine that theoretical equivalence numerically. Specifically, we want to write out various conditional expectations that should be equivalent theoretically and show that the estimated values are indeed equivalent.</p>
<p>Let’s start by displaying the two models on the same table. You have to be very careful doing this (so you don’t accidentally mis-label variables), but we can re-name the variable labels for each model so that they are the same (e.g., rename <code>aBA</code> and <code>bBA</code> to both be <code>BA</code>) and thus display on the same row of the stargazer table. We’ll make a copy of the model results that we use specifically for this purpose. Then we’ll rename the coefficients to have the same names. Then we’ll display them using stargazer.</p>
<hr />
<p><strong>UN-COMMENT-OUT the following code after you estimate the Beta Model v1</strong></p>
<div class="sourceCode" id="cb731"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb731-1"><a href="dummy-variables-part-1.html#cb731-1" aria-hidden="true" tabindex="-1"></a>alphaModelStargazer <span class="ot"><-</span> alphaModel</span>
<span id="cb731-2"><a href="dummy-variables-part-1.html#cb731-2" aria-hidden="true" tabindex="-1"></a>betaModelStargazer <span class="ot"><-</span> betaModel</span>
<span id="cb731-3"><a href="dummy-variables-part-1.html#cb731-3" aria-hidden="true" tabindex="-1"></a><span class="fu">names</span>(alphaModelStargazer<span class="sc">$</span>coefficients) <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"(Intercept)"</span>, <span class="st">"BA"</span>, <span class="st">"Masters"</span>, <span class="st">"PhD"</span>)</span>