class: center, middle, inverse, title-slide # Lecture 1: Introduction to Econometrics ## ECON 480 - Econometrics - Fall 2018 ### Ryan Safner ### August 27, 2018 --- class: inverse, center, middle # What is Econometrics? --- # Why Everyone, Yes *Everyone*, Should Learn Statistics .center[.image-40[]] --- # Why Everyone, Yes *Everyone*, Should Learn Statistics .center[.image-30[]] --- # We're Not so Good at Statistics - Votes in the U.S. House of Representatives in favor of passing the Civil Rights Act of 1964: | Democrat | Republican | |----------|------------| | 61% | 80% | -- - Simple enough: "on average, Republicans tended to vote for passage more than Democrats" --- # We're Not so Good at Statistics - Broken down further by Northern vs. Southern states: | |Democrat | Republican | |-------|----------|------------| | **North** | 94% | 85% | | | (145/154)| (138/162) | | **South** | 7% | 0% | | | (7/94) | (0/10) | | **Overall** | 61% | 80% | | | (152/248) | (138/172) | - What's going on? -- - A far greater proportion of Democrats (94/248, 38%) than Republicans (10/172, 6%) were from the South -- - The 7% of southern Democrats voting *for* the Act dragged down the Democrats' *overall* percentage more than the 0% of southern Republicans --- # Simpson's Paradox .content-box-red[ .red[**Simpson's Paradox**:] The correlation between two variables can change (even reverse!) when additional variables are considered] .center[] --- # Simpson's Paradox .pull-left[ .content-box-red[ .red[**Simpson's Paradox**:] The correlation between two variables can change (even reverse!) when additional variables are considered] ] .pull-right[ .center[] ] --- class: inverse, center, middle # Economic Theory --- # Economic Theory and Economic Models - Economic theorizing often involves building a .content-box-green[formal model] to relate economic phenomena and build intuitions -- .content-box-green[ .green[**Example**]: Becker (1968) famously models crime as a rational choice: `$$y = f(x_1,x_2,x_3,x_4,x_5,x_6,x_7)$$` | Thing | Thing 2 | |-------|------------------------------------| | `\(x_1\)` | Hours spent on criminal activities | | `\(x_2\)` | Hourly wages for legal employment | ] - We can at least predict the "sign" of each relationship between `\(y\)` and each `\(x_i\)` (then estimate the quantitative impact) | Thing | Thing 2 | |-------|------------------------------------| | `\(x_1\)` | Hours spent on criminal activities | | `\(x_2\)` | Hourly wages for legal employment | --- class: blank background-image: url(https://www.dropbox.com/s/dg69zmfgg020onj/bitcoinpriceapril2019.png?raw=1) background-position: 50% 50% --- # Example Code .pull-left[ ```r ggplot(data = gapminder, aes(x = gdpPercap, y = lifeExp, color = continent, fill= continent))+ geom_point()+geom_smooth(method = "lm") + * scale_x_log10()+ylab("Life Expectancy (Years)")+ * xlab("Log GDP/Capita") ``` ] .pull-right[ <!-- --> ] --- class: inverse, center, middle # About this Class --- # This Class Is <!-- --> --- # This Class Is <!-- --> --- # Example <table> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:right;"> mpg </th> <th style="text-align:right;"> cyl </th> <th style="text-align:right;"> disp </th> <th style="text-align:right;"> hp </th> <th style="text-align:right;"> drat </th> <th style="text-align:right;"> wt </th> <th style="text-align:right;"> qsec </th> <th style="text-align:right;"> vs </th> <th style="text-align:right;"> am </th> <th style="text-align:right;"> gear </th> <th style="text-align:right;"> carb </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Mazda RX4 </td> <td style="text-align:right;"> 21.0 </td> <td style="text-align:right;"> 6 </td> <td style="text-align:right;"> 160 </td> <td style="text-align:right;"> 110 </td> <td style="text-align:right;"> 3.90 </td> <td style="text-align:right;"> 2.620 </td> <td style="text-align:right;"> 16.46 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> 4 </td> </tr> <tr> <td style="text-align:left;"> Mazda RX4 Wag </td> <td style="text-align:right;"> 21.0 </td> <td style="text-align:right;"> 6 </td> <td style="text-align:right;"> 160 </td> <td style="text-align:right;"> 110 </td> <td style="text-align:right;"> 3.90 </td> <td style="text-align:right;"> 2.875 </td> <td style="text-align:right;"> 17.02 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> 4 </td> </tr> <tr> <td style="text-align:left;"> Datsun 710 </td> <td style="text-align:right;"> 22.8 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> 108 </td> <td style="text-align:right;"> 93 </td> <td style="text-align:right;"> 3.85 </td> <td style="text-align:right;"> 2.320 </td> <td style="text-align:right;"> 18.61 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> 1 </td> </tr> <tr> <td style="text-align:left;"> Hornet 4 Drive </td> <td style="text-align:right;"> 21.4 </td> <td style="text-align:right;"> 6 </td> <td style="text-align:right;"> 258 </td> <td style="text-align:right;"> 110 </td> <td style="text-align:right;"> 3.08 </td> <td style="text-align:right;"> 3.215 </td> <td style="text-align:right;"> 19.44 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 1 </td> </tr> <tr> <td style="text-align:left;"> Hornet Sportabout </td> <td style="text-align:right;"> 18.7 </td> <td style="text-align:right;"> 8 </td> <td style="text-align:right;"> 360 </td> <td style="text-align:right;"> 175 </td> <td style="text-align:right;"> 3.15 </td> <td style="text-align:right;"> 3.440 </td> <td style="text-align:right;"> 17.02 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 2 </td> </tr> <tr> <td style="text-align:left;"> Valiant </td> <td style="text-align:right;"> 18.1 </td> <td style="text-align:right;"> 6 </td> <td style="text-align:right;"> 225 </td> <td style="text-align:right;"> 105 </td> <td style="text-align:right;"> 2.76 </td> <td style="text-align:right;"> 3.460 </td> <td style="text-align:right;"> 20.22 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 1 </td> </tr> </tbody> </table> --- # Example II .pull-left[ ``` ## ## Call: ## lm(formula = hwy ~ displ, data = mpg) ## ## Residuals: ## Min 1Q Median 3Q Max ## -7.1039 -2.1646 -0.2242 2.0589 15.0105 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 35.6977 0.7204 49.55 <2e-16 *** ## displ -3.5306 0.1945 -18.15 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 3.836 on 232 degrees of freedom ## Multiple R-squared: 0.5868, Adjusted R-squared: 0.585 ## F-statistic: 329.5 on 1 and 232 DF, p-value: < 2.2e-16 ``` ] .pull-right[ <!-- --> ] --- # Example III .pull-left[ ``` ## ## Call: ## lm(formula = hwy ~ displ, data = mpg) ## ## Residuals: ## Min 1Q Median 3Q Max ## -7.1039 -2.1646 -0.2242 2.0589 15.0105 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 35.6977 0.7204 49.55 <2e-16 *** ## displ -3.5306 0.1945 -18.15 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 3.836 on 232 degrees of freedom ## Multiple R-squared: 0.5868, Adjusted R-squared: 0.585 ## F-statistic: 329.5 on 1 and 232 DF, p-value: < 2.2e-16 ``` ] .pull-right[ <table style="text-align:center"><tr><td colspan="2" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"></td><td><em>Dependent variable:</em></td></tr> <tr><td></td><td colspan="1" style="border-bottom: 1px solid black"></td></tr> <tr><td style="text-align:left"></td><td>hwy</td></tr> <tr><td colspan="2" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">displ</td><td>-3.531^***</td></tr> <tr><td style="text-align:left"></td><td>(0.195)</td></tr> <tr><td style="text-align:left"></td><td></td></tr> <tr><td style="text-align:left">Constant</td><td>35.698^***</td></tr> <tr><td style="text-align:left"></td><td>(0.720)</td></tr> <tr><td style="text-align:left"></td><td></td></tr> <tr><td colspan="2" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">Observations</td><td>234</td></tr> <tr><td style="text-align:left">R²</td><td>0.587</td></tr> <tr><td style="text-align:left">Adjusted R²</td><td>0.585</td></tr> <tr><td style="text-align:left">Residual Std. Error</td><td>3.836 (df = 232)</td></tr> <tr><td style="text-align:left">F Statistic</td><td>329.453^*** (df = 1; 232)</td></tr> <tr><td colspan="2" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left"><em>Note:</em></td><td style="text-align:right">^*p<0.1; ^**p<0.05; ^***p<0.01</td></tr> </table> ] --- .pull-left[ - Probability a student gets between a 65 and 85: ``` ## [1] 0.6826895 ``` ] .pull-right[ <!-- --> ] --- # DAGs <!-- --> <!-- -->