SA3_RSolution_Econ140

ECON 140: Section 3 (OLS) Question 3: Dummy variables regression Load required libraries Load dataset # Set working directory getwd () ## [1] "/Users/jonathanold/Dropbox/ECON_140_SPRING_2024/Section Assignments" setwd ( "/Users/jonathanold/Library/CloudStorage/GoogleDrive-jonathan_old@berkeley.edu/My Drive/_Berkeley # Load dataset mexico_data = read.csv ( "../Datasets/Mexico.csv" ) head (mexico_data) ## year state sector sex age ind_lang educ_years hrs_wk inc_m USDist_km ## 1 2010 1 Services 1 30 0 12 48 3600 600.6932 ## 2 2010 1 Services 0 16 0 9 98 4286 557.6143 ## 3 2010 1 Agriculture 0 19 0 10 24 1286 616.0118 ## 4 2010 1 Manufacturing 0 29 0 12 45 4286 550.4415 ## 5 2010 1 Services 0 38 0 9 40 4600 597.9345 ## 6 2010 1 Services 0 50 0 13 30 8000 561.4097 # Create summary statistics table, export as LaTeX stargazer ( data= mexico_data, type= "latex" , title= "Summary Statistics" , summary.stat = c ( "n" , "mean" , "sd" , "min" , "median" , "max" ), out= "Summary Table.tex" ) # To display table, use \input{"Summary Table.tex"} Table 1: Summary Statistics Statistic N Mean St. Dev. Min Median Max year 1,000 2,010.000 0.000 2,010 2,010 2,010 state 1,000 17.963 7.961 1 17 32 sex 1,000 0.337 0.473 0 0 1 age 1,000 36.527 13.524 12 35 80 ind_lang 1,000 0.151 0.358 0 0 1 educ_years 1,000 8.295 4.452 0 9 19 hrs_wk 1,000 45.447 20.039 1 48 168 inc_m 1,000 4,890.467 13,662.750 8 3,429 400,000 USDist_km 1,000 702.982 274.254 6.609 738.099 1,348.003 1

Get means and difference in means # How to create a dummy variable using an ifelse condition mexico_data = mexico_data %>% mutate ( rich = ifelse (inc_m > 3000 , 1 , 0 )) # Using tidyR syntax to generate mean of income by indigenous language mexico_data %>% group_by (ind_lang) %>% summarize ( mean (inc_m)) ## # A tibble: 2 x 2 ## ind_lang mean(inc_m) ## <int> <dbl> ## 1 0 5309. ## 2 1 2537. # Using base R syntax to generate mean of income by indigenous language mean1 = mean (mexico_data $ inc_m[mexico_data $ ind_lang == 1 ]) mean0 = mean (mexico_data $ inc_m[mexico_data $ ind_lang == 0 ]) mean_diff = mean1 - mean0 mean_diff ## [1] -2771.968 mean1 ## [1] 2537.066 mean0 ## [1] 5309.034 The average monthly income in the group of indigenous language speakers is 2537, and in the group of non-indigenous language speakers, it is 5309. The difference between the two is -2772. Run OLS regression # Running and outputting linear regression ols_results = summary ( lm (inc_m ~ ind_lang , data= mexico_data)) ols_results ## ## Call: ## lm(formula = inc_m ~ ind_lang, data = mexico_data) ## ## Residuals: ## Min 1Q Median 3Q Max ## -5301 -2738 -1452 291 394691 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 5309.0 467.9 11.347 <2e-16 *** ## ind_lang -2772.0 1204.1 -2.302 0.0215 * ## --- ## Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 ## ## Residual standard error: 13630 on 998 degrees of freedom ## Multiple R-squared: 0.005282, Adjusted R-squared: 0.004286 ## F-statistic: 5.3 on 1 and 998 DF, p-value: 0.02153 2

30 40 50 60 70 45000 55000 65000 dataset$age dataset$wage_yearly linear_regression = summary ( lm (wage_yearly ~ age , data= dataset)) print (linear_regression) ## ## Call: ## lm(formula = wage_yearly ~ age, data = dataset) ## ## Residuals: ## Min 1Q Median 3Q Max ## -9149.7 -2174.3 -180.6 2068.6 13537.9 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 46193.351 223.323 206.84 <2e-16 *** ## age 143.556 4.524 31.73 <2e-16 *** ## --- ## Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 ## ## Residual standard error: 3217 on 2998 degrees of freedom ## Multiple R-squared: 0.2514, Adjusted R-squared: 0.2511 ## F-statistic: 1007 on 1 and 2998 DF, p-value: < 2.2e-16 # We use the function I() to create quadratic terms and interactions. quadratic_regression = lm (wage_yearly ~ age + I (age ˆ 2 ) , data= dataset) summary (quadratic_regression) ## ## Call: ## lm(formula = wage_yearly ~ age + I(age^2), data = dataset) ## ## Residuals: ## Min 1Q Median 3Q Max ## -7930.0 -2100.8 -318.6 2011.6 14186.3 4

## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 28155.2161 764.3662 36.84 <2e-16 *** ## age 961.9520 33.6772 28.56 <2e-16 *** ## I(age^2) -8.5927 0.3509 -24.49 <2e-16 *** ## --- ## Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 ## ## Residual standard error: 2937 on 2997 degrees of freedom ## Multiple R-squared: 0.3762, Adjusted R-squared: 0.3758 ## F-statistic: 903.7 on 2 and 2997 DF, p-value: < 2.2e-16 # We can use cplot to create two types of plots: # 1. Predict wages by age (the estimated regression function) cplot (quadratic_regression, "age" , what = "pred" , main = "Predicted yearly wages, by age" ) 30 40 50 60 70 48000 50000 52000 54000 Predicted yearly wages, by age age Predicted value # 2. The marginal "effect" of age (the derivative of the estimated regression function): cplot (quadratic_regression, "age" , what = "effect" , main = "Average Marginal Effect of age" ) 5