Model

What is the difference between black, white, and hispanic wages through each education level?

To answer the question of the difference in wages among black, white, and hispanic workers across different education levels, we first analyze the wage data using a Bayesian regression model. For this initial model, we use the following formula:

\[ \text{wage} = \beta_{0} + \beta_{1} \times \text{education}_i + \beta_{2} \times \text{year}_i \]

Characteristic	Beta	95% CI 1
less_than_hs	2.6	0.73, 4.6
high_school	-4.8	-8.6, -0.89
some_college	-5.1	-7.9, -2.3
bachelors_degree	3.5	1.9, 5.1
advanced_degree	1.4	0.43, 2.4
1 CI = Credible Interval

We observe the impact of different education levels on average hourly wages. Next, we calculate the effect of education level and ethnicity on wages using the following model:

\[ \text{wage} = \beta_{0} + \beta_{1} \times \text{education}_i + \beta_{2} \times \text{ethnicity}_i \]

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: high_school ~ white_less_than_hs + white_high_school + white_some_college + white_bachelors_degree + white_advanced_degree + black_less_than_hs + black_high_school + black_some_college + black_bachelors_degree + black_advanced_degree + hispanic_less_than_hs + hispanic_high_school + hispanic_some_college + hispanic_bachelors_degree + hispanic_advanced_degree 
   Data: large_data (Number of observations: 50) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Regression Coefficients:
                          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
Intercept                    -0.70      0.46    -1.63     0.22 1.00     3655
white_less_than_hs            0.02      0.04    -0.07     0.11 1.00     2644
white_high_school             0.75      0.07     0.62     0.87 1.00     2557
white_some_college            0.16      0.05     0.06     0.25 1.00     2733
white_bachelors_degree       -0.08      0.02    -0.12    -0.04 1.00     3102
white_advanced_degree        -0.00      0.01    -0.03     0.02 1.00     3221
black_less_than_hs            0.05      0.03    -0.01     0.11 1.00     3544
black_high_school             0.13      0.03     0.07     0.20 1.00     2750
black_some_college            0.02      0.03    -0.03     0.07 1.00     3059
black_bachelors_degree       -0.01      0.02    -0.04     0.03 1.00     3041
black_advanced_degree         0.02      0.01     0.01     0.04 1.00     2967
hispanic_less_than_hs        -0.09      0.04    -0.16    -0.02 1.00     2689
hispanic_high_school          0.09      0.03     0.02     0.16 1.00     3281
hispanic_some_college         0.02      0.03    -0.03     0.07 1.00     2750
hispanic_bachelors_degree    -0.00      0.01    -0.02     0.02 1.00     3171
hispanic_advanced_degree     -0.01      0.00    -0.02    -0.00 1.00     2923
                          Tail_ESS
Intercept                     3271
white_less_than_hs            2654
white_high_school             2834
white_some_college            2896
white_bachelors_degree        2679
white_advanced_degree         2591
black_less_than_hs            3002
black_high_school             2482
black_some_college            2815
black_bachelors_degree        2657
black_advanced_degree         2724
hispanic_less_than_hs         2426
hispanic_high_school          2853
hispanic_some_college         2910
hispanic_bachelors_degree     2860
hispanic_advanced_degree      3054

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.05      0.01     0.04     0.07 1.00     2153     2377

Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

This model includes the ethnicity variable to account for differences between black, white, and hispanic workers, providing a more comprehensive analysis.

Characteristic	Beta	95% CI 1
white_less_than_hs	0.02	-0.07, 0.11
white_high_school	0.75	0.62, 0.87
white_some_college	0.16	0.06, 0.25
white_bachelors_degree	-0.08	-0.12, -0.04
white_advanced_degree	0.00	-0.03, 0.02
black_less_than_hs	0.05	-0.01, 0.11
black_high_school	0.13	0.07, 0.20
black_some_college	0.02	-0.03, 0.07
black_bachelors_degree	-0.01	-0.04, 0.03
black_advanced_degree	0.02	0.01, 0.04
hispanic_less_than_hs	-0.09	-0.16, -0.02
hispanic_high_school	0.09	0.02, 0.16
hispanic_some_college	0.02	-0.03, 0.07
hispanic_bachelors_degree	0.00	-0.02, 0.02
hispanic_advanced_degree	-0.01	-0.02, 0.00
1 CI = Credible Interval

In summary, we find that higher education levels generally correspond to higher wages. However, there are significant differences in wages among black, white, and Hispanic workers at each education level. This relationship highlights the importance of considering both education and ethnicity when analyzing wage disparities in the USA.