Hedonic Regression of Salary on Skill Aggregates

Estimating the salary elasticity of skill aggregates

One might be interested in the association between our skill clusters and salary. Here we perform a hedonic wage regression to estimate the elasticity of salary with respect to five skill aggregates: Analytical, Management, STEM, Social, and Technical skills. A non-exhaustive list of caveats:

  1. We identify associations, not causal effects: Increasing a skill by 1% will not increase your salary by the reported elasticity.
  2. Salaries are not determined by skills alone: omitted “other” determinants will bias the estimates when correlated with skills.
  3. The influence the skill clusters have on salary are not likely to be additive: the influence of one skill cluster on salary is likely to depend on the level of other skill clusters.

Diagnostic Plots

Code 
par(mfrow=c(2,2))
plot(mod)

Added Variable Plot for Analytical Skills

Code 
av_plot_gg(mod, "log(Analytical)", data = tbbl)

Added Variable Plot for Management Skills

Code 
av_plot_gg(mod, "log(Management)", data = tbbl)

Added Variable Plot for STEM Skills

Code 
av_plot_gg(mod, "log(STEM)", data = tbbl)

Added Variable Plot for Social Skills

Code 
av_plot_gg(mod, "log(Social)", data = tbbl)

Added Variable Plot for Technical Skills

Code 
av_plot_gg(mod, "log(Technical)", data = tbbl)

Regression Results

Code 
robust_se <- sqrt(diag(vcovHC(mod, type = "HC3")))


stargazer(mod, type = "html",
          se = list(robust_se),
          title = "Hedonic Regression of Wages on Skill Aggregates (HC3 Standard Errors)",
          dep.var.labels = "Log Salary",
          covariate.labels = c("Log Analytical Skills", "Log Management Skills", 
                               "Log STEM Skills", "Log Social Skills", "Log Technical Skills"),
          digits = 3,
          omit.stat = c("f", "ser"),
          no.space = TRUE)
Hedonic Regression of Wages on Skill Aggregates (HC3 Standard Errors)
Dependent variable:
Log Salary
Log Analytical Skills 1.864***
(0.292)
Log Management Skills 0.388***
(0.125)
Log STEM Skills -0.134**
(0.064)
Log Social Skills -1.064***
(0.165)
Log Technical Skills 0.004
(0.033)
Constant 6.816***
(0.603)
Observations 500
R2 0.403
Adjusted R2 0.397
Note: p<0.1; p<0.05; p<0.01

Compare to Regression on 35 (un-clustered) Skills

Code 
all_skills <- skills|>
  select(NOC=NOC2021, name=Skill, value=`Level Score`) |>
  mutate(value=value+1)|>
  pivot_wider()|>
  inner_join(wages)|>
  unite(noc, NOC, `Occupation Title`, sep = ": ")|>
  column_to_rownames("noc")|>
  na.omit()

response <- "salary"
log_response <- paste0("log(`", response, "`)")
# Get independent variables (exclude response)
indep_vars <- setdiff(names(all_skills), response)

# Create formula terms: log(`var name`)
log_vars <- paste0("log(`", indep_vars, "`)")

# Build the formula
fmla <- reformulate(termlabels = log_vars, response = log_response)

# Fit model
all_model <- lm(fmla, data = all_skills)

print(fmla)
log(salary) ~ log(`Active Learning`) + log(`Active Listening`) + 
    log(`Complex Problem Solving`) + log(Coordination) + log(`Critical Thinking`) + 
    log(`Equipment Maintenance`) + log(`Equipment Selection`) + 
    log(Installation) + log(Instructing) + log(`Judgment and Decision Making`) + 
    log(`Learning Strategies`) + log(`Management of Financial Resources`) + 
    log(`Management of Material Resources`) + log(`Management of Personnel Resources`) + 
    log(Mathematics) + log(Monitoring) + log(Negotiation) + log(`Operation and Control`) + 
    log(`Operations Analysis`) + log(`Operations Monitoring`) + 
    log(Persuasion) + log(Programming) + log(`Quality Control Analysis`) + 
    log(`Reading Comprehension`) + log(Repairing) + log(Science) + 
    log(`Service Orientation`) + log(`Social Perceptiveness`) + 
    log(Speaking) + log(`Systems Analysis`) + log(`Systems Evaluation`) + 
    log(`Technology Design`) + log(`Time Management`) + log(Troubleshooting) + 
    log(Writing)
Code 
par(mfrow=c(2,2))
plot(all_model)

Tie-fighter plot of skill elasticities

Code 
coef_df <- coeftest(all_model, vcov = vcovHC(all_model, type = "HC3"))|>
  tidy()|>
  filter(term != "(Intercept)")|>
  mutate(term=str_remove_all(term, "log\\("),
         term=str_remove_all(term, "\\)"),
         term=str_remove_all(term, "`"))|>
  full_join(clusters, by = c("term" = "Skill")) 

ggplot(coef_df, aes(x = estimate, y = fct_reorder(term, estimate))) +
  geom_vline(xintercept = 0, lwd = 2, color = "white") +
  geom_point() +
  geom_errorbarh(aes(xmin = estimate - std.error, xmax = estimate + std.error), height = 0.2) +
  labs(
    x = "Coefficient Estimate (+/-1 HC3 SE)",
    y = NULL,
    title = "Skill elasticities from Hedonic Wage Regression"
  )+
  facet_wrap(~cluster_name, ncol = 1, scales = "free_y")