Income Distribution & Inequality

The skill premium

The skill premium is the wage ratio of skilled to unskilled workers, \(\omega = w_s/w_u\). It is set by relative supply and relative demand:

\[\omega = D \cdot \left(\frac{L_u}{L_s}\right)^{1/\sigma}\]

• \(L_s/L_u\) = relative supply of skilled workers. More skilled workers (education) → \(\omega\) falls.
• \(D\) = relative demand for skill. Skill-biased technical change (SBTC) raises \(D\) → \(\omega\) rises.
• \(\sigma\) = how easily firms substitute the two types.

Try it. Educate more workers (raise the skilled share) and the premium falls. Turn up SBTC and it rises — the race between education and technology.

#| standalone: true
#| viewerHeight: 520

library(shiny)
ui <- fluidPage(
  tags$head(tags$style(HTML("body{font-family:'Inter',system-ui,sans-serif;}
    .sb{background:#f0f4f8;border-radius:6px;padding:12px 14px;margin-top:10px;font-size:14px;line-height:1.85;} .sb b{color:#1f3b73;}"))),
  sidebarLayout(
    sidebarPanel(width=4,
      sliderInput("s","Skilled share of workers:",min=0.1,max=0.9,value=0.4,step=0.05),
      sliderInput("D","Relative demand for skill  D (SBTC):",min=0.5,max=3,value=1.5,step=0.1),
      sliderInput("sig","Substitutability  σ:",min=1,max=5,value=2,step=0.5),
      uiOutput("sb")),
    mainPanel(width=8, plotOutput("plot",height="440px"))))
server <- function(input,output,session){
  prem <- function(s,D,sig) D*((1-s)/s)^(1/sig)
  output$plot <- renderPlot({
    sg <- seq(0.1,0.9,length.out=200); wg <- prem(sg,input$D,input$sig)
    par(mar=c(4.2,4.6,1,1))
    plot(sg,wg,type="l",col="#1f3b73",lwd=3,xlab="Skilled share of workers",ylab="Skill premium  w_s / w_u",
         las=1,bty="l",cex.lab=1.1,ylim=c(0.5,max(wg)*1.05))
    abline(h=1,col="#9aa4b2",lty=3)
    points(input$s,prem(input$s,input$D,input$sig),pch=19,col="#1c6b4a",cex=1.7)
  })
  output$sb <- renderUI({ w<-prem(input$s,input$D,input$sig)
    HTML(sprintf("<div class='sb'>Skill premium <b>w_s/w_u = %.2f</b><br>%s</div>",
      w, if(w>1) sprintf("Skilled workers earn <b>%.0f%% more</b>.",100*(w-1)) else "Premium below 1 (skilled no longer scarce).")) })
}
shinyApp(ui,server)

What to notice

• Slide the skilled share up → the premium falls: expanding education compresses inequality (Goldin & Katz’s “race”).
• Turn up SBTC (D) → the whole curve shifts up: technology that favors skill widens inequality.