In my last post, I found that experience has a significant impact on the salary of engineers. Is the significance of experience on wages unique to engineers or are there similar correlations in other occupational groups?

I will use the same model in principal as in my previous post to calculate the significance of age. I will not use sex as an explanatory variable since there are occupational groups that do not have enough data for both genders. I will also use a polynomial of degree three since this provides a significant model fit for some occupational groups.

There are still occupational groups with too little data for regression analysis. More than 30 posts are necessary to fit both age and year.

The R-value from the Anova table is used as the single value to discriminate how much the age and salary correlates. For exploratory analysis, the Anova value seems good enough.

In the figure below I will also use the estimate for the year to see how much the salaries are raised each year for the different occupational groups holding age as constant.

library (tidyverse)
## -- Attaching packages -------------------------------------------- tidyverse 1.2.1 --
## v ggplot2 3.2.0     v purrr   0.3.2
## v tibble  2.1.3     v dplyr   0.8.3
## v tidyr   0.8.3     v stringr 1.4.0
## v readr   1.3.1     v forcats 0.4.0
## -- Conflicts ----------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library (broom)
library (car)
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
## 
##     recode
## The following object is masked from 'package:purrr':
## 
##     some
library (polynom)

readfile <- function (file1){read_csv (file1, col_types = cols(), locale = readr::locale (encoding = "latin1"), na = c("..", "NA")) %>%
  gather (starts_with("19"), starts_with("20"), key = "year", value = salary) %>%
  drop_na() %>%
  mutate (year_n = parse_number (year))
}

The data table is downloaded from Statistics Sweden. It is saved as a comma-delimited file without heading, 000000D2.csv, http://www.statistikdatabasen.scb.se/pxweb/en/ssd/.

The table: Average basic salary, monthly salary and women´s salary as a percentage of men´s salary by sector, occupational group (SSYK 2012), sex and age. Year 2014 – 2018 Monthly salary All sectors

tb <- readfile("000000D2.csv") %>%
  rowwise() %>%
  mutate(age_l = unlist(lapply(strsplit(substr(age, 1, 5), "-"), strtoi))[1]) %>%
  rowwise() %>%
  mutate(age_h = unlist(lapply(strsplit(substr(age, 1, 5), "-"), strtoi))[2]) %>%
  mutate(age_n = (age_l + age_h) / 2)

summary_table = 0
anova_table = 0

for (i in unique(tb$`occuptional  (SSYK 2012)`)){
  temp <- filter(tb, `occuptional  (SSYK 2012)` == i)
  if (dim(temp)[1] > 30){
    model <-lm (log(salary) ~ year_n + poly(age_n, 3), data = temp)
    summary_table <- rbind (summary_table, mutate (tidy (summary (model)), ssyk = i))
    anova_table <- rbind (anova_table, mutate (tidy (Anova (model, type = 2)), ssyk = i))
  }
}

merge(summary_table, anova_table, by = "ssyk", all = TRUE) %>%
  filter (term.y == "poly(age_n, 3)") %>%
  filter (term.x == "year_n") %>%
  ggplot () +
    geom_point (mapping = aes(x = estimate, y = statistic.y)) +
    labs(
      x = "Increase in salaries (% / year)",
      y = "F-value for age"
    ) 

Figure 1: The significance of experience on the salary in Sweden, a comparison between different occupational groups, Year 2014 – 2018

The table with all occupational groups sorted by F-value in descending order.

merge(summary_table, anova_table, by = "ssyk", all = TRUE) %>%
  filter (term.y == "poly(age_n, 3)") %>%
  filter (term.x == "year_n") %>%
  select (ssyk, estimate, statistic.y) %>%
  rename (`F-value for age` = statistic.y) %>%
  rename (`Increase in salary` = estimate) %>%
  arrange (desc (`F-value for age`)) %>%
  knitr::kable(
    booktabs = TRUE,
    caption = 'Correlation for F-value (age) and the yearly increase in salaries with age held as constant')

Let’s check what we have found.

temp <- tb %>%
  filter(`occuptional  (SSYK 2012)` == "234 Primary- and pre-school teachers")
 
temp %>%
  ggplot () +
    geom_point (mapping = aes(x = year_n,y = salary, colour = age)) +
    facet_grid(. ~ sex) +   
    labs(
      x = "Year",
      y = "Salary (SEK/month)"
    ) 

Figure 2: Highest F-value, Primary- and pre-school teachers

model <-lm (log(salary) ~ year_n + poly(age_n, 3, raw = T), data = temp)

summod <- tidy(summary (model))

temp %>%
  ggplot () +
    geom_point (mapping = aes(x = age_n,y = age_n * summod$estimate[3] + summod$estimate[4] * age_n^2 + summod$estimate[5] * age_n^3)) +
    labs(
      x = "Age",
      y = "Salary"
    )

Figure 3: Model fit, Primary- and pre-school teachers, Correlation between age and salary

pdx <- deriv(as.polynomial(c(0, summod$estimate[3], summod$estimate[4], summod$estimate[5])))

temp %>%
  ggplot () + 
    geom_point (mapping = aes(x = age_n, y = summod$estimate[2] + pdx[1] + pdx[2] * age_n + pdx[3] * age_n^2)) +
    labs(
      x = "Age",
      y = "Salary raise (%)"
    )

Figure 4: Model fit, Primary- and pre-school teachers, The derivative for age

temp <- tb %>%
  filter(`occuptional  (SSYK 2012)` == "821 Assemblers")

temp %>%
  ggplot () +
    geom_point (mapping = aes(x = year_n,y = salary, colour = age)) +
    facet_grid(. ~ sex) +   
    labs(
      x = "Year",
      y = "Salary (SEK/month)"
    ) 

Figure 5: Lowest F-value, Assemblers

model <-lm (log(salary) ~ year_n + poly(age_n, 3, raw = T), data = temp)

summod <- tidy(summary (model))

temp %>%
  ggplot () +
    geom_point (mapping = aes(x = age_n,y = age_n * summod$estimate[3] + summod$estimate[4] * age_n^2 + summod$estimate[5] * age_n^3)) +
    labs(
      x = "Age",
      y = "Salary"
    )

Figure 6: Model fit, Assemblers, Correlation between age and salary

pdx <- deriv(as.polynomial(c(0, summod$estimate[3], summod$estimate[4], summod$estimate[5])))

temp %>%
  ggplot () + 
    geom_point (mapping = aes(x = age_n, y = summod$estimate[2] + pdx[1] + pdx[2] * age_n + pdx[3] * age_n^2)) +
    labs(
      x = "Age",
      y = "Salary raise (%)"
    )

Figure 7: Model fit, Assemblers, The derivative for age

temp <- tb %>%
  filter(`occuptional  (SSYK 2012)` == "161 Financial and insurance managers")

temp %>%
  ggplot () +
    geom_point (mapping = aes(x = year_n,y = salary, colour = age)) +
    facet_grid(. ~ sex) + 
      labs(
        x = "Year",
        y = "Salary (SEK/month)"
      ) 

Figure 8: Highest yearly salary increase, Financial and insurance managers

model <- lm (log(salary) ~ year_n + poly(age_n, 3, raw = T), data = temp)

summod <- tidy(summary (model))

temp %>%
  ggplot () +
    geom_point (mapping = aes(x = age_n,y = age_n * summod$estimate[3] + summod$estimate[4] * age_n^2 + summod$estimate[5] * age_n^3)) +
    labs(
      x = "Age",
      y = "Salary"
    )

Figure 9: Model fit, Financial and insurance managers, Correlation between age and salary

pdx <- deriv(as.polynomial(c(0, summod$estimate[3], summod$estimate[4], summod$estimate[5])))

temp %>%
  ggplot () + 
    geom_point (mapping = aes(x = age_n, y = summod$estimate[2] + pdx[1] + pdx[2] * age_n + pdx[3] * age_n^2)) +
    labs(
      x = "Age",
      y = "Salary raise (%)"
    )

Figure 10: Model fit, Financial and insurance managers, The derivative for age

temp <- tb %>%
  filter(`occuptional  (SSYK 2012)` == "523 Cashiers and related clerks")
temp %>%
  ggplot () +
    geom_point (mapping = aes(x = year_n,y = salary, colour = age)) +
    facet_grid(. ~ sex) + 
    labs(
      x = "Year",
      y = "Salary (SEK/month)"
  )

Figure 11: Lowest yearly salary increase, Cashiers and related clerks

model <-lm (log(salary) ~ year_n + poly(age_n, 3, raw = T), data = temp)

summod <- tidy(summary (model))

temp %>%
  ggplot () +
    geom_point (mapping = aes(x = age_n,y = age_n * summod$estimate[3] + summod$estimate[4] * age_n^2 + summod$estimate[5] * age_n^3)) +
    labs(
      x = "Age",
      y = "Salary"
    )

Figure 12: Model fit, Cashiers and related clerks, Correlation between age and salary

pdx <- deriv(as.polynomial(c(0, summod$estimate[3], summod$estimate[4], summod$estimate[5])))

temp %>%
  ggplot () + 
    geom_point (mapping = aes(x = age_n, y = summod$estimate[2] + pdx[1] + pdx[2] * age_n + pdx[3] * age_n^2)) +
    labs(
      x = "Age",
      y = "Salary raise (%)"
    )

Figure 13: Model fit, Cashiers and related clerks, The derivative for age

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