The significance of education on the salary in Sweden, a comparison between different occupational groups

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In my last post, I found that education has a significant impact on the salary of engineers. Is the significance of education 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 education. I will not use sex as an explanatory variable since there are occupational groups that do not have enough data for both genders. Searching through the different occupational groups I will fit education with a polynomial of degree one. I am interested in occupational groups where a longer education also results in higher salaries. Because of that, I will use the numerical approximation from my last post instead of using the categorical predictor. A polynomial of higher degree than one would result in a better fit but the problem with oscillation and overfitting made me settle for degree one. A straight line as a function also has the advantage that the average increase in salary for each education year is directly given from the model.

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

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

In the figure below I will also use the estimate for education to see how much the salaries are raised by education for the different occupational groups holding year 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 (splines)
#install_github("ZheyuanLi/SplinesUtils")
library (SplinesUtils)

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, 000000CY.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 educational level (SUN). Year 2014 – 2018 Monthly salary All sectors

tb <- readfile("000000CY.csv")

numedulevel <- read.csv("edulevel.csv") 

numedulevel %>%
  knitr::kable(
  booktabs = TRUE,
  caption = 'Initial approach, length of education')

Table 1: Initial approach, length of education
level.of.education eduyears
primary and secondary education 9-10 years (ISCED97 2) 9
upper secondary education, 2 years or less (ISCED97 3C) 11
upper secondary education 3 years (ISCED97 3A) 12
post-secondary education, less than 3 years (ISCED97 4+5B) 14
post-secondary education 3 years or more (ISCED97 5A) 15
post-graduate education (ISCED97 6) 19
no information about level of educational attainment NA

tbnum <- tb %>% 
  right_join(numedulevel, by = c("level of education" = "level.of.education")) %>%
  filter(!is.na(eduyears))

## Warning: Column `level of education`/`level.of.education` joining character
## vector and factor, coercing into character vector

summary_table = vector()
anova_table = vector()

for (i in unique(tbnum$`occuptional  (SSYK 2012)`)){
  temp <- filter(tbnum, `occuptional  (SSYK 2012)` == i)
  if (dim(temp)[1] > 30){
    model <- lm (log(salary) ~ year_n + eduyears, 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 == "eduyears") %>%
  filter (term.x == "eduyears") %>%
  mutate (estimate = (exp(estimate) - 1) * 100) %>%
  ggplot () +
    geom_point (mapping = aes(x = estimate, y = statistic.y)) +
    labs(
      x = "Increase in salaries (% / year of education)",
      y = "F-value for education"
    )


The significance of education on the salary in Sweden, a comparison between different occupational groups, Year 2014 - 2018

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

The table with all occupational groups sorted by Increase in salary in descending order.

merge(summary_table, anova_table, by = "ssyk", all = TRUE) %>%
  filter (term.y == "eduyears") %>%
  filter (term.x == "eduyears") %>%
  select (ssyk, estimate, statistic.y) %>%
  mutate (estimate = (exp(estimate) - 1) * 100) %>%
  rename (`F-value for education` = statistic.y) %>%
  rename (`Increase in salary` = estimate) %>%
  arrange (desc (`Increase in salary`)) %>%
  knitr::kable(
    booktabs = TRUE,
    caption = 'Correlation for F-value (education) and the increase in salaries for each year of education')

Table 2: Correlation for F-value (education) and the increase in salaries for each year of education
ssyk Increase in salary F-value for education
151 Health care managers 11.3222562 615.8861538
221 Medical doctors 10.2650113 70.5835974
121 Finance managers 9.9172689 32.7350353
261 Legal professionals 9.7834120 48.1004817
122 Human resource managers 9.0394770 103.8231602
161 Financial and insurance managers 8.6603822 19.2527280
231 University and higher education teachers 7.5276294 141.4796497
132 Supply, logistics and transport managers 6.6969576 87.6384397
137 Production managers in manufacturing 6.5378753 65.2842719
123 Administration and planning managers 6.2977859 129.4982036
136 Production managers in construction and mining 6.2192630 57.8361291
129 Administration and service managers not elsewhere classified 5.6522431 74.9238199
131 Information and communications technology service managers 5.1937185 95.3092758
159 Other social services managers 5.1920288 355.8557670
134 Architectural and engineering managers 4.6458339 186.5137309
262 Museum curators and librarians and related professionals 4.4638502 294.6004878
332 Insurance advisers, sales and purchasing agents 4.2505985 57.1999444
179 Other services managers not elsewhere classified 4.0931013 44.9824826
235 Teaching professionals not elsewhere classified 3.9957394 189.3385229
311 Physical and engineering science technicians 3.9729301 134.6441603
234 Primary- and pre-school teachers 3.8498852 140.3499938
233 Secondary education teachers 3.7146273 167.3564935
125 Sales and marketing managers 3.6489071 17.5675213
241 Accountants, financial analysts and fund managers 3.3820710 49.5445027
242 Organisation analysts, policy administrators and human resource specialists 3.1833018 94.6038730
213 Biologists, pharmacologists and specialists in agriculture and forestry 2.9242020 93.6360138
321 Medical and pharmaceutical technicians 2.7274994 130.1793959
133 Research and development managers 2.5377568 28.8355719
173 Retail and wholesale trade managers 2.4736675 5.9078862
335 Tax and related government associate professionals 2.3658837 41.8703194
214 Engineering professionals 2.3546977 140.9367261
243 Marketing and public relations professionals 2.3458276 31.1353096
232 Vocational education teachers 2.3303514 27.2589020
334 Administrative and specialized secretaries 2.2765069 20.8078772
342 Athletes, fitness instructors and recreational workers 2.1279403 24.0465329
266 Social work and counselling professionals 2.0818202 46.6894573
331 Financial and accounting associate professionals 2.0726916 8.1402279
411 Office assistants and other secretaries 2.0115047 60.8893100
523 Cashiers and related clerks 1.8137124 13.9599411
524 Event seller and telemarketers 1.7261688 13.0208742
251 ICT architects, systems analysts and test managers 1.5958484 81.4664709
819 Process control technicians 1.4963794 40.1366829
962 Newspaper distributors, janitors and other service workers 1.3940863 38.9982657
812 Metal processing and finishing plant operators 1.3878292 12.9570916
432 Stores and transport clerks 1.2376483 43.6773646
341 Social work and religious associate professionals 1.1195539 60.5012820
531 Child care workers and teachers aides 1.0815506 16.6066709
264 Authors, journalists and linguists 1.0636388 5.4839869
333 Business services agents 1.0019699 3.5614940
522 Shop staff 0.9835325 9.4858527
351 ICT operations and user support technicians 0.9821077 7.4180769
441 Library and filing clerks 0.9770931 17.5562894
941 Fast-food workers, food preparation assistants 0.8675015 15.3917476
611 Market gardeners and crop growers 0.8014313 6.0302572
817 Wood processing and papermaking plant operators 0.7291227 7.4060017
217 Designers 0.7088900 1.8475401
831 Train operators and related workers 0.5548934 3.3520151
932 Manufacturing labourers 0.5533498 4.2142587
343 Photographers, interior decorators and entertainers 0.5498463 0.6786136
513 Waiters and bartenders 0.5489340 2.0997794
312 Construction and manufacturing supervisors 0.5475032 1.3980603
534 Attendants, personal assistants and related workers 0.5264678 28.8067668
515 Building caretakers and related workers 0.5221112 6.8499176
815 Machine operators, textile, fur and leather products 0.4691193 2.1375421
422 Client information clerks 0.3886323 1.7115048
533 Health care assistants 0.3239149 4.1630503
818 Other stationary plant and machine operators 0.2957261 1.0364217
512 Cooks and cold-buffet managers 0.2548134 0.9265992
711 Carpenters, bricklayers and construction workers 0.2417011 0.1572365
218 Specialists within environmental and health protection 0.2397413 0.4222318
961 Recycling collectors 0.1921605 0.8568597
541 Other surveillance and security workers 0.1812197 0.4153472
511 Cabin crew, guides and related workers 0.1658380 0.2150479
723 Machinery mechanics and fitters 0.1410149 0.2170183
821 Assemblers 0.0644892 0.0858323
813 Machine operators, chemical and pharmaceutical products 0.0326476 0.0217158
833 Heavy truck and bus drivers 0.0309875 0.0482259
816 Machine operators, food and related products 0.0069780 0.0017000
532 Personal care workers in health services -0.0383003 0.1216850
352 Broadcasting and audio-visual technicians -0.0705932 0.0171995
814 Machine operators, rubber, plastic and paper products -0.1428982 0.2504506
722 Blacksmiths, toolmakers and related trades workers -0.1569686 0.4841203
732 Printing trades workers -0.3543764 0.5477171
911 Cleaners and helpers -0.3859718 4.5299051
834 Mobile plant operators -0.3979938 5.1952942
216 Architects and surveyors -0.6970606 1.2794827
516 Other service related workers -0.7106422 1.0123452
265 Creative and performing artists -1.4326841 6.0250927

Let’s check what we have found.

temp <- tbnum %>%
  filter(`occuptional  (SSYK 2012)` == "151 Health care managers")

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


Highest increase in salary, 151 Health care managers

Figure 2: Highest increase in salary, 151 Health care managers

modelcont <- lm (log(salary) ~ year_n + bs(eduyears, degree = 1), data = temp)

contspline <- RegBsplineAsPiecePoly(modelcont, "bs(eduyears, degree = 1)")

tibble(eduyears = seq(11, 19, by=0.1)) %>%
  ggplot () + 
    geom_point (mapping = aes(x = eduyears,y = predict(contspline, eduyears))) +
  labs(
    x = "Years of education",
    y = "Salary"
  )


Model fit, Health care managers, Correlation between education and salary

Figure 3: Model fit, Health care managers, Correlation between education and salary

tibble(eduyears = seq(11, 19, by=0.1)) %>%
  ggplot () + 
    geom_point (mapping = aes(x = eduyears,y = (exp(predict(contspline, eduyears, deriv = 1)) - 1) * 100)) +
  labs(
    x = "Years of education",
    y = "Salary difference (%)"
  )


Model fit, Health care managers, The derivative for educaton

Figure 4: Model fit, Health care managers, The derivative for educaton

temp <- tbnum %>% 
  filter(`occuptional  (SSYK 2012)` == "265 Creative and performing artists")

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


Lowest increase in salary, 265 Creative and performing artists

Figure 5: Lowest increase in salary, 265 Creative and performing artists

modelcont <- lm (log(salary) ~ year_n + bs(eduyears, degree = 1), data = temp)

contspline <- RegBsplineAsPiecePoly(modelcont, "bs(eduyears, degree = 1)")

tibble(eduyears = seq(11, 15, by=0.1)) %>%
  ggplot () + 
    geom_point (mapping = aes(x = eduyears,y = predict(contspline, eduyears))) +
  labs(
    x = "Years of education",
    y = "Salary"
  )


Model fit, Creative and performing artists, Correlation between education and salary

Figure 6: Model fit, Creative and performing artists, Correlation between education and salary

tibble(eduyears = seq(11, 15, by=0.1)) %>%
  ggplot () + 
    geom_point (mapping = aes(x = eduyears,y = (exp(predict(contspline, eduyears, deriv = 1)) - 1) * 100)) +
  labs(
    x = "Years of education",
    y = "Salary difference (%)"
  )


Model fit, Creative and performing artists, The derivative for education

Figure 7: Model fit, Creative and performing artists, The derivative for education

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