1. Research question

In Thailand, the difference in wage comes from many factors, they can be education, experience, living region, industry and even gender. With a job like engineer that already requires high quality candidates from the start, I want to study to what extent the level of education and experience affect income.

I also incorporated gender factor to see whether there was any inequality in income between the two sexes in Thailand. And if there is, can the difference between education and experience between male and female engineers be used to explain this trend. In 1985, Thailand’s government has officially announced its commitment to promote women’s rights and improve gender inequality. After 13 years in implementation, it’s vital to assess whether the equality still exists, at least in a smaller scale like engineering job.

2. Theoretical background

Conventionally, factors like education level, years of experience, past experience, living region, marital status, etc. account greatly for the change in wage. More educational background indicates an engineer who can handle complex tasks better, thus results in a better wage. Similarly, the longer an engineer spend time working, the more experienced and skillful he or she gets, which should also result in a better wage. After studying the effects of education and experience on wage, I introduce gender into the equation. If other factors are controlled, then any disparity in wage (if there is any) must due to the difference in gender.
A basic multiple regression model can be used to investigate this question:
\(log(wage) = \beta_0 + \beta_1 male + \beta_k X_k + u_i\)

Where:
+ log(wage) is the natural log of wage, our dependent variable and be represented by \(lwage\)
+ \(male\) is indicator of observation’s gender, \(male\) = 1 if subject is male and = 0 if subject is female.
+ \(X_k\) is a combination of non-gender factors. In this case, it consists of variables: \(educ\) as years of education, \(exper\) as years of experience in current occupation, \(pexper\) as years of experience in past occupations.

3. Description of the data

library(wooldridge)
library(table1)
## 
## Attaching package: 'table1'
## The following objects are masked from 'package:base':
## 
##     units, units<-
library(stargazer)
## 
## Please cite as:
##  Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.
##  R package version 5.2.2. https://CRAN.R-project.org/package=stargazer
library(knitr)
data("engin")
enginm <- subset(engin, male == 1)
enginf <- subset(engin, male == 0)
engin1 <- engin
engin1$male <- factor(engin1$male, levels=c(1,0),labels=c("Male","Female"))
label(engin1$swage)       <- "starting wage"
label(engin1$educ)       <- "years of education"
label(engin1$exper)     <- "years of experience"
label(engin1$pexper) <- "years of past experience"
table1(~ swage + educ + exper + pexper | male, data=engin1, overall="Total")
Male
(N=213)		 Female
(N=190)		 Total
(N=403)
starting wage
Mean (SD) 20900 (8600) 12900 (2610) 17200 (7630)
Median [Min, Max] 16500 [11400, 60000] 12100 [9750, 30000] 15000 [9750, 60000]
years of education
Mean (SD) 15.0 (2.66) 12.3 (2.09) 13.7 (2.77)
Median [Min, Max] 15.0 [8.00, 20.0] 12.0 [8.00, 16.0] 14.0 [8.00, 20.0]
years of experience
Mean (SD) 13.4 (1.83) 13.6 (1.66) 13.5 (1.75)
Median [Min, Max] 14.0 [11.0, 17.0] 14.0 [6.00, 17.0] 14.0 [6.00, 17.0]
years of past experience
Mean (SD) 12.6 (9.25) 9.88 (11.6) 11.3 (10.5)
Median [Min, Max] 10.0 [1.00, 38.0] 4.00 [0, 40.0] 8.00 [0, 40.0]

The data is collected in 1998 with 403 observations, among which 190 observations are female and 213 are male, so the representation of genders is quite balance. The description of the data is as follows:
(a) For male engineers:
- The average starting wage is 20,900 (Thai baht/month)
- The average years of education is 15, with observations who have 12 years or more of education is 203 (95% of male population), of which 31 have completed college degree and 48 have completed graduate degree, so 79 of them have 16 years of more of education.
- The average years of experience is 13.4, with the minimum of 11 years.
- Their past experience is quite diverse, with the average of 12.6 years.
(b) For female engineers:
- The average starting wage is 12,900 (Thai baht/month), this is significantly lower than their male counterparts.
- The average years of education is only 12.3. Observations who have completed 12 years or more of education is 168 (88.4% of female population), among which only 17 observations have earned college degree and 0 of them have graduate degree. Furthermore, 22 female engineers had to drop highschool, which is double than that of male engineers (10). Overall, female engineers are less educated than male engineers.
- The average years of experience for female engineers is about 13.6, approximately equal to male engineers.
- However, female engineers overall have less experience in the past than male engineers, with average years of past experience is around 9.88.

From the preliminary results, it is reasonable to anticipate that \(male\) variable will have a positive effect on wage. \(educ\) and \(exper\) should also have positive effects on wage.

4. Model estimation

model1 <- lm(lwage ~ male + swage + educ + exper, data=engin)
model2 <- lm(lwage ~ male + swage + educ + exper + pexper, data=engin)
stargazer(model1, model2, type = "text")
## 
## =====================================================================
##                                    Dependent variable:               
##                     -------------------------------------------------
##                                           lwage                      
##                               (1)                      (2)           
## ---------------------------------------------------------------------
## male                        0.102***                 0.120***        
##                             (0.022)                  (0.021)         
##                                                                      
## swage                      0.00003***               0.00004***       
##                            (0.00000)                (0.00000)        
##                                                                      
## educ                        0.034***                 0.026***        
##                             (0.005)                  (0.005)         
##                                                                      
## exper                       0.016***                 0.018***        
##                             (0.005)                  (0.005)         
##                                                                      
## pexper                                              -0.006***        
##                                                      (0.001)         
##                                                                      
## Constant                    9.045***                 9.145***        
##                             (0.086)                  (0.083)         
##                                                                      
## ---------------------------------------------------------------------
## Observations                  403                      403           
## R2                           0.800                    0.822          
## Adjusted R2                  0.798                    0.820          
## Residual Std. Error     0.181 (df = 398)         0.171 (df = 397)    
## F Statistic         397.018*** (df = 4; 398) 366.673*** (df = 5; 397)
## =====================================================================
## Note:                                     *p<0.1; **p<0.05; ***p<0.01

Both models are statistically significant. The only difference between the 2 models is I included \(pexper\) in the latter, which produced a better \(R^2\) and smaller Residual standard error. In this case, past experience has a small negative impact on current wage. This is quite reasonable since the longer one spent time at the previous work, the less time he/she has for the current work, which justifies a lower wage. As model 2 can explain better for the change in wage, we should pick it as the primary model for further analysis.

Model’s verification:
The chosen estimation model is:
\(\hat{\log(wage)}\) = 9.145 + 0.12 \(male\) + 0.00004 \(swage\) + 0.026 \(educ\) + 0.018 \(exper\) - 0.0006 \(pexper\)
\(obs\) = 403, \(R^2\) = 0.822
All explanatory variables are statistically significant.

+ Testing for Multicollinearity
I assess this potential problem with variance inflation factor (VIF). If the VIF is equal to 1 there is no multicollinearity among factors, but if the VIF is greater than 1, the predictors may be moderately correlated. A VIF between 5 and 10 indicates high correlation of the explanatory variable and that may be problematic.

car::vif(model2)
##     male    swage     educ    exper   pexper 
## 1.468501 2.246526 2.187864 1.014172 1.090357

In this case, each explanatory variable has vif > 1 and < 5, so there exists a certain degree of multicollinearity but it is not a problem.

+Testing for residual’s normality

x <- resid(model2)
h<-hist(x, breaks=20, col="yellow", xlab="Model residuals",
   main="Residual histogram distribution with Normality Curve")
xfit<-seq(min(x),max(x),length=40)
yfit<-dnorm(xfit,mean=mean(x),sd=sd(x))
yfit <- yfit*diff(h$mids[1:2])*length(x)
lines(xfit, yfit, col="blue", lwd=2)

The residual appears to follow normal distribution, then we should be able to calculate the confidence intervals.

From the verfications above, it can be concluded that our model is suitable for analysis.

5. Results and Interpretation

Estimation results:
\(\hat{\log(wage)}\) = 9.145 + 0.12 \(male\) + 0.00004 \(swage\) + 0.026 \(educ\) + 0.018 \(exper\) - 0.0006 \(pexper\)
\(obs\) = 403, \(R^2\) = 0.822

The independent variables can explain for 82.2% the change in wage.
Education and Years of experience has positive effects on an engineer’s wage. 1 additional year of education can increase wage by 2.6% (with 95% confidence intervals is [1.6% ; 3.6%]), whereas 1 additional year of experience can increase wage by 1.8% (with 95% confidence intervals is [0.8% ; 2.8%]).

More notably, all else equal, being a male engineer helps increase wage by 12% (with 95% confidence intervals is [7% ; 16%]. This is a very important result. It shows that there are some indications of gender inequality in engineering job in Thailand. Looking at the table in 3, we see that the significant differences between male and female engineers are starting wage and education, since their years of experience are roughly the same. Female engineers on average have lower level of education, thus make them relatively less productive than male engineers. In a demanding job like engineer, education matters.

In conclusion, we see that among many factors that affect wage like education, experience but factor that has the most impactful effect is being male or not. The above data shows that inequality still exists in Thailand engineering job market, where male engineers earn substantially more than female engineers (about 12%), mainly due to the fact that male engineers are more educated. To improve gender equality, women’s access to education, especially higher education needs to be more emphasized and supported by the government.