CHAPTER IV. RESULTS
4.2 AGE EFFECTS ON THE TRAJECTORY OF WAGE
In this section, null model of this research is firstly proposed and models of age effects are presented as follows.
4.2.1 Null Model
As mentioned in the previous chapter, the simplest model is a null model without any explanatory variables, with only a grand mean (𝛾00) and two variations: intercept variations among groups [u0𝑗] and within group variations [ε
𝑖𝑗].
The results show that the grand mean (𝛾00 =453.03, p<.001), intercept variations among groups (𝜏002 =520.79, p<.001), and within-group variations (𝜎𝜀2=204.96, p<.001) are all significantly different from zero. Intra-class correlation coefficient (ICC) is calculated by:
ICC𝑦 = 𝜏2
𝜏2+ 𝜎2= 520.79
520.79 + 204.96 = 0.718
As demonstrated in the calculation of ICC, variance among groups explain 71.8% of total variance, a percentage that reminds us in our research to observe variance among individuals.
4.2.2 Age Effects on the Trajectory of Wage without Covariates
To begin our discussion on the APC effects on the trajectory of wage, the age effect is the most primary and widely studied one. As a result, our models for the wage variable include not only age but its contextual variables (the mean value of age), displayed in both the linear growth model and the quadratic growth model in Table6. All models estimated the fixed effects—in Ma1, Ma3, Ma5 and Ma6—as well as the random effects—in Ma2, Ma4 and Ma7; as a whole, there are 7 models. (Syntax of Mplus of Ma6 and Ma7 are listed in Appendix I and II, respectively)
Table 6 summarizes the estimated age effects and contextual effects for the wage. The results of Ma1 indicate that when only fixed effects are considered, the linear effect of age for the wage was positive but insignificant (age1=0.005, p>.05), suggesting that the mean wage for everyone remains quite the same as they age. However, if random effects
(tau1=4.165, p<.001) were taken into account, it reveals that linear effects of age are
actually significantly different among individuals, but overall, average wage rises as people age.
41 Table 7
Results of age effects on wage
M0 Ma1 Ma2 Ma3 Ma4 Ma5 Ma6 Ma7
Fixed effect
Intercept(b00) 453.03** 453.03** 453.00** 453.01** 452.99** 458.52** 453.19** 453.29**
age1(b10) -- 0.005 0.257** 3.736** 3.920** -- 3.736** 3.990**
age2(b20) -- -- -- -0.042** -0.046** -- -0.042** -0.046**
mage1(b01) -- -- -- -- -- 0.108* 3.768** 4.328**
mage2(b02) -- -- -- -- -- -0.047** -0.047** -0.053**
Random effect
Eplson 204.96** 204.96** 158.41** 194.95** 157.12** 204.91** 194.94** 157.17**
Tau0 520.79** 520.79** 533.80** 523.47** 533.78** 472.84** 476.07** 484.23**
Tau1 -- -- 4.165** -- 19.45** -- -- 18.80**
Tau2 -- -- -- -- 0.003** -- -- 0.003**
Model Fit
BIC 263502 263513 260519 262176 259825 263004 261684 259300
Note. *p<.05. **p<.01. ‘age1’ and ‘age2’ respectively represents the within effects of linear and quadratic forms of age. ‘mage1’ and ‘mage2’ respectively denotes the between effects of linear and quadratic forms of age.
Moreover, when considering the quadratic growth model of age on the trajectory of wage, both Ma3 (age2=-0.042, p<.001) and Ma4 (age2=-0.046, p<.001) still show significantly negative results, and indicating an increase from young to middle age but a decrease toward older age. Ma4 has an estimation on random effects of the curvature, which is significant at p<.001, meaning that the rate of people’s wage going upward and then going downward is again significantly different.
Contextual variables are the mean value of age and age square, labeled as mage1 and mage2, variables that are transformed from level one variables to explain the individual differences of intercepts in level two equation.
In Ma5, only level two variables, mage1 and mage2, are included, without any variations within individuals. The square term of this quadratic growth model is also significantly negative (mage2=-0.047, p<.001). Adding the age and age square variables in Ma6 and Ma7, respectively, did not affect the results. Both the square of age (Ma6: age2=-0.042, p<.001; Ma7: age2=-0.046, p<.001) and of the mean age (Ma6: mage2=-0.047,
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p<.001; Ma7: mage2=-0.053, p<.001) remain significantly negative, and they didn’t differ much in estimates, either. As a whole, there is a quite robust curvilinear relationship between age and wage, where wage rises from young to middle age but declines toward older age.
Additionally, after taking random effects into considerations in Ma7, both slope
variance and curvature variance are significant at p<.001, revealing individual differences in these coefficients. In other variances, variances among individuals (Tao0) were significant in all models at p<.001—from Ma1 to Ma7—as well as variances within individuals (Eplson), indicating significant differences in comparing individually and tracking personally. With the lowest BIC, Ma7 is the best to fit the data; therefore, in the next discussions of premium effects, the research is going to base on this model.
4.2.3 Age Effects on the Trajectory of Wage with Covariates
As shown in Table 7 model Map, adding human capital factors to Ma7 did not affect the estimates for age effects considerably. However, when those are controlled, the estimates for both age and age square variables dropped a little but still remained significant, inferring that part of the age effects actually come from the effects of those premium factors.
Moreover, compared from model M1, the model of pure human capital premium effects, the effect of education year is stronger in Map than in M1. It revealed the fact that controlling the effects of age would magnify the effect of education, that the rise of wage is not only because of aging but because of the accumulation of education.
43 Table 8
Premium effects of age on wage
M0 Ma7 M1 Map
Fixed effect
Intercept(b00) 453.03** 453.29** 389.37** 353.77**
age1(b10) -- 3.99** -- 3.79**
age2(b20) -- -0.046** -- -0.042**
mage1(b01) -- 4.328** -- 4.542**
mage2(b02) -- -0.053** -- -0.047**
sex -- -- 11.197** 11.089**
eduyear -- -- 3.135** 3.626**
wh -- -- 0.238** 0.256**
Random effect
Eplson 204.96** 157.17** 195.34** 131.04**
Tau0 520.79** 484.23** 324.17** 266.65**
Tau1 -- 18.80** -- 14.231**
Tau2 -- 0.003** -- 0.002**
Tau3 -- -- -- 0.233**
Model Fit
BIC 263502 259300 256801 251091
Note. *p<.05. **p<.01. ‘age1’ and ‘age2’ respectively represents the within effects of linear and quadratic forms of age. ‘mage1’ and ‘mage2’ respectively denotes the between effects of linear and quadratic forms of age. ‘sex’ means gender, ‘eduyear’ represents years of education and ‘wh’ equals to working hours.
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