The matching approach and matched dataset
This paper uses propensity score matching (Nonparametric Preprocessing for Parametric Causal
Inference), which is a statistical technique in which a treatment case is matched with one or more control
cases, based on each instance’s propensity score, in order to ensure two groups are matched (see Figures 4
and 5). This paper will use R software to run the matching approach, by applying the software package
‘Matchit’. To be more specific, we control the rationale of the treatment group population to control group
population group as 1:1, i.e. 1,423 (solo self-employed): 1,423 (employees) and 348 (self-employed with
hiring employees): 348 (employees). Before being matched, it is observed that the self-employed are more
often male, older, with better mental health and less educated than wage-paid workers, whereas for
education, contradictory evidence has been found in the earlier literature (Van der Sluis et al., 2008). The
self-employed without employees have lower incomes than wage-paid workers, whereas the self-
employed with employees have higher incomes than the salary workers (corresponding to earlier studies
such as Sorgner et al., 2014). All these variables are closely associated with work-related stress. After
being matched, it can be seen that the demographical differences among control variables are largely
reduced; the T-test p-values results (Table 12) show no significant differences in demographic variables
between the solo self-employed and employees and between the SEE group and employees. The
difference of variable distance between the two groups is largely reduced after matching as well (the SEE
vs Employees: before matching: 0.07, after matching: 0; the Solo SE vs Employees: before matching:
0.19, after matching: 0.13). Also, the distribution of propensity scores tends to be similar between the two
groups after matching.
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Figure 4 Distribution of Propensity Scores: Solo Self-employed VS Employees
Figure 5 Distribution of Propensity Scores: Self-employed withHiring employees VS Employees
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Table 12 Mean, Mean Differences, T-test of Control Variables Before and After Matching
Sole SE VS Employees Solo SE VS Employees
SEE Employees Solo SE Employees
N=348 N=1972 N=1423
N=1972
Before matched After matched Before matched After matched
mean
mean T-test Mean differences mean T-test Mean differences
mean
mean T-test
Mean differences
Mean T-test Mean differences
Control Variables
Distance 0.21 0.14 0.21 0.53 0.34 0.40
Age 50.07 44.82 0 5.25 50.34 0.76 -0.27 49.78 44.82 0 4.96 48.84.98 0.42 0.94
Sex 0.31 0.53 0 -0.22 0.30 0.87 0.01 0.40 0.53 0 -0.13 0.44 0.72 -0.04
Single 0.00 0.01 0 -0.01 0.00 0.99 0 0.01 0.01 0 0 0.02 0.76 -0.01
Education 2.9 2.6 0.01 0.3 2.77 0.58 0.13 2.86 2.6 0 0.26 2.81 0.24 0.05
Physical Health 52.75 53.09 0.42 -0.34 53.01 0.81 -0.26 52.13 53.09 0 -0.96 52.90 0.19 -0.77
Mental Health 51.57 50.66 0.04 0.91 51.53 0.90 0.04 52.37 50.66 0 1.71 51.86 0.05 0.51
Job Income 3999.26 2327.73 0 1671.53 3653.8 0.78 345.46 1916.41 2327.73 0 -411.32 1934.52 0.04 18.11
SE stands for the Self-employed
Solo SE stands for Solo Self-employment
SEE stands for Self-employed with hiring employees
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Table 13 Mean, Mean Differences, T-test of Variables: Solo SE VS SEE
SEE
Solo SE
mean mean mean differences T-test
Work-related stress
Job Anxiety 3.11 2.22 -0.89 0
Job Depression 1.28 0.92 -0.36 0.03
Job Demands 42.59 32.33 10.26 0
Job Control 6.26 6.63 0.37 0
Social support 16.38 16.08 0.30 0.8
Control Variables
Age 50.07 49.78 0.29 0.65
Sex 0.31 0.40 -0.09 0.04
Single 0.00 0.01 -0.01 0.02
Education 2.9 2.86 0.04 0.71
Physical Health 52.75 52.13 0.62 0.17
Mental Health 51.57 52.37 -0.8 0.08
Job Income 3999.26
1916.41
2082.85 0
Solo SE stands for Solo Self-employment
SEE stands for Self-employed with hiring employees
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Table 14 Mean, Mean Differences, T-test of Independent and Dependent Variables Before and After Matching
Self-employed with hiring employees VS Employees Sole Self-employed VS Employees
SEE SE Employees
Solo SE
Employees
Before matched After matched Before matched After matched
mean mean T-test Mean differences mean T-test
Mean differences
mean mean T-test Mean differences mean T-test Mean differences
Work-related stress
Job Anxiety 3.11 2.93 0.47 0.18 2.45 0.04 -0.26 2.22 2.93 0 0.71 2.63 0 0.41
Job Depression 1.28 1.52 0.35 0.24 1.13 0.04 -0.27 0.92 1.52 0 0.6 1，35 0 0.43
Job Demand 42.59 31.19 0 11.4 32.42 0 10.17 32.33 31.19 0.04 1.14 30.66 0.01 1.67
Job Control 9.26 9.37 0.11 -3.11 9.36 0.1 -3.1 9.63 9.37 0.16 -2.74 9.17 0 -0.46
Social Support 16.38 16.15 0.46 0.17 16.69 0.71 -0.31 16.08 16.35 0.66 -0.17 21.87 0.79 -5.79
Solo SE stands for Sole Self-employment
SEE stands for Self-employed with hiring employees
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Table 15 Means, Standard Deviations, and Bivariate Correlations (After matched)
(n=3743)
Mean SD (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
Job Anxiety 2.67 2.45
Job Depression 1.27 2.07 0.02
Job Demand 32.69 15.65 -0.04* -0.08***
Job Control 8.04 3.63 0.04* 0.16*** 0.08***
Social support 16.14 2.32 0.02 0.29*** 0.27*** 0.01
Age 47.19 11.52 -0.05** -0.08*** 0.05** -0.08*** -0.02
Sex 0.46 0.5 0.01 0.11*** -0.01 -0.17*** 0.03 -0.08***
Single 0.02 0.11 0 0.04* -0.14*** -0.35*** -0.07*** 0.07*** -0.03
Education 2.73 1.82 -0.04* 0.02 -0.02 -0.02 0.05** -0.01 -0.04** 0.04*
Physical Health 52.69 7.99 -0.04* -0.09*** -0.01 0.02 0.02 0.04* 0.14*** -0.06*** -0.01
Mental Health 51.40 8.13 0.03* -0.05** -0.01 0.06*** -0.05** 0.01 -0.18*** 0.01 0.03 -0.15***
Log(Job Income) 2326.76 2483.29 -0.01 0.45*** -0.12*** 0.02 0.13*** -0.09*** 0.13*** -0.10*** -0.12*** 0.07*** -0.17***
SE 0.47 0.5 -0.01 -0.10*** 0.03 0.27*** -0.04* 0.02 -0.04** -0.21*** -0.04* -0.09*** 0.13*** 0.03
SEE 0.10 0.29 0.06** 0.06*** 0.03* -0.10*** 0.03* -0.45*** 0.11*** -0.04** -0.01 0.02 -0.04* 0.03 -0.19***
*** p<.001; ** p<.0.01; * p<.05
SEE stands for Self-employed with hiring employees
SE stands for Self-employment
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