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4. Model
In order to evaluate the impact of implementation of the Labor Pension Act on
layoff rate, employees are divided into treatment and reference groups, to apply the difference in differences strategy as described before. Besides, whether an employee has been laid off also divides employees into two groups. One of them cover employees who have ever been laid off in the last year due to business recession, shutdown or personnel adjustment, and the corresponding outcome variable LAYOFF is assigned the value of 1. The other group covers employees who have not been laid off in the last year and hence the corresponding outcome variable is assigned the value of 0.Since the outcome variable LAYOFF, which indicates whether an employee has ever been laid off is a binary variable, probit regression is estimated as follows:
𝐿𝐴𝑌𝑂𝐹𝐹∗ = 𝛽𝑋 + γ1𝐿𝑆𝐴 + 𝛾2𝐼𝑀𝑃 + 𝛾3𝐿𝑆𝐴 ∗ 𝐼𝑀𝑃 + 𝜀 𝐿𝐴𝑌𝑂𝐹𝐹 = 1 if 𝐿𝐴𝑌𝑂𝐹𝐹∗ > 0, 𝑎𝑛𝑑 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒.
where the first line of the regression models is the latent regression with the standard normally distributed error term 𝜀, and the second line is an index function which depends on the value of the latent variable LAYOFF*.
To control the individual characteristics, variables such as monthly income, gender, years of education, age, job seniority, household size, head of household and working area are all included in the vector 𝑋. Besides, all of the control variables are based on the job corresponding to the first observation year.
To be specific, years of education are defined by the average number of years required in Taiwan to complete the corresponding highest education. 0 years are
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assigned to those who have not ever attended formal education before; 6 years to elementary school; 9 years to junior high school; 12 years to senior high school; 16 years to college, 18 years to master degree and 22 years to doctoral degree.
Household size means the number of members over the age of 15 in the family.
Job seniority is measured in years as the education. Whether an employee is the head of the household or not is indicated as a dummy variable. Besides, working area of the employee is controlled by setting three dummy variables which indicate northern area, central area, southern area and the eastern area. Also, when the sample analyzed includes the year of 2008, then dummy variable is set to control the possible effect caused by the subprime crisis.
The main variables used to derive the difference in difference estimates are LSA, IMP and their interaction term LSA*IMP. LSA is a dummy variable which indicates application of the Labor Standards Act and takes the value of one if an employee is covered under the Labor Standards Act. IMP is a dummy variable which takes the value of one when the observation is investigated in the period after implementation of Labor Pension Act. Moreover, the interaction term LSA*IMP takes value of one when the employee is covered under the Labor Standards Act and also belongs to the period after the policy change.
The expected difference of layoff rates of the reference group before and after the policy change is
E(LAYOFF|LSA = 0, IMP = 1) − E(LAYOFF|LSA = 0, IMP = 0) = 𝛾2
and the expected difference of layoff rates of the treatment group before and after the policy change is
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E(LAYOFF|LSA = 1, IMP = 1) − E(LAYOFF|LSA = 1, IMP = 0) = 𝛾2+ 𝛾3
Therefore, difference in differences estimate is
[E(LAYOFF|LSA = 1, IMP = 1) − E(LAYOFF|LSA = 1, IMP = 0)]
−[E(LAYOFF|LSA = 0, IMP = 1) − E(LAYOFF|LSA = 0, IMP = 0)]
= (𝛾2+ 𝛾3) − 𝛾2 = 𝛾3
which is just the coefficient of the interaction term LSA*IMP and exactly indicates the effect of the Labor Pension Act.
Usually, the common trends assumption has to be satisfied when applying the difference in differences method. Referring to Joshua and Jöhn-Steffen (2008), Figure 1 illustrates the conceptions of the common trends assumption and the deviation induced by the treatment. From Figure 1, one can see that the reference group only faces the trend effect, and the treatment group faces both trend effect and treatment effect. In order to find the treatment effect, one has to specify these two effects by taking the trend of the reference group as the counterfactual measure of the treatment group. Therefore, the trend faced by the treatment group and reference group have to be the same; otherwise the counterfactual measurement could be biased, causing inaccuracy in difference in differences estimates. Here, common trends assumption requires that the trend of layoffs before implementation of the Labor Pension Act should be the same for all employees, irrespective of whether they are covered by the Labor Standard Act or not.
Data of multiple periods are used to investigate the common trends assumption.
Table A4 shows the proportion of laid off employees from 2000 to 2011 and Figure 2 plots all of them to show the long run trends. From Figure 2, one can see that the
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layoff proportions of the treatment group declined gradually before implementation of LPA. After implementation of LPA, its trend became noisy. At first, it continued to decline from 2006 to 2007, but then rose dramatically in 2008 which is the year of the subprime crisis. After 2008, it declined again and reached the same level as the reference group.
Figure 1: Casual Effects in the Difference In Differences Model Source: Angrist, J., and S. Pischke (2008), p172
Figure 2: Proportions of Laid off Employees from 2000 to 2011 Note: The dash line indicates the time of implementation of Labor Pension Act.
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250
Layoff Proportions (Reference Group) Layoff Proportions (Treatment Group) treatment
effect
layoff trend in reference group layoff trend in treatment group
counterfactual layoff trend in treatment group
time after
before layoff
rate
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Like the treatment group, layoffs of the reference group also declined before implementation of LPA, except for the period from 2003 to 2004. After LPA, it has a relatively stable trend compared with the treatment group. Therefore, it seems that employees not covered by LSA can provide a good measure of counterfactual layoff rate before implementation of the LPA.
However, there are still some facts that need to be addressed before analyzing results of the regressions. Actually, using the fact whether employees are covered by LSA as the standard of segregating employees into treatment and reference groups can cause some bias in results.
First, implementation of the Labor Pension Act did not force all employees who were originally covered under the Labor Standards Act to choose the Labor Pension Act. Only employees who had never worked before or changed the job after implementation of LPA were forced to choose it. As a result, employees who were originally under the Labor Standards Act may still choose LSA so that the severance pay would not change when they are laid off. Such kinds of situations can cause inconsistencies within the treatment group. That is, some employees in the treatment group may not be affected by the reduction of severance pay. To deal with such kinds of situations, employees who tend to choose LSA rather than LPA are eliminated according to some specific conditions. Section 6 describes the process in detail.
Second, given that most of the employees who are not covered by the Labor Standards Act are public servants, selection bias may be a problem. Most employees in the public sector are generally risk averse and they do not tend to expose themselves to situations which may induce layoff. Therefore, the effect of the change of time may not be the same for the treatment group and the reference group. That is, the common trends assumption may be violated. However, Figure 2 shows that the trends for treatment and reference group seem to evolve similarly before the
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implementation of LPA. Hence, such kinds of problems might not affect the results so much.
Third, implementation of LPA may lead to reallocation of job. But this concern could be eliminated by comparing the shares of the two groups over the entire period from 2000 to 2011, as showed in Figure 3. The share of reference the group is 11% on average, and the share of the treatment groups is 89% on average. It seems shares of the two groups are very stable and do not have any apparently large change.
Figure 3: Shares of Reference Group and Treatment Group from 2000 to 2011 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
share of reference group share of treatment group
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