Simulating histories within dynamic microsimulation models

Many countries today are facing the prospect of rapid demographic change in the decades ahead and numerous research papers have been devoted to the analysis of the implications of an ageing population. A number of microsimulation models have been developed to study this issue linked with social security, retirement incomes, and pension reforms. In order to generate an accurate and stable projection for elderly earnings and pensions, it is essential to include some historical information in the dataset, a luxury that many modellers do not have.

Microsimulation models are usually categorised as either “static” or “dynamic”. Static models, e.g. EUROMOD (Mantovani et al., 2007), are mostly arithmetic models that evaluate the immediate distributional impact upon individuals/households of possible policy changes, whilst Dynamic models, e.g. DESTINIE, PENSIM, SESIM (Bardaji et al., 2003; Curry, 1996; Flood, 2007), extend the static model by allowing individuals to change their characteristics as a result of endogenous factors within a model (O’Donoghue, 2001). Dynamic microsimulation models in theory, could offer more insights than static models as they usually integrate long-term projections and behaviour simulations; however, they are costly to develop and require a baseline dataset that is both rich in variables and historical information. These demanding requirements unfortunately are rarely matched by the existing data availability (Harding, 2007) and therefore compromises are often made in order to make the simulation possible.

This paper investigates longitudinal data availability issues in microsimulation and proposes a viable alternative by simulating a plausible and consistent history using a typical household survey panel from Ireland. The following section discusses the base dataset issues in dynamic microsimulation models and the potential alternatives. Section 3 describes the dataset used in the back simulation and Section 4 explains the modelling procedure of the back simulation, and followed by a description of the alignment technique used in Section 5. The three sections following report the results of the back simulation together with the validations, for employment status, pension memberships and earnings, respectively. A conclusion and discussion are provided in the final section of this paper.

This back simulation module is primarily modelled based on the 1994-2001 Living in Ireland Survey (LII) dataset along with some external statistics extracted from the pension questionnaire section of the 2002 Quarterly Household National Survey (QHNS), and the Irish census reports since 1930s.

The LII survey constitutes the Irish component of the European Community Household Panel (ECHP) and is a representative household panel survey that was conducted yearly on the Irish population between 1994 and 2001 (eight waves). The data contains panel information on demographics, employment, and other social economic characteristics for around 3,500 households in each wave. In 2000, an additional 1,500 households were brought into the dataset to compensate for the attrition since 1994. Table 1 lists some descriptive information of key demographic and employment variables in the LII dataset.

Besides the LII survey, the back simulation module also uses the information gathered from the QHNS survey, which is a nationwide household survey designed to produce quarterly labour force estimates in Ireland since 1997. In the first quarter of 2002, a special module dedicated to pension savings was added to the survey. QHNS is used in the back simulation mostly for alignments when estimating occupational and private pensions. Census reports prior to 1994 were used in the back simulation module in order to align certain important history aggregates.

This section describes the methodology used in the back simulation. While a back simulation model may use some historical information to refine the outcome, it also has a higher requirement on the output quality. Since the main purpose of this back simulation model is to recreate each individual career trajectory, it demands a high accuracy of the model prediction as the pension eligibility is highly sensitive to the past employment status. In a forward microsimulation model, one would typically use some kind of aggregated values (e.g. mean, standard deviation of the distribution) to evaluate the quality of the simulation. The predicted value does not need to be correct at the individual level as long as the distributions are reasonable. Nonetheless, in the case of backward simulation, one needs to ensure that the values are sensible at the individual level due to the longitudinal consistency requirement while maintaining the reasonable distribution shape at each crosssectional level.

Compared with a forward dynamic microsimulation model, a back simulation model could be more complex as it is designed to exploit more information both from historical values and retrospective information. In order to create a panel dataset that is as close as possible to the real history, three methodologies are used in back simulations:

• Deterministic simulation

• Semi-stochastic simulation

• Stochastic simulation

The deterministic simulation generates the part of the history that is directly determined by retrospective variables and ensures that the generated history is perfectly consistent with the reported values. For instance, if an individual reports starting work at age 20, it is safe to assume that this individual was in work that particular year. The variables used in deterministic simulation include the age when an individual begins to work, the year in which an individual quit their previous job, the number of years spent in their current employment status (e.g. length of current job, unemployment etc.) and the number of years spent in each employment status.

Semi-stochastic simulation recreates certain historical events from retrospective variables in conjunction with some reasonable assumptions. While the deterministic simulation pinpoints the timing of some major events in history, it gives only incomplete information regarding employment trajectory. Semi-stochastic simulation is still largely based on the reported retrospective variables but might involve some assumptions. For instance, since most women take maternity leave when giving birth, it is reasonable to simulate a career profile interrupted in the year of childbirth with a high probability. Another example would be “back to work” social welfare benefit, which usually implies a period of unemployment for the years preceding claiming the benefit.

Stochastic simulation is designed to fill the parts of the history that cannot be inferred from deterministic and semi-stochastic processes and it recreates the history through the predictions of estimated econometric models with random components. This method is similar to a regular dynamic microsimulation model, such as DYNAMOD2 and SAGE (King et al., 1999; Zaidi, 2004), with the difference being that the back simulation model ages the population in a reversed direction and is subject to a much more restricted alignment procedure for consistency reasons. An outline of the simulation steps are provided in the Appendix 1.

Alignment is a commonly used method for calibrating microsimulation models so that aggregate outputs from the model match the external projections or values. This is partially due to insufficient knowledge regarding microbehaviour to specify a fully dynamic model. Simulation models, if unbounded, may over or under predict the occurrence of a certain event, even in a well-specified discrete model (Duncan & Weeks, 2000). Therefore, although in theory alignment might be controversial (as a perfectly specified model with perfect data should not need any alignment), it is a de facto common practice for microsimulation models (see for example DYNACAN, CORSIM, and LIAM).

In the back simulation module, alignment shapes the earnings and the distribution of employment status in a way that is both consistent with historical census information and retrospective information. There are two types of alignments applied in this model; one is a cross-sectional alignment and the other a longitudinal alignment.

This section evaluates the back-simulation of discrete (mainly employment status) variables. It recreates labour force participation and job nature (public or private sector, employed or selfemployed), crucial information for future pension projection. Figure 1 illustrates their simulation order within the module. Among the discrete variables, the module simulates:

• In-work, Employment Sector (Public/Private)

• Self-employment

• Various pension memberships

Figure 1

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The simulations are based on the complete sample of the 1994 population in the LII survey. Since the model does not generate historical profiles for people who have died before 1994, the simulated sample is not representative of the population prior to 1994. This implies that the average age in the earlier years of the simulation is significantly lower than the average age in the sample. Therefore, outputs are presented mostly by age group or cohort group in order to avoid misunderstandings.

As discussed in the earlier section, the main goal of the back simulation model is to recreate a sensible history for all individuals in the dataset. Therefore, it is essential that the model output can replicate what actually happened. In an ideal world, the model output should be compared with the actual data to see how well the model performs. However, the lack of real historical data is the very reason that the back simulation is required. In addition, it is not feasible to compare the model with other back simulation approaches, e.g. statistical matching method, in this particular case, as synthetic history recreation is the only option due to the data limitation. Therefore, the results of the model are mainly compared with the known benchmarks: the census reports and the pension eligibilities. A success replication of this information would suggest the simulated historical profiles are sensible at both aggregate and individual level.

6.1 In-work ratio

The evolution of the in-work ratio is reproduced in Figure 2 and Figure 3. As the graphs show, the male employment rate alters little over time except for a gradual fall of late career employment since the introduction of the retirement pension system in the 1970s. The female employment rate is 40%~50% lower than the male employment rate throughout the simulated history. The simulation indicates that the female labour participation rate is much higher before the age of 35 than for other age groups.

Figure 2

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Figure 3

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Figure 4 and Figure 5 further examine the simulated historical in-work proportion and offer a comparison with the census values to validate the simulation. As discussed earlier, the crosssectionals in the simulated period are not population representative due to the missing values of deceased individuals. Therefore, census values were adjusted based on the sample’s demographic features. In order to isolate the change of demographic composition, graphs are presented by cohorts.

Figure 4

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Figure 5

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The figures confirm that the simulated values roughly match the estimations from the census data with a deviation of around 5 percentage points on average. The simulation seems to work better for later cohorts than the earlier ones, however this difference may partially be caused by the longitudinal alignment procedure where the adjustments may not be perfectly balanced, and the inconsistencies in retrospective variables, where the data quality declines as age increases. Nonetheless, it is safe to say that the simulated ratios move in the same direction as the census values.

The back simulation module not only aims at providing a reasonable profile at the crosssectional level, but also a historical trajectory that is consistent with retrospective variables. Figure 6 illustrates the difference between the simulated number of years in work and the reported values. As shown, the longitudinal inconsistency in the simulation is well controlled; in total, over 83% of the individuals were simulated with an error no greater than 1 year, and over 89% of the observations have a difference of less than 2 years. A few extreme cases are also spotted with an error greater than 10 years. These observations typically report no working history but with old age pension entitlement. In this case, the model overrides the report of zero working year in favour of the observed pension eligibilities. On average, the absolute simulation errors for males are slightly larger than those for females. A possible reason is that males generally have longer career trajectories, which increase the computation complexity in balancing the crosssectional and longitudinal alignments. The longer career trajectory also implies that the measurement error of the retrospective values like reported years of work might be bigger for males. As a result, the quality of the simulation could be negatively affected due to the inconsistent reported values.

Figure 6

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6.2 Employment sectors and self-employment

Figure 7 and Figure 8 depict the historical evolution of public sector employment by age. As shown, there is a gradual growth of public sector workers for all age groups, a trend that is consistent for both males and females. However, the increase of females working in the public sector is faster compared with male workers, especially for workers in their early and midcareer stages.

Figure 7

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Figure 8

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Regarding the self-employed, Figure 9 and Figure 10 reveal the different preferences amongst different age groups. From the graphs it can be seen that the self-employment rates increase dramatically for males above the age of 35 over time and this stabilises around 30%, while the self-employment rate for males under 35 is just above 12% most of the time. The raise slope of the curve in the earlier part of the history may be contributed to by the limited number of observations for the age group. For females, the self-employment ratio is more or less stable within each age group except for a moderate decline for workers over 50 years old. Despite the drop, this late-career age group has a self-employment rate of around 30%, which is more than 20 percentage points higher compared with other groups. The differences are mainly due to the dropped female labour participation at later ages. Since the average age of retirement for female employee is lower than the male counterparts, the proportion of the self-employed workers increases after age 50. The graphs demonstrate that workers under the age of 35 have the least preference towards self-employment, a preference which is observed in both the simulated histories and the original dataset.

Figure 9

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Figure 10

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According to Irish pension regulations, individuals retiring at the age of 65 or later are entitled to a retirement or old age social welfare pension (RP and OAP, respectively), which can either be contributory or means-tested. The state pension system consists of a social insurance pension introduced for those aged 70+ in 1961 and a retirement pension for those aged 65 introduced in 1970 (O’Donoghue, 2002). Individuals may be entitled to additional pensions depending on their jobs and personal choices. The back simulation module replicates the pension system by simulating each individual’s participation in pension schemes and calculating their eligibility for a state pension once an individual retires.

7.2 Occupational pension membership

Occupational and private pensions are simulated through well-specified logit models and the results are aligned with the information extracted from the QNHS and LII survey². Figure 11 describes the development of occupational pension membership by cohorts. It seems that later cohorts are more willing to participate in occupational pension schemes, which might imply an increase in the occupational pension coverage in Ireland over time, which in turn is consistent with the history of Irish pension reforms.

Figure 11

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Analysing the trend for the cohort prospectively shows the dynamics of pension participation across time for the different cohort groups. Nonetheless, it does not reveal the dynamics of age preference, which is tightly linked with career development. Figure 12 discloses the shift of preference of same age groups across time. As suggested, mid-career individuals appear to be participating more actively then those in other groups. It seems that the age group closest to retirement has the lowest participation rate, which could due to the differences in career trajectories, availability of the pension options for this cohort and other reasons.

Figure 12

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In addition to employment statuses, the back simulation module also provides monetary income histories for all individuals. Labour earnings are simulated using the models mentioned in Section 4, while other non-labour income is assumed stable over time as they do not affect pension memberships. Figure 13 and Figure 14 demonstrate the dynamics of the average labour income over lifetime in this back simulation by analysing the earnings of three different cohorts. The average earning curve, as shown by the earlier cohorts, has the distinctive shape of a quadratic function, which matches the expectation of classic human capital theory. Female earnings seem to have a more flat mid-career profile, which may be due to the career interruption caused by maternity leave.

Figure 13

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Figure 14

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Figure 15 and Figure 16 give an overview of the evolution of earnings across the different age groups. As can be seen, average earnings increase steadily due to the increasing level of education. This is also confirmed by the cohort graphs shown earlier, where the younger cohorts demonstrate higher peak values. Male earnings are substantially different depending on the stage of their career. The average earnings by age 50 or above can be more than 50% higher compared to a male aged 20–35, but the difference is a lot smaller for female workers.

Figure 15

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Figure 16

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As discussed above, the preparation of the base dataset is one of the most important elements in every dynamic microsimulation model. However, finding a long historical panel dataset with all the necessary variables is often infeasible. This paper develops an algorithm to simulate a historical panel for the LII dataset to fill in the missing history.

The back simulation module extracts retrospective information from the LII survey and applies a dynamic microsimulation in a reversed direction to simulate population histories. Due to the nature of historical simulation, the longitudinal consistency requirement is high and difficult to achieve when compared with a forward dynamic microsimulation. The method proposed in this paper solves this problem by introducing extra calibrations and alignments at both the crosssectional and longitudinal levels. The overall result of the simulated panel, as described in the earlier sections, matches the labour market history to a fairly high degree based on the macro statistics calculated. The simulated values follow the observed trend quite closely, and are able to pick up the dynamics of different types of pension eligibility across time and cohorts. Nevertheless, further validation of the long-term trajectories of the employment and earnings produced by the model might be necessary, although there is little reliable data to compare the results with for the earlier half of 20th century.

The back simulation method could potentially offer many benefits for microsimulation modellers. By expanding the longitudinal information while maintaining consistencies with a panel dataset with limited waves, it offers a viable alternative to the dilemma of base dataset choice as described by Cassells et al. (2006) and Zaidi and Scott (2001). The generated historical panel could consequently enhance the accuracy and stability of the forward dynamic simulation by feeding in information on career trajectory. Given the extensive retrospective information modelled, the back simulated panel has a much higher data quality than a simple synthetic panel. Since only standardized survey questions and macro statistics are used in the simulation, this proposed back simulation method could be potentially replicated in other datasets that include retrospective questions, e.g. ECHP, BHPS, German Socio-Economic Panel (GSOEP), FFS. The method could help modellers to run a life-cycle based simulation without using a scarce long panel. In addition, the historical panel provides many important insights, e.g. the dynamics of career trajectories, which would otherwise be easily overlooked in the original dataset.

The exploration of a back simulation method as described in this paper is still in its early stages and the current algorithm could be further improved. Future work is planned to improve the following aspects of the back simulation model:

• Simulation of the deceased cohort of the population in order to align historical statistics more accurately, as the current version does not generate a representative historical population.

• Develop an improved algorithm for the cross-sectional/longitudinal alignment to alleviate the impact of inaccurate responses for retrospective questions.

• Understand the robustness of the model and the standard errors of the results. Further analysing the variations in the model would enhance the credibility of the model, especially when stochastic components are used.

In spite of the shortcomings inherent in the current version of this model, this paper shows that reconstructing historical information is feasible based on standard household survey dataset and census information, providing there is some retrospective information in the dataset that can be used for modelling. From a practical point of view, the simulated panel is the only available historical panel dataset for Ireland, which offers the possibilities of investigating life-cycle income profiles together with a dynamic microsimulation model.

1. Estimate models

   1. Employment (in-work/out-of-work) model

   2. Self-employed model

2. Impute social economic status variables for each year in the original dataset (1994-2001)

   1. Impute the number of years in education, employment, sickness, home care duties and retirement using regression in 1994 by sex group

   2. Update these variables to 1995–2001

   3. Consistency check for major social economic variables during the years 1994–2001

3. Generate historical data using known information

   1. Demographic information (e.g. year of birth)

   2. Maternity information (based on child age)

   3. Job information (e.g. year of starting first job, last job, total number of years worked etc.)

   4. Pension information (e.g. total pension contribution, pension entitlements)

   5. Others (e.g. school, geographic information)

4. Deterministic back simulation (in/out work)

   1. Create age information

   2. b. Infer working status from retrospective variables

      1. Must be out of work before year of starting work

      2. Must be in work in the year of starting work

      3. Must be in work since the current job started

      4. Must be in work in the year of quitting previous job

      5. Must be unemployed since current unemployment started

5. Semi-stochastic back simulation

   1. Assuming a 75% chance that a woman will be “out of work” in the year of giving birth to a child

   2. State pensioners must start work before the age of 56

   3. “Back to work” beneficiaries must have been unemployed for 2 years

6. Fill the gap of unallocated working status for history using stochastic simulation

   1. Replace the unknown working status to “in work” if the number of known working years is lower than the total work years

      1. Error term is stochastic. The ranking is based on the sum of the error terms and the personal effect in the model

      2. The status is aligned with census data by interacting with the ranking

   2. Impute the working status if there is still a gap between the reported number of years in work and the simulated years of in work

   3. Set the rest of the employment statuses to “not in work” if the simulated number of years in work is consistent with the reported values

   4. Adjust any differences

7. Simulate/Generate the variables that LIAM will use

   1. Demographic information (age, alive, maternity)

   2. Education information (based on the age of leaving full time education)

   3. Marriage information

      1. Calculate the year in which an individual married

      2. Assume that an individual married at age 25 if the current marital status is separated, divorced or widowed.

   4. d. Prepare employment information

      1. Self-employment

         1. Estimate the probability of being self-employed (1994–2001)

         2. Read the historical values of self-employment and smooth the curve using moving average method

         3. Use the stochastic term and personal effect to predict the probability of selfemployment, align data with estimates.

      2. Public sector

         1. Assume that people stick with the same sector as reported in 1994

         2. Do not allow for small gaps in public sector employment

         3. Store alignment data by sex education and cohort

         4. Use stochastic term and personal effect to predict the probability of staying within the public sector, and align the data using saved values

      3. Final adjustments to smooth labour participation history

8. Calculation for pay related social insurance (PRSI) pension entitlement

   1. Create a variable for the contributory class in the PRSI system for state pensions

      1. Public servants are treated as employees if they joined the job after 1995

      2. Public servant pensions are eligible for those who joined the work before 1995

   2. Calculate the eligibility for a PRSI pension for the rest

      1. Self-employed are assumed to only be insured after 1988

      2. Public sector are assumed to only be insured after 1995

      3. Calculate the pension credit

9. Longitudinal Alignment

   1. Compare simulated PRSI pension entitlement with the actual entitlement

   2. Modify the history while keeping the cross-sectional alignment of the labour market participation, self-employed and pension coverage ratio stable

   3. Repeat the above procedure several times until the consistency is satisfactory

10. Simulate earnings (for employees and self-employed)

    1. Estimate the wage model (random effect model)

    2. Record the standard deviation of random effects and the error term

    3. Simulate the wage for each group with a stochastic term that shares the standard deviation of estimated random effects

    4. Align the average earnings by sex, education level and age group to the year 2000 values

11. Simulate occupational pension membership using the equation estimated using the 1994-2001 data and calibrated using the QNHS samples.

    1. Calculate the probability of receiving an occupational pension, employee personal pension and self-employed personal pension for each age and sex group

    2. Estimate the occupational/self-employed/personal pension model using existing data

    3. Align it with the probability breakdown calculated from the QHNS sample for both the existing dataset (LII) values and the simulated historical values

    4. Correction for the unlikely event of an inconsistency between the occupational pension status and the employment status

    5. Final adjustment and alignment

12. Calculate the value of the DC Occupational pension fund

    1. Model contribution in a similar manner as wages and align with observed contribution rate (split into two rates, pre-1995 and post-1995)

    2. Calculate the pension fund value from the 1930s using assumed interest rates

    3. Calculate the contributions for each pension type

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Author details

1. Jinjing Li

   Maastricht University / UNU-MERIT, The Netherlands

   For correspondence

   Jinjing.Li@natsem.canberra.edu.au

2. Cathal O’Donoghue

   Rural Economy and Development Programme, Teagasc, Ireland

   For correspondence

   cathal.odonoghue@nuigalway.ie