Figures and data in Using trajectory analysis to test and illustrate microsimulation outcomes

Abstract

We propose a new data-driven way of testing and visualizing dynamic microsimulation outcome data. The proposed statistical methodology is based on trajectory analysis (Nagin, 1999), which can be used to identify several sub-populations from a population measured longitudinally. We briefly introduce the statistical basis of trajectory analysis and discuss its use in the context of microsimulation. Finally, we report our results from the Finnish microsimulation model ELSI (Tikanmäki et al., 2014; Tikanmäki et al., 2015) to illustrate the possibilities and benefits of this technique. Trajectory analysis is available in many statistical software packages (e.g., SAS, R, Stata and Mplus). We conclude that trajectory analysis is a useful tool for investigating microsimulation outcomes.

This article contains 5 figures and 3 tables.

Figures

**Figure 1.** Structure of the ELSI microsimulation model

**Figure 3.** Earnings trajectories, k=5

Tables

Table 1. BIC scores and number of sub-groups k

Outcome	3	4	5	6
Earnings (N=3,325)	−50288.7	−48178.8	−45974.7	−46375.9
Education (N=13,173)	−549399.6	−544342.9	−537412.2	−535026.8
Pension (N=10,761)	−834881.4	−811092.8	−786210.9	786234.1

Notes: BIC = log(L) −.5 * log(n) k, where L = log likelihood, n = sample size and k = number of parameters.

Table 2. Composition of earnings trajectories at age 60, per cent

	G1 (8%)	G2 (11%)	G3 (17%)	G4 (29%)	G5 (35%)	Total
Active first year	0.8	2.3	2.3	0.5	3.4	2.1
Active second year	0.4	0.6	0.7	0.3	0.9	0.6
Active (working)	2.3	51.1	1.2	89.9	54.2	50.6
Unemployed or in education	1.5	9.7	6.2	1.6	10.4	6.5
Sickness benefits	.	1.1	0.4	.	2.5	1.1
Partial disability pension and active	.	1.4	0.2	2.3	0.4	1
Partial disability pension and non-active	0.8	1.1	0.9	.	0.7	0.6
Full disability pension	23.4	2.8	26.9	0.5	2.9	7.9
Full disability pension second year	1.1	1.4	3.4	.	2	1.6
Old-age pension	.	.	0.5	0.1	0.7	0.4
Only national disability pension	15.5	.	.	.	.	1.2
Out of labor markets I	18.9	1.4	17.2	0.3	1.8	5.3
Out of labor markets II	14.3	.	2.5	.	0.8	1.9
Inactive	5.7	18.8	30.8	1.5	15.5	13.8
Deceased	15.5	8.2	6.9	2.8	3.8	5.5
Total	100	100	100	100	100	100

Outcome	Groups	${\hat{β}}_{0}$	$S E ({\hat{β}}_{0})$	${\hat{β}}_{1}$	$S E ({\hat{β}}_{1})$	${\hat{β}}_{2}$	$S E ({\hat{β}}_{2})$	${\hat{β}}_{3}$	$S E ({\hat{β}}_{3})$
Earnings	1	−0.60816	0.93616	0.17156	0.07229	−0.00845	0.00173	0.00008	0.00001
Earnings	2	10.77241	0.7512	−1.05243	0.05715	0.03048	0.00135	−0.00026	0.00001
Earnings	4	−24.0041	0.69707	1.88334	0.05421	−0.04084	0.00128	0.00026	0.00001
Earnings	5	2.89272	0.93197	−0.55508	0.08212	0.02763	0.00225	−0.00029	0.00002
Education	1	150.7634	13.69866	−23.324	1.03504	0.60943	0.01352	−0.00442	0.00018
Education	2	−38.2479	1.84202	1.95442	0.10906	−0.03343	0.00214	0.00019	0.00001
Education	3	−1.40435	0.08235	0.09431	0.00638	−0.00206	0.00016	0.00001	0.00000
Education	4	−3.82746	0.09413	0.27969	0.00712	−0.00568	0.00017	0.00004	0.00000
Education	5	−6.14041	0.09384	0.46159	0.00701	−0.00958	0.00017	0.00006	0.00000
Education	6	−34.1529	1.02762	2.02103	0.06446	−0.03841	0.00133	0.00024	0.00001
Pension	1	1352.226	1.29912	−66.1983	0.03537	1.07053	0.0006	−0.00572	0.00001
Pension	2	−220.279	3.93005	5.68868	0.15254	−0.03308	0.00196	−0.00003	0.00001
Pension	3	−464.879	3.77328	14.13735	0.14801	−0.12224	0.00197	0.00024	0.00001
Pension	4	27.60321	4.88433	−1.86771	0.19721	0.03987	0.00262	−0.00025	0.00001
Pension	5	−127.459	2.91581	3.18956	0.10992	−0.01691	0.00136	−0.00002	0.00001