Table 1.
Structure of state transition matrices, Q(x).
Fig 1.
Age-specific annual survival probabilities.
Annual survival (the number alive at age x + 1/ the number alive at x) for those above (red) and below (blue) the poverty threshold at age x. a, b and c differ in threshold income used to define poverty, 1×, 2×, and 3× the ‘official’ poverty income level, respectively. The green vertical lines in each panel are the seams between data-sets utilized: NLSY79 pre-1994, NLSY79 post-1994 and HRS (at age 33 and 50).
Fig 2.
Age-specific conditional probabilities of being above the poverty threshold.
Annual probability of being above the poverty threshold at age x + 1 for those below (red) or above (blue) the poverty threshold at age x, conditional on survival. a, b, and c, differ in the threshold income used to define poverty, 1×, 2×, and 3× the ‘official’ poverty income level, respectively. The green vertical lines in each panel are the seams between data-sets utilized: NLSY79 pre-1994, NLSY79 post-1994 and HRS (at age 33 and 50).
Fig 3.
Predicted proportion of individuals that are below the poverty threshold.
Black lines are the predicted proportion of individuals of age x that are below the poverty threshold according to the dominant eigenvector of the cumulative Q(x) matrix Qcum(x), the cumulative unconditional state transition matrix for age x. Red lines represent population projections for those below poverty with five different initial cohort distributions: (from top to bottom) 970,000, 750,000, 500,000, 250,000, and 30,000 individuals below poverty threshold in an initial cohort of 1,000,000 individuals. Regardless of initial cohort, the proportion of individuals below poverty (red lines) converge to the dominant eigenvector of Qcum(x) with age. a, b, and c, differ in the threshold income used to define poverty, 1×, 2×, and 3× the ‘official’ poverty income level, respectively. The green vertical lines in each panel are the seams between data-sets utilized: NLSY79 pre-1994, NLSY79 post-1994 and HRS (at age 33 and 50).
Fig 4.
The average remaining life expectancies and remaining years in poverty.
Average remaining life expectancies (solid lines) and expected years in poverty (dashed lines) conditional on surviving to age x based on state at age x (red = below threshold, blue = above threshold). a, c, and e, differ in the threshold income used to define poverty, 1×, 2×, and 3× the ‘official’ poverty income level, respectively. The ratio of the average remaining life in poverty (or below 2× poverty or 3× the ‘official’ poverty threshold) to total average remaining life are graphed in panels (b), (d) and (f). In other words, this is the proportion of average remaining life below a specified threshold. All values are calculated from the fundamental matrix (see section B of S1 Theory). The dashed green vertical lines in each panel are the seams between data-sets utilized: NLSY79 pre-1994, NLSY79 post-1994 and HRS (at age 33 and 50).
Fig 5.
The variance of remaining life expectancy, conditional on surviving to a specific age.
a, c, and e depict the variance of remaining life expectancy conditional on surviving to age x based on state at age x (red = below threshold, blue = above threshold). The age-specific coefficient of variation (the standard deviation divided by the mean) for state (red = below threshold, blue = above threshold) at age x are graphed in panels (b), (d) and (f). The dashed green vertical lines in each panels are the seams between data-sets utilized: NLSY79 pre-1994, NLSY79 post-1994 and HRS (at age 33 and 50).
Fig 6.
Cohort simulations of 10,000 individuals lifetime trajectories.
The right column is a ‘snapshot’ of 100 individuals between the ages of 50 and 60 with mortality around 60. Red is the above income threshold state, green is below the income threshold, and blue is death. The first column is the entire cohort and is in the shape of a survivorship curve for all three rows. The first row of panels has a threshold at 1× poverty income threshold, second row is 2× and third row is 3× poverty income threshold.
Fig 7.
Cohort simulations of 10,000 individuals: Distributions of residence times and ages of transitions.
The initial cohort is the same for each row but each row is a separate simulation with a particular income threshold in place. Distributions of the years an individual spends in the lower income state are depicted in panels a, d, and g. The panels in the second column are distributions of ages of entry into the lower income state. The panels in the third column are distributions of ages of exit from the lower income state. The first row of panels has a threshold at 1× poverty income threshold, second row is 2× and third row is 3× poverty income threshold. The dashed green vertical lines in panels in the last two columns are the seams between data-sets utilized: NLSY79 pre-1994, NLSY79 post-1994 and HRS (at age 33 and 50).