Finance and Economics Discussion Series: Accessible versions of figures for 2015-117

Taxing Capital? The Importance of How Human Capital is Accumulated

Accessible version of figures


Figure 1: Life Cycle Frisch Labor Supply Elasticity in Endogenous Model.

This figure has two panels to compares the baseline model, where the U.S. tax policy is exogenous, with the LBD and LOD models, where the U.S. tax policy is endogenous.
Left panel: The y-axis shows the Frisch Elasticity spanning from 0.45 to 0.8. The x-axis shows age from 20 to 100. The baseline model (exogenous) is a flat solid line at 0.5 Frisch Elasticity from age 20 to 65. The LBD model starts with a Frisch Elasticity around 0.485 at age 20 and gradually increases to 0.5 at age 59. It then sharply increases to 0.73 by age 65 (where both lines end).
Right panel: The y-axis shows the Frisch Elasticity from 0.46 to 0.53. The x-axis shows age from 20 to 100. The baseline model (exogenous) is a flat solid line at 0.5 Frisch Elasticity from age 20 to 65. The LOD model starts at age 20 with a Frisch Elasticity of 0.528 and decreases to 0.5 by age 37. It then continues to decrease to 0.47 at age 65. Both lines end at age 65.

Return to text.


Figure 2: Effect of LOD Elasticity on Young Labor Supply

This figure compares the percent of time endowed to supplying labor from ages 20 to 35 between the exogenous and the LOD models. The y-axis runs from 0.345 to 0.385 (aka 34.5 percent to 38.5 percent), and the x-axis runs from age 20 to 35 in increments of 5. Both models begin at age 21, with the exogenous model showing a time endowment of just above 0.365 and the LOD model showing a time endowment of just above 0.355. The models dip down at a constant rate, reaching time endowments at age 23 of 0.355 and 0.345 respectively. At this point, both the exogenous and LOD models, reaching maximum time endowments around age 31 of 0.385 and just above 0.375 respectively. Both models then begin the decrease, with the exogenous model plateauing around 0.375 at age 35, and the LOD model decreasing until roughly 0.37 at age 35.

Return to text.


Figure 3: Actual and Exogenous Life Cycle Profiles

This figure has four panels. All panels compare the actual life cycle profile to the exogenous model’s life cycle profile in various economic dimensions. The x-axis of each panel runs from age 20 to age 100, while the y-axes vary.
Top left panel: Compares labor, as measured by the percent of time spent working, between the actual and exogenous model. The y-axis begins at 0 percent of time spent working to 0.4, or 40% of time spent working. The model begins at age 20 around 0.35 percent, while the actual data begins near 0.3. The former begins to decrease steadily around age 30, until age 65 when the time endowment reaches 0.25. At this point, the exogenous model drops straight down to 0. By contrast, the actual profiles in the data rise from age 20 to age 40, peaking around 0.36 time working, and then decrease steadily, reaching a time endowment of 0.2 at age 65 and flattening out to near 0 by age 90.
Top right panel: Compares earnings, as measured in thousands of dollars, between the actual and exogenous model. The y-axis ranges from 0 to 60 thousand dollars. The exogenous model begins at age twenty with earnings just under 30 thousand, increasing to 50 thousands by age 40 and decreasing back to 30 thousand by age 65. The actual profiles in the data begin near 20 thousand, increase to just above 50 thousand by age 50 and then begin to decrease gradually, reaching 30 thousand by age 65 and 10 thousand by age 80 with substantial static in earnings until age 90.
Bottom left panel: Compares consumption, as measured in thousands of dollars, between the actual and exogenous model. The y-axis ranges from 20 to 45 thousand dollars. The exogenous model begins at 20 thousands at age 20 and increases steadily to a peak between 40 and 45 thousand dollars of consumption around age 75. After this point, the model drops quickly to somewhere between 20 and 25 thousand dollars of consumption at age 90 and remains after that. The actual profiles in the data begin just above 35 thousand at age 20 and increase more sharply to just under 40 thousand at age 45, after which point, consumption drops gradually to just under 25 thousand at age 90.
Bottom right panel: Compares savings, as measured in hundreds of thousands of dollars, between the actual and exogenous model. The y-axis ranges from 0 to 3.5 (aka 0 to $350,000). Both the exogenous model and the actual profiles in the data begin around 0 at age 20 and increase to a peak near 3 at age 60. The actual profiles in the data are much more jagged, while the exogenous model produces a smooth curve. After this maximum, exogenous model decreases to 0 at age 90, while the actual data ends around 2 at age 90.

Return to text.


Figure 4: Life Cycle Profiles under Baseline-Fitted U.S. Tax Policy.

This figure has four panels. Each panel compares aspects of life cycle profiles in the baseline-fitted policy (tax policy is exogenous) with the LBD, LOD with working and training, and LOD with working models.
Top-left panel: Compares percent of endowed hours worked across age groups for the four models. For the baseline model, the percent of endowment worked starts around 0.36 at age 20. After an initial slight dip, the percent of endowed hours worked increases to around 0.375 around age 30, then decreases to about 0.24 by age 65. The LBD model starts at 0.375 at age 20, increases to 0.388 around age 30, then decreases to close to 0.15 by age 65. The LOD model with working and training starts around 0.37 at age 20, dips slightly and increases to 0.375 by age 30, then decreases to 0.24 by age 65—closely following the baseline model. The LOD model with working starts at 0.33 at age 20, briefly dips to 0.325 then increases to 0.348 shortly after age 30. It then decreases to 0.24 by age 65—constantly below, but converging to, the baseline model.
Top-right panel: Compares consumption across age groups. The baseline model starts at 0.3 at age 20, increases constantly to 0.62 around age 70 when it smoothly begins to decrease. By age 80, it is falling sharply to level off at 0.34 around age 91. The LBD model begins around 0.31, increases constantly to 0.59 around age 70 (falling below the baseline consumption level around age 45). It then smoothly begins to decrease, eventually dropping quickly until leveling off abruptly at 0.335 around age 91. The LOD model begins around 0.275, increases constantly to 0.59 around age 70. It then smoothly begins to decrease, eventually dropping quickly until leveling off abruptly at 0.32 around age 91.
Bottom-right panel: Asset Holdings Under Baseline. Compares asset holdings across ages. The baseline (exogenous) model resembles a bell-curve. It starts at zero at age twenty, increases to 4.2 around age 60 then decreases to zero around age 92. The LBD model starts at zero at age twenty and follows the baseline model closely. It reaches its maximum around age 58 around 4.22 and then decreasing slightly quicker than the baseline model, but ultimately reaching zero at age 92. The LOD model also follows a bell-curve shape. It starts at zero at age twenty and increases (slightly below the exogenous model) until reaching its maximum asset holding level of 4.1 around age 62. It then decreases following the baseline model very closely until reaching zero at age 92.
Bottom-right panel: Age-specific Human Capital Under Baseline. Compares productivity across ages. The baseline (exogenous) model begins at age twenty with productivity 1, increases fairly constantly to productivity 1.7 around age 30, increases constantly from there to 1.94 at age 40, increases constantly from there to 1.96 at age 50, decreases constantly from there to 1.87 at age 60, and finally decreases constantly from there to just above 1.6 at age 65. The LBD model begins at age twenty with productivity 1, increases fairly constantly to productivity 1.59 around age 30, increases constantly from there to 1.87 at age 40, increases constantly from there to 2.0 at age 50, decreases constantly from there to 1.83 at age 60, and finally decreases constantly from there to just above 1.6 at age 65. The LOD model begins at age twenty with productivity 1, increases fairly constantly to productivity 1.6 around age 30, increases from there to 1.93 at age 40, increases from there to 2.0 at age 49, decreases from there to 1.83 at age 60, and finally decreases constantly from there to just above 1.61 at age 65.

Return to text.


Figure 5: Life Cycle Profiles in the Exogenous Model.

This figure has three panels. Each panel compares aspects of life cycle profiles in the baseline (exogenous) policy with those under the optimal policy.
Top-left panel: Compares percent of endowed hours worked across age groups for the two policies. For the baseline policy, the percent of endowment worked starts at 0.365 for age 20, decreases to around 0.358 at age 23 then increases to about 0.375 at age 30. From ages 20 to 30 years, the line for the optimal policy increases from 0.355 to 0.38, being above the baseline policy line from around age 25 to 30. From 30 years to around 65 years (where the lines ends), both lines decrease to end with around 0.235 of endowed hours worked. The optimal policy line is slightly higher than the baseline policy line throughout this decline.
Top-right panel: Compares consumption for different age groups between the two models. At age 20, the baseline policy line begins around 0.3 and the optimal policy line also begins at 0.3. The baseline policy line increases in consumption with age fairly constantly until age 60 when the increase slows and smoothly begins to decrease. It then decreases at an accelerating rate until around age 92 when it abruptly becomes constant just blow 0.35. The optimal policy line follows the contour of the baseline policy line. Throughout it is a little bit above the baseline policy line. At the peak, the optimal policy line is around 0.63, while the peak of the baseline policy line is closer to 0.61.
Bottom panel: Compares Asset holdings across ages for the two policies. Both have the same bell-curve shape. They start at zero at age 20, smoothly increase until age 60 and then decrease until around age 92. However, the optimal policy line falls slightly below the baseline policy line between ages 20 and 35. After 35, it is slightly above the baseline policy line at every age except for the tail that approaches age 100 where assets are equal to zero (approaching 20 and 100 years). At the peak, the baseline policy line is around 4.3 and the optimal policy line is around 4.5.

Return to text.


Figure 6: Life Cycle Profiles in the LBD Model.

This figure has four panels. Each panel compares aspects of life cycle profiles in the baseline (exogenous) policy with those under the optimal policy.
Top-left panel: Compares percent of endowed hours worked across age groups for the two policies. For the baseline policy, the percent of endowment worked starts at 0.375 for age 20, increases to about 0.39 at age 30. From ages 20 to 23 years, the line for the optimal policy decreases from 0.375 to 0.37 and then increases to 0.39 at age 35, being above the baseline policy line from around age 30 and on. From 35 years to around 65 years (where the lines ends), both lines decrease to end with around 0.2 of endowed hours worked. The optimal policy line is slightly higher than the baseline policy line throughout this decline.
Top-right panel: Compares consumption for different age groups between the two policies. At age 20, the baseline policy line begins around 0.3 and the optimal policy line also begins at 0.3. The baseline policy line increases in consumption with age fairly constantly until age 60 when the increase slows and smoothly begins to decrease. It then decreases at an accelerating rate until around age 92 when it abruptly becomes constant just blow 0.35. The optimal policy line follows the contour of the baseline policy line. Throughout it is a little bit above the baseline policy line. At the peak, the optimal policy line is around 0.62, while the peak of the baseline policy line is closer to 0.6.
Bottom-left panel: Compares Asset holdings across ages for the two policies. Both have the same bell-curve shape. They start at zero at age 20, smoothly increase until age 60 and then decrease until around age 92. However, the optimal policy line falls slightly below the baseline policy line between ages 20 and 45. After 45, it is slightly above the baseline policy line at every age except for the tail that approaches age 100 where assets are equal to zero (approaching 20 and 100 years). At the peak, the baseline policy line is around 4.2 and the optimal policy line is around 4.5.
Bottom-right panel: Compares productivity across ages for the baseline and optimal policy lines. The baseline policy line begins at productivity one at age 20 and increases fairly constantly to 1.9 around age 40. Here, its increases gradually slows and begins to decrease until age 65, where production is 1.63. For the baseline policy line, the peak production is just below 2 around age 50. The optimal policy line follows the baseline policy line closely. It is almost indistinguishable from the baseline policy until age 35, when it rises slightly above the baseline policy line and continues a little above but following the contour of the baseline policy line. It peaks at 2.1 around age 50. It terminates at age 65 with a production 1.63.

Return to text.


Figure 7: Life Cycle Profiles in the LOD Model.

This figure has six panels. Each panel compares aspects of life cycle profiles in the baseline (exogenous) policy with those under the optimal policy.
Top-left panel: Compares percent of endowed hours worked plus hours of training across age groups for the two policies. For the baseline policy, the percent of endowment worked starts at 0.37 for age 20, dips slightly to 0.365 around age 23 and then increases to about 0.375 at age 30. From ages 20 to 23 years, the line for the optimal policy decreases from 0.37 to 0.364 and then increases to 0.378 at age 35, being above the baseline policy from around age 30 and on. From 30 years to around 65 years (where the lines ends), both lines decrease to end with around 0.23 of endowed hours worked. The optimal policy line is slightly higher than the baseline policy throughout this decline.
Top-right panel: Compares consumption for different age groups between the baseline and the optimal in the LOD model. At age 20, the baseline policy begins around 0.275 and the optimal policy line also begins at 0.275. The baseline policy increases in consumption with age fairly constantly until age 60 when the increase slows and smoothly begins to decrease. It then decreases at an accelerating rate until around age 92 when it abruptly becomes constant around 0.325. The optimal policy line follows the contour of the baseline policy line. Throughout it is a little bit above the baseline policy line. At the peak, the optimal policy line is around 0.62, while the peak of the baseline policy line is closer to 0.6.
Middle-left panel: Compares Asset holdings across ages between the baseline and the optimal in the LOD model. Both have the same bell-curve shape. They start at zero at age 20, smoothly increase until age 60 and then decrease until around age 92. However, the optimal policy line increases and decreases slightly faster than the baseline policy from age 40 and on. After 40, it is slightly above the baseline policy at every age except for the tail that approaches age 100 where assets are equal to zero (approaching 20 and 100 years). At the peak, the baseline policy line is around 4.1 and the optimal policy line is around 4.3.
Middle-right panel: Compares human capital across ages for the baseline and optimal policies. The two policy lines follow each other exactly. They begin at productivity 1 at age 20 and increase fairly constantly to 1.9 around age 40. Here, the increase gradually slows and begins to decrease until age 65, where production is 1.63. Their peak is around 1.95 around age 45.
Bottom-left panel: Compares percent of endowment of time spend in training across ages in the LOD model. Both policies are very close across all ages. They start at 0.04 and decrease fairly constantly to zero around age 65. They remain at zero for the remainder.
Bottom-right panel: Compares percent of endowment spent working across ages in the LOD model. The baseline policy line starts at 0.33 at age 20, decreases slightly to 0.327 around age 23 and then smoothly increases to peak at 0.345 around ate 35. It then decreases to 0.235 at age 65. The optimal policy line starts at 0.335 at age 20, decreases to 0.323 around age 24, then smoothly increases to its peak of 0.35 around age 35 and decreasing to 0.235 at age 65—remaining above the baseline policy line from age 30 and on.

Return to text.


Figure 8: Flatter Labor Supply Profile

This figure compares the labor supply across the exogenous, actual and alternative exogenous I models as measured in the percent of endowment spent working. The y-axis ranges from 0.15 to 0.4. The exogenous model begins at 0.36 at age 20 and increases to a peak around 0.375 near age 35, at which point it decreases steadily to 0.24 at approximately age 65. The actual data profiles begin at 0.3 at age 20 and increase to a maximum of about 0.36 at age 40, only to decrease sharply beginning at age 45 and ending below 0.2 by age 65. Finally, the alternative exogenous I model begins around 0.34 at age twenty and increases to a peak of just above 0.35 at age 35 and then decreases slowly to just under 0.35 at age 50. At this point, the alternative exogenous model decreases more rapidly to just below 0.2 by age 65.

Return to text.


Figure 9: Labor Supply in Alternative Exogenous

This figure compares the labor supply across the exogenous, LBD and alternative exogenous II models as measured in the percent of endowment spent working. The y-axis ranges from 0.15 to 0.4. The exogenous model begins at 0.36 at age 20 and increases to a peak around 0.37 near age 35, at which point it decreases steadily to 0.24 at approximately age 65. The LBD model begins at 0.375 at age 20 and increase to a maximum of about 0.39 at age 35, decreasing gradually to 0 by age 65. Finally, the alternative exogenous II model begins around 0.39 at age 20 and decreases throughout the age range, more slowly at first and then more quickly after age 40 when the time endowment equals 0.375 to end up at 0 by age 65.

Return to text.