2.4.1 Preferences

A representative individual of ability a and generation t experiences utility in the j-th period of life through the instantaneous utility function described in equation (12).

(12)$$u( {c_{\,ja}^t , \;\ell_{\,ja}^t } ) = \ln ( {c_{\,ja}^t } ) + \gamma _j\displaystyle{{{( \ell _{\,ja}^t ) }^{1-\theta }} \over {1-\theta }}\;\;\;\forall {\rm \;}j = 1, \;2, \;3, \;4, \;5; \;\;\;\forall a = L, \;M, \;H$$

with $\gamma _1 = \gamma _2 = 0, \;\;\;\gamma _j > 0{\rm \;}\forall {\rm \;}j = 3, \;4, \;5$ and θ > 0 (θ ≠ 1)

Instantaneous utility is thus increasing in consumption $c_{ja}^t$ and leisure time $\ell _{ja}^t$ experienced in that period. Preferences are logarithmic in consumption and iso-elastic in leisure with the intertemporal elasticity of substitution in leisure being 1/θ. γ _j indicates the age-dependent utility value of leisure relative to consumption. Young and middle-aged individuals do not value leisure and, as a result, will opt to not allocate any time to leisure.

Each individual in the model maximizes their expected lifetime utility, described by equation (13). In this equation, β denotes the discount factor determining the present value of future utility, while $\pi _j^t$ has been defined in Section 2.1 as the unconditional probability to reach age j.

(13)$$U^t = \mathop \sum \limits_{\,j = 1}^5 \beta ^{\,j-1\;}\pi _j^t \;u( {c_{\,ja}^t , \;\ell_{\,ja}^t } ) $$

2.4.2 Time constraints

Every period is of the same fifteen-year length. We normalize this length to 1. Depending on the specific age and ability of an individual, time is allocated to either work (n), education (e) or leisure (ℓ). Equations (14) to (17) state the time constraints in each period.

(14)$$\;n_{1a}^t = 1-e_{1a}^t \;{\rm with}\;e_{1L}^t = 0$$

(15)$$n_{2a}^t = 1$$

(16)$$\ell _{3a}^t = 1-n_{3a}^t $$

(17)$$\ell _{\,ja}^t = 1\;\;for\;j = 4, \;5$$

Young individuals in equation (14) allocate their time to either work (n) or education (e). Individuals of low innate ability do not study when young $( e_{1L}^t = 0)$. They are assumed to have zero productivity of schooling at the tertiary level. In later stages of life no one studies. Middle-aged individuals in equation (15) only work. Whereas young and middle-aged individuals have no leisure, retired individuals in their fourth and fifth period of life have only leisure, as expressed in equation (17). The statutory retirement age is 65. The generation of age 50 to 64 (j = 3) is the only generation in our model that is able to choose, in equation (16), what share $\ell _{3, a}^t$ of time they allocate towards non-productive activities. Leisure time when older $\ell _{3a}^t$ can be considered attainable through either reducing hours worked while still employed or through entering into early retirement schemes.

2.4.3 Budget constraints

Each individual enters the model with zero assets. Equations (18)–(20) state the budget constraints with which individuals of generation t are confronted in different periods of life.

(18)$$\eqalign{( {1 + \tau_c} ) c_{\,ja}^t + \omega _{\,ja}^t = & \;w_{a, t + j-1}h_{\,ja}^t n_{\,ja}^t ( {1-\tau_{wja, t + j-1}} ) \cr & \quad + ( {1 + r_{t + j-1}( {1-\tau_{ci}} ) } ) \omega _{\,j-1, a}^t + iht_{t + j-1} + tra_{t + j-1}\;{\rm for}\;j = 1, \;2} $$

(19)$$\eqalignno{( {1 + \tau_c} ) c_{3a}^t + \omega _{3a}^t & = w_{a, t + 2}h_{3a}^t n_{3a}^t ( {1-\tau_{w3a, t + 2}} ) + bw_{a, \;t + 2}h_{3a}^t ( {1-n_{3a}^t } ) ( {1-\tau_{w3a, t + 2}} ) \cr & \quad + ( {1 + r_{t + 2}( {1-{\rm \tau }_{ci}} ) } ) \omega _{2a}^t + iht_{t + 2} + tra_{t + 2}} $$

(20)$$\eqalign{( {1 + \tau_c} ) c_{ja}^t + \omega _{ja}^t = & \;pp_{ja}^t + ( {1 + r_{t + j-1}( {1-\tau_{ci}} ) } ) \omega _{j-1, a}^t + iht_{t + j-1} \cr & \quad + tra_{t + j-1}\;{\rm for}\;j = 4, \;5} $$

Individuals allocate their disposable resources to either consumption $c_{ja}^t$ or the accumulation of non-human wealth. We denote by $\omega _{ja}^t$ the stock of wealth held by an individual of ability a at the end of the j-th period of their life. Consumption is taxed at rate τ _c. The right-hand sides of equations (18) and (19) show individuals' available resources during active life. These include after-tax labor income, non-employment benefits (only when older), non-human wealth accumulated in the previous period and the after-tax return on it, accidental inheritances (iht _t) and lump-sum transfers from the government (tra _t).

After-tax labor income rises in the real remuneration w _a per unit of effective human labor provided by an individual of ability a, the human capital of that individual $h_{ja}^t$, and the fraction of time spent working $n_{ja}^t$. It falls in the average tax rate on labor income τ _wja. Since we model a progressive labor income tax system (cf. infra), tax rates depend on the ability and age of individuals. When older, at model age j = 3, individuals may choose to reduce their working time. In line with reality in many countries, they may then receive a benefit that is proportional to the time not spent working. This benefit can be thought to reflect both early retirement benefits (for those no longer working) and benefits in the context of phased retirement schemes (for older employees reducing work hours). The level of the benefit is a fraction of the net labor income an individual would receive if they worked. The policy parameter b indicates the net replacement rate.

If individuals survive into the next period t + 1, they lend out their unconsumed resources from period t to firms or the government. Individuals are paid back at the end of period t + 1 and remunerated at the after-tax real interest rate r(1 − τ _ci), with τ _ci a proportional capital income tax. At the end of the fifth period (80–94), all remaining individuals fully consume their remaining resources $( \omega _{5a}^t = 0)$. This way, individuals in the final period of life do not die with debt nor do they willingly leave bequests. In other stages of life, individuals are allowed to have negative values $\omega _{ja}^t$.

During retirement, in equation (20), an individual receives old-age pension benefits, $pp_{4a}^t$ and $pp_{5a}^t$. The pension system in the model is of the pay-as-you-go type. Equation (21) describes the formation of these benefits as a function of the individual's net labor income in the past. The replacement rate is denoted by ρ. We impose that each of the three periods of active life are equally important for the calculation of the pension assessment base.

(21)$$pp_{4a}^t = pp_{5a}^t = \rho \left\{{\displaystyle{1 \over 3}\mathop \sum \limits_{j = 1}^3 \Big[ {w_{a, t + j-1}h_{ja}^t n_{ja}^t ( {1-\tau_{wja, t + j-1}} ) } \Big] } \right\}$$

Finally, if individuals do not survive the transition to the following period, the unconsumed part of their disposable resources is not lent out to firms in the next period. In equation (22), IHT _t indicates the total mass of unconsumed resources at the end of period t of individuals who do not reach the next period of their life. This total inheritance mass IHT _t will be immediately distributed on an equal basis among all individuals in the form of a lump-sum transfer. The inheritance per person at the end of period t (iht _t) is given by equation (23)Footnote ².

(22)$$IHT_t = \mathop \sum \limits_{j = 1}^4 \mathop \sum \limits_{a = L, M, H} \Big( {1-sr_{\,j + 1}^{t + 1-j} } \Big) \;\pi _j^{t + 1-j} N_{1a}^{t + 1-j} \omega _{ja}^{t + 1-j} $$

(23)$$iht_t = \displaystyle{{IHT_t} \over {N_1^t + \pi _2^{t-1} N_1^{t-1} + \pi _3^{t-2} N_1^{t-2} + \pi _4^{t-3} N_1^{t-3} + \pi _5^{t-4} N_1^{t-4} }}\;$$

2.4.4 Human capital formation

Individuals of different ability enter the model with different initial levels of human capital. The human capital of young individuals of the high ability type is normalized to h ₀. Young individuals of medium and low ability dispose of only a fraction ${\rm \varepsilon }_a$ of this level.

(24)$$\;h_{1, a}^t = \varepsilon _ah_0\;\;with\;\varepsilon _L < \;\varepsilon _M < \;\varepsilon _H = 1$$

This heterogeneity in individuals upon entering the model can be thought to reflect both differences in innate ability at birth and heterogeneous learning outcomes in primary and secondary education. Neither h ₀ nor ${\rm \varepsilon }_a$ varies across generations such that equation (24) is not a source of long-term growth or of fluctuations in the skill premium.

In the first period of life, medium and high ability individuals can allocate time to increasing their level of human capital (reflecting participation in tertiary education between the ages of 20 and 34). Equation (25) describes the human capital production function. It is identical to that of Bouzahzah et al. (Reference Bouzahzah, de la Croix and Docquier2002) and Buyse et al. (Reference Buyse, Heylen and Van de Kerckhove2017), among others. Equations (26) and (27) indicate that human capital never depreciates. We have in mind that learning by doing at work may counteract depreciation.

(25)$$h_{2a}^t = h_{1a}^t ( {1 + \phi {\left[{e_{1a}^t }\right]}^\sigma } ) \;\;\forall a = M, \;H\;{\rm and}\;\phi > 0, \;\;0 < \sigma \le 1$$

(26)$$h_{2L}^t = h_{1L}^t $$

(27)$$h_{3a}^t = h_{2a}^t \;\forall a = L, \;M, \;H$$

2.4.5 Optimality conditions for savings, education and work

Individuals in the model maximize their expected lifetime utility (equation 13) subject to the budget and time constraints (equations (14) to (27)) by optimally choosing consumption in each period of active life and the share of time spent working when aged 50 to 64. Medium and high ability individuals also choose the amount of time spent at educational activities when aged 20 to 34. The relevant optimality conditions are described in online Appendix E.

3.1.1 Technology and preference parameters

The rate of physical capital depreciation is assumed to be the same for traditional capital and automation capital. We impose δ _k = δ _p = 0.714, which implies a yearly depreciation rate of around 8% because of the fifteen-year length of one model period. Similarly, we impose β = 0.8, which reflects a rate of time preference of 1.5% per year. We assume the share parameter α for traditional capital in the production function for final goods to be equal to 0.25. The idea is that before tasks were technologically automatable $( \xi _a = 1, \;\forall a = L, \;M, \;H)$, the share of capital in national income was constant and equal to the share parameter of the Cobb-Douglas production function α. This is thought to reflect the historical constancy of the labor share (Kaldor, Reference Kaldor, Lutz and Hague1961; Keynes, Reference Keynes1939). With regard to the level of the constant initial wage share, our value of 0.75 is consistent with the findings of Johnson (Reference Johnson1954) and Gollin (Reference Gollin2002).

The elasticity of substitution s between labor (tasks) of different ability types is set equal to 1.5. The empirical labor literature consistently documents values between 1 and 2 (Caselli & Coleman, Reference Caselli and Coleman2006). For the value of the intertemporal elasticity of substitution in leisure (1/θ) we follow Rogerson (Reference Rogerson2007). He puts forward a reasonable range for θ in macro studies from 1 to 3. In line with this, we impose θ to be equal to 2. This choice implies an elasticity of labor supply which is much higher than the very low elasticities typically found in micro studies. Given our macro focus, however, these micro studies may not be the most relevant ones (Fiorito and Zanella, Reference Fiorito and Zanella2012; Rogerson and Wallenius, Reference Rogerson and Wallenius2009). Several parameters in our model relate to human capital production. For the elasticity of human capital with respect to education time (σ) we choose a conservative value of 0.3. This value is within the range considered by Bouzahzah et al. (Reference Bouzahzah, de la Croix and Docquier2002) and Docquier and Paddison (Reference Docquier and Paddison2003). For the values of the relative initial human capital of medium and low ability individuals (relative to the initial human capital of high ability individuals, $\varepsilon _M$ and $\varepsilon _L$), we follow Buyse et al. (Reference Buyse, Heylen and Van de Kerckhove2017). They looked at the distribution of PISA science test scores in OECD countries. From the robust pattern they observed in relative scores of weaker and median performers relative to better performers, they derived $\varepsilon _L = 0.67$ and $\varepsilon _M = 0.84$. The initial level of human capital with which high ability individuals enter the model is normalized to one (h ₀ = 1). We calibrated all remaining parameters by imposing that the model matches key recent data for the US.

The relative taste for leisure of individuals during the final period of active life (γ ₃) is set to generate an employment rate among older workers, averaged over the three ability groups (n ₃) of 57.4%. This is the fraction of potential hours that were actually worked by all individuals aged 50 to 64 in the US during the 2005–2019 period (for more details, see online Appendix D). The exogenous growth rate of A _t is the only source of long-term per capita growth in the model, which is why x is set to match the average yearly growth rate of potential GDP per person of working age. This was 1.35% in the US for the years between 2005 and 2019, leading to a value of x of 0.228. We calibrate the efficiency parameter in the human capital production function ϕ such that the model accurately predicts the 2005–2019 data on the average aggregate participation in education of individuals between 20 and 34.

For the calibration of the share parameters of the three different ability types of labor (tasks) relevant to the production of final output (η _L, η _M, η _H), our target values are the pre-tax wages of young workers of low and medium education relative to the wages of young workers of high education. More specifically, we target data published by the OECD (Education at a Glance 2020) for the wages of 25- to 34-year-old individuals whose highest degree is of the upper secondary level or lower (ISCED 3 or lower) and of individuals with short-cycle tertiary education (ISCED 5), relative to the wages of individuals with at least a bachelor's degree (ISCED 6 or higher). This educational division best approximates our modeling assumption that individuals with low ability do not participate in tertiary education, while those of medium and high ability do.Footnote ³ This results in values for η _L and η _M respectively. The value for η _H then follows as η _H = 1 − η _L − η _M.

3.1.2 Automation parameters

We identify five parameters relating to automation. These are the shares of automatable tasks by ability type 1 − ξ _a (for a = L, M, H), the elasticity of substitution between automatable and non-automatable tasks κ, and the productivity of automation capital J. They are determined such that our model replicates five facts or well-informed hypotheses. A first one is that 25% of tasks of low ability are automatable. A second and third are that the fractions of automatable tasks of medium and high ability equal respectively 85% and 48% of the fraction of automatable tasks of low ability. A fourth one is that due to automation the labor share in the US fell from 75% to about 70% in 2005–2019. The fifth one is the finding of Acemoglu and Restrepo (Reference Acemoglu and Restrepo2022) that if the demographic structure in the US were the same as in Germany, robot density in the US would be 52% higher. We now clarify these facts or hypotheses in greater detail.

3.1.3 Shares of automated tasks: 1 − ξ _a for a = L, M, H

The basis of our calibration is the work of Arntz et al. (Reference Arntz, Terry and Ulrich2016) and Popescu et al. (Reference Popescu, Petrescu, Sabie and Muşat2018). Both studies reveal clear heterogeneity between ability types in the share of tasks 1 − ξ _a that are automatable. Unlike most other studies, Arntz et al. (Reference Arntz, Terry and Ulrich2016) adopt a task-based approach to estimate the share of jobs and individuals at high risk of automation. This makes their results a more reliable point of reference for us to start from. More precisely, they report for the three groups in the US with the lowest ISCED levelsFootnote ⁴ estimated shares of workers at high risk of automation equal to 100%, 44%, and 19% respectively. Weighing these shares with the relative size of these three low education groups (US Census Bureau, Current Population Survey), we obtain that 25.3% of, what we label, low ability individuals are employed in highly automatable occupations. If we assume a one-to-one relationship between the task content of jobs and the education level of those who execute them, it follows that a share of 25% of low ability tasks are automatable (1 − ξ _L).

Taking this 25% for 1 − ξ _L as our benchmark, similar shares of tasks of medium and high ability that are automatable can be derived fairly easily from Popescu et al. (Reference Popescu, Petrescu, Sabie and Muşat2018). They build on the work of Frey and Osborne (Reference Frey and Osborne2017) and also estimate the probability of job automation by education level.Footnote ⁵ We impose that the relative levels of future automation probabilities that they report, are also reflected in the share of tasks of each ability that are already automated. In practice, this results in two conditions demanding that the share of medium ability (high ability) tasks that are automated is 84.7% (48.0%) of the share of low ability tasks that are automated. In absolute terms, it then follows that we impose a value for 1 − ξ _M equal to 21% and a value for 1 − ξ _H equal to 12%. We thus assume that the same ability bias expected in future automation has been present in the automation technologies up to now. Compared to the findings of Arntz et al. (Reference Arntz, Terry and Ulrich2016), Popescu et al. (Reference Popescu, Petrescu, Sabie and Muşat2018) put forward relatively small differences in job automatability between education levels. By opting for their estimates to serve as calibration targets, our model is conservative in the sense that it is less likely to overestimate the skill-biased effects of automation.

3.1.4 Efficiency parameter of automation capital J

With the three shares of automated tasks (1 − ξ _a) fixed above, the efficiency parameter J determines the share of income that is a remuneration for automation capital (equation 40).

(40)$$\displaystyle{{\partial Y_t} \over {\partial P_t}}\displaystyle{{P_t} \over {Y_t}} = ( {1-\alpha } ) \left({\displaystyle{{K_t} \over {H_t}}} \right)^\alpha \mathop \sum \limits_{a = L, M, H} \left\{{\eta_a{\left({\displaystyle{{H_t} \over {H_{a, tot, t}}}} \right)}^{1/s }( 1-\xi_a) {\left({\displaystyle{{H_{a, tot, t}} \over {P_t}}} \right)}^{1/\kappa}J} \right\}\displaystyle{{P_t} \over {Y_t}}$$

Since traditional capital K _t and the total execution of tasks H _t are combined in a Cobb-Douglas production function with an output elasticity of traditional capital of 0.25, the share of human labor in the national income is 0.75 minus automation capital's income share. As indicated earlier, before tasks became technologically automatable $( \xi _a = 1, \;\forall a = L, \;M, \;H)$, automation capital's share of income was zero (equation 40) and the labor share of income was a constant 0.75. We then calibrate the constant parameter value J such that – with given values of 1 − ξ _a and the demographic parameters – the labor share that our model produces in the US for the 2005–2019 model period is lower than this original 0.75 as a result of automation. More specifically, we will target a value for the US labor share in this period of 0.701. That is precisely half of the fall from the initial 0.75 to the level of 0.652 that Gutiérrez (Reference Gutiérrez2017)Footnote ⁶ finds for the US labor share (excluding the real estate, finance and non-business sectors) for 2010–2014. In imposing that the automation of tasks was the driving force behind 50% of the fall in the labor share, we are in line with the findings of Karabarbounis and Neiman (Reference Karabarbounis and Neiman2014), Dao et al. (Reference Dao, Das, Koczan and Lian2017) and Bergholt et al. (Reference Bergholt, Furlanetto and Maffei-Faccioli2022). This approach yields a value for J equal to 20.1.

We derive and discuss the inequality conditions that have to hold such that it is strictly cheaper for firms to execute automatable tasks by automation capital in Appendix A, part 1. For the value of J that we obtained, these conditions are satisfied for each ability level.

3.1.5 Elasticity of substitution between automated and non-automated tasks: κ

Our calibration imposes constant parameter values for 1 − ξ _a and J over all periods. This choice reflects our focus on non-technological automation at the intensive margin, as argued in sub-section 2.3. In response to aging (increased life expectancy and scarcity of young workers), firms can substitute automated tasks for tasks executed by humans. The elasticity of substitution between automated and non-automated tasks κ is crucial in this respect. We calibrate κ such that aging induces automation to the extent that is found by the empirical study of Acemoglu and Restrepo (Reference Acemoglu and Restrepo2022). They find that if the US had the same demographic trends as Germany – keeping all other things equalFootnote ⁷ – “the gap in robot adoption between the two countries would be 50% smaller” (p. 2). Practically, we use the data for 2014 that Acemoglu and Restrepo (Reference Acemoglu and Restrepo2022) present on the size of the robotics gap between Germany and the US: Germany's relative lead in robotics was approximately 103.6%. Acemoglu and Restrepo (Reference Acemoglu and Restrepo2022) thus more generally find that if the US had the demographic structure of Germany, their robot density would be 51.8% higher (half of 103.6%). For our calibration, we therefore impose that applying German demography to the US and keeping all other things equal leads to a rise in the baseline automation density of 51.8% at the end of the 2005–2019 period. This is the target value for our calibration. It yields a value of κ equal to 6.04.

The explanation for why the longer life expectancy and the scarcity of workers in Germany relative to the US contribute to the higher adoption of robotics in Germany is twofold. Note that as automated and non-automated tasks substitute better for one another (a higher κ), both explanations for why aging stimulates automation gain in strength. First, the literature finds that increased longevity and reduced fertility have a net positive effect on total savings (e.g., Carvalho et al., Reference Carvalho, Ferrero and Nechio2016). In our closed economy model, increased national savings translate to lower interest rates and capital deepening for all types of capital. The fall in the cost of capital will result into automation capital deepening more so when κ is higher, since a higher elasticity of substitution with labor counteracts diminishing returns to capital (Palivos & Karagiannis, Reference Palivos and Karagiannis2010). Irmen (Reference Irmen2021) too finds that, in the long run, a rise in longevity stimulates automation. Second, Abeliansky and Prettner (Reference Abeliansky and Prettner2023) outline how a fall in fertility can generate a relative shortage of human labor supply that can encourage the adoption of automation technologies. While automation capital is only a q-substitute for low and medium ability labor (cf. infra), it can be shown that an equal fall in the labor supply of all ability types positively affects the marginal product of automation capital (while, of course, reducing the marginal product of traditional capital) for the calibrated parameter values. Given the no-arbitrage condition, a fall in fertility will thus stimulate the accumulation of automation capital.Footnote ⁸ The automation-enhancing effect of a fall in fertility will be stronger in case of a higher value for κ, since the derivative of the marginal product of automation capital with respect to the human labor input will be more negative in case of a higher κ.

3.1.6 Automation at the intensive margin and the effect on wages: q-substitutes?

In this sub-section, we show that our model succeeds in creating heterogeneous wage effects related to a rise in P (non-technological automation at the intensive margin) despite the common elasticity of substitution κ. The main driver of this result is the difference in the shares of total tasks that are automated 1 − ξ _a. Equation (41), derived in Appendix B, determines whether a rise in the input of automation capital in the production function has a positive or negative effect on the real hourly wage per unit of effective labor for an individual of ability a. The continuity condition for symmetry of the mixed second order derivatives is met, such that equation (41) also indicates whether the marginal product of automation capital is decreasing or increasing in the amount of human labor of type a.

(41)$$\eqalign{sgn\left({\displaystyle{{\partial w_{a, t}} \over {\partial P_t}}} \right) \!& = \ sgn\left[{\left\{{( 1 \!- \!\xi_a) {\left({\displaystyle{{H_{a, tot, t}} \over {P_t}}} \right)}^{1/\kappa }} \right\}\left\{{\left({\displaystyle{1 \over s} \! - \!\alpha } \right)\eta_aH_t^{{-}1} {\left({\displaystyle{{H_t} \over {H_{a, tot, t}}}} \right)}^{1/s} \!+\! \left({\displaystyle{1 \over \kappa}-\displaystyle{1 \over s}} \right)H_{a, tot, t}^{{-}1} } \right\}} \right. \cr & \left. { + \left({\displaystyle{1 \over s}-\alpha } \right)H_t^{{-}1} \sum\limits_{\,j\ne a} {\left\{{\eta_j( 1-\xi_j) {\left({\displaystyle{{H_t } \over {H_{j, tot, t}}}} \right)}^{1/s}{\left({\displaystyle{{H_{j, tot, t}} \over {P_t}}} \right)}^{1/\kappa }} \right\}} } \right]} $$

Equation (41) consists of two terms that have distinct interpretations. The first term indicates the effect of a rise in P on the wage of workers of ability a through the increased execution of automatable tasks of type a. This is the direct displacement effect. The degree to which automated tasks can substitute for non-automated tasks of the same ability type a – embodied by the elasticity of substitution κ – plays a crucial role here. For our calibrated parameter values, this first effect is negative for all ability types. It will be more negative for the low and medium ability workers, however, since a larger share of tasks performed by them are automated (larger 1 − ξ _a). This is not the whole story though. The second term indicates the effect of a rise in P on the wage of workers performing tasks of type a through the increased execution of automatable tasks of a type different from a.Footnote ⁹ This is the indirect productivity effect. The elasticity of substitution s between the different ability types plays a large role in determining the sign of this second effect. For our calibrated parameter levels, tasks of different ability types are q-complements and the effect will be positive.

The net effect of this non-technological automation at the intensive margin is negative for low and medium ability workers, but positive for high ability workers given the calibration. Automation capital is thus only a q-substitute for low and medium ability human labor, since, for workers of high ability, the negative displacement effect of automation is more than fully compensated by the increased execution of complementary tasks.