The Race Between Machine and Man: Implications of Technology for Growth, Factor Shares and Employment

May combine two claims.

In the static model with fixed capital and exogenous technology, automation lowers employment and the labor share and can lower wages, while creating new tasks has the opposite effects.

“In a static version where capital is fixed and technology is exogenous, automation reduces employment and the labor share, and may even reduce wages, while the creation of new tasks has the opposite effects.”

• Also stated in: § 1 Introduction · hedged

  “here automation always reduces the labor share and employment, and may even reduce wages.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

Proposition 2 shows that when technology constrains task allocation (I*=I<I), automation lowers the relative factor price W/R, the labor share, and employment, whereas new tasks raise all three.

“The main implication of Proposition 2 is that the two types of technological changes-automation and the creation of new tasks-have polar implications.An increase in I-an improvement in automation technology-reduces W/R, the labor share and employment (unless I * = I < I and firms are not constrained by technology in their automation choice), while an increase in N -the creation of new tasks-raises”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

For n above the threshold, the effective wage in the least complex labor task rises with n, the effective wage in the most complex labor task falls with n, asymptotic employment and labor share rise with n, and if the rise in n comes from more automation, capital also rises.

“• For n > n(ρ), w I (n) is increasing and w N (n) is decreasing in n.Moreover, the asymptotic values for employment and the labor share are increasing in n.Finally, if the increase in n is caused by an increase in I, the capital stock also increases.”

May combine two claims.

For the unique interior BGP when the innovation ratio exceeds the upper threshold, the BGP is globally stable if theta is zero and locally stable if theta is positive.

“Proposition 6 also shows that, for κ I κ N > κ, the unique interior BGP is globally stable provided that the intertemporal elasticity of substitution is infinite (i.e., θ = 0), and locally stable otherwise (i.e., when θ > 0).”

May combine two claims.

The elasticity of substitution between capital and labor is sigma when technology constrains automation, but sigma_free when it does not, and sigma_free exceeds sigma.

“This additional margin of adjustment implies that σ free > σ.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

With heterogeneous skills, new tasks help skilled workers directly and at first raise inequality.

“while new tasks directly benefit skilled workers and at first increase inequality as well.”

• AssumptionThe authors state this as an assumption: Skilled labor has a comparative advantage in new tasks.

May combine two claims.

In the unconstrained case, more new tasks always raise the equilibrium wage but can lower the rental rate, while more automation has no effect on factor prices.

“That is, an increase in N (more new tasks) always increases the equilibrium wage but may reduce the rental rate, while an increase in I (greater technological automation) has no effect on factor prices.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

More equilibrium automation raises capital's share and lowers labor's share in the aggregate production function, while new task creation has the reverse effect.

“An increase in I * -which corresponds to greater equilibrium automation-increases the share of capital and reduces the share of labor in this aggregate production function, while the creation of new tasks does the opposite.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

In the technology-constrained case, more new tasks (higher N) always raise the equilibrium wage but can lower the rental rate, while more automation (higher I) always raises the rental rate but can lower the equilibrium wage.

“That is, a higher N always increases the equilibrium wage but may reduce the rental rate, while a higher I always increases the rental rate but may reduce the equilibrium wage.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

The evolution of n is determined by relative profitability: n rises if the value of new tasks exceeds the value of automation and falls if the reverse holds.

“Equation (28) implies that ṅ(t) > 0 if and only if κ N V N (t) > κ I V I (t), and ṅ(t) < 0 if and only if κ N V N (t) < κ I V I (t).”

May combine two claims.

If the discount rate exceeds the critical value, new task creation grows at rate Delta, automation grows at least as fast, and n is below the threshold, there is a unique globally stable interior BGP with n* equal to n(rho) and I* above I.

“3. (Interior BGP with eventual automation) if ρ > ρ, Ṅ (t) = ∆ and İ(t) ≥ ∆ with ρ + (θ -1)A∆ > 0, and n(t) < n(ρ), then there exists a unique and globally stable BGP.In this BGP n * (t) = n(ρ) and I * (t) = I(t) > I(t).”

• AssumptionThe authors state this as an assumption: The comparative advantage schedule satisfies gamma(i) equals e to the power A i, with A positive.
• AssumptionThe authors state this as an assumption: In the dynamic model before the full model, the path of technology represented by I(t) and N(t) is exogenous.

The quote only partly states this claim.

Under Assumptions 1', 2, and 4, there is a scientist supply threshold below which the model has different BGP types depending on rho and the ratio of automation to new-task innovation productivity.

“Proposition 6 (Equilibrium with endogenous technological change) Suppose that Assumptions 1 ′ , 2, and 4 hold.Then, there exists S such that, when S < S, we have:foot_18”

• AssumptionThe authors state this as an assumption: The comparative advantage schedule satisfies gamma(i) equals e to the power A i, with A positive.
• AssumptionThe authors state this as an assumption: Assumption 4: sigma is greater than zeta.

May combine two claims.

Under natural assumptions, the interior balanced growth path is stable: if automation outpaces new task creation, market forces reduce later automation and accelerate new task creation.

“Under natural assumptions, this (interior) balanced growth path is stable, so that when automation runs ahead of the creation of new tasks, market forces induce a slowdown in subsequent automation and more rapid countervailing advances in the creation of new tasks.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.

May combine two claims.

In the technology-constrained case, automation always raises aggregate output but its effect on the equilibrium wage is ambiguous.

“The most important result in Proposition 3 is that, when I * = I < I, automation-an increase in I-always increases aggregate output, but has an ambiguous effect on the equilibrium wage.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

In the unconstrained case, new tasks raise productivity, but further automation technologies do not.

“That is, new tasks increase productivity, but additional automation technologies do not.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

The static equilibrium output is a CES combination of capital and labor with elasticity sigma, and its share parameters depend on automation and new task technologies.

“Equation ( 12) shows that aggregate output is a CES aggregate of capital and labor, with the elasticity between capital and labor being σ.The share parameters are endogenous and depend on the state of the two types of technologies in the economy.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

More new tasks always raise productivity and the equilibrium wage, and if their productivity gains are small, they can lower the rental rate.

“Finally, Proposition 3 shows that an increase in N always increases productivity and the equilibrium wage (recall that Assumption 3 imposes that R > W γ(N ) ), and when the productivity gains from the creation of new tasks are small, it can reduce the rental rate.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

In the technology-constrained case, there is a threshold K > K such that automation raises the equilibrium wage if K < K and lowers it if K > K.

“In particular, there exists K > K such that an increase in I increases the equilibrium wage when K < K and reduces it when K > K.”

• AssumptionThe authors state this as an assumption: Labor has a strict comparative advantage in tasks with higher indices.
• AssumptionThe authors state this as an assumption: The demand for labor and capital is homothetic, which holds if either η approaches 0 or ζ equals 1.
• AssumptionThe authors state this as an assumption: The capital stock is below a threshold K defined by R = W/γ(N), ensuring that new tasks are adopted immediately.

May combine two claims.

Over the long run, the productivity effect raises the real wage, yet automation still lowers the labor share.

“Although the real wage in the long run increases because of this productivity effect, automation always reduces the labor share.”

May combine two claims.

Standardization can curb rising inequality, and the paper identifies when this force is enough to restore stable inequality in the long run.

“but also points out that standardization may limit the increase in inequality, and characterizes the conditions under which this force is sufficient to restore stable inequality in the long run.”

• AssumptionThe authors state this as an assumption: Skilled labor has a comparative advantage in new tasks.

The quote only partly states this claim.

If the discount rate exceeds the minimum and new task creation grows at rate Delta, there is a unique globally stable no-automation BGP in which all tasks use labor and the capital share is zero.

“4. (No automation) if ρ > ρ min and Ṅ (t) = ∆ with ρ + (θ -1)A∆ > 0, then there exists a unique and globally stable BGP.In this BGP all tasks are produced with labor, and the capital share is zero.”

• AssumptionThe authors state this as an assumption: The comparative advantage schedule satisfies gamma(i) equals e to the power A i, with A positive.
• AssumptionThe authors state this as an assumption: In the dynamic model before the full model, the path of technology represented by I(t) and N(t) is exogenous.

May combine two claims.

In the second extension, which reintroduces creative destruction of earlier innovators' profits, the results resemble the baseline, but uniqueness and stability of the balanced growth path require stronger conditions.

“The results in this case are similar, but the conditions for uniqueness and stability of the balanced growth path are more demanding.”

May combine two claims.

In the task-based framework, automation is always capital-biased, reducing both the wage-rental ratio and the labor share.

“here automation is always capital-biased (that is, it reduces both W/R and the labor share)”

Classified as probably not a substantial claim. May combine two claims.

All qualitative results remain true and are proved under the more general Assumption 2′.

“All of our qualitative results remain true and will be proved under this more general assumption.”

• AssumptionThe authors state this as an assumption: Assumption 2′: one of the following holds: (i) η→0, or (ii) ζ=1, or (iii) γ(N−1)/γ(N) 2+2σ+η > |σ−ζ|.

May combine two claims.

Lemma A2 part 1: If ρ∈[ρ_min,ρ], there is a decreasing function n(ρ) such that for all n>n(ρ), w_I(n)>ρ+δ+θg>w_N(n), and ρ+δ+θg=w_N(n(ρ)); n(ρ_min)=1 and n(ρ)=0.

“If ρ ∈ [ρ min , ρ], there is a decreasing function n(ρ) : [ρ min , ρ] → (0, 1] such that, for all n > n(ρ) we have w I (n) > ρ + δ + θg > w N (n), and ρ + δ + θg = w N ( n(ρ)).”

May combine two claims.

In the interior equilibrium, automated tasks are eventually but not immediately produced with capital, with n*(t)=n(ρ)>n(t).

“Interior equilibrium in which automated tasks are eventually but not immediately produced with capital: n * (t) = n(ρ) > n(t).”

May combine two claims.

If ρ < ρmin, then for all n in [0,1], wI(n) ≥ wN(n) > ρ+δ+θg, so new tasks do not raise aggregate output and are not adopted.

“4. If ρ < ρ min , for all n ∈ [0, 1] we have w I (n) ≥ w N (n) > ρ + δ + θg, which implies that new tasks do not increase aggregate output and will not be adopted for any n ∈ [0, 1].”

May combine two claims.

Controlling for demographic trends and average years of schooling reduces the coefficient of new job titles but leaves it highly significant, and the estimated contribution of new job titles is 6.62% of the 17.5% growth from 1980 to 2007.

“Although this covariate reduces the magnitude of the coefficient of the share of new job titles, our estimate for β remains highly significant.The contribution of new job titles is now estimated at 6.62% out of the 17.5% growth between 1980 and 2007.”

May combine two claims.

When σ_const is at most 1, ω increases with n, and n also raises employment.

“Because ∂ω ∂N > 0 and w ′ I (n) > 0, we have that, whenever σ const ≤ 1, ω is increasing in n.Moreover, because the BGP level of employment is given by the increasing function L LR (ω), n raises employment too.”

May combine two claims.

For n below n(ρ), v_I(n) is positive while v_N(n) is negative, v_I decreases with n, and v_N increases with n.

“Because w N (n)e gτ > ρ + δ + θg and w I (n)e gτ > ρ + δ + θg for all τ ≥ 0, it follows that, in this region, v I (n) > 0 > v N (n) as claimed.Moreover, the derivatives for w I (n) and w N (n) in equation (A7) imply that, in this region, both w I (n) and w N (n) are decreasing in n.Thus, in this region, v I (n) is decreasing and v N (n) is increasing in n.”

May combine two claims.

Reweighting the data by the 1980 employment share weakens the relationship between new job titles and employment growth, making it statistically insignificant, and this insignificance is driven by a few large outlier occupations.

“This weakens the relationship of interest, and the share of novel tasks and jobs is no longer statistically significant.However, this lack of significance is driven by a few large occupations that are outliers in the estimated relationship.”

May combine two claims.

There exists a positive threshold S_2 such that for S below S_2, κ_N v_N(n) exceeds κ_I v_I(n), which is positive, and v_I(n) is of order g.

“Thus, there exists S 2 > 0 such that for S < S 2 , κ N v N (n) > κ I v I (n) > 0 as claimed, and v I (n) = O(g).”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Under Assumption 4, the demand for intermediates increases with both capital and labor, so X_K and X_L are positive.

“Moreover, we have X K , X L > 0-that is, the demand for intermediates increases with K and L.”

• AssumptionThe authors state this as an assumption: Assumption 4 holds, imposing σ > ζ and ensuring that capital and labor are complements to intermediates.

The quote only partly states this claim.

When θ = 0, the balanced growth path is globally saddle-path stable.

“We now analyze the stability properties of the system and show that the BGP is globally saddlepath stable.”

• AssumptionThe authors state this as an assumption: Assumptions 1', 2', and 4 hold.

May combine two claims.

If ξ<1, in the unique BGP, W_H/W_L diverges to infinity, the share of tasks performed by low-skill workers converges to zero, and capital and high-skill workers perform a constant share of tasks.

“If ξ < 1, in the unique BGP we have lim t→∞ W H (t)/W L (t) = ∞, the share of tasks performed by low-skill workers converges to zero, and capital and high-skill workers perform a constant share of tasks.”

May combine two claims.

Controlling for log employment at the start of the decade raises the coefficient of interest to 0.560, and the estimated contribution of new tasks and job titles to growth is 9.8%.

“The coefficient of interest increases slightly to 0.560 and continues to be precisely estimated.The log of employment at year t appears with a negative coefficient, which indicates that smaller occupations tend to grow more over time.The quantitative contribution of new tasks and job titles remains very similar to column 1, increasing slightly to 9.8%.”

May combine two claims.

Under the conditions of Lemma A3, when n is at most n(ρ) and ρ exceeds ρ, κ_N v_N(n) is greater than κ_I v_I(n), and κ_I v_I(n) is O(g).

“if n ≤ n(ρ) (and ρ > ρ), we have κ N v N (n) > κ I v I (n) = O(g)”

• AssumptionThe authors state this as an assumption: Assumptions 1', 2', and 4 hold.

The quote only partly states this claim.

Excluding the three outlier occupations from the weighted regression produces a pattern similar to the specification that controls for demographics and schooling.

“In column 6, we exclude these three occupations from our analysis, and obtain a similar pattern to that of column 4.”

May combine two claims.

Under the conditions of Lemma A3, when n is below n(ρ) and ρ is below ρ, κ_I v_I(n) is positive while κ_N v_N(n) is negative; in this region v_I(n) decreases with n and v_N(n) increases with n.

“If n < n(ρ) (and ρ < ρ), we have κ I v I (n) > 0 > κ N v N (n). Moreover, in this region, v I (n) is decreasing and v N (n) is increasing in n.”

• AssumptionThe authors state this as an assumption: Assumptions 1', 2', and 4 hold.

May combine two claims.

If ξ=1, in the unique BGP W_H and W_L grow at the same rate as the economy, the wage gap W_H/W_L remains constant, and capital, low-skill and high-skill workers perform constant shares of tasks.

“If ξ = 1, in the unique BGP W H (t) and W L (t) grow at the same rate as the economy, the wage gap, W H (t)/W L (t), remains constant, and capital, low-skill and high-skill workers perform constant shares of tasks.”

May combine two claims.

With labor market frictions, the welfare effect of automation is ambiguous, while the welfare effect of new tasks is positive.

“Then: dW dI = Ce -ν(L) 1-θ F I F -L W C -ν ′ (L) ε L ω ∂ω ∂I * ≶ 0. dW dN = Ce -ν(L) 1-θ F N F + L W C -ν ′ (L) ε L ω ∂ω ∂N > 0.”

• AssumptionThe authors state this as an assumption: Assumptions 1, 2, and 3 hold, and I* = I > I, for the welfare analysis in Proposition 9.

May combine two claims.

When σ_const is greater than 1, ω increases with n, and n also raises employment.

“Because ∂ω ∂I * < 0 and w ′ N (n) < 0, we have that, whenever σ const ≥ 1, ω is increasing in n.Moreover, because the BGP level of employment is given by the increasing function L LR (ω), n raises employment too.”

May combine two claims.

Lemma A1: If Assumption 2' holds, ω(I*,N,K) is decreasing in I* and increasing in N.

“Lemma A1 If Assumption 2 ′ , ω(I * , N, K) is decreasing in I * and is increasing in N .”

May combine two claims.

Without labor market frictions, welfare increases with both automation and the creation of new tasks.

“Then: dW dI = Ce -ν(L) 1-θ F I F > 0, dW dN = Ce -ν(L) 1-θ F N F > 0.”

• AssumptionThe authors state this as an assumption: Assumptions 1, 2, and 3 hold, and I* = I > I, for the welfare analysis in Proposition 9.

May combine two claims. The quote only partly states this claim.

Lemma A2 part 2: If ρ∈[ρ,ρ_max], there is an increasing function n(ρ) such that for all n>n(ρ), w_I(n)>ρ+δ+θg>w_N(n) and ρ+δ+θg=w_I(n(ρ)); n(ρ_max)=1 and n(ρ)=0.

“If ρ ∈ [ρ, ρ max ], there is an increasing function n(ρ) : [ρ, ρ max ] → (0, 1] such that, for all n > n(ρ) we have w I (n) > ρ + δ + θg > w N (n) and ρ + δ + θg = w I (n(ρ)).”

May combine two claims.

Around g equal to zero, the system of differential equations is Lipschitz continuous, with bounded derivatives around the balanced growth path.

“Around g = 0, the above system of differential equations is Lipschitz continuous (on their righthand side, the equations for ċ, k, ṅ and v have bounded derivatives around the BGP {c B , k B , n B , v B }.”

May combine two claims.

The only possible BGP has k(t)=kB, c(t)=cB, and L(t)=LB>0; it satisfies transversality and is the unique BGP.

“Hence, the only possible BGP is one in which k(t) = k B , c(t) = c B and L(t) = L B > 0.Moreover, in view of the fact that ρ + (θ -1)A∆ > 0, this candidate BGP satisfies the transversality condition (19), and is indeed the unique BGP.”

May combine two claims.

When the labor market is fully competitive, automation increases overall welfare because productivity gains raise welfare and reduced employment has no first-order welfare cost.

“When the labor market is fully competitive as in our baseline model, this reduction in employment has no first-order welfare cost for the representative household (which was previously setting the marginal cost of labor supply equal to the wage).As a result, automation increases overall welfare.”

Classified as probably not a substantial claim.

In the all-labor case, all tasks are always produced with labor, so n*(t)=1.

“All tasks are always produced with labor: n * (t) = 1.”

The quote only partly states this claim.

Under Assumptions 1′, 2′′, and 4, there exists S such that when S<S, for ρ<ρ there is a BGP with n(t)=0 and all tasks produced with capital.

“1 (Full automation) For ρ < ρ, there is a BGP in which n(t) = 0 and all tasks are produced with capital.”

May combine two claims.

Induced capital accumulation makes automation's impact on the labor share worsen over time if σconst > 1 and ease if σconst < 1.

“The induced capital accumulation implies that the impact of automation on the labor share worsens over time if σ const > 1 and eases if σ const < 1.”

May combine two claims.

When the automation-to-new-task innovation ratio is below the lower threshold, the automation value curve is not steep enough relative to the new-task curve, the curves never intersect, automation is unprofitable even at n equal to one, all tasks use labor, capital is redundant, and growth comes from labor-augmenting endogenous technology.

“When κ I κ N < κ, κ I v I (n) is not sufficiently steep relative to κ N v N (n), and the two never intersect.This means that even at n = 1, it is not profitable to create new automation technologies, and all tasks will be produced with labor.In this BGP, capital becomes redundant, and growth is driven by endogenous technological change increasing labor's productivity as in the standard quality l”

• cites Aghion and Howitt, 1992Not checked yet

  Not checked in the free run.

• cites Grossman and Helpman, 1991Not checked yet

  Not checked in the free run.

May combine two claims.

The short-run effect of new tasks on the rental rate of capital is ambiguous, so the capital accumulation response is also ambiguous.

“Because the short-run impact of new tasks on the rental rate of capital is ambiguous, so is the response of capital accumulation.”

May combine two claims. The quote only partly states this claim.

Stability comes from factor prices guiding technological direction: greater automation lowers the profitability of further automation, while the productivity effect makes new-task value rise with n, and the upper-threshold condition makes the automation value curve steeper.

“The critical economic force generating stability is that, as noted above, it is factor prices that guide the direction of technological change.”

May combine two claims.

Not all shocks leave labor's long-run prospects unchanged; with multiple steady states or changes such as a large rise in B or a fall in rho, the economy can shift to full automation with disastrous consequences for labor.

“This does not, however, imply that all shocks will leave the long-run prospects of labor unchanged.For one, this would not necessarily be the case in a situation with multiple steady states, and certain changes in the environment (for example, a large increase in B or a decline in ρ), can shift the economy from the region in which there is a unique interior BGP to the region with full automation,”

May combine two claims.

If zeta exceeds sigma, technologies working with more expensive factors are more profitable, and the present discounted values from innovation are negative.

“When the opposite holds and ζ > σ, we have the paradoxical situation where technologies that work with more expensive factors are more profitable, and consequently, in this case the present discounted values from innovation is negative.”

May combine two claims.

When rho is below the critical value, for n below the threshold it is not optimal to create new tasks, so a full-automation BGP exists and labor becomes redundant.

“Panel A of Figure 8 illustrates the first part of Proposition 6 (which parallels the first part of Proposition 4): when ρ < ρ, κ I v I (0) is above κ N v N (0) for n < n(ρ).In this region it is not optimal to create new tasks.Consequently, there exists a BGP with full automation, meaning that all tasks will be automated and produced with capital.”

May combine two claims.

v_N(n) also rises with n because w_N(n) falls with n due to the productivity effect and the constant long-run rental rate.

“However, v N (n) is also increasing in n because, as explained in the previous section, w N (n) is decreasing in n owing to the productivity effect and the fact that the rental rate is constant in the long run.”

Classified as probably not a substantial claim. May combine two claims.

The assumption that sigma exceeds zeta ensures innovations are directed toward technologies using cheaper factors and that the present discounted values from innovation are positive.

“This ensures that innovations are directed towards technologies that allow firms to produce tasks by using the cheaper (or more productive) factors, and consequently, that the present discounted values from innovation are positive.”

• AssumptionThe authors state this as an assumption: Assumption 4: sigma is greater than zeta.

May combine two claims.

Automation also has a negative displacement effect: it shrinks the range of tasks done by labor, and concentrating workers in fewer tasks pushes wages down.

“This negative effect occurs because automation contracts the set of tasks performed by labor.Because tasks are subject to diminishing returns in the aggregate production function, (1), bunching workers into fewer tasks puts downward pressure on the wage.”

May combine two claims.

Faster automation relative to new task creation may come from faster I growth, producing stagnant or lower short-run wages while capital adjusts, or from slower N growth, producing low output and wage growth.

“Faster automation relative to the creation of new tasks might be driven by an acceleration in the rate at which I(t) advances, in which case we would have stagnant or lower wages in the short run while capital adjusts to a new higher level.Alternatively, it might be driven by a deceleration in the rate at which N (t) advances, in which case we would also have low growth of aggregate output and w”

May combine two claims.

Automation creates a positive productivity effect: cheaper capital replaces expensive labor, raising productivity and labor demand in tasks not yet automated.

“On the one hand, there is a positive productivity effect captured by the term d ln Y | K,L : by substituting cheaper capital for expensive labor, automation raises productivity, and hence the demand for labor in the tasks that are not yet automated.”

May combine two claims.

When rho exceeds the critical value, at n equal to zero or below the threshold the automation value curve lies below the new-task value curve, so full automation is impossible and any BGP must profitably create new labor-intensive tasks.

“In this case, at n = 0 (or at any n ≤ n(ρ)), κ I v I (n) is strictly below κ N v N (n), and thus a full automation BGP is not possible, and the two curves can only intersect for n ∈ (n(ρ), 1], implying that in any BGP, utilizing and creating new labor-intensive tasks will be profitable.”

May combine two claims.

If the elasticity of substitution is below one, capital accumulation softens but does not fully offset the short-run fall in the labor share; if it is above one, capital accumulation further lowers the labor share even though it raises the wage.

“If σ < 1, the resulting capital accumulation mitigates the shortrun decline in the labor share but does not fully offset it (this is the case depicted in the figure).If σ > 1, capital accumulation further depresses the labor share-even though it raises the wage.”

May combine two claims.

Automation lowers long-run employment and the labor share but always raises the long-run equilibrium wage.

“Automation reduces employment and the labor share in the long run, but always increases the long-run equilibrium wage.”

May combine two claims.

A permanent increase in N raises the wage, aggregate output, employment, and the labor share in both the short run and the long run.

“In this case, new tasks increase the wage (because w I (n) is increasing in n), aggregate output, employment, and the labor share, both in the short and the long run.”

May combine two claims.

In the task-based framework, automation can raise productivity while at the same time lowering wages.

“The fact that automation may increase productivity while simultaneously reducing wages is a key feature of the task-based framework developed here.”

May combine two claims.

When the automation-to-new-task innovation ratio is above the upper threshold, the automation value curve is steep enough relative to the new-task curve, the curves intersect exactly once, and there is a unique interior BGP with n strictly between zero and one.

“Conversely, when κ I κ N > κ, the curve κ I v I (n) is sufficiently steep relative to κ N v N (n) so that the two curves necessarily intersect and can only intersect once.Hence there exists a unique interior BGP (interior in the sense that now the BGP level of n is strictly between 0 and 1, and thus some tasks are produced with labor and some with capital).”

May combine two claims.

If occupations with more new job titles had not grown faster than occupations with no novel jobs, employment growth from 1980 to 2007 would have averaged 8.66% instead of the actual 17.5%, implying that about 8.84% of the 17.5% growth is accounted for by new job titles.

“If occupations with more new job titles did not grow any faster than the benchmark category with no novel jobs, employment growth from 1980 to 2007 would B-1 have been, on average, 8.66% instead of the actual 17.5%, implying that approximately 8.84% of the 17.5% growth is accounted for by new job titles”

May combine two claims.

When employment is below its unconstrained optimum, the planner values new tasks more and automation less.

“Thus, when the level of employment is below its unconstrained optimum, the planner values the introduction of new tasks more because they raise the marginal product of labor and ease the constraint on total employment.Likewise, the planner values automation less because she recognizes that by reducing employment automation has a first-order cost on workers.”

May combine two claims.

With creative destruction, v_CD_I(n) is decreasing in n, so automating tasks makes further automation more profitable.

“Unlike the previous case with no creative destruction, we now have that v CD I (n) is decreasing in n.As more tasks are automated, the rental rate remains unchanged and newlyautomated tasks will be replaced less frequently”

• AssumptionThe authors state this as an assumption: New technologies do not infringe the patents of the products they replace.

May combine two claims.

The market does not recognize the first-order costs of automation or the first-order benefits of new tasks; only factor prices determine the incentives to introduce these technologies.

“Importantly, the market does not recognize the first-order costs from automation or the first-order benefits from introducing new tasks.As the expressions for V N and V I show, only factor prices-not the extent of frictions in the labor market-determine the incentives to introduce these technologies.”

May combine two claims.

When ρ exceeds ρ and n(t) is at most n(ρ), all scientists are employed to create new tasks, so ṅ is positive and bounded away from zero, which contradicts n(t) < n(ρ).

“Therefore, in this region this region we always have that all scientists will be employed to create new tasks, and thus ṅ > 0 (and is uniformly bounded away from zero).But this contradicts n(t) < n(ρ).”

• AssumptionThe authors state this as an assumption: Assumptions 1', 2', and 4 hold.

May combine two claims. The quote only partly states this claim.

When ξ<1, both automation and creation of new tasks increase inequality, with automation displacing low-skill workers ahead of high-skill workers and new tasks directly benefiting high-skill workers.

“When ξ < 1, this extension confirms the pessimistic scenario about the implications of new technologies for wage inequality and the employment prospects of low-skill workers-both automation and the creation of new tasks increase inequality”

Classified as probably not a substantial claim.

Under Assumption 1'', because Γ is increasing, low-skill worker productivity in a task is greater the longer the task has existed.

“because Γ is increasing, it implies that the productivity of low-skill workers in a task is greater when that task has been in existence for longer.”

May combine two claims. The quote only partly states this claim.

When labor market frictions are present and the direction of technological change is endogenized, there is a force toward excessive automation; the decentralized equilibrium devotes too much effort to improving automation relative to the social planner.

“when labor market frictions are present and the direction of technological change is endogenized, there will be a force towards excessive automation.”

• AssumptionThe authors state this as an assumption: Labor market frictions also constrain the social planner's choices.

May combine two claims.

When ρ is below ρ and n is below n(ρ), the only possible balanced growth path in that region has n(t) = 0, and no interior balanced growth path exists with n between 0 and n(ρ).

“Thus, the only possible BGP in this region must be one with n(t) = 0.No interior BGP exists with n ∈ (0, n(ρ)).”

• AssumptionThe authors state this as an assumption: Assumptions 1', 2', and 4 hold.

May combine two claims.

When ξ=1, automation increases inequality in both short and long run, while creation of new tasks that permanently lowers n increases inequality in short run but reduces it in long run.

“Consequently, automation increases inequality both in the short and the long run, while the creation of new tasks that leads to a permanently lower level of n increases inequality in the short run, but reduces it in the long run.”

May combine two claims.

A permanent increase in N raises the wage gap in the short run but reduces it in the long run, while a permanent increase in I raises the wage gap both in the short and long run.

“Consequently, a permanent increase in N raises the wage gap W H (t)/W L (t) in the short run, but reduces it in the long run, while a permanent increase in I raises the wage gap both in the short and the long run.”

May combine two claims.

Under Assumption 1'' and ξ∈(0,1], the ratio of low-skill to high-skill productivity is increasing in task index, implying high-skill workers have a comparative advantage in higher-indexed tasks.

“Second, because of standardization and the assumption that ξ ∈ (0, 1], the ratio ,t) is increasing in i.This implies that high-skill workers have a comparative advantage in higher-indexed tasks, as these tasks have had little time to be standardized.”

May combine two claims.

When ρ is below ρ, a technology path with n(t) = 0 yields balanced growth, all tasks are produced with capital, V_I and V_N are zero, and this path is consistent with the equilibrium allocation of scientists, so the resulting balanced growth path is an equilibrium with endogenous technology.

“Proposition 4 shows that for ρ < ρ, a path for technology with n(t) = 0 yields balanced growth.Moreover, along this path all tasks are produced with capital, which implies that V I (t) = V N (t) = 0. Thus, a path for technology in which n(t) = 0 is consistent with the equilibrium allocation of scientists.The resulting BGP is an equilibrium with endogenous technology.”

• cites Proposition 4Not checked yet

  Not checked in the free run.

• AssumptionThe authors state this as an assumption: Assumptions 1', 2', and 4 hold.

May combine two claims. The quote only partly states this claim.

With creative destruction, v_CD_N(n) is increasing in n because the effective wage in new tasks is decreasing in n and an increase in n raises the present discounted value of profits from new tasks.

“Moreover, v CD N (n) continues to be increasing in n.This is for two reasons: first, as before, the productivity effect ensures that the effective wage in new tasks, w N (n), is decreasing in n”

• AssumptionThe authors state this as an assumption: New technologies do not infringe the patents of the products they replace.

Probably not a substantial claim: may not pass S3 (load-bearing).

The relationship depicted in Figure 1 is robust.

“Additional information on the data and our sample is provided in Appendix B, where we also document in detail the robustness of the relationship depicted in Figure1.”

May combine two claims. The quote only partly states this claim.

When ρ exceeds ρ, an interior balanced growth path requires n(t) = n, and each interior balanced growth path corresponds to a solution of equation (29) in the interval (n(ρ), 1).

“Thus, a necessary and sufficient condition for an interior BGP is (29) in the text.Consequently, each interior BGP corresponds to a solution to this equation in (n(ρ), 1).”

• AssumptionThe authors state this as an assumption: Assumptions 1', 2', and 4 hold.

Probably not a substantial claim: may not pass S3 (load-bearing).

Following Acemoglu (2003), a binding minimum wage indexed to income can also yield a quasi-labor supply curve.

“Following Acemoglu (2003), another way in which we could obtain a quasilabor supply curve is if there is a binding minimum wage.”

• cites Acemoglu (2003)Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

An efficiency-wage model provides a micro-foundation for the quasi-labor supply expression used in the main text.

“Efficiency wages: Our first micro-foundation relies on an efficiency wage story.”