Joao Guerreiro (Northwestern University), Sergio Rebelo (Northwestern University, NBER and CEPR), Pedro Teles (Católica-Lisbon School of Business & Economics, Banco de Portugal and CEPR)

1. 1/56
Should Robots Be Taxed?
Joao Guerreiro, Sergio Rebelo, and Pedro Teles
November 2017
Should Robots Be Taxed? Joao Guerreiro, Sergio Rebelo, and Pedro Teles

2. Should robots be taxed?
A rise in automation will increase income inequality by eliminating the
jobs of routine workers.
Is there a role for policy?
Develop model with heterogeneous households: routine and
non-routine.
Perform optimal policy exercises.
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3. Outline
1. Model of automation
Static model. Dynamic considerations discussed at the end
2. Equilibrium with current tax system (status-quo equilibrium)
3. First-best solution
4. Mirrleesian second-best solution
5. Optimal policy with simple income taxes
6. Welfare comparison
7. Endogenous occupational choice
8. Relation to public finance literature
9. Conclusion
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4. 4/56
Model
Should Robots Be Taxed? Joao Guerreiro, Sergio Rebelo, and Pedro Teles

5. Model of automation
Two representative households,
One with routine workers, j = r,
The other with non-routine workers, j = n.
Preferences
Uj = u(Cj ) − v(Nj ) + g(G),
Cj = consumption, Nj = hours worked, G = government spending.
Budget constraint
Cj ≤ wj Nj − T(wj Nj ),
wj =wage rate worker type j,
T(·) = income tax schedule.
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6. Robot producers
Robots are an intermediate input. Final good producers can use
robots in tasks i ∈ [0, 1].
Robots for each task i are produced by competitive firms.
Cost of producing a robot φ units of output. Identical across tasks.
Problem of firm that produces robots to automate task i is
πi = max
xi
pi xi − φxi .
It follows that
pi = φ.
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7. Final good producers
A representative firm hires non-routine labor (Nn).
For each task i, hire routine labor (ni ) or buy intermediate goods (xi )
which we refer to as robots.
Production function:
Y = A
m
0
xρ
i di +
1
m
nρ
i di
1−α
ρ
Nα
n ,
CES aggregator for tasks and Cobb-Douglas in tasks and non-routine
labor.
Each task may be produced by robots or routine workers (perfect
substitution).
Since tasks are symmetric, assume first m are automated, and last
(1 − m) use routine workers.
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8. Final good producers
Representative firm problem is to choose {xi , ni , m, Nn} to maximize
π = Y − wnNn − wr
1
m
ni di −
m
0
(1 + τx )φxi di.
τx = linear tax on robots.
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9. Final good producers
xi = x constant in [0, m].
ni = n constant in (m, 1].
If wr = (1 + τx )φ, there’s partial automation (m ∈ [0, 1]).
With partial automation the levels of routine labor and robots are the
same: x = n.
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10. Government
Government chooses
Income taxation, T(·).
Tax on robots, τx .
Government spending, G.
Budget constraint:
G ≤ T(wr Nr ) + T(wnNn) +
m
0
τx φxi di.
Tax schedule is the same for both types of workers.
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11. Market clearing
Routine labor:
1
m
ni di = Nr .
Output market:
Cr + Cn + G ≤ A
m
0
xρ
i di +
1
m
nρ
i di
1−α
ρ
Nα
n −
m
0
φxi di.
Cost of robot production subtracted from final output.
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12. Competitive equilibrium
The share of production of non-routine workers is the same as with a
Cobb-Douglas production function
wnNn
Y
= α.
But for routine workers it is multiplied by (1 − m)
wr Nr
Y
= (1 − α)(1 − m).
An increase in automation increases pre-tax income inequality
Reduces the income share of routine workers,
Keeps constant income share of non-routine workers.
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13. With partial automation
With partial automation, total routine labor supplied is split equally
by 1 − m non-automated tasks:
ni =
Nr
1 − m
, for i ∈ (m, 1] ,
Robots in the first m tasks are used at the same level.
Equilibrium level of automation is
m = 1 −
(1 + τx )φ
(1 − α)A
1/α
Nr
Nn
.
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14. With partial automation
Wage rates are given by technological parameters (independent of
preferences)
wn = α
A1/α(1 − α)
1−α
α
[(1 + τx )φ]
1−α
α
,
wr = (1 + τx )φ.
Tax on robots increases wage of routine, but decreases wage of
non-routine.
In that way, this instrument affects the relative wage.
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15. 15/56
Status-quo equilibrium
Should Robots Be Taxed? Joao Guerreiro, Sergio Rebelo, and Pedro Teles

16. Status-quo equilibrium
Heathcote, Storesletten and Violante (2014) propose after-tax income
function
y(wj Nj ) = λ(wj Nj )1−γ
,
T(wj Nj ) = wj Nj − λ(wj Nj )1−γ
.
λ controls the level of taxation (higher λ implies lower average taxes).
γ controls the progressivity of the tax code (γ > 0 implies
progressivity).
HSV estimates using PSID data
γ = 0.185 (income taxes close to linear),
R2
is 0.92.
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17. Status-quo equilibrium
Functional form for utility function:
Uj = log(Cj ) + θ log(1 − Nj ) + χ log(G).
θ = 1.63, which implies Nj = 1/3.
χ = 0.25.
Policy:
Government sets its spending to 20 percent of output
Sets γ = 0.185 and adjusts λ to balance budget
Robots are not taxed, τx = 0.
Production parameters:
A = 1, α = 0.5 (symmetry).
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18. Status-quo equilibrium
Only non-routine workers benefit from automation.
Consumption of routine workers goes to zero.
Full automation never occurs.
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19. 19/56
First-best allocation
Should Robots Be Taxed? Joao Guerreiro, Sergio Rebelo, and Pedro Teles

20. First-best allocation
Planner maximizes average utility
V =
1
2
Ur +
1
2
Un,
Possible interpretation: ex-ante, workers do not know whether they are
routine or non-routine, planner maximizes expected utility.
subject to resource constraints
Cr + Cn + G ≤ Y − φ
m
0
xi di,
Y = A
m
0
xρ
i di +
1
m
nρ
i di
1−α
ρ
Nα
n ,
1
m
ni di = Nr .
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21. First-best allocation
Agents have equal consumption in the first best.
More productive agents work more.
⇒ When types are not observable, this allocation cannot be
implemented
High productivity agents would pretend to be low productivity.
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22. First-best allocation
Routine workers have higher utility than non-routine.
Routine workers always benefit from automation.
Non-routine workers eventually benefit.
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23. First-best allocation
While interesting as a benchmark, the first best is not implementable
when there are restrictions on the tax system.
For that reason we will turn to plans that satisfy restrictions:
Informational restrictions, in the spirit of Mirrlees (1971);
Instrument restrictions, in the tradition of Ramsey (1927).

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Mirrleesian optimal taxation
Should Robots Be Taxed? Joao Guerreiro, Sergio Rebelo, and Pedro Teles

25. Mirrleesian optimal taxation
Government does not observe agent’s type or labor supply.
Government observes an agent’s total income. Incentive compatible
income taxation.
Robot taxes are assumed to be proportional, τx .
Guesnerie (1995): non-linear taxes on intermediate inputs create
arbitrage opportunities. Difficult to implement.
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26. Mirrleesian optimal taxation
In Mirrlees (1971) differences in agents’ productivities are exogenous.
In our model, productivity differences are endogenous and depend on
τx .
Key question: is it optimal to distort production decisions by taxing
the use of robots to redistribute income from non-routine to routine
workers to increase social welfare?
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27. Mirrleesian optimal taxation
Planner’s problem:
W (τx ) = max
1
2
[u(Cr ) − v (Nr ) + g(G)]
+
1
2
[u(Cn) − v (Nn) + g(G)] ,
subject to resource constraint
Cr + Cn + G ≤ wnNn
τx + α
α(1 + τx )
+
wr Nr
1 + τx
.
and two incentive compatibility (IC) constraints
u(Cn) − v (Nn) ≥ u(Cr ) − v (wr Nr /wn) ,
u(Cr ) − v (Nr ) ≥ u(Cn) − v (wnNn/wr ) .
Optimal choice of τx requires W (τx ) = 0.
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28. Mirrleesian optimal taxation
Proposition
In the optimal plan, when automation is incomplete (m < 1) robot taxes
are strictly positive (τx > 0).
Increasing τx generates a first-order gain from loosening the
informational restriction of the non-routine worker:
u(Cn) − v(Nn) ≥ u(Cr ) − v
wr
wn
Nr .
If τx < 0, a marginal increase in τx is also in the direction of
production efficiency.
If τx = 0, a marginal increase in τx induces output losses, but only
second order.
A planner that chooses τx ≤ 0 can always improve its objective with a
marginal increase in τx .
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29. Mirrleesian optimal taxation - with full automation
With full automation, Yr = 0 and m = 1, the IC of the non-routine
worker becomes
u(cn) − v(nn) = u(cr )
Robot taxes no longer affect this constraint.
Routine and non-routine workers have the same utility.
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30. Mirrleesian optimal taxation
Modest levels of robot taxes. These become zero once routine workers
are replaced by robots.
With full automation agents have the same utility. Planner cannot
further transfer towards routine workers.
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Simple income tax systems
Should Robots Be Taxed? Joao Guerreiro, Sergio Rebelo, and Pedro Teles

32. Simple taxes
The Mirrleesian plan may be a big deviation from the income tax
systems that we observe in actual economies.
How close to the Mirrleesian second best can an empirically plausible
tax function take us?
Is there a simple modification of such tax system that would generate
a large improvement?
⇒ Restrictions on instruments - Ramsey tradition
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33. Simple taxes
Optimal tax policy when the tax schedule has form proposed by
Heathcote, Storesletten and Violante (2014)
T(wj Nj ) = wj Nj − λ(wj Nj )1−γ
,
With this formulation the ratio of consumptions is
Cr
Cn
=
(1 − α)(1 − m)
α
1−γ
.
Two ways to make ratio Cr /Cn closer to one.
Raise τx which leads to a fall in the level of automation, m.
Reduces production efficiency.
Make γ closer to one, i.e. make the tax system more progressive.
Reduces incentives to work.
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34. Simple taxes
Cr
Cn
=
(1 − α)(1 − m)
α
1−γ
.
The planner will balance making the system more progressive and
distorting m downwards.
Full automation is never optimal.
That would lead the routine worker to consume zero.
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35. Simple taxes
High taxes on robots = high production distortions.
Both agents eventually benefit from automation.
Full automation never occurs.
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36. Simple taxes
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37. Simple taxes with lump-sum transfers
The previous tax system leads to very high taxation of robots, large
production inneficiency.
Simple modification: allow for lump-sum rebates, Ω.
T(wj Nj ) = wj Nj − λ(wj Nj )1−γ
− Ω.
In this case, the ratio of consumptions is given by
Cr
Cn
=
[(1 − α)(1 − m)]1−γ + ω
α1−γ + ω
,
ω =
Ω
λY 1−γ
.
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38. Simple taxes with lump-sum transfers
Cr
Cn
=
[(1 − α)(1 − m)]1−γ + ω
α1−γ + ω
.
Lump-sum rebate helps redistributing income
Agents receive income even if they do not work
⇒ Full automation is possible.
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39. Simple taxes with lump-sum transfers
Full automation is recovered.
Robot taxes are zero after full automation (since Nr = 0 robot taxes do
not help redistribution).
The utility of routine gets closer to non-routine.
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40. Simple taxes with lump-sum transfers
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41. Welfare comparison - routine workers
How much would we have to increase consumption in the status-quo
with m = 0?
Status-quo is the only equilibrium where they are always hurt by
further automation.
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42. Welfare comparison - non-routine workers
Best equilibrium is status-quo, they are the only ones to benefit from
decreasing automation costs.
Apart from first best they are always better off by further automation.
First-best planner can induce non-routine to work more, and
temporarily lose with automation. 42/56

43. 43/56
Endogenous occupational choice
Should Robots Be Taxed? Joao Guerreiro, Sergio Rebelo, and Pedro Teles

44. Endogenous occupational choice
Suppose now that agents can move between occupations.
Household type θ has preferences over the two occupations.
u(Cθ) − v(Nθ) + g(G) − Oθθ.
Oθ = 1 if household becomes non-routine, and Oθ = 0 otherwise.
If θ < 0 the household prefers non-routine occupations.
If θ > 0 the household prefers routine occupations.
The agent receives the wage wn if he decides to become non-routine
and wr if he decides to become routine.
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45. Endogenous occupational choice
Agents choose both their occupation and the number hours worked.
There are two incentive constraints:
Intensive margin - labor supply IC
u(Cθ) − v(Nθ) ≥ u(Cθ ) − v
wθ
wθ
Nθ .
Extensive margin - occupation choice IC
u(Cθ) − v(Nθ) − Oθθ ≥ u(Cθ ) − v(Nθ ) − Oθ θ.
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46. Endogenous occupational choice
In the optimum, agents that choose the same occupation have the
same levels of consumption and hours of work.
The extensive margin incentive compatibility is summarized by a
threshold rule
θ∗
= [u(Cn) − v(Nn)] − [u(Cr ) − v(Nr )].
Agents with θ > θ∗
choose to be routine workers.
Agents with θ ≤ θ∗
become non-routine.
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47. Endogenous occupational choice
We assume that θ is drawn from a normal distribution with mean zero
and standard deviation σ.
Half of the population prefers non-routine work.
The other half prefers routine work.
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48. Endogenous occupational choice - First best
For lower σ: more agents become non-routine.
For lower σ: everyone works less and has higher consumption.
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49. Endogenous occupational choice - Mirrlees Optimal Taxes
When occupation switching costs are lower: redistribute by inducing
more agents to become non-routine.
There is less of a need to resort to robot taxes.
Worse deal for the remaining routine.
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50. Endogenous occupational choice - Mirrlees Optimal Taxes
With σ = 1, redistribution by moving agents to non-routine ⇒ More
non-routine than in first best.
With σ = 2, direct redistribution and more robot taxes ⇒ Less
non-routine than in first best.
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51. 51/56
Back to taxation of intermediate
goods
Should Robots Be Taxed? Joao Guerreiro, Sergio Rebelo, and Pedro Teles

52. Back to taxation of intermediate goods
Diamond & Mirrlees (1971)
Assumes that government can tax different goods at different rates.
In our model this assumption would allow taxing routine and
non-routine workers at different rates.
When direct tax discrimination is not possible, robots will be taxed
provided this helps treating different agents differently.
Atkinson & Stiglitz (1976)
Assumes that labor types are perfect substitutes.
This implies that intermediate goods do not interact differently with
different labor types.
These assumptions do not hold in our model.
Robots are substitutes for routine workers and complements for
non-routine workers.
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53. Robots as capital
Robots are durable goods.
Taxing robots creates intertemporal distortions, in addition to
production inneficiency.
Intertemporal distortions might be optimal for reasons orthogonal to
the ones studied in this paper:
To confiscate the initial stock, if the set of tax instruments is limited.
Because the elasticities of the marginal utility of consumption and
labor are time varying.
With idiosyncratic risks, there may be insurance motives.
As a capital good, robots would be taxed by a capital income tax
without full deduction of investment.
South Korea will limit tax incentives for investment in automated
machines, as part of a revision of tax laws. Effective begining of 2018.
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54. Conclusions
With current U.S. tax system, a sizable fall in automation costs leads
to large rise in income inequality.
Routine-worker wages fall to make them competitive with automation.
Only non-routine workers benefit from advances in automation.
Full automation never occurs: routine workers always supply labor as
their income and consumption approach zero.
Inequality can be reduced by raising marginal tax rates paid by
high-income individuals and by taxing robots to raise the wages of
routine workers.
Eventually both agents benefit from advances in automation.
Full automation never occurs.
This solution involves a substantial efficiency loss.
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55. Conclusions
Mirrleesian optimal income tax can reduce inequality at a smaller
efficiency cost.
Lower taxes on robots.
Full automation occurs for relatively high automation costs.
However, this tax system can be complex and difficult to implement.
Simpler approach with large gains: amend tax system to include
lump-sum rebates.
Solution get closer to Mirrleesian solution.
When costs of automation are sufficiently low, routine workers stop
working and live off transfers.
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56. Conclusions
With endogenous occupational choice:
The planner can switch agents between occupation to redistribute.
For lower switching costs:
More agents change to non-routine occupations
There is less of a role for robot taxes.
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