Imposición Óptima Teoría y Aplicación - aaep.org.ar · Imposición Óptima Teoría y Aplicación Iván Werning, MIT Conferencia Rolf Mantel Tucumán, Noviembre, 2016 Reunión

Imposición Óptima Teoría y Aplicación

Iván Werning, MIT

Conferencia Rolf Mantel Tucumán, Noviembre, 2016

Reunión de la Asociación Argentina de Economía Política

Impuestos ÓptimosImpuestos…

intervención estatal del mercado por excelenciaefectos…

distorsiones vs. redistribucióncompensar fallas de mercado

Hoy: desigualdad en aumento ¿mayor redistribución? Vasta literatura sobre impuestos óptimos…

teoría relacionada…equilibrio generaldiseño de mecanismos

medición y estimación de elasticidades

Hoy: repaso de la teoría tradicional y más reciente (en el margen, comparación con impuestos en Argentina)

Impuestos: un tema muy cargado políticamente e ideológicamente¿Qué puede aportar la teoría de impuestos óptimos?

Impuestos Óptimos

Impuestos: un tema muy cargado políticamente e ideológicamente¿Qué puede aportar la teoría de impuestos óptimos?

Imposible: resolver todos los conflictos y desacuerdosFactible…

aclarar conceptos básicos sugerir qué medir: interacción entre teoría y trabajo empíricoacercar posiciones y permitir debate más informado

recomendar un menú de opciones razonables en vez de dictar “óptimo”ciudadano vs. economista

Impuestos Óptimos

Introduction❖ Introduction❖Motivation❖Contribution❖Results

Model

Main Results

Applications

Conclusions

Pareto Efficient Income Taxation - p. 4

Pareto Frontier

vH

vL

VH+ VL

Hoja de Ruta

sofisticacióninstrumentosimpositivos

sofisticaciónmodelo

lineal nonlinear diseño demecanismos

estático

dinámico

incertidumbre

fricciones de mercado

DiamondMirrlees

Chamley Judd

Mirrlees

New DynamicPublic FinanceSimulaciones

Politica Fiscal Ciclica y Políticas Macroprudenciales

= mi investigación con diferentes colaboradores: Farhi, Schuer, Straub

compromiso perfecto

inconsistencia temporal

economia politica

normativo vs. positivo

Diamond-MirrleesModelo de equilibrio generalImpuestos linealesDos casos…

agente representativo + sin impuesto de suma fija (Ramsey)agentes heterogeneous + impuesto suma fija

Diamond-MirrleesEstado

(impuestos t=q-p)Firmas

(precios p)

Consumidores/Trabajadores

(precios q)

Diamond-MirrleesResultado #1. Producción Eficiente, en la frontera de producción:

Implicancias…no distorsionar bienes intermediosno influir en decisiones tecnológicas e.g. Robots producción Estatal a mismos precios que privadaapertura comercial is óptima, aun con efectos distributivos

Intuicióntecnología con rendimientos constantes a escala firmas sin rentas extraordinarias;única distorsión entre Estado y consumidores

Argentina: Producción Eficiente?IVAImpuestos al trabajo y aportesGananciasBienes personales

Impuesto al Ingresos BrutosImpuesto al cheque Aranceles y trabas al comercio internacionalTrabas y regulaciones a la adopción tecnológicaSubsidios a energíaSubsidios regionales ?

Resultado #2. Formula…

Elasticidad inversa si… … escasa utilidadIntuición: aumento proporcional

Diamond-Mirrlees

(indice de disuasión) (efecto redistributivo)

Impuestos UniformesResultado #3. Impuestos uniformes

punto de referencia útil pero homoteticidad le quita aplicabilidad

Atkinson-Stiglitz: Con un impuesto no lineal (flexible) sobre misma conclusion sin homoteticidad de G.

subutilidad homotética

ArgentinaEspeciales: autos, telefonos, combustibles, cigarrillos, alcohol IVA

regular 21%aumentada 27% (agua, electricidad, gas natural)reducidas 10.5% (carne, frutas, harinas)exentos: libros, leche, medicamentos, comedores escolares

Incidencia distributiva resultados mixtos (Artana et al)innecesarios si aplican resultados anteriores

¿Se aplica Atkinson-Stiglitz?Ganancias es un impuesto no-lineal…… pero de limitada participación… inflexibilidad politica?

Devolución del 15% del IVA (impuesto no lineal)




estático

dinámico

incertidumbre


DiamondMirrlees

Chamley Judd

Mirrlees



MirrleesDos bienes

consumotrabajo (en unidades efectivas)

Heterogeneidad en capacidades de trabajo (via preferencias)

Distribution continua Tecnologia lineal

MirrleesImpuesto no-lineal al trabajoRestricción presupuestaria de agentes:

Pregunta: ¿cuál es el T óptimo?método tradicional: programación dinámica via control optimoScheuer-Werning (2016): aplicación de Diamond-Mirrlees! Truco: tratar cada nivel de y como un bien separado

Formula de Mirrlees

Saez (2001)

Scheuer-Werning

Definimos…el bien como: 1 - H(y)el impuesto como el impuesto marginal

Hay que calcular…

misterios: ¿una sola elasticidad y qué hace la densidad ahí?

[Diamond-Mirrlees]

[Mirrlees]

misterio resulto: una sola elasticidad y densidad

Mirrlees

No sabemos los coeficientes de Paretotípico: Utilitarista ¿qué cardinalidad?Rawls: maximizar el mínimootra solución: test de eficiencia

Ignorando efectos ingreso, el impuesto superior satisface

coeficiente de Pareto de distribución del ingreso

w

T (w)

h(w)

w0

Rol de la Densidad de Ingreso

si densidad declina rápidoefecto indirecto más benefico

impuesto no eficiente!

Alicuota Superior

Diamond-Saez: cálculo aproximado usando esta formula

Elasticidad: ~0.25Parametro de Pareto: ~1.5Impuesto optimo superior: ~75%

Conclusion: ¿teoría sugiera impuesto alto en práctica? Scheuer-Werning: ojo con superestrellas

SuperestrellasFenomeno de superestrellas (Rosen 1981)

pequeñas diferencias de talento, grandes diferencias de ingresodesigualdad en la cola superior del ingreso

Ejemplos: espectaculos, deportes, escritores, finanzas, CEOs, entrepreneurs, abogados…

¿Impuestos mayores a Superestrellas…

…dada la distribución del ingreso?…dada la distribución de talento?

SuperestrellasTrabajadores (igual que antes)

talentoutilidad

Tecnologíafirmasproducción (supermodular)

Matching uno-a-uno

Equilibrio: salario endogeno

Gabaix/Landier (2008), Terviö (2008)

Equilibrio

W(y)

U2

U3

U1

y

c

Figure 1: Convex equilibrium earnings schedule.

ment models, is fundamental to the superstar effects on the earnings schedule. To see this,differentiate to obtain

W 00(y) = Ayx(s(G(y)), y) · s

0(G(y)) · G0(y) + Ayy(s(G(y)), y). (6)

By supermodularity, the first term is positive, providing a force for the earnings schedule tobe convex in effort. When A is linear in y, then A(q, y) = a(x)y for some increasing functiona and so W 0(y) = a(s(G(y))) is increasing in y. In this case, output is linear in y at thefirm level, but earnings are convex, W 00(y) > 0, as individuals with higher y get matched tohigher-x firms, which is reflected in the earnings schedule. This is illustrated in Figure 1.

2.3 Two Examples based on Gabaix-Landier

Before turning to optimal taxation, it is useful to illustrate superstar equilibria in our model.We do so by adapting the CEO application in Gabaix and Landier (2008). Given their focus,their framework takes the distribution of effort y as given (“talent” in their terminology).We provide two specific examples with endogenous effort that deliver this distribution inequilibrium. We return to Gabaix-Landier’s specification and our two examples repeatedly.

Individual CEOs produce CSby when matched with a firm of size S and supplying efforty, for some parameter b > 0. Firm size is a function of the rank, 1 � x, according to Zipf’slaw: S = C(1 � x)�1; the distribution of x is uniform on [0, 1]. It follows that

A(x, y) = (1 � x)�by,

for some normalization of C. Gabaix-Landier find that the CEO earnings distribution fea-tures a Pareto tail: Letting n denote the rank of a CEO in the earnings distribution (i.e., n

12

Q: ¿tasas más altas para superestrellas?

I. …dada la distribución del ingreso ?

II. …dado la distribución de talento ?

# 1. Misma condición que en Mirrlees: elasticitidad y distribución del ingreso

# 2. Elasticidad más alta! Tasa más baja

# 3. Efecto de superestrellas: neutral, misma tasa!desigualdad sube, pero elasticidad sube.

Diamond-MirrleesDiamond-Mirrlees:

una pista: tecnología no aparece en fórmula…pero indirectamente, elasticidad depende de q…

En nuestro contexto, de W(y). Para que lado va?

Principio de Le Chatelier: elasticidad más alta

U

W(y)

y

c

U

W(y)

y

c

Figure 3: Compensated earnings elasticity with superstar effects (left) and without (right).

F(w0), the additional convexity is due to supermodularity of the output function Byq

> 0;thus, it is driven precisely by superstar effects.

This is particularly transparent when B is linear in y. Then by (6) the adjustment becomes

F(w0) = 1 � #

c(w0)

W 00(y0)y0W 0(y0)

W 0(y0)y0W(y0)

2 [0, 1). (26)

The fixed-assignment elasticity ignores the convexity of the earnings schedule. As Figure 3shows, a convex earnings schedule leads to higher compensated response in effort; implyinga higher response in earnings.

Gabaix-Landier Economy. We can illustrate the magnitude of this adjustment using theGabaix-Landier parameterization from Section 2.3. By (9), the elasticities of the earningsschedule and the marginal earnings schedule are

W 0(y)yW(y)

=1

br � 1y

b � yand

W 00(y)yW 0(y)

=br

br � 1y

b � y.

Substituting this in the adjustment factor (26) gives17

#

c(w) =#

c(w)1 � br#

c(w). (27)

By Proposition 2, in equilibrium #

c(w) is restricted to values that ensure the denominator ispositive.

17Note that the framework in Gabaix and Landier (2008) indeed features an output function A(x, y) that islinear in y. Hence (26) applies.

24

superestrella

U

W(y)

y

c

U

W(y)

y

c

Figure 3: Compensated earnings elasticity with superstar effects (left) and without (right).

F(w0), the additional convexity is due to supermodularity of the output function Byq

> 0;thus, it is driven precisely by superstar effects.

This is particularly transparent when B is linear in y. Then by (6) the adjustment becomes

F(w0) = 1 � #

c(w0)

W 00(y0)y0W 0(y0)

W 0(y0)y0W(y0)

2 [0, 1). (26)

The fixed-assignment elasticity ignores the convexity of the earnings schedule. As Figure 3shows, a convex earnings schedule leads to higher compensated response in effort; implyinga higher response in earnings.

Gabaix-Landier Economy. We can illustrate the magnitude of this adjustment using theGabaix-Landier parameterization from Section 2.3. By (9), the elasticities of the earningsschedule and the marginal earnings schedule are

W 0(y)yW(y)

=1

br � 1y

b � yand

W 00(y)yW 0(y)

=br

br � 1y

b � y.

Substituting this in the adjustment factor (26) gives17

#

c(w) =#

c(w)1 � br#

c(w). (27)

By Proposition 2, in equilibrium #

c(w) is restricted to values that ensure the denominator ispositive.

17Note that the framework in Gabaix and Landier (2008) indeed features an output function A(x, y) that islinear in y. Hence (26) applies.

24

salario fijo

Ajuste por Superestrellas

0 0.1 0.2 0.3 0.4 0.50

1

2

3#

(b = 1)

#

(b = 12)

#

#

0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

11+r#

(b = 1)

11+r#

(b = 12)

11+r#

#

Figure 5: Unadjusted and adjusted earnings elasticities (left panel) and upper bound on toptax rate using unadjusted and adjusted earnings elasticities (right panel).

Effort Elasticities. Using (39) and (40), the required adjustment (23) and (25) for the effortelasticity at any point in the distribution simplifies to

#

c =#

c

br�1

brn1r

�b�1� br#

c. (44)

The adjustment now depends on the rank n (and we omitted the dependence of #

c and #

c onn to simplify notation). Note that for the bottom (n = 1) the effort elasticity adjustment is thesame as the fixed-assignment elasticity adjustment (43); this reflects the fact that W 0(y)y

W(y) = 1for the lowest worker. The adjustment is larger, for a given #

c, for lower n as we move upthe distribution towards the top; this is because W 0(y)y

W(y) increases with y.If br < 1, then at the top, as n ! 0,

#

c =#

c

1 � br � br#

c > #

c, (45)

since Lemma 2 ensures that the denominator is positive. We see that the adjustment is in-creasing in the superstar parameter b and vanishes if b = 0. For a given earnings distribu-tion and hence parameter r, this implies a lower upper bound on the set of Pareto efficienttop marginal tax rates t (based on, for instance, (17) in the absence of income effects).

If br > 1, as supported by Gabaix-Landier, then, since brn1r

�b ! • as n ! 0, the

and Sleet, 2015, in their empirical analysis). In that case, and using their preferred elasticity of .25, Diamondand Saez (2011) find a top tax rate of 73% to be revenue-maximizing. If this elasticity ignores superstar effectsand b = 1, however, the correct elasticity is .4 and the revenue-maximizing top tax rate falls to 62%.

33

Ingresos Bajos

Dos margenes laboralesextensivo (participación)intensivo

Mirrlees = intensivoParticipación importante para ingresos bajos

Margen ExtensivosPreferences

elasticidad de participación

Si margen intensivo es cero…

(Diamond 1980; Chone-Laroque, 2011)

negativo para y bajo

posible: impuestos marginales negativos

NIT vs EITC1040 QUARTERLY JOURNAL OF ECONOMICS

a. Negative Income Tax (NIT) b. Earned Income Tax Credit (EITC)

"Phasing-out Region

Phasing-out Region

Subsdy Regon

Break Even W Subsidy Region Point

z Break Even

xW

Point a,

Guaranteed InCerme

<t<

4/ •5 line 450 line

0 0 Earnings w Earnings w

FIGURE I

contrast, the evidence of responses along the intensive margin seems much more limited. Most estimates of hours of work elasticities conditional on working are small (see Pencavel [1986] and Blundell and MaCurdy [1999] for surveys). The aim of this paper is to show that the margin of the behavioral response is a key element to take into consideration when designing an optimal transfer scheme.

The optimal income tax literature has developed models to analyze the design of transfer programs but has focused, following the seminal contribution of Mirrlees [1971], almost exclu- sively on the intensive margin of response. Mirrlees [1971] showed that, in that context, the optimal tax marginal tax rates at any income level cannot be negative. Moreover, numerical simulations have shown that, in this model, optimal rates at the bottom are very high (see, e.g., Tuomala [1990] and Saez [2001]). Redistribution thus takes the form of a guaranteed income level that is taxed away at substantial rates as depicted in Figure Ia. Such a transfer scheme is known as a Negative Income Tax (NIT) program: it provides the largest transfers to the lowest income earners who are presumably the most in need of support. In accordance with the theory, many European countries use NIT- type programs to redistribute toward zero or low income earners. In the United States there is no universal income support program. However, most categorical transfer programs such as Tem- porary Assistance for Needy Families (TANF) for single mothers, Food Stamps, Disability Insurance, and Supplemental Social Se- curity Income for the old are also designed as NIT programs.

This content downloaded from 193.157.190.179 on Wed, 17 Feb 2016 17:34:02 UTCAll use subject to JSTOR Terms and Conditions

Saez (2002)

Argentina?

Europa EEUU

ArgentinaImpuesto a las Ganancias

tasas progresivas históricamente, fracción muy chica de contribuyentes

Historia reciente…inflación + sin ajuste de Ganancias mayor participaciónampliación muy resistidaingresos bajos…

subsidios con otros programas de asistencia (AUH, etc)otras intervenciones (e.g. precios) o transferencias ad hoc

¿Conveniencia de consolidar?Propuestas de reformas: ¿ampliar y hacer más progresivo?




estático

dinámico

incertidumbre


DiamondMirrlees

Chamley Judd

Mirrlees



Impuestos al Capital¿Qué diría Diamond-Mirrlees?

capital es un bien más en el primer periodo y está fijoresultado: impuesto al capital de 100% en el periodo inicial, i.e. expropiaciónimpuestos uniformes al consumo intertemporal (bajo homotéticidad): cero impuesto al capital a futuro

Atkinson-Stiglitz: similar (sin homotéticidad)

Problema de inconsistencia temporal

Chamley: restricciones al impuesto al capital (y al consumo)

Chamley Judd ¿ Deberíamos gravar al capital ? NO, de acuerdo a...

Chamley (1986)agente representativohorizonte infinito

Judd (1985)trabajadores vs. capitalistassin mercado de crédito

Resultados: impuesto cero al capital en estado estacionario, i.e. largo plazo?

Intuición? Elusiva...

QuejasSupuestos cuestionados (Banks-Diamond)

agente representativo?horizonte infinito para el consumidor?elasticidad implicit infinita?sin incertidumbre individual?capacidad fiscal para distinguir capital vs. trabajo?

AlternativasNew Dynamic Public Finance: incertidumbre otros...

Chamley-Judd se mantiene como punto de referencia importante para defender postura de cero impuesto al capital

Straub-WerningCuestionan los resultados mismos…

demuestra results/proofs incompleteconclusiones opuestas cuando Elasticidad Intertemporal < 1

¿Qué paso?asumían convergencia a un estado estacionario interior

Judd: no converge a un estado estacionario (aun sin restricciones)Chamley: impuesto al capital en cota superior para siempre

Chamley 1986Modelo

modelo neoclassico agente representativofactores: trabajo y capital

cota superior para impuesto a los ingresos de capital

restringir impuestos al consumo ya que imitan expropiación al capital

Resultado...impuesto al capital cero en estado estacionariocon utilidad CRRA: resuelve la transición

Chamley 1986Chamley (1986, Theorem 2)Suppose and additive CRRA utility. There exists a T < ∞ such thata. for t < Tb. for t >T

solución de Bang-bang¿No puede ser T = ∞ ?

Chamley proof: “The bounds cannot be binding forever, or marginal utility would grow to infinity, which is absurd.”

???

Chamley 1986

T = •

T < •

k0

b0

Figure 4: Graphical representation of Proposition 8.

(b) for t > T capital income is untaxed: rt = r⇤t and tt = 0;

(c) T < •.

At a crucial juncture in the proof of this claim, Chamley (1986) states in support of part(c) that “The constraint rt � 0 cannot be binding forever (the marginal utility of privateconsumption [...] would grow to infinity [...] which is absurd).”28 Our next propositionestablishes that there is nothing absurd about this within the logic of the model and that,quite to the contrary, part (c) of the above claim is incorrect: indefinite taxation, T = •,may be optimal.

Proposition 8. Suppose t = 1 and preferences given by (11) with s > 1. Fix any initial capitalk0. There exists b < b such that for initial government debt b0 2 [b, b] the optimum has tt = t

for all t � 0, while for b > b0 there is no equilibrium.

Here b represents the peak of a “Laffer curve”, above which there is no equilibrium.The proposition states that for intermediate debt levels it is optimal to tax capital indefi-nitely. Since these points are below the peak of the Laffer curve, indefinite taxation is notdriven by budgetary need—there are feasible plans with T < •, however, the plan withT = • is simply better. This is illustrated in figure 4 with a qualitative plot of the set ofstates (k0, b0) for which indefinite capital taxation is optimal. Although this propositiononly considers t = 1, as in Chamley (1986), it is natural to conjecture that lower values oft make the optimality of T = • more likely.

Our next result assumes g = 0 and constructs the solution for a set of initial conditionsthat allow us to guess and verify its form.

28It is worth pointing out, however that although Chamley (1986) claims T < • it never states that T issmall. Indeed, it cautions to the possibility that it is quite large saying “the length of the period with capitalincome taxation at the 100 per cent rate can be significant.”

26

T = ∞ óptimo!debajo de máximo de Lafferintuición?

Indefinite Taxation.Suppose and additive CRRA utility and Fix initial capital . There there exists so that

Chamley (1986, Theorem 2)Suppose and additive CRRA utility. There exists a T < ∞ such thata. for t < Tb. for t >T

Chamley 1986

Intuición para T= ∞no estamos en Diamond-Mirrleesacá hay restricciones al impuesto al capital y estas pueden estar “activas” para siempre

Judd 1985Capitalistas

Trabajadores

Tecnología

TaxesTransferencias al trabajador

Impuesto al capital

100 200 3000

1

2

100 200 300

2 %

4 %

6 %

8 %

10 %

0.75 0.9 0.95 0.99 1.025 1.05 1.1 1.25

Figure 1: Optimal time paths over 300 years for capital stock (left panel) and wealth taxes(right panel) for various value of s. Note: tax rates apply to gross returns not net returns,i.e. they represent an annual wealth tax.

zero-tax steady state. Our numerical method is based on the Bellman equation (4) and isdescribed in the appendix.

To clarify the magnitudes of the tax on wealth, consider an example: if R⇤ = 1.04 s sothat the before-tax net return is 4%, then a tax on wealth of 1% represents a 25% tax onthe net return, a tax of 4% represents a tax rate of 100% on net returns, etcetera.

A few things stand out in Figure 1. First, the results confirm what we showed theoret-ically in Proposition 3, that for s > 1 capital converges to kg = 0.0126. In the figure thisconvergence is monotone12 and relatively steady, taking around 200 years for s = 1.25.The asymptotic tax rate is very high, approximately 1 � R/R⇤ = 85%, and outside thefigure’s range. Of course, this implies that the before-tax return R⇤ = f 0(kg) + 1 � d at kg

is exorbitant, because the after-tax return is still R = 1/b.Second, for s < 1, the path for capital is not monotonic13 and eventually converges to

the zero-tax steady state and the tax rate converges to zero. However, the convergence isrelatively slow, especially for values of s near 1. This makes sense, since, by continuity,for any period t, the solution should converge to that of the logarithmic utility case ass ! 1.14 By implication, for s < 1 the rate of convergence to the zero-tax steady statemust be zero as s " 1. To further punctuate this point, Figure 2 shows the number ofyears it takes for the tax on wealth to drop below 1% as a function of s 2 (1

2 , 1). As s risesit takes longer and longer and as s " 1 it takes an eternity.

The logarithmic case leaves other imprints on the solutions for s 6= 1. Returning to

12This depends on the level of initial capital. For lower levels of capital the path first rises then falls.13This is possible because the state variable has two dimensions, (kt, Ct�1). At the optimum, for the same

capital k, consumption C is initially higher on the way down than it is on the way up.14Recall that, by Proposition 1, the logarithmic solution converges to positive taxation as t ! •.

13

0.5 0.6 0.7 0.8 0.9 10

500

1,000

1,500

Figure 2: Time elapsed (in years) until tax on wealth falls below 1% for s 2 (12 , 1). The

solid line uses the solution of the nonlinear model, the dashed line uses an approximationfrom the linearized model below.

Figure 1, for both s < 1 and s > 1 we see that over the first 20-30 years, the path ap-proaches the steady state of the logarithmic utility case, associated with a tax rate around1 � R

R⇤ = 1 � b = 5%. The speed at which this takes place is relatively quick, which isexplained by the fact that for s = 1 it is driven by the standard rate of convergence in theneoclassical growth model. The solution path then transitions much more slowly eitherupwards or downwards, depending on whether s < 1 or s > 1.

An Intuition based on the Intertemporal Manipulation of Saving Incentives. Whydoes the tax rise for s > 1 and fall for s < 1? Why are these dynamics relatively slow fors near 1?

To address these questions about normative results, it helps to back up and reviewdifferences in the following positive exercise. Start from a constant tax on wealth andimagine an unexpected announcement for higher future taxation. How do capitalists re-act today? There are substitution and income effects pulling in opposite directions. Whens > 1 the substitution effect is weaker and capitalists increase present savings, to partiallyoffset the drop in future consumption.15 When s < 1 the substitution effect is strongerand capitalists decrease present savings, substituting towards current consumption. Inthe logarithmic case, s = 1, the two effects cancel out, so that present consumption andsavings are unaffected.

Returning to the normative questions, increasing savings is desirable when capital iscurrently being taxed, so as to augment the tax base. When s < 1, this can be accom-

15This does not imply that the supply for savings “bends backward”. For instance, if the interest ratewere lowered permanently then wealth would rises over time, even with s > 1. Higher values of s aresimply associated with a less elastic savings response. Although there is no consensus, the case with s > 1is usually considered the empirically plausible one.

14

years until wealth tax < 1%

Resultados!




estático

dinámico

incertidumbre


DiamondMirrlees

Chamley Judd

Mirrlees



NDPFAusente hasta ahora: incertidumbre individual

Evidencia empirica: muy importante!Políticas públicas: seguros sociales (desempleo, incapacidad, etc.)

New Dynamic Public Finance…efecto de incertidumbre individual sobre impuestos y seguros socialesmetodología: diseño de mecanismos

Resultados…impuestos al ahorro/capitalimpuestos al trabajo que suben con la edadotros: duración de seguros de desempleo etc.

hoy

Inverse EulerSin incertidumbre… Atkinson-Stiglitz: impuesto cero al ahorroCon incertidumbre… Inverse Euler

impuesto positivo al ahorro

compromiso perfecto


economia politica





estático

dinámico

incertidumbre


DiamondMirrlees

Chamley Judd

Mirrlees



Desigualdad FuturaAtkinson-Stigliz otra vez…

Nuevo: imponemos restricción o objetivo

Dos interpretaciónes…intergeneracional: impuesto a la herencia (a=0)problema de economia political: reducir desigualdad (a>0)

función concava

Interpretación I: Intergeneracional

Lecture Note 14.471: Estate Taxation

Iván Werning, MIT

November 2013

• Here...

– we review the basic argument in Farhi Werning (2010; QJE)

– we can do so quickly because we will use the same trick we used in the previ-ous lecture

• Utility, parents and kids

Up(q0) = u(c0(q0)) + bu(c1(q0)) � h(y0(q0), q)

Uc(q0) = u(c1(q0))

where b � 0 is an altruism parameter

• Cost per agentC(u0(q0)) + qC(u1(q0)) � y0(q0)

• Pareto Frontier

A

vc

vp

Figure 1: Pareto frontier between ex-ante utility for parent, vp, and child, vc.

interior point since parents are altruistic.

This paper explores other e�cient points, those on the downward sloping section of the

Pareto frontier. Indeed, to the right of point A, a role for estate taxation emerges. Our main

result is that e�cient estate taxation has two crucial features.

The first feature concerns the shape of marginal tax rates: we show that estate taxation

should be progressive. That is, more fortunate parents, leaving larger bequests, should face

a higher marginal tax on their bequests. Since more fortunate parents face lower returns

on their bequests than the less fortunate ones, their bequests are more similar than would

be otherwise. This mechanism generates mean reversion in consumption across generations,

which helps lowers consumption inequality for newborns. This arrangement still provides

incentives to parents, since the child’s consumption varies with that of the parent, but it

now varies less than one-for-one. In this way, progressive estate taxation mitigates the

inheritability of luck within a dynasty.

Note that our result characterizes the optimal shape of the marginal tax rates on bequests,

but does not imply that the overall tax system should be progressive. In fact, our analysis

has nothing to say about the shape of labor income taxes. Moreover, our results on the

estate tax apply regardless of the amount of redistribution across parents with di�erent

productivities. Our stark conclusion regarding the progressivity of estate taxation contrasts

with the well-known lack of sharp results regarding the shape of the optimal income tax

schedule (Mirrlees, 1971; Seade, 1982; Tuomala, 1990; Ebert, 1992; Diamond, 1998; Saez,

2001).1

1Mirrlees’s (1971) seminal paper established that for bounded distributions of skills the optimal marginal

3

1

Generación actual:

Generación futura:

Interpretación II: Economía Politica

Hoy: decidimos impuestos de hoy y mañanaMañana: si las cosas están mal, reformamos

igualamos consumo……pero perdemos fracción recursos

Inconsistencia temporal: incentivos ya fueron…Natural: democracia o revoluciones

ResultadoModelo

Resultados

impuesto progresivonegativo para pobrespositivo para ricos si a > 0

c0 c1

intuición: reflejo de reversion

a la media

ArgentinaPaíses desarrollados…

impuestos a las transferencias y herenciabajos o nulos impuestos a la riqueza (sacando impuestos a los ingresos del capital)

ArgentinaImpuestos a la riqueza: bienes personalessin impuestos a herencia

Piketty: propone impuesto a la riqueza 1-2% internacional

compromiso perfecto


economia politica





estático

dinámico

incertidumbre


DiamondMirrlees

Chamley Judd

Mirrlees



ConclusionTeoría de Imposición Óptima: muy fructífera…

resultados tradicionales aún muy útilesavances recientes…

extensiones para cuantificar (alicuota superior)revisar resultados anteriores (Chamley-Judd)

nuevas ideas, nuevos resultados (superestrellas, incertidumbre, etc.)

Argentina…dista de satisfacer algunos principios básicos¿a la vanguardia en otras?necesidad de reformas

Documents

Imposición Óptima Teoría y Aplicación - aaep.org.ar · Imposición Óptima Teoría y Aplicación Iván Werning, MIT Conferencia Rolf Mantel Tucumán, Noviembre, 2016 Reunión