Pareto Improving Structural Reforms_IMF OECD WB Conference Sept 2020

Pareto improving structural reforms Gilles Saint-Paul (PSE & NYUAD)

March 3, 2019

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

1 / 48

Introduction

Standard view: If a reform is e¢ cient, side transfers can make everybody better-o¤ Example: Delpla-Wyplosz recommendation for rent buyback But side transfers are costly to the budget And taxes are distortionary Does this result hold under distortionary taxation?

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

2 / 48

A negative intuition

Aggregate gains from reform are small relative to their distributive e¤ects "triangle" vs "rectangle"

Welfare losses from distortionary taxation of the same order of magnitude as losses from regulation

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

3 / 48

An example

Price pegged above equilibrium market price. p (x ) = inverse demand function, c (x ) = marginal cost function. Îť = welfare cost of public funds.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

4 / 48

Reform Reform reduces price. by dp, Change in consumer surplus dCS = p 0 (x )xdx > 0.

Change in producer surplus dPS = (p (x ) c (x ) + p 0 (x )x )dx.

Need to transfer dPS to producers Additional taxes must be such that dT = λdT dPS = 1dPSλ .

Total e¤ect on social welfare dCS + dPS

λdT =

p

c + λxp 0 .

1 λ

For this to work we need that λ where η D = markup.

p xp 0

Gilles Saint-Paul (PSE & NYUAD) ()

p c µ 1 = ηD , 0 xp µ

(1)

is the elasticity of demand and µ = p/c is the Pareto improving structural reforms

March 3, 2019

5 / 48

Replacing regulation by taxes

Consider a tax d τ on the good itself Revenues xd τ Output loss dx = d τ/p 0 < 0.

Welfare gain (p

c )d τ/p 0 < 0, i.e.

p c xp 0

per unit of tax collected.

Hence total cost of public funds cannot exceed η D

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

µ 1 µ .

March 3, 2019

6 / 48

Basic setup

There is a continuum of consumers-producers over [0, 1], indexed by i.

Consumers with index i are endowed with a speci…c labor input which only allows them to produce good i.

All consumers have the same utility function, given by U (fcij g, li ) =

Gilles Saint-Paul (PSE & NYUAD) ()

Z 1 0

1/α

cijα dj

Pareto improving structural reforms

γ

li , γ

March 3, 2019

7 / 48

Production

Each good j is produced with a linear technology, yj = lj .

=)Wages coincide with prices

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

8 / 48

Regulation

A fraction r of the goods are regulated.

Goods such that i > r are unregulated.

Their (common by symmetry) price is normalized to 1.

Goods such that i < r are regulated at pR > 1.

People such that i < r cannot supply more than an amount of labor lĚ&#x201E;

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

9 / 48

The structure of individual choice Indirect utility function V (R, l, p ) = where p = (rpR 1

R p

lγ , γ

α α

+1

r)

1 α α

.

Demand for nonregulated goodscN (R, p ) = Rp 1 Demand for regulated goods

(2)

α α

1

α

cR (R, p ) = Rp 1 α pR 1

α

Labor supply (constrained if i < r ): l (w /p ) = Gilles Saint-Paul (PSE & NYUAD) ()

w p

1 γ 1

Pareto improving structural reforms

.

March 3, 2019

10 / 48

Non regulated households Labor supply l = lN = p

1 γ 1

.

Consumption of nonregulated goods cNN = p 1

α α

1 γ 1

(3)

Consumption of regulated goods cNR = p 1

α α

1 γ 1

1

pR 1

α

Utility uN =

Gilles Saint-Paul (PSE & NYUAD) ()

1

1 γ

p

Pareto improving structural reforms

γ γ 1

March 3, 2019

11 / 48

Regulated households’consumption

Nonregulated goods: α

cRN = p 1 α pR l̄

(4)

Regulated goods: α

α

cRR = p 1 α pR 1 α l̄

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

12 / 48

Equilibrium regulated labor supply Write down that supply equals demand for any nonregulated good.

Walras’s law, demand then consistent with l̄ in regulated sectors. lN = rcRN + (1

r )cNN .

Substituting, l̄ = p

1 γ 1

1

pR 1 α ,

(5)

Yields equilibrium utility

uR

= V (pR l̄, l̄, p ) = p

γ γ 1

pR 1

α α

1 1 γα p γ R

= JuN

Gilles Saint-Paul (PSE & NYUAD) ()

(6) (7)

Pareto improving structural reforms

March 3, 2019

13 / 48

Extensive reform

Fraction of regulated sectors reduced to r 0 < r .

Size of reform â&#x2C6;&#x2020;r = r

r0

Lumpsum transfer T to each household i such that r 0 < i

r.

General proportional tax on labor income Ď&#x201E;.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

14 / 48

Nonregulated households Let p 0 = new price level.

Income = l (1

τ)

Labor supply: 1 γ 1

l = lN0 = p 0

1

(1

τ) γ 1 .

(8)

Utility uN0

=

1 γ

1

They bene…t from the i¤ uN0

τ p0

γ γ 1

.

(9)

uN , i.e.

1

Gilles Saint-Paul (PSE & NYUAD) ()

1

τ

p0 . p

Pareto improving structural reforms

(10)

March 3, 2019

15 / 48

Deregulated households By linearity of indirect utility function, their labor supply is the same as for nonregulated, lN0 = (p 0 (1

1 γ 1

τ ))

.

Disposable income RD0 = T + p 0

1 γ 1

(1

τ) γ

γ 1

Utility uD0 = They gain i¤ uD0 T

T + 1 p0

1 γ

p0

γ γ 1

(1

γ

τ) γ 1 .

(11)

uR , i.e. p

Gilles Saint-Paul (PSE & NYUAD) ()

0

1 γ

1

γ 1 γ

"

p0 p

γ γ 1

J

Pareto improving structural reforms

(1

τ) γ

γ 1

#

.

March 3, 2019

(12) 16 / 48

Nonderegulated households Income RR0 = l̄ 0 pR (1 Utility is uR0 =

pR l̄ 0 (1 p0

τ) l̄ 0γ . γ

τ)

(13)

Computing l̄ 0 : r 0 l̄ 0 pR (1

τ) = p0

1 γ 1

(1

τ) γ

1 1

Government’s BC T ∆r = τ (1

r 0 )p 0

h

1 γ 1

r 0 pR 1

(1

α α

+ τ (1

τ) γ

1 1

r 0)

i

T ∆r .

+ τr 0 pR l̄ 0 .

(14)

(15)

Allows to compute 1

l̄ 0 = pR 1 α p 0 Gilles Saint-Paul (PSE & NYUAD) ()

1 γ 1

(1

τ) γ

Pareto improving structural reforms

1

(16)

1 March 3, 2019

17 / 48

Condition for reform to be Pareto-improving LEMMA 1 – For any r 0 < r , the reform can be implemented in a Pareto-improving way if and only if there exists some τ 2 [0, 1] such that 1 and, T

p

0

1 γ

1

γ 1 γ

for T =

τ (1

"

p0 , p

τ

γ γ 1

p0 p

J 1

τ) γ 1 p0 ∆r

1 γ 1

(1

τ) γ

γ 1

#

.

(19)

α 1 α

.

(20)

If so, the reform is called viable.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

18 / 48

The La¤er curve PROPOSITION 1 – (i) There exists a unique tax rate τ max 2 (0, 1) which maximizes the utility of the deregulated agents, uD0 , which is hump-shaped in τ. (ii) This tax rate is equal to α

τ max

(γ 1)(p 0 1 α ∆r ) . = α γp 0 1 α (γ 1)∆r

(21)

(iii) Assume p

γ

r (γ

1),

(22)

then τ max

1

p 0 /p for all r 0

r.

(iv) Assume (22) is violated. Then there exists a unique r̃ 2 (0, r ) such that r 0 r̃ , τ max 1 p 0 /p.

.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

19 / 48

A possibility result

PROPOSITION 2 – (i) All reforms are viable (ii) If τ max 1 p 0 /p then there exists τ c 2 (0, 1 p 0 /p ] such that a reform is viable if and only if τ c τ 1 p 0 /p, 0 (iii) If τ max < 1 p /p then there exists τ c 2 (0, τ max ] such that a reform is viable if and only if τ c τ 1 p 0 /p, furthermore all reforms such that τ max < τ are Pareto-dominated by τ = τ max .

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

20 / 48

Why?

Ď&#x201E; = 1 p 0 /p leaves real wage, labor supply and utility unchanged for NR and ND Aggregate gains from reform all go to the D rgoups But gains are positive Because relative price distortions are reduced Because employment goes up for the D groups

For distortions to prevent viability, compensatory taxes should reduce labor supply.

Not true here.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

21 / 48

Intensive reforms Now assume prices of all regulated goods are uniformly lowered to pR0 < pR .

LEMMA 2 – For any pR0 < p 0 , the reform can be implemented in a Pareto-improving way if and only if there exists some τ 2 [0, 1] such that p0 1 τ (23) p holds as well as

τ (1

1

τ) γ 1 p

0

α

1 α

r

1

γ γ

γ γ 1

p (1 τ ) p0

J

J

0

!

p0 p

γ γ 1

, (24)

with at least one strict inequality where 0

J = Gilles Saint-Paul (PSE & NYUAD) ()

0

γpR

α 1 α

γ

0

pR 1

γ 1 α

Pareto improving structural reforms

.

(25) March 3, 2019

22 / 48

Intensive reforms are viable too

PROPOSITION 3 – (i) All reforms are viable (ii) If τ max 1 p 0 /p then there exists τ c 2 (0, 1 p 0 /p ] such that a reform is viable if and only if τ c τ 1 p 0 /p, 0 (iii) If τ max < 1 p /p then there exists τ c 2 (0, τ max ] such that a reform is viable if and only if τ c τ 1 p 0 /p, furthermore all reforms such that τ max < τ are Pareto-dominated by τ = τ max .

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

23 / 48

Notations

There are q = n + r goods, indexed by i = 1, ...q.

Vectors denoted by x, whose components xi .

Matrices denoted by M and their components by mij .

If f () : Rp ! Rn , its gradient rf is a matrix (∂fi /∂xj ).

If f () : Rp ! R, rf is a line vector to remain consistent with the preceding de…nition.

hx, yi = ∑i xi yi , x y =(xi yi ), x y =(xi /yi ) In particular hx, yi = hx z, y zi .

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

24 / 48

Preferences

Continuum of agents of total mass 1 Same utility function but di¤er by skills.

For each i, a mass 1/q of agents have skills speciâ&#x20AC;Śc to sector i Utility is U (c,l ) = u (c) v (l ), where v 0 , v 00 > 0 and u is homogeneous of degree one.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

25 / 48

The structure of demand

Let pi be the price of good i.

Consumer demand is ci = RĎ&#x2C6;i (p), where R is expenditure.

We have that

hp, Ď&#x2C6;(p)i = 1, 8p.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

(26)

March 3, 2019

26 / 48

Walrasian labor supply

Aggregate hedonic price level to 1, Hence utility can be rewritten as R

v (l ).

Labor supply is l = Îť (w ), where Îť = v 0

1

and w is the real wage.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

27 / 48

Production

Production yi in sector i only uses the speciâ&#x20AC;Śc labor input li and unit labor requirement is equal to 1 yi = li .

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

28 / 48

Regulation

N = f1, ..., n g nonregulated sectors

R = fn + 1, ..., q g regulated sectors.

In deregulated sectors, the price adjusts to clear markets.

In regulated sectors, the price is â&#x20AC;Śxed by law above the competitive level, Output is determined by demand Supply is rationed.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

29 / 48

Pre-reform resouce allocation Output equals demand in all sectors l=Y ψ (p) Output equals supply in all nonregulated sectors lN = λ(pN ) Aggregate p normalized to 1 u (ψ(p)) = 1.

Remarks: Unknows: Y , pN , l.

By construction, total income always equals total expenditure, Y = hp, li .

Distribution of income is R = p l.

Income shares s = p ψ (p) Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

30 / 48

Distortion size

For prices to be above equilibrium in regulated sectors, we need that v 0 (li ) < pi for i 2 R. Let Ď&#x2030;i = 1

v 0 (li ) 2 [0, 1). pi

Ď&#x2030; i is a measure of distortions in sector i.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

31 / 48

De…ning reforms Pure structural reform (PSR) pR is replaced by pR + dpR .

Structural reform with …scal adjustment (SRFA): 0 = p + dp , pR is replaced by pR R R income in each sector taxed at rate d τ i , (possibly negative) lump-sum transfer to sector i, dTi .

Government budget constraint

hs, dτ i Y = h1, dTi

(27)

Structural reform with side transfers (SRST): SRFA such that dτ = 0.

Budget constraint becomes

h1, dTi = 0.

(28)

Feasible structural reform (FSR) SRFA such that dT Gilles Saint-Paul (PSE & NYUAD) ()

0.

Pareto improving structural reforms

March 3, 2019

32 / 48

Post-reform equilibrium allocation of output and labor

l0 = Y ψ (p0 ) 0 lN

0 λ(pN

= u (ψ(p )) = 1,

(29)

(1N dτ N ))

(30)

0

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

(31)

March 3, 2019

33 / 48

Key observation: taxes not distortionary in regulated sectors

In regulated sectors, supply is constrained by demand.

Therefore activity is not reduced by a marginal proportional tax.

As a result, the feasibility constraint dTi regulated sectors.

0 is irrelevant for

Lump-sum tax can be replaced by proportional tax, with no e¤ect on equilibrium

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

34 / 48

Equivalence DEFINITION 1 – Let ρ0 = (dpR 0 , dτ 0 , dT0 ) and ρ1 = (dpR 1 , dτ 1 , dT1 ) be two SRFAs. They are equivalent [ρ0 ρ1 ] if and only if l00 = l10 , 0

R00 ψ(p0 )T

= R10 ψ(p10 )T .

DEFINITION 2 – Let ρ0 = (dpR 0 , dτ 0 , dT0 ) and ρ1 = (dpR 1 , dτ 1 , dT1 ) be two SRFAs. They are production-equivalent [ρ0 ρ1 ] if and only if l00 = l10 , p00 = p10 .

Clearly, if two reforms are production-equivalent and deliver the same distribution of income (R00 =R10 ), then they are equivalent.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

35 / 48

Distortions may limit feasibility only for N groups

Two reforms yielding the same net taxes for R agents are equivalent: LEMMA 3 – Let ρ0 = (dpR 0 , dτ 0 , dT0 ) and ρ1 = (dpR 1 , dτ 1 , dT1 ) be two SRFAs.. Assume that dτ N 0 = dτ N 1 , dTN 0 = dTN 1 , and dTR 0 Y sR 0 dτ R 0 = dTR 1 Y sR 1 dτ R 1 . Then ρ0 ρ1 .

If reform is feasible for N agents, equivalent feasible reform can be implemented: LEMMA 4 – For any SRFA ρ such that dTN such that ρ̃ ρ.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

0, there exists an FSR ρ̃

March 3, 2019

36 / 48

Taxing away consumer gains

DEFINITION 3 – An SRFA is N-neutral if and only if dTN = 0 and dτ N = dpN

pN .

(32)

In an N-neutral reform, dlN = 0.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

37 / 48

N neutral reforms are viable if aggregate welfare goes up

The e¤ect on utilitarian social welfare is dW = hs ω, dl Y

li .

Consequently, aggregate social welfare goes up if and only if

hs ω, dl

li > 0.

(33)

Assume an SRFA ρ0 is N-neutral and satis…es (33). Then there exists an N-neutral FRS ρ1 such that (i) ρ0 ρ1 , and (ii) ρ1 is Pareto-improving.

Hence Pareto and Utilitarian criteria coïncide for N-neutral reforms

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

38 / 48

Existence of Pareto-improving structural reform

PROPOSITION 6 â&#x20AC;&#x201C; For any r-vector dz there exists an N-neutral SRFA such that dlR = dz.

Corollary â&#x20AC;&#x201C; There exists a Pareto-improving FSR. N-neutral reform can be constructed to generate any vector of employment growth in R sectors Such vector can be chosen to be positive By (33), social welfare goes up Hence Pareto-improving FSR exists.

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

39 / 48

But: Does FSR involve deregulation?

PROPOSITION 7 – Let sR = hsR , 1i , pi σ = min σi = [rψ]ii > 0, i ψi and η = max

i ,j ,i 6=j

pj [rψ]ij ψi

0.

Consider a nonzero r-vector of price reductions dx xm = max dx > 0, x̄Y = hsR , dxi /sR > 0, and σR = hsR , σ R dxi / hsR , dxi > 0.

Assume η<

1 q

1

min(

1

sR 2

σ,

0. Let

x̄Y σR ) xm

(34)

Then (i) there exist a N-neutral SRFAs such that dpR pR = dx and (ii) These reforms are such that dlR > 0, implying that they satisfy (33).

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

40 / 48

Conditions for Pareto-improving deregulation

Price cross-elasticities of demand small enough relative to own price elasticities structural reform not too unbalanced: maximum reduction in a regulated price not too large relative to average.

If this holds reform can be implemented In a Pareto improving way So that employment grows in all regulated sectors

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

41 / 48

If regulated prices indexed on aggregate price level the nonregulated have rents

ND no longer beneâ&#x20AC;Śts from induced fall in p For them not to lose, they must pay lower taxes than NR For nobody to lose, NR must have rents This reduces T , making compensation less e¢ cient

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

42 / 48

ND rent falls, taxes must leave rents to NR Now uR0 = uN0 J 0 , where 0

J =

α 1 α

γ(pR /pN0 )

γ

(pR /pN0 ) 1

γ 1 α

< J.

ND viability condition becomes 1 uR0

τ

pN pN0

J J0

γ 1 γ

,

uR =) uN0 > uN .

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

43 / 48

Partial reform never viable if regulation not too strict PROPOSITION 8 – There exists p̄ > 1 such that for any pR 2 (1, p̄ ), the only viable reform is r 0 = 0. α 0.3

γ 1.2

r 0.2

0.3

1.2

0.8

1.2

0.5 0.5 0.2

-2

1.2

0.2

0.3

2

0.2

∆r 0 0.2 0 0.5 0 0.2 0 0.2 0 0.2

pRm 2.17 1.67 1.09 ∞ 1.5

pRc 1.18 1.2 1.06 1.07 1.05 1.05 1.42 1.47 1.15 1.17

Table 1 Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

44 / 48

Example 1

People only consume a subset of the goods which di¤ers across people in a random way

They di¤er by their type = proportion of regulated goods consumed.

Type r

h (r )

r̄ = total proportion of regulated goods Under reform, r̄ falls to r̄ 0 = λr̄ , with λ 2 [0, 1).

Reform is assumed to a¤ect people proportionally: r 0 = λr .

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

45 / 48

Example 1 (Ctd) Îť 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Table

Ď&#x201E; (%) 7.6 6.7 5.8 4.9 4.1 3.3 2.6 1.9 1.3 0.7 2

fraction of winners (%) among nonregulated non deregulated 60.8 85.0 61.8 86.7 63.0 88.4 64.4 90.0 65.4 91.7 66.7 95.0 67.3 95.0 68.3 96.7 67.5 96.7 65.2 91.7

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

46 / 48

Example 2

Goods are on a circle, indexed by j mod .1.

Agents are uniformly distributed over this circle They all consume a fraction ρ of the goods, located in an interval Agent located at x consumes goods [x, x + ρ mod 1].

The distribution of preferences is independent of the allocation of producers to sectors.

The regulated goods are those such that j 2 [0, r̄ ].

We assume 1

r̄ > ρ > r̄ .

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

March 3, 2019

47 / 48

Now reform scope matters crucially r̄ 0 0 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 Table 3

τ (%) 9.6 8.5 7.4 6.4 5.4 4.4 3.5 2.6 1.7 0.9 –ρ

fraction of winners (%) among nonregulated non deregulated 46 45 45.8 46 45.7 45 45.3 46 44.8 45 44.3 44 43.5 43 42.7 43 41.9 43 40.8 40 = 0.4, pR = 1.4, r̄ = 0.3

Gilles Saint-Paul (PSE & NYUAD) ()

Pareto improving structural reforms

total 62.2 60.5 58.7 56.8 54.7 52.6 50.2 47.9 45.7 42.4

March 3, 2019

48 / 48