CES Lecture 3 Nigar Hashimzade - CESifo Group Munich · 2019-12-12 · Overall e⁄ect on growth is...

Issues in optimal �scal policyCES Lecture 3

Nigar Hashimzade

Durham and IFS

29/11/2016

Nigar Hashimzade (Durham and IFS) Fiscal policy 29/11/2016 1 / 45

Optimal �scal policies

Fiscal policies: taxation, government spending, and government debt

Taxation: tax structureI Tax base; tax rates; tax administration

Government spending: compositionI Public goods (production and consumption)I Investment (physical and human capital)I Redistribution (subsidies for consumption or production)

Government debt: important in dynamic/stochastic context(will not be discussed this time)

E¢ ciency�equity trade-o¤

Optimality criteria


Optimal taxation

First-best tax system: no distortion of economic choices

Second-best: issues to considerI Extent of distortionsI Administrative costsI Political economy

Tax reformsI Start with the existing tax systemI Implement a revenue-neutral (welfare-neutral) changeI Calculate change in welfare (revenue)

Examples: individual vs corporate income tax; income vs consumption tax;progressivity; salience; etc.


Optimal spending

Objective: maximize social welfareI Issues with de�nition

Alternative objective: minimize distortionsI Marginal cost of public funds

�Partial�approachI Induce desired behaviour

All of these, of course, applies to optimal taxation.

Tax expenditure vs government spending(Behavioural and political considerations)


Outline

Focus: public spending as an input in production

Barro (1990) model

Extentions and applications:I Optimal composition of stock and �ow of public input in production;I Optimal composition of two di¤erent public inputs (�ows);I National and supra-national public spending (�scal federation).

Empirical �ndings


Barro (JPE 1990)

This is a version of Romer�s AK model where government investmentcomplements private investment.

Public investment (e.g. in infrastructure or in schools) is funded fromincome tax

I Negative e¤ect

It increases marginal productivity of private investmentI Positive e¤ect

Overall e¤ect on growth is non-monotoneI La¤er-type curve in the growth rate

Engine of growth: marginal productivity of capital is constant in total(private plus public) capital, while it remains diminishing in privatecapital.


Barro (JPE 1990)A simpli�ed version

Production function:Y = AK 1�αG α

The law of motion of private capital:�K = s (1� τ)Y � δK

I Output (income) is taxed at a �at constant rateI Savings rate can be endogenized using consumer utility(e.g., in�nitely-lived representative consumer with some well-de�nedinter-temporal preferences)

Government budget constraint:

G = τY

This gives, upon substitution,

Y = eAK , where eA � A 11�α τ

α1�α


Barro (JPE 1990)The growth rate of capital stock:

�K = s (1� τ)Y � δK = s (1� τ) eAK � δK

g =

�KK= s (1� τ) eA� δ = sA

11�α (1� τ) τ

α1�α � δ

For exogenous savings, the growth rate is maximal when τ = α.For endogenous savings, assume a representative consumer maximizes

U =Z ∞

0

C 1�σ � 11� σ

e�ρtdt

subject to the budget and technology constraints,

�K = (1� τ)Y � CY = AK 1�αG α

(for simplicity, δ = 0).


Barro (JPE 1990)Decentralized solution

Important: the consumer takes the tax rate as given and ignores hiscontribution into the public good.Solving optimization problem gives

γ =

�CC=1σ[(1� τ)YK � ρ] =

1σ

�(1� α) (1� τ)AK�αG α � ρ

�Note: the consumer recognizes the negative e¤ect of tax on thegrowth rate (1� τ #) but ignores the positive e¤ect (G ")Upon substitution,

γ =1σ

h(1� α)A

11�α (1� τ) τ

α1�α � ρ

iThe growth rate is maximal when τ = α.

I Clearly, since the positive externality is ignored, this will be lower thansocially optimal tax rate.

This is also the utility-maximizing growth rate (as long as fα, θ, ρgare such that the utility remains bounded: ρ > γ (1� σ)).


Barro (JPE 1990)Social optimum

In the social optimum the consumer utility is maximized subject tothe resource constraint:

maxU =Z ∞

0

C 1�θ � 11� θ

e�ρtdt

s.t.�K = Y � G � C = A 1

1�α (1� τ) τα1�α � C .

The optimal growth rate is

γ� =

�CC=1σ

hA

11�α (1� τ) τ

α1�α � ρ

iI This di¤ers from the competitive growth rate:

γ =1σ

h(1� α)A

11�α (1� τ) τ

α1�α � ρ

iI For any given τ = G

Y the competitive growth rate is lower. However,the growth-maximizing (and the utility-maximizing) tax rate is thesame: τ = α.


Application 1: Optimal composition of governmentspending

Ghosh & Roy (2004); Ghosh & Gregoriu (2008); Devarajan et al. (1996)Underlying idea:

In Barro�s model public input is a �ow, i.e. public services.I Maintenance of law and order; maintenance of infrastructure etc.

Alternatively, public input can be a stock (e.g., as in Turnovsky, 1997)I Infrastructure; public health etc.

Payo¤ to investment in public services is immediate;

Payo¤ to investment in public capital comes with a lag;

There may be di¤erent inputs of the same type (e.g., two types ofservices) with di¤erent productivity;

Optimal �scal policy includes characterization of the optimal mix, oroptimal composition of government spending.


Composition of government spending

Why is this important?

Need to prioritize when allocating the budget

ObjectivesI Economic growthI Social welfareI Redistribution

Implications of budget cuts

Public choice issues


Model 1. Optimal mix of public capital and public services.

Technology:Y =

�G αSG

1�αF

�1�βK β

Preferences:U =

Z ∞

0lnC (t) e�ρtdt

Private budget constraint:

�K = (1� τ)Y � C


�GS + GF = τY


Decentralized equilibriumConsumer�s optimization gives Euler�s equation for the consumptionpath (Ramsey rule):

ρ+

�CC= (1� τ)YK

Government�s optimization gives productive e¢ ciency condition:

YGF = 1

(same as in Barro�s model: MC = MB) and Ramsey rule:

ρ+

�CC= YGS

Along the BGP all real variables grow at the same constant rate,

γ = (1� τ)YK � ρ = (1� τ) βx β�1 � ρ

Here x � KG αSG

1�αF

and g � GSGF. Let θ � GF

�G S+GF

.


Optimal �scal policy in decentralized equilibrium

First-order conditions give a system of equations for the optimal �scalpolicy parameters and the associated growth rate.In an interior equilibrium

θe =1

(1� α)�1 � ρg e

τe = (1� β) [1� (1� α) ρg e ]

g e =

"αβ

(1� α) ββ (1� β)1�β (1� τe )β

# 1α(1�β)+β

xe =�(1� α) (1� β) (g e )α�� 1

β

γe =α

(1� α) g e� ρ

There is no closed-form solution, but these equations allow comparisonwith the �rst-best outcome.


Social planner�s optimum

Social planner chooses the path for consumption, private capitalinvestment, public services, and public capital investment to maximize theutility of the representative consumer. In the optimum

ρ+

�CC= YGS = YK

Along the BGP all real variables grow at the same constant rate,

γ = YK � ρ = βx β�1 � ρ.

Same as in Barro�s model:the decentralized equilibrium and the socialoptimum di¤er because of the tax wedge.


Social planner�s optimumThe solution is given by

θ� =1

(1� α)�1 � ρg �

τ� = (1� β) [1� (1� α) ρg �]

g � =

"αβ

(1� α) ββ (1� β)1�β

# 1α(1�β)+β

x� = [(1� α) (1� β) g �α]� 1

β

γ� =α

(1� α) g �� ρ

These equation are exactly the same as in the decentralized equilibriumexcept for the equation for g . Clearly, for τ 2 (0, 1) g e > g �. Therefore:

xe < x�, τe < τ�, γe < γ�, θe > θ�, and se < s�.

Slower accumulation of private capital in the decentralized equilibrium,compared to the social optimum, leads to the lower growth rate.Nigar Hashimzade (Durham and IFS) Fiscal policy 29/11/2016 17 / 45

ComparisonThe government uses sub-optimal share of output for public goodproduction, because the distortionary tax used to �nance public goodcauses deadweight loss;Consumers ignore the externality of their individual contribution tothe public good:

(1� τ)YK < YK

(individual payo¤ is lower than the social payo¤);The government tries to compensate for the externality by making theindividual payo¤ higher; hence, sets τ lower;This requires adjusting g upwards to maintain the Euler equationsimultaneously with the Ramsey rule.Final points:

I An additional policy tool allows to adjust θ and τ to correct, partially,the distortion observed with only �ow or only stock of public good;

I Social optimum can be achieved with a lump-sum tax or aconsumption tax.


Model 2. Optimal mix of two kinds of public services.

Technology:

Y =�

αK�η + βG�η1 + δG�η

2

��1/η

α > 0; β � 0; δ � 0; α+ β+ δ = 1; η � �1

Preferences:

U =Z ∞

0

C 1�σ � 11� σ

e�ρtdt

Private budget constraint:

�K = (1� τ)Y � C


G1 + G2 = τY

Let φ = G1/ (τY ) = 1� G2/ (τY ) .Nigar Hashimzade (Durham and IFS) Fiscal policy 29/11/2016 19 / 45

Decentralized equilibriumStandard solution of the optimization problem describes thedecentralized equilibrium.We can focus on the BGP equilibrium and assume τ = Const.

γ ��CC=1σ

0@α (1� τ)

"ατη

τη � βφ�η � δ (1� φ)�η

#� 1+ηη

� ρ

1AHow does the change in the composition of government spendinga¤ect the growth rate?

dγ

dφ> 0 () φ

1� φ<

�β

δ

�θ

where θ =1

1+ ηis the elasticity of substitution.

Important: the sign of the e¤ect depends on the technology and onthe initial shares.


Properties of the dececentralized equilibriumLet β > δ, i.e. G1 is more productive than G2.

dγ

dφ> 0 () φ

1� φ<

�β

δ

�θ

An increase in φ (rebalance towards a more productive public input)may not increase growth rate if the initial share is su¢ ciently high.Let φ� be the �critical value�: dγ

dφ > 0 for φ < φ� and dγdφ < 0 for

φ > φ�,

φ�

1� φ�=

�β

δ

�θ

;dφ�

dθ= (1� φ�)

�β

δ

�θ

lnβ

δ> 0

I Higher substitutability between two types of public inputs makes itmore likely that rebalancing towards the more productive inputincreases economic growth.

I Conversely, lower substitutability makes such rebalancing less likely toincrease growth, even when the initial share of more productive input islow.(Extreme case: Leontie¤ production function, θ = 0).


Properties of the dececentralized equilibriumThe e¤ect of τ on the growth rate is non-monotone,

dγ

dτT 0 i¤ τ S τ�

The growth-maximizing tax rate, for given shares, τe (φ), solves

τ1+η

βφ�η + δ (1� φ)�η + ητ = 1+ η

(In the Cobb-Douglas case, τe = β+ δ, � same as in the Barro�sbenchmark model).With more than two types of public inputs: assume the share ofcomponent i is raised by reducing the share of component j , and noother shares change. Then the growth rate will increase i¤

βθi

φi>

βθj

φj.


Optimal mix of public inputs

Standard assumptions:

Government chooses tax rate and shares so as to maximize the utilityof the representative consumer,

The representative consumer chooses consumption path to maximizeutility, taking government policies as given.

Productive e¢ ciency,YG1 = YG2 = 1,

gives the optimal mix:G1G2=

�β

δ

�θ

Since η � �1, the optimal share of the more productive input ishigher.


Growth rate and the e¤ect of productivityOptimal tax rate and optimal shares:

τe = βθ + δθ; φe =βθ

βθ + δθ

The maximal growth rate in a decentralized economy:

γe =α�1/η

h1� βθ � δθ

i� ρ

σ

An increase in the productivity of a more productive input haspositive e¤ect on growth and negative e¤ect on the optimal tax rate:(

dγe

d β > 0dτe

d β < 0i¤ β > γ.

An increase in the productivity of one input raises the optimal shareof that input:

dφe

dβ> 0.


Implications for empirical studies

Cross-country regressions may show positive, negative, or insigni�cante¤ect of government spending on per capita output growth

I Di¤erent countries can be above or below the optimal level

Regressions with disaggregated government spending may showpositive or negative e¤ect of di¤erent categories

I This depends on the relative productivity of di¤erent categoriesI Conversely, the sign can be used to identify �productive�and�unproductive� categories of spending


Application 2: Spill-overs across jurisdictions in a �scalfederation

Hashimzade & Myles (2010)Model:

Two countries, �home�and �foreign�

Each government provides public input (stock) in production

Positive externality across the border

Y = F�K ,G ,G

�I For example,

Y = AK α�G ρΓ1�ρ

�1�α, Γ = G + G

The solution is messy, but we can get some insight from the analysis ofthe balanced growth path (BGP) equilibrium.


Optimality: growth rate or welfare?

It can be shown that

In a single-country case utility is strictly increasing in the growth rate,I Utility-maximization is equivalent to growth-maximization

In the two-country case utility depends non-monotonically on (theown country�s) growth rate


Cooperation

In a non-cooperative setting two governments choose tax ratessimultaneously, each maximizing their own consumers�welfare

I This creates an additional distortion: positive externality on theneighbour is ignored;

I Thus, three sources of ine¢ ciency: distortionary tax; public input;positive externality across jurisdictions.

In a cooperative setting two governments choose tax ratessimultaneously to maximize the sum of home and foreign consumers�welfare

I This removes one distortion;I However, both types of country-level distortions remain.


Coordination

A supra-national authority (SNA) can achieve a further improvement:I Stage 1. SNA announces proportions (say, θ and θ) of national taxrevenue to be collected into the federal budget;

I Stage 2. Each government chooses optimal tax rate in anon-cooperative way;

I Stage 3. SNA announces how the federal budget will be dividedbetween two jurisdictions (say, in proportions µ and 1� µ);

I Stage 4. Investment and production take place.


Comparison

In the non-cooperative case the tax rate is the lowest; the growth rateand the utility levels are the lowest

Tax rates chosen cooperatively are higher; the growth rate and theutility levels are higher

The redistribution policy of SNA is matching grants: θ, θ < 0I Since the non-cooperative tax rates are too low, the SNA matchinggrant achieves an improvement by making the governments raise taxes;

I Matching grants are funded by a �federation tax�

Still, not the �rst-best outcome (because of the distortionary tax onconsumers)


Issues in empirical workRomp and de Haan (2007); Bom and Ligthart (2014)How to de�ne public capital?

Publicly-owned tangible capital stock excluding military structuresand equipment

I �Core�and �Non-core� componentsI Core infrastructure: roads/railways/airports; utilities; hospitals; schoolbuildings/other public buildings

I Transportation is the largest component

This can be provided by the central or local governmentI Many studies include provision at all levelsI Others include two components separately

The de�nition is especially important because of inter-regionalspill-over e¤ectsThe e¤ect of public capital on private output can be estimated usingproduction function approach

I Empirical elasticities vary around 0.08 in the short run to around 0.2 inthe long run for core infrastructure; the average is around 0.1.


Empirical studies: an overviewEarly studies: summarized, e.g., in Kneller et al. (1998) � see nexttwo slides.

I Aschauer (1989): public capital played a role in productivity fall in theUS in 1970s and 1980s;

I Levine and Renelt (1992), Easterly and Rebelo (1993): signs andmagnitudes of coe¢ cient on �scal variables are sensitive to modelspeci�cation;

I Kneller et al. (1998, 1999): correction for omitted variable bias.Disaggregated expenditure into productive/unproductive and taxationinto distortionary/non-distortionary.

Later studies: disaggregation and institutional framework areimportant.

I Arslanalp et al. (2010), Gupta et al. (2014): e¢ ciency in transformingpublic expenditure into capital.

In general, large e¤ects found in some early studies were unreliablebecause of reverse causality, heterogeneity, and other methodologicaland econometric issues.Attempts to address these issues were made in later studies.


Taxation and growth (Kneller et al., 1998)


Government spending and growth (Kneller et al., 1998)


Interpretation of coe¢ cients

There is an argument (Kneller et al., 1999) that in the previous literatureinterpretation of the coe¢ cients ignored the government budget constraint.

Standard interpretation: ceteris paribus

However, not all components of public expenditure or public revenuesare included

An increase in an included compoment of expenditure requiresI A decrease in the omitted component(s) of expenditure and/orI An increase in the omitted component(s) of revenue

Ceteris paribus interpretation leads to a bias in the estimated e¤ect


Interpretation of coe¢ cients

True model:

g = α+K

∑i=1

β(i )Z (i ) +M

∑m=1

δ(m)X (m) + ε

Budget constraint:M

∑m=1

X (m) = 0

To avoid perfect multicollinearity omit one component and estimate

g = α+K

∑i=1

β(i )Z (i ) +M�1∑m=1

γ(m)X (m) + ε

Thenγ(m) = δ(m) � δ(M ) for m = 1, . . . ,M � 1.

The bias can be avoided by omitting a �neutral�category, e.g.non-distortionary tax or non-productive expenditure.


Kneller et al., 1999

Disaggregation:I Distortionary taxation: income, pro�t, social security contibutions,payroll, manpower, property

I Non-distortionary taxation: domestic goods and servicesI Productive expenditure: general public services, defence, education,health, housing, transport, communication

I Unproductive expenditure: social security and welfare, recreation,economic services

I �Other revenues�; �Other expenditures�

Data: 1970-1995 panel of 22 OECD countries;

Estimation: 5-year averages (98 obs.); two-way FE

After correcting for the bias caused by omitted components:(1) distortionary taxation reduces growth; non-distortionary taxation doesnot; (2) productive government expenditure enhances growth;unproductive expenditure does not.


Budget structure and growthAfonso and Alegre, 2011Economic model: several categories of public spending in the productionfunction and the utility function

Cobb-Douglas production function with direct public capital input(Yt = AK α

t Lγt G

β1t)

Capital-enhancing spending, e.g. infrastructure as public subsidy tothe cost of private capital (G2t = (1� s)Kt)Labour-enhancing spending, e.g. investment in education etc.(Lt = w

µt G

ν3tN

ηt )

Public good in the utility function (U = ∑ βtC θt G

1�θ4t )

Three linear taxes: labour income tax, corporate pro�t tax, andconsumption tax.The solution of the consumer optimization problem (taking policies asgiven) allows to characterize the e¤ect of the tax rates and budgetstructure on output, productivity, and growth.


Empirical speci�cationEconometric model: autoregressive distributed lag, to account for dynamice¤ects

yit = µi + vt +p

∑j=1

λjyi ,t�j +M

∑m=1

q

∑s=0

δ(m)s f (m)i ,t�s +

K

∑k=1

ρ(k )z (k )it + εit

Data: panel 1971-2006 for 15 EU member statesEstimation: GMM (Arrellano and Bond), to account for endogeneityof policy variablesLong-run e¤ect for each �scal variable:

θ(m) =∑qs=0 δ

(m)s

1�∑pj=1 λj

Dependent variable: 4 speci�cationsPer capita GDP growthLabour productivity growthTFP growthMoving average GDP


Empirical speci�cation

Fiscal variables

Expenditures (functional classi�cation): economic a¤airs; health;education; social protection.

Expenditures (economic classi�cation): consumption; compensationof employees; social transfers; subsidies; investment.

Revenues: direct taxation; social contributions; indirect taxation;public de�cit.

Controls (as in Kneller et al., 1999)

Private investment (% of GDP)

Terms of trade

Labour force growth rate

Population growth rate


Estimation results


Adjusted public expenditure

Gupta et al. (2014)This paper re-apprises the relationship between public capital and growthusing adjustment for the e¢ ciency of public investment.

Important: in developing countries private investment is more e¢ cientthan public investment

I Large number of failed public projectsI Likely because of poor institutional framework

Constructed Public Investment Measurement Index (PIMI)I Allows to separate four stages of public investment process: appraisal,selection, implementation, evaluation

Estimated e¤ect of (1) adjusted public investment on growth and of(2) each of the stages on capital accumulation and growth.


Data, methods, and resultsData: 1960-2010 panel for 71 countries, capital stock constructed frominvestment with adjustment for e¢ ciency:

Git = (1� δit )Gi ,t�1 + qi Iit , qi 2 [0, 1]E¢ ciency parameter is proxied by PIMI (overall e¢ ciency) and di¤erentcomponents/sub-indices (e¢ ciency at each of the four stages).


Data, methods, and resultsMethod: a Cobb-Douglas production function is estimated by static FEand by system GMM (Blundell & Bond)Results:

Factor share of public capital Implied marginal productivityUnadjusted Adjusted Unadjusted Adjusted

Static FEAll 0.189 0.197 0.42 0.88MIC 0.197 0.226 0.36 0.71LIC 0.193 0.187 0.50 1.04System GMMAll 0.233 0.154 0.52 0.69MIC 0.167 0.162 0.30 0.51LIC 0.253 0.143 0.65 0.80

Table: E¤ect of public capital on output


Conclusions

Economic growth will remain an important objective.

Growth-enhancing policies are important for e¢ ciency reasons.

They can also facilitate redistributive, equity-enhancing policies.

Measurement has improved but still not perfect.

Quantitative and qualitative improvements in data availability (longerperiods; micro-level data; surveys) open new avenues for research.


Date post:	01-Apr-2020
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

CES Lecture 3 Nigar Hashimzade - CESifo Group Munich · 2019-12-12 · Overall e⁄ect on growth is...

Documents