Advanced Macroeconomics II

Fiscal Policy

Lorenza Rossi(Spring 2014)

University of PaviaPart of these slides are based on Jordi Galì slides for Macroeconomia

Avanzada II.

University of Pavia and CREI ()University of Pavia Part of these slides are based on Jordi Galì slides for Macroeconomia Avanzada II. 1

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Outline

Fiscal Policy in the Real business cycle model

Debt Dynamics

The e¤ects of �scal shocks

Fiscal evidence on countries debt and debt consolidation

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Public Expenditure: provision of public goods and servises.Redistributive issues

- expenditure for goods and servises.- transfer: redistributive (unemployment subsidies, pensions)- subsidies: �rms subsidies- interests on public debt

Taxes: Finance the provision of public goods and servises. Redistributiveand incetive issues

- consumption taxes- capital income taxes- pro�ts taxes- labor income taxes

The di¤erence between public expenditure and taxes is the de�cit,�nanced through the emission of public debtFiscal policy decision =) A¤ects the level of the economic activity.

! Fiscal policy is exogenous: independent from �uctuations! Fiscal policy is used as an instrument of business cycle stabilization

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Fiscal Policy in the RBC model

GOVERNMENT BUDGET CONSTRAINT: with a balanced budget

The Government runs a balanced budgetExample I: with only lump-sum taxes

Gt = Tt

Example II: with lump-sum taxes and labor income taxed

Gt = Tt + τnwtNt

Gt can be represented by an AR(1) process

ln�GtG

�= ρg ln

�Gt�1G

�+ εg ,t

If G does not enter into the utility function, i.e. U (Ct ,Gt ,Nt ) oralternatively it does not enter into �rms�production function, i.e.Y = AF (N,K ,G ) =)it is a pure waste for the economy. In thiscase government expenditure is nonproductive.

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IRFS to a government spending shock in the basic RBC

5 10 15 20 25 30 35 40­0.05

0

0.05

0.1

0.15y

5 10 15 20 25 30 35 40­0.2

­0.15

­0.1

­0.05

0c

5 10 15 20 25 30 35 40­4

­3

­2

­1

0

1i

5 10 15 20 25 30 35 400

0.05

0.1

0.15

0.2

0.25n

5 10 15 20 25 30 35 40­0.1

­0.08

­0.06

­0.04

­0.02

0w

5 10 15 20 25 30 35 40­0.2

­0.15

­0.1

­0.05

0k

5 10 15 20 25 30 35 400

2

4

6

8x 10

­3 r

5 10 15 20 25 30 35 400

0.5

1

1.5spesa

Result: government spending implies a large crowding-out e¤ect onprivate consumption

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IRFS to a government spending shock in the basic RBC

The RBC model predicts a decline in private consumption in responseto a rise in government spending. (crowding out e¤ect onconsumption)

With in�nitely-lived Ricardian households, an increase in(nonproductive) government spending purchases (�nanced by currentor future lump-sum taxes), lowers the present value of after-taxincome, and thus generates a negative wealth e¤ect on consumption(Aiyagari et al., 1990; Baxter and King, 1993; Christiano andEichenbaum, 1992).

The quantity of labor supplied at any given wage increases.

Equilibrium: lower consumption, lower real wage, higher employment(increase in hours) and higher output.

The increase in employment leads, if su¢ ciently persistent, to a risein the expected return to capital, and may trigger a rise ininvestment. Otherwise investment decrease.

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Fiscal Policy in the RBC model

GOVERNMENT BUDGET CONSTRAINT: general form

Government budget constraint In period t:

Gt + (1+ rt�1)Bgt�1 = τntwtNt + Tt + B

gt

Household budget constraint of the RBC model modi�es as follows:

Ct + Bt = (1� τnt )wtNt + (1+ rt�1)Bt�1 +Dt � Tt

De�nitions:

Gt : public expenditureBGt : stock of Government Bond - Public Debt (one period, risk free)rt : interest rate on public debt.τnt : labor income taxTt : lump-sum tax (no distorsionary).University of Pavia and CREI ()

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Fiscal Policy in the RBC model

The equation for the labor supply becomes:

Un,t + (1� τnt )wtUc ,t = 0

For U (Ct ,Nt ) =C 1�σt1�σ � v

N+ϕt

1+ϕ , in log-deviation from the steady state

bwt = σbct + ϕbnt � τn

1� τnbτnt

where τn is the steady state of the labor income tax.

The production function

Yt = AtN1�αt

in log-deviation byt = at + (1� α) bntUniversity of Pavia and CREI ()

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Equilibrium

Goods marketYt = Ct + Gt

in log-deviations byt = (1� sg )bct + sg bgt .where sg � G/Y .Labor market

σbct + ϕbnt � τn

1� τnbτnt = bat � αbnt

Bonds market bbt = bbgtbrt = σEtf∆bct+1gTechnology byt = bat + (1� α) bnt

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Equilibrium output

From the labor market, equilibrum after some algebra,

σ (1� α) + (1+ ϕ) (1� sg )(1� sg ) (1� α)

byt = bat � (1� α) + 1+ ϕ

(1� α)

�+σ

sg1� sg

bgt � τn

1� τnbτnt

solving for bytbyt =

(1� sg ) (1+ ϕ)

σ (1� α) + (1+ ϕ) (1� sg )bat

+(1� α) σsg

σ (1� α) + (1+ ϕ) (1� sg )bgt +

��

(1� sg ) (1� α)

σ (1� α) + (1+ ϕ) (1� sg )

�τn

1� τnbτnt

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Equilibrium of hours, consumption and real wage

Substituting the equilibrium output into the production function we�nd bnt = n (bgt , bτnt ,bat ).Substituting byt into the aggregate resource constraint we �ndbct = c (bgt , bτnt ,bat )Finally substituting bnt and bct into the labor supply we �ndbwt = w (bgt , bτnt ,bat )Find bct = c (bgt , bτnt ,bat ) , bnt = n (bgt , bτnt ,bat ) and bwt = w (bgt , bτnt ,bat )by your ownFinally we also know that

brt = σEtf∆ct+1g

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Discussion

- E¤ects of di¤erent �scal shocks (τnt , gt)- Ricardian Equivalence Ricardiana- Fiscal rules and Stabilization policies- Structural De�cit: a big European Problem

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Empirical evidence on the e¤ects of �scal shocks

Identi�cation problem: simultaneity.

Discretionary changes in taxes are likely to a e¤ect GDPcontemporaneously, but aggregate �uctuations will alsocontemporaneously a¤ect commonly used tax measures (such as taxrevenues).

Consider the following

∆yt = α0 + b∆τt + ut

Any measure τt which is a function of factors also contemporaneouslya¤ecting output, cannot be used to consistently identify the e¤ects oftax changes. The chosen tax measure would be contemporaneouslycorrelated with the error term ut , violating the standard requirementfor consistent estimation of the coe¢ cients.

Blanchard and Perotti (2002). Try to identify only the "structural"shocks to revenues: uncorrelated with contemporaneos shocks.

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Empirical evidence on the e¤ects of �scal shocks

The Macroeconomic E¤ects of Tax Changes: Romer & Romer (AER2010)

- narrative approach- exogenous tax changes:

� legislated changes (not automatic)� tax changes introduced for:

- need to reduce the public de�cit inherited- aim to achieve a long-term debt target

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Empirical evidence on the e¤ects of �scal shocks - Romer andRomer 2010 AER

Equations estimated:

∆yt = α+K

∑k=0

βk∆Tt�k + ut

and

∆yt = α+K

∑k=0

βk∆T at�k +K

∑k=0

γk∆T it�k + ut

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Empirical evidence on the e¤ects of �scal shocks - Romer andRomer 2010 AER

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Empirical evidence on the e¤ects of �scal shocks - Romer andRomer 2010 AER

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Empirical evidence on the e¤ects of �scal shocks - Romer andRomer 2010 AER

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Debt Dynamics

Understanding the E¤ects of Government Spending on Consumption:Galí, López-Salido y Vallés (JEEA 2007)

- A model with both standard Ricardian and liquidity constrainedhouseholds (consume all their disposable income)

- Public expenditure (purchases of good and services)

gt =K

∑k=1

φ0kxt�k + εgt

- Macroeconomic E¤ects:

zt =K

∑k=0

βk εgt�k + ut

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The E¤ects of Government Spending Shocks - Galì, Lopez-Salidoand Vallet JEEA 2007

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The E¤ects of Fiscal Consolidation

E¤ects of Fiscal Consolidation: IMF WEO Oct. 2010)

- 15 Countries, 1980-2009- 173 countries-year �scal consolidation measures (aim: de�cit

reduction)- Equations estimated:

zt = α+K

∑k=0

βk ft�k + ut

zt :GDP, unemployment

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The E¤ects of Fiscal Consolidation - IMF WEO October 2010

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The E¤ects of Fiscal Consolidation - IMF WEO October 2010

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The E¤ects of Fiscal Consolidation - IMF WEO October 2010

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The E¤ects of Fiscal Consolidation - IMF WEO October 2010

Factors that usually soften the short-term impact of �scalconsolidation.

Central banks cut of interest rates and the currency falls in value. Thishelps cushion the impact on consumption and investment, and boostsexports.Fiscal consolidation is less costly when markets are more concernedabout �scal sustainability.Consolidations based on spending cuts are less painful than those basedon tax hikes. This is largely because Central banks cut interest ratesmore after spending cuts.

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The E¤ects of Fiscal Consolidation - IMF WEO October 2010

FISCAL CONSOLIDATION IN THE LONG RUN: �scalconsolidation has a positive impact on output. In particular, lowerdebt tends to reduce real interest rates and debt service costs, whichallows for future tax cuts. By boosting private investment, thisincreases output in the long term.

The authors�simulations suggest that the contraction in output maybe more than twice as large as their baseline estimate when centralbanks cannot cut interest rates, and when the adjustment issynchronized across all countries. Nevertheless, for economiesconsidered at high risk of sovereign default, short-term negativee¤ects are likely to be smaller.

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Debt Dynamics

Bgt = (1+ rt�1)Bgt�1 + Gt � τntWtNt � Tt

De�nition of De�cit:

DEFt � Bgt � Bgt�1 = rt�1Bgt�1 + Gt � τntWtNt � Tt

De�nition of Primary De�cit:

DEF pt � Gt � τntWtNt � TtDEF pt � Gt � Tt

or

DEF �t � rt�1Bgt�1 + G (Y �t )� T (Y �t )DEF p,�t � G (Y �t )� T (Y �t )

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Debt DynamicsDe�nitions

bgt � Bgt /Yt ; deft � DEFt/Yt ; def pt � DEF pt /Yt

def �t � DEF �t /Y �t ; def p,�t � DEF p,�t /Y �t ; gt �Yt � Yt�1Yt�1

De�cit and discretionary �scal policy

deft = rt�1bgt�1 + def

p,�t + cyclical comp.

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Debt Dynamics I

Considering the de�cit:

Bgt = Bgt�1 +DEFt

or, as a share of output

bgt =1

1+ gt�1bgt�1 + deft

thus∆bgt = �

gt�11+ gt�1

bgt�1 + deft

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Debt Dynamics I

Stationarity condition:

∆bgt = �g

1+ gbgt�1 + def

ifg > 0

In the steady state:

bg =1+ gg

def

show the phase diagram

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Debt Dynamics I: Phase Diagram with g > 0

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Debt Dynamics II

Considering the primary de�cit:

Bgt = (1+ rt�1)Bgt�1 +DEF

pt

as a share of output

bgt =�1+ rt�11+ gt�1

�bgt�1 + def

pt

thus

∆bgt =�rt�1 � gt�11+ gt�1

�bgt�1 + def

pt

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Stationarity condition

∆bgt =�r � g1+ g

�bgt�1 + def

p

if:r < g

Steady State:

bg =1+ gg� r def

p

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Dynamics of Primary Debt: r < g

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Dynamics of Primary Debt: r < g

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Dynamics of Primary Debt: r > g

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Dynamics of Primary Debt: r�bgt�1

�

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Alternatives to an adjustment of the primary de�cit

Higher growth

Default or debt restructuring (or in�ation)

"Financial Repression"

Sale of public assets (40% of GDP in advanced economies)

Empirical Evidence

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Government Balance: Fiscal Monitor 2014

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Fiscal Balance: Fiscal Monitor 2014

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Fiscal Trend: Fiscal Monitor 2014

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Public Debt: Fiscal Monitor 2014

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Trend in Public Debt: Fiscal Monitor 2014

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Gross Financing Needs: Fiscal Monitor 2014

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