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Fiscal austerity in emerging market economies

Chetan Dave ORCID logo, Chetan Ghate, Pawan Gopalakrishnan and Suchismita Tarafdar

Abstract

We build a small open economy RBC model with financial frictions to analyse spending and tax based fiscal consolidations in emerging market economies (EMEs). We show that if government spending is a substitute to private consumption in household utility, a spending based fiscal consolidation has an expansionary effect on output. In contrast, tax based consolidations are always contractionary irrespective of the strength of substitutability between government and private consumption. Our findings support the results in the World Economic Outlook (2010), USA: International Monetary Fund, that tax based consolidation measures are more costly (in terms of GDP losses) than spending based consolidations. We calibrate the model to India and calculate the fiscal multipliers associated with spending and tax based fiscal consolidations. Our paper identifies new mechanisms that underlie the dynamics of fiscal reforms and their implications for successful fiscal consolidations.

JEL Classification: E32; E62

Corresponding author: Chetan Dave, Department of Economics, University of AB, 8-14 Tory Building, Edmonton, T6G 2H4, AB, Canada,

Acknowledgements

We thank Monisankar Bishnu, Patrick Blagrave, Piyali Das, Stephen Wright, and seminar participants at the 13th Annual Conference on Growth and Development (2017) at ISI Delhi, the 2018 SERI Conference at IIM Bangalore, the DSGE Workshop at Indira Gandhi Institute of Development Research, Ashoka University, CAFRAL, IIM Kolkata, the 2018 Annual International Conference on Macroeconomic Analysis and International Finance (Crete), Virginia Tech, the 2018 World Bank South Asia Workshop on Fiscal Policy, and the 2018 Delhi Macroeconomics Workshop for helpful comments. We also thank the Editor and two anonymous referees for useful comments. We are grateful to PPRU (the Policy Planning Research Unit) for financial assistance related to this project. The views and opinions expressed in this article are those of the authors and do not necessarily reflect the views of the institutes they belong to.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: We are grateful to PPRU (the Policy Planning Research Unit) for financial assistance related to this project.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Technical Appendix

This appendix provides the derivation of the linear system comprising the model we analyse. We note that this model is built for use with HP-filtered data and as such does not feature deterministic trends.

A.1 The Household’s problem

A representative household maximizes utility:

max { C t , H t , B t , D t , K t } E 0 t = 0 β t [ μ ln ( C t χ C t 1 + ζ G t ) + ( 1 μ φ 1 φ 2 ) ln ( 1 H t ) + φ 1 ln ( D t ) + φ 2 ln ( B t ) ] ,

where β ∈ (0,1), G t C S S P ( G ¯ , ρ G , σ G ) and subject to,

C t + K t ( 1 δ ) K t 1 + ϕ 2 K t 1 [ K t K t 1 1 ] 2 + B t + κ 1 2 Y t [ B t Y t B ¯ Y ¯ ] 2 + D t + κ 2 2 Y t [ D t Y t D ¯ Y ¯ ] 2 = ( 1 τ w ) W t H t + ( 1 τ k ) R t K t 1 + R t 1 P B t 1 + R t 1 G D t 1 + T t

where CSSP denotes a covariance stationary stochastic process. The Lagrangian of the problem, where Λ t is the multiplier on the household budget constraint, is

max { C t , H t , B t , D t , K t }   L = [ t = 0 β t [ μ ln ( C t χ C t 1 + ζ G t ) + ( 1 μ φ ) ln ( 1 H t ) + φ ln ( D t ) ] ] [ t = 0 β t Λ t [ C t + K t ( 1 δ ) K t 1 + ϕ 2 K t 1 [ K t K t 1 1 ] 2 + B t + κ 1 2 Y t [ B t Y t B ¯ Y ¯ ] 2 + D t + κ 2 2 Y t [ D t Y t D ¯ Y ¯ ] 2 [ ( 1 τ w ) W t H t + ( 1 τ k ) R t K t 1 + R t 1 P B t 1 + R t 1 G D t 1 + T ] t ] ]

and the FONC are, for C t , H t , K t , B t and D t respectively,

Λ t = μ C t χ C t 1 + ζ G t χ μ C t + 1 χ C t + ζ G t + 1 ( 1 τ w ) Λ t W t = 1 μ φ 1 φ 2 1 H t E t { β Λ t + 1 [ ( 1 δ ) ϕ 2 [ K t + 1 K t 1 ] 2 + ϕ K t + 1 K t [ K t + 1 K t 1 ] + ( 1 τ k ) R t + 1 ] = Λ t [ 1 + ϕ [ K t K t 1 1 ] ] } E t { β Λ t + 1 R t P = Λ t [ 1 + κ 1 [ B t Y t B ¯ Y ¯ ] ] φ 2 B t } E t { β Λ t + 1 R t G = Λ t [ 1 + κ 2 [ D t Y t D ¯ Y ¯ ] ] φ 1 D t } .

The household problem therefore delivers the following system of 7 equations:

Λ t = μ C t χ C t 1 + ζ G t χ μ C t + 1 χ C t + ζ G t + 1 ( 1 τ w ) Λ t W t = 1 μ φ 1 φ 2 1 H t E t { β Λ t + 1 [ ( 1 δ ) ϕ 2 [ K t K t 1 1 ] 2 + ϕ K t + 1 K t [ K t K t 1 1 ] + ( 1 τ k ) R t + 1 ] = Λ t [ 1 + ϕ [ K t K t 1 1 ] ] } E t { β Λ t + 1 R t P = Λ t [ 1 + κ 1 [ B t Y t B ¯ Y ¯ ] ] φ 2 B t } E t { β Λ t + 1 R t G = Λ t [ 1 + κ 2 [ D t Y t D ¯ Y ¯ ] ] φ 1 D t } C t + K t ( 1 δ ) K t 1 + ϕ 2 K t 1 [ K t K t 1 1 ] 2 + B t + κ 1 2 Y t [ B t Y t B ¯ Y ¯ ] 2 + D t + κ 2 2 Y t [ D t Y t D ¯ Y ¯ ] 2 = ( 1 τ w ) W t H t + ( 1 τ k ) R t K t 1 + R t 1 P B t 1 + R t 1 G D t 1 + T t where  G t C S S P ( G ¯ , ρ G , σ G )

in 15 parameters { β , χ , μ , ζ , φ 1 , φ 2 , δ , ϕ , κ 1 , κ 2 , τ w , τ k , G ¯ , ρ G , σ G } and 13 variables { C t , G t , H t , D t , K t , B t , Y t , W t , R t , R t P , R t G , T t , Λ t } .

A.2 The Firm’s problem

The firm seeks to maximize it’s profits given by,

max { K t 1 , H t }   Y t R t K t 1 ( 1 θ ) W t H t θ W t H t R t 1 P ,

subject to

Y t = A t K t 1 α H t 1 α A t C S S P ( A ¯ , ρ A , σ A )

This optimization yields 2 First order conditions,

( 1 α ) Y t H t = W t [ ( 1 θ ) + θ R t 1 P ] α Y t K t 1 = R t

The firm problem therefore delivers the following system of 4 equations:

( 1 α ) Y t H t = W t [ ( 1 θ ) + θ R t 1 P ] α Y t K t 1 = R t Y t = A t K t 1 α H t 1 α A t C S S P ( A ¯ , ρ A , σ A )

with the addition of 5 parameters { θ , α , A ¯ , ρ A , σ A } and 1 variable (A t ) to the household system.

A.3 Government budget constraint

The government budget constraint is given by

G t + T t = τ w W t H t + τ k R t K t + D t R t 1 G D t 1 ,

where

R t G = ξ R t * exp ( D t Y t D ¯ Y ¯ ) R t P = Γ R t G R t * C S S P ( R ¯ * , ρ R * , σ R * )

The specification for government behavior therefore delivers 4 additional equations to the system so far:

G t + T t = τ w W t H t + τ k R t K t + D t R t 1 G D t 1 R t G = ξ R t * exp ( D t Y t D ¯ Y ¯ ) R t P = Γ R t G R t * C S S P ( R ¯ * , ρ R * , σ R * )

with the addition of 5 parameters { ξ , Γ , R ¯ * , ρ R * , σ R * } and 1 variable ( ( R t * ) ) to the system given by the household and firm problems.

A.4 The nonlinear system

Collecting across economic actors, the system of expectational difference equations is

(N1) Λ t = μ C t χ C t 1 + ζ G t χ μ C t + 1 χ C t + ζ G t + 1

(N2) ( 1 τ w ) Λ t W t = 1 μ φ 1 φ 2 1 H t

(N3) E t { β Λ t + 1 [ 1 δ ϕ 2 [ K t + 1 K t 1 ] 2 + ϕ K t + 1 K t [ K t + 1 K t 1 ] + ( 1 τ k ) R t + 1 ] = Λ t [ 1 + ϕ [ K t K t 1 1 ] ] }

(N4) E t { β Λ t + 1 R t P = Λ t [ 1 + κ 1 [ B t Y t B ¯ Y ¯ ] ] φ 2 B t }

(N5) E t { β Λ t + 1 R t G = Λ t [ 1 + κ 2 [ D t Y t D ¯ Y ¯ ] ] φ 1 D t }

(N6) C t + K t ( 1 δ ) K t 1 + ϕ 2 K t 1 [ K t K t 1 1 ] 2 + B t + κ 1 2 Y t [ B t Y t B ¯ Y ¯ ] 2 + D t + κ 2 2 Y t [ D t Y t D ¯ Y ¯ ] 2 = ( 1 τ w ) W t H t + ( 1 τ k ) R t K t 1 + R t 1 P B t 1 + R t 1 G D t 1 + T t

(N7) ( 1 α ) Y t H t = W t [ ( 1 θ ) + θ R t 1 P ]

(N8) α Y t K t 1 = R t

(N9) Y t = A t K t 1 α H t 1 α

(N10) G t + T t = τ w W t H t + τ k R t K t + D t R t 1 G D t 1

(N11) R t G = ξ R t * exp ( D t Y t D ¯ Y ¯ )

(N12) R t P = Γ R t G

(N13) G t C S S P ( G ¯ , ρ G , σ G )

(N14) A t C S S P ( A ¯ , ρ A , σ A )

(N15) R t * C S S P ( R ¯ * , ρ R * , σ R * )

which is a nonlinear system of (15) equations in:

  • 25 parameters { β , χ , μ , ζ , φ 1 , φ 2 , δ , ϕ , κ 1 , κ 2 , τ w , τ k , θ , α , Γ , ξ , G ¯ , A ¯ , R ¯ * , ρ G , ρ A , ρ R * , σ G , σ A , σ R * } and,

  • 15 variables {C t , H t , D t , K t , B t , Y t , W t , R t , R t P , R t G , T t , Λ t , G t , A t , R * t }.

A.5 The Nonstochastic Steady State

Assume that the steady state values A ¯ , G ¯ and R ¯ * are in hand, then R ¯ G is in hand from Eq. (11) above:

R t G = ξ R t * exp ( D t Y t D ¯ Y ¯ ) R ¯ G = ξ R ¯ * .

Equation (3) above yields the expression for R ¯ :

E t { β Λ t + 1 [ 1 δ ϕ 2 [ K t + 1 K t 1 ] 2 + ϕ K t + 1 K t [ K t + 1 K t 1 ] + ( 1 τ k ) R t + 1 ] = Λ t [ 1 + ϕ [ K t K t 1 1 ] ] } R ¯ = 1 β ( 1 δ ) β ( 1 τ k ) ,

and finally Eq. (12) above yields the expression for R ¯ P :

R t P = Γ R t G R ¯ P = Γ R ¯ G

The remaining (9) equation system in the steady state is

Λ ¯ = μ ( 1 χ ) ( 1 χ ) C ¯ + ζ G ¯ ( 1 τ w ) Λ ¯ W ¯ = 1 μ φ 1 φ 2 1 H ¯ β Λ ¯ R ¯ P = Λ ¯ φ 2 B ¯ β Λ ¯ R ¯ G = Λ ¯ φ 1 D ¯ C ¯ + δ K ¯ + B ¯ + ( 1 R ¯ G ) D ¯ = ( 1 τ w ) W ¯ H ¯ + ( 1 τ k ) R ¯ K ¯ + R ¯ P B ¯ + T ¯ ( 1 α ) Y ¯ ( 1 θ + θ R ¯ P ) H ¯ = W ¯ W ¯ H ¯ Y ¯ = 1 α 1 θ + θ R ¯ P α Y ¯ K ¯ = R ¯ Y ¯ = A ¯ K ¯ α H ¯ 1 α G ¯ + T ¯ = τ w W ¯ H ¯ + τ k R ¯ K ¯ + D ¯ R ¯ G D ¯

from which we need to determine the steady state values for C t , H t , D t , K t , Y t , W t , T t , B t and Λ t . Combining the 5th and 9th equations in the above system eliminates

T ¯ = τ w W ¯ H ¯ + τ k R ¯ K ¯ + D ¯ R ¯ G D ¯ G ¯

and yields

Λ ¯ = μ ( 1 χ ) ( 1 χ ) C ¯ + ζ G ¯ ( 1 τ w ) Λ ¯ W ¯ = 1 μ φ 1 φ 2 1 H ¯ Λ ¯ = φ 2 B ¯ ( 1 β R ¯ P ) D ¯ = φ 1 ( Λ ¯ β Λ ¯ R ¯ G ) G ¯ + ( 1 R ¯ P ) B ¯ = W ¯ H ¯ + ( R ¯ δ ) K ¯ C ¯ W ¯ = ( 1 α ) Y ¯ ( 1 θ + θ R ¯ P ) H ¯ α Y ¯ K ¯ = R ¯ Y ¯ = A ¯ K ¯ α H ¯ 1 α

Next, we can eliminate K ¯ = α Y ¯ R ¯

(18) Y ¯ = A ¯ ( α Y ¯ R ¯ ) α H ¯ 1 α

(19) Y ¯ = ( A ¯ ( α R ¯ ) α ) 1 1 α H ¯

(20) Y ¯ = ϑ 1 H ¯ , ϑ 1 = ( A ¯ ( α R ¯ ) α ) 1 / 1 α

yielding

Λ ¯ = μ ( 1 χ ) ( 1 χ ) C ¯ + ζ G ¯ ( 1 τ w ) Λ ¯ W ¯ = 1 μ φ 1 φ 2 1 H ¯ Λ ¯ = φ 2 B ¯ ( 1 β R ¯ P ) D ¯ = φ 1 ( Λ ¯ β Λ ¯ R ¯ G ) G ¯ + ( 1 R ¯ P ) B ¯ = W ¯ H ¯ + ( R ¯ δ ) K ¯ C ¯ W ¯ = ( 1 α ) ϑ 1 ( 1 θ + θ R ¯ P ) = ϑ 2

Then letting ϑ 3 = 1−μφ 1φ 2

C ¯ = μ Λ ¯ ζ G ¯ 1 χ H ¯ = ( 1 τ w ) ϑ 2 Λ ¯ ϑ 3 ( 1 τ w ) ϑ 2 Λ ¯ B ¯ = ( 1 β R ¯ P ) φ 2 Λ ¯ D ¯ = ( 1 β R ¯ G ) φ 1 Λ ¯ ϑ 6 Λ ¯ 2 ϑ 5 Λ ¯ + ϑ 4 = 0 Λ ¯ = ϑ 5 ± ϑ 5 2 4 ϑ 4 ϑ 6 2 ϑ 6 ϑ 4 = R ¯ ϑ 2 ( 1 χ ) φ 2 ϑ 3 + ( 1 χ ) φ 2 ( R ¯ δ ) α ϑ 1 ϑ 3 + R ¯ ϑ 2 μ ( 1 τ w ) ( 1 χ ) φ 2 ϑ 5 = [ R ¯ ϑ 2 ( 1 χ ) φ 2 ϑ 2 ( 1 τ w ) + ( 1 χ ) φ 2 ( R ¯ δ ) α ϑ 1 ( 1 τ w ) ϑ 2 + R ¯ ϑ 2 ( 1 τ w ) φ 2 ζ G ¯ R ¯ ϑ 2 ( 1 τ w ) ( 1 χ ) φ 2 G ¯ ] ϑ 6 = R ¯ ϑ 2 ( 1 τ w ) ( 1 χ ) ( 1 R ¯ P ) ( 1 β R ¯ P ) .

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Supplementary material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2019-0042).

Received: 2019-04-17
Accepted: 2020-08-04
Published Online: 2020-09-17

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